Grade 3 Mathematics Curriculum Document 2016 …...1 Grade 3 Mathematics Curriculum Document...

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Grade 3 Mathematics Curriculum Document

2016-2017

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Table of Contents Cover Page Pg. 1 Table of Contents Pg. 2 Trouble Shooting Guide Pg. 3 Best Practices in the Math Classroom Pg. 4 Problem Solving 4-Square Model Pg. 6 Problem Solving with Pictorial Modeling/ Strip Diagrams Pg. 7 Number Sense/ Number Talks Pg. 8 Year at a Glance Pg. 17 TEKS Spiraling Checklist Pg. 18 Mathematics Process Standards Pg. 21 Math Instructional Resources Pg. 22 Bundle 1: Representing and Comparing Whole Numbers Pg. 24 Bundle 2: Addition and Subtraction of Whole Numbers Pg. 31 Bundle 3: Multiplication and Division of Whole Numbers (Understanding Multiplication and Division) Pg. 39 Bundle 4: Multiplication and Division of Whole Numbers (Expanding and Mastering Multiplication and Division) Pg. 51 Bundle 5: Fractions Pg. 56 Bundle 6: Geometry Pg. 66 Bundle 7: Measurement Pg. 70 Bundle 8: Data Analysis Pg. 77 Bundle 9: Personal Financial Literacy Pg. 82 Bundle 10: STAAR Review and Testing Pg. 87 Bundle 11: Extended Learning Pg. 87

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Trouble Shooting Guide

• The 2015-2016 Mathematics Curriculum Document for Grade 3 includes the following features:

• The NISD Curriculum Document is a TEKS-Based Curriculum.

• Year at a Glance Indicating Bundle Titles and Number of Days for Instruction

• Color Coding: Green- Readiness Standards, Yellow- Supporting Standards, Blue- Process Standards,

Purple- ELPS, Strike-Out- Portion of TEKS not Taught in Current Bundle

• NISD Math Instructional Focus Information

• The expectation is that teachers will share additional effective resources with their campus Curriculum &

Instructional Coach for inclusion in the document.

• The NISD Curriculum Document is a working document. Additional resources and information will be

added as they become available.

• **Theresourcesincludedhereprovideteachingexamplesand/ormeaningfullearningexperiencestoaddresstheDistrictCurriculum.InordertoaddresstheTEKStotheproperdepthandcomplexity,teachersareencouragedtouseresourcestothedegreethattheyarecongruentwiththeTEKSandresearch-basedbestpractices.Teachingusingonlythesuggestedresourcesdoesnotguaranteestudentmasteryofallstandards.Teachersmustuseprofessionaljudgmenttoselectamongtheseand/orotherresourcestoteachthedistrictcurriculum.

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NISD Math Focus

Best Practices in the Math Classroom • Teaching for Conceptual Understanding: Math instruction should focus on developing a true understanding of the math concepts being

presented in the classroom. Teachers should avoid teaching “quick tricks” for finding the right answers and instead focus on developing student understanding of the “why” behind the math. Math is not a list of arbitrary steps that need to be memorized and performed, but is, rather, a logical system full of deep connections. When students see math as a set of disconnected steps to follow they tend to hold many misconceptions, make common mistakes, and do not retain what they have learned. However, when students understand the connections they have fewer misconceptions, make less errors, and tend to retain what they have learned.

• Developing Student Understanding through the Concrete-Pictorial-Abstract Approach: When learning a new math concept, students should be taken through a 3-step process of concept development. This process is known as the Concrete-Pictorial-Abstract approach. During the concrete phase, students should participate in hands-on activities using manipulatives to develop an understanding of the concept. During the pictorial phase, students should use pictorial representations to demonstrate the math concepts. This phase often overlaps with the concrete phase as students draw a representation of what they are doing with the manipulatives. During the abstract phase, students use symbols and/or numbers to represent the math concepts. This phase often overlaps with the pictorial phase as students explain their thinking in pictures, numbers, and words. If math concepts are only taught in the abstract level, students attain a very limited understanding of the concepts. However, when students go through the 3-step process of concept development they achieve a much deeper level of understanding.

• Developing Problem Solving Skills through Quality Problem Solving Opportunities: Students should be given opportunities to develop their problem solving skills on a daily basis. One effective approach to problem solving is the think-pair-share approach. Students should first think about and work on the problem independently. Next, students should be given the opportunity to discuss the problem with a partner or small group of other students. Finally, students should be able to share their thinking with the whole group. The teacher can choose students with different approaches to the problem to put their work under a document camera and allow them to talk through their thinking with the class. The focus of daily problem solving should always be Quality over Quantity. It is more important to spend time digging deep into one problem than to only touch the surface of multiple problems.

• Developing Problem Solving Skills through Pictorial Modeling: One of the most important components of students’ problem solving development is the ability to visualize the problem. Students should always draw a pictorial representation of the problem they are trying to solve. A pictorial model helps students to better visualize the problem in order to choose the correct actions needed to solve it. Pictorial modeling in math can be done with pictures as simple as sticks, circles, and boxes. There is no need for detailed artistic representations. One of the most effective forms of pictorial modeling is the strip diagram (or part-part-whole model in lower grades). This type of model allows students to see the relationships between the numbers in the problem in order to choose the proper operations.

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• Developing Students’ Number Sense: The development of number sense is a critical part of a student’s learning in the mathematics classroom. The ability to reason about numbers and their relationships allows students the opportunity to think instead of just following a rote set of procedures. The standard algorithms for computation may provide students with a quick answer, but they do not allow for development of student thinking and reasoning. The standard algorithms should not be abandoned completely, but should be used as one of many ways of approaching a computation problem. It is, however, very important that students have the opportunity to develop their number sense through alternative computation strategies before learning the standard algorithm in order to prevent students from having a limited view of number relationships.

• Creating an Environment of Student Engagement: The most effective math classrooms are places in which students have chances to interact with their teacher, their classmates, and the math content. Students should be given plenty of opportunities to explore and investigate new math concepts through higher-order, rigorous, and hands-on activities. Cooperative learning opportunities are critical in order for students to talk through what they are learning. The goal should be for the student to work harder than the teacher and for the student to do more of the talking.

• Higher Level Questioning: The key to developing student thinking is in the types of questions teachers ask their students. Teachers should strive to ask questions from the top three levels of Bloom’s Taxonomy to probe student thinking.

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NISD Math Focus

Developing Problem Solving through a 4-Square Model Approach • The 4-square problem solving model should be used to help guide students through the problem solving process. It is important that

students complete step 2 (pictorial modeling) before attempting to solve the problem abstractly (with computation). When students create a visual model for the problem they are better able to recognize the appropriate operation(s) for solving the problem.

Dragon Problem Solving 1. What is the problem asking?

2. This is how I see the problem. (pictorial/ strip diagram)

3. This is how I solve the problem. (computation)

4. I know my work is correct because... (justify)

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NISD Math Focus

Developing Problem Solving through Pictorial Modeling/ Strip Diagrams Part-Part-Whole: Addition and Subtraction

Whole Unknown Alan had some marbles. He lost 12 of them. Then he had 32 left. How many did he have to begin with?

? 12 32

Part Unknown Steven had 122 peanuts. He ate 71 of them. How many peanuts are left?

122 71 ?

Another Part Unknown Some adults and 12 children are on a bus. There are 31 people on the bus. How many adults are on the bus?

31 ? 12

Comparison: Addition and Subtraction

How Much More Unknown Alex has 47 toy cars. Keisha has 12 toy cars. How many more cars does Alex have than Keisha?

47 12 ?

Smaller Quantity Unknown Fran spent $84 which was $26 more than Alice spent. How much did Alice spend?

84 ? 26

Larger Quantity Unknown Barney has 23 old coins. Steve has 16 more old coins than Barney. How many old coins does Steve have?

? 23 16

Equal Parts: Multiplication and Division

Whole Unknown Kim has 4 photo albums. Each album has 85 pictures. How many photos are in her 4 albums?

? 85 85 85 85

Amount for Each Part Unknown Pam put the same number of apples in each of 4 bags. She ended up with 52 apples in bags. How many apples did she put in each bag?

52 ? ? ? ?

Number of Equal Parts Unknown Fred bought some books. Each book cost $16. He spent $48 on books. How many books did he buy?

48 16

Comparison: Multiplication and Division

Larger Quantity Unknown Raul has 17 markers. Linda has 3 times as many. How many markers does Linda have?

? 17 17 17 17

Smaller Quantity Unknown Maria has 24 cards. She has 3 times as many cards as Jamal has. How many cards does Jamal have?

24 ? ? ? ?

Number of Times as Many Unknown Ann’s teacher is 39 years old. Ann is 13 years old. Ann’s teacher is how many times as old as Ann?

39 13 13

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NISD Math Focus

Developing Number Sense through Number Talks

What is a Number Talk? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.

Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.

A Rationale for Number Talks

http://www.mathsolutions.com/documents/9781935099116_ch1.pdf

Number Talks 6-Weeks Focus

Operation Strategies 1st 6-Weeks Addition Breaking Each Number Into its Place Value (Decomposing Each Number), Making Landmark

or Friendly Numbers, Doubles/ Near-Doubles, Making Tens, Compensation, Adding Up in Chunks (Decomposing One Number)

2nd 6-Weeks Subtraction Adding Up, Removal or Counting Back, Place Value and Negative Numbers, Keeping a Constant Difference, Adjusting One Number to Create and Easier Problem

3rd 6-Weeks Multiplication Repeated Addition or Skip Counting, Making Landmark or Friendly Numbers, Partial Products, Doubling and Halving, Breaking Factors into Smaller Factors

4th 6-Weeks Addition Breaking Each Number Into its Place Value (Decomposing Each Number), Making Landmark or Friendly Numbers, Doubles/ Near-Doubles, Making Tens, Compensation, Adding Up in Chunks (Decomposing One Number)

5th 6-Weeks Subtraction Adding Up, Removal or Counting Back, Place Value and Negative Numbers, Keeping a Constant Difference, Adjusting One Number to Create and Easier Problem

6th 6-Weeks Division Repeated Subtraction or Sharing/ Dealing Out, Multiplying Up, Partial Quotients, Proportional Reasoning

* Highlighted strategies must be introduced. Other strategies may be used with teacher discretion.

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Number Talks

Addition Strategy Examples Strategy Example(s)

Breaking Each Number Into its Place Value (Decomposing Each Number)

116 + 118 (100 + 10 + 6) + (100 + 10 + 8) 100 + 100 = 200 10 + 10 = 20 6 + 8 = 14 200 + 20 + 14 = 234

Making Landmark or Friendly Numbers

116 + 118 +2 116 + 120 = 236 236 – 2 = 234

Doubles/ Near-Doubles 116 + 118 -2 -3 115 + 115 = 230 230 + 4 = 234

Making Tens 116 + 118 (110 + 4 + 2) + (110 + 8) 110 + 110 + (2 + 8) + 4 110 + 110 + 10 + 4 230 + 4 = 234

116 + 118 (110 + 6) + (110 + 4 + 4) 110 + 110 + (6 + 4) + 4 110 + 110 + 10 + 4 = 234

Compensation 116 + 118 - 2 +2 114 + 120 = 234

116 + 118 +4 -4 120 + 114 = 234

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Adding Up in Chunks (Decomposing One Number)

116 + 118 116 + (100 + 10 + 4 + 4) 116 + 100 = 216 216 + 10 = 226 226 + 4 = 230 230 + 4 = 234

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Number Talks

Subtraction Strategy Examples Strategy Example(s)

Adding Up 123 – 59 59 + 1 = 60 60 + 40 = 100 100 + 23 = 123 1 + 40 + 23 = 64

Removal or Counting Back

123 – 59 123 – (10+10+10+10+10+3+6)

123- 59 123 – (20+30+3+6) 123 -20 = 103 103 – 30 = 73 73 – 3 = 70 70 – 6 = 64

123 – 59 123 – (50 + 9) 123 – 50 = 73 73 – 9 = 64

Place Value and Negative Numbers

123 – 59

100 20 3 - 50 9

100 -30 -6

100 – 30 – 6 100 – 30 = 70 70 – 6 = 64

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Keeping a Constant Difference

123 – 59 123 + 1 = 124 - 59 + 1 = - 60 64

300 – 78 300 – 1 = 299 - 78 – 1 = - 77 222

Adjusting One Number to Create and Easier Problem

123 – 59 123 123 -59 + 1 = - 60 63 + 1 = 64

123 – 59 123 123 - 59 – 6 = - 53 70 – 6 = 64

123 – 59 123 + 6 = 129 - 59 -59 70 – 6 = 64

123 – 59 123 – 4 = 119 -59 -59 60 + 4 = 64

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Number Talks

Multiplication Strategy Examples Strategy Example(s)

Repeated Addition or Skip Counting

6 x 15 15 + 15 + 15 + 15 + 15 + 15 15 + 15 = 30 30 + 15 = 45 45 + 15 = 60 60 + 15 = 75 75 + 15 = 90

6 x 15 15 + 15 + 15 + 15 + 15 + 15 2 x 15 = 30 2 x 15 = 30 90 2 x 15 = 30

6 x 15 15 + 15 + 15 + 15 + 15 + 15 6 x 10 = 60 6 x 5 = 30 90

Making Landmark or Friendly Numbers

9 x 15 9 groups of 15 + 1 (group of 15) 10 x 15 = 150 150 – 15 = 135

Partial Products 12 x 9 (10 + 2) x 9 10 x 9 = 90 2 x 9 = 18 90 + 18 = 108

12 x 9 (6 + 6) x 9 6 x 9 = 54 6 x 9 = 54 54 + 54 = 108

12 x 9 12 x (5 + 4) 12 x 5 = 60 12 x 4 = 48 60 + 48 = 108

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Doubling and Halving

Breaking Factors into Smaller Factors

8 x 25 (4 x 25) + (4 x 25) 100 + 100 = 200

8 x 25 (2 x 4) x 25 2 x (4 x 25) 2 x 100 = 200

8 x 25 8 x (5 x 5) (8 x 5) x 5 40 x 5 = 200

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Number Talks

Division Strategy Examples Strategy Example(s)

Sharing/ Dealing Out 30 ÷ 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

5 x 6 = 30

30 ÷ 5

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

5 x 6 = 30 First Deal: 5 x 2 = 10

Second Deal: 5 x 2 = 10 Third Deal: 5 x 2 = 10

Multiplying Up 72 ÷ 8 8 x 5 = 40 8 x 4 = 32 8 x 9 = 72 72 ÷ 8 = 9 72 ÷ 8

8 x 5 = 40

8 x 4 = 32

76 ÷ 4 4 x 10 = 40 4 x 5 = 20 4 x 4 = 16 4 x 19 = 76 76 ÷ 4 = 19

4 x 10 = 40

4 x 5 = 20 4 x 4 = 16

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Partial Quotients 56 ÷ 4 40 ÷ 4 = 10 16 ÷ 4 = 4 56 ÷ 4 = 14

88 ÷ 4 40 ÷ 4 = 10 40 ÷ 4 = 10 8 ÷ 4 = 2 88 ÷ 4 = 22

Proportional Reasoning 88 ÷ 4 88 ÷ 4 = 44 ÷ 2 = 22 ÷ 1 = 22

88 44 22 ---- = ---- = ----- = 22 4 2 1

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Year at a Glance First Semester Second Semester 1st 6-Weeks 4th 6-Weeks

• Bundle #1- Representing and Comparing Whole Numbers (10 days)

• Bundle #2- Addition and Subtraction of Whole Numbers (19 days)

• Bundle #5 (cont.)- Fractions (18 days/ continued from 3rd 6-weeks)

• Bundle #6- Geometry (15 days)

• Bundle #7- Measurement (19 days/ continued in 5th 6-weeks)

2nd 6-Weeks 5th 6-Weeks • Bundle #3- Multiplication and Division of Whole Numbers

(Understanding Multiplication and Division) (34 days/ continued in 3rd 6-weeks)

• Bundle #7- Measurement (19 days/ continued from 4th 6-weeks)

• Bundle #8- Data Analysis (10 days)

• Bundle #9- Personal Financial Literacy (4 days)

• Bundle #10- STAAR Review and Testing (15 days/ continued in 6th 6-weeks)

3rd 6-Weeks 6th 6-Weeks • Bundle #3 (cont.)- Multiplication and Division of Whole

Numbers (Understanding Multiplication and Division) (34 days/ continued from 2nd 6-weeks)

• Bundle #4- Multiplication and Division of Whole Numbers (Expanding and Mastering Multiplication and Division) (15 days)

• Bundle #5- Fractions (18 days/ continued in 4th 6-weeks)

• Bundle #10- STAAR Review and Testing (15 days/ continued from 5th 6-weeks)

• Bundle #11- Extended Learning (17 days)

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TEKS Spiraling Checklist

*The following checklist is intended to assist with planning for spiraled review of previously taught material. The lavender shaded boxes indicate the 6-weeks in which the TEKS are introduced/taught. For each 6-weeks following initial instruction, there are six boxes in which to indicate when the TEKS were reviewed. For documentation purposes, the date the TEKS were reviewed can be written in the provided boxes. TEKS can be reviewed through center activities, problem of the day, entry/exit tickets, mini-lessons, etc.

1st 6-Weeks 2nd 6-Weeks 3rd 6-Weeks 4th 6-Weeks 5th 6-Weeks 6th 6-Weeks 3.2A

3.2B

3.2C

3.2D

3.3A

3.3B

3.3C

3.3D

3.3E

3.3F

3.3G

3.3H

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3.4A

3.4B

3.4C

3.4D

3.4E

3.4F

3.4G

3.4H

3.4I

3.4J

3.4K

3.5A

3.5B

3.5C

3.5D

3.5E

3.6A

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3.6B

3.6C

3.6D

3.6E

3.7A

3.7B

3.7C

3.7D

3.7E

3.8A

3.8B

3.9A

3.9B

3.9C

3.9D

3.9E

3.9F

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Mathematical Process Standards • Process standards MUST be integrated within EACH bundle to ensure the success of students.

3.1A 3.1B 3.1C 3.1D 3.1E 3.1F 3.1G apply mathematics to problems arising in everyday life, society, and the workplace

use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution

select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

create and use representations to organize, record, and communicate mathematical ideas

analyze mathematical relationships to connect and communicate mathematical ideas

display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

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Math Instructional Resources

Resource Print/Online Description EnVision Both Textbook Adoption https://www.pearsontexas.com/#/ Motivation Math Both Supplemental Curriculum https://www.mentoringminds.com/customer/account/login/ Engaging Mathematics Print Collection of Mini-Lessons for All TEKS from Region IV http://www.region4store.com/catalog.aspx?catid=1171582 Reasoning Mind (STAAR Readiness) Online Online STAAR Supplemental Curriculum http://www.rmcity.org/ Think Through Math Online Online Supplemental Curriculum https://lms.thinkthroughmath.com/users/sign_in\ Thinking Blocks Online Online Problem Solving Practice with Strip Diagrams http://www.mathplayground.com/thinkingblocks.html 3rd Grade Math Games Print Collection of Engaging and Low-Prep Math Games for Skill

Practice http://maccss.ncdpi.wikispaces.net/file/view/3rdgrade_GAMES_8.22.14.pdf/519547204/3rdgrade_GAMES_8.22.14.pdf Epic! For Educators Online Search for Literature Connections for Math Content https://www.getepic.com/educators Number Talks (Sherry Parrish) Print Develop Number Sense Through a Daily Number Talk

Routine TEKSing Toward STAAR Print STAAR Based Supplemental Curriculum Lessons for Learning (North Carolina) Print Collection of Engaging and Rigorous Math Lessons http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade3-2014new.pdf/559562521/CCSSMathTasks-Grade3-2014new.pdf Math Learning Center (Bridges) Print Collection of Engaging and Rigorous Math Lessons http://catalog.mathlearningcenter.org/catalog/supplemental-materials-elementary/lessons-activities-grade-3-free NCTM Illuminations Online Search for Engaging and Rigorous Math Lessons by Grade

and Topic http://illuminations.nctm.org/ Math Coach’s Corner Online Math Blog from a Master Texas Math Teacher, Coach, and

Consultant http://www.mathcoachscorner.com/ Promethean Planet Online Tools and Lessons for Interactive Whiteboard http://www.prometheanplanet.com/en-us/ Interactive Math Glossary Online TEA Interactive Math Glossary http://www.texasgateway.org/resource/interactive-math-glossary?field_resource_keywords_tid=math%20teks&sort_by=title&sort_order=ASC&items_per_page=5

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TEKS Information for Teachers TEA STAAR Resources Online TEA Information Regarding STAAR Math http://tea.texas.gov/student.assessment/staar/math/ TEA Math Resources Online TEA Supporting Information for Math TEKS http://tea.texas.gov/Curriculum_and_Instructional_Programs/Subject_Areas/Mathematics/Resources_for_the_Revised_Mathematics_TEKS/ Lead4Ward Resources Online Math TEKS Instructional Resources and Supporting

Information http://lead4ward.com/resources/ TEKS Resource System Online Math TEKS Instructional Resources and Supporting

Information http://www.teksresourcesystem.net/module/profile/Account/LogOn

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Course: Grade 3 Math Bundle 1: Representing and Comparing Whole Numbers

Dates: August 22nd- September 2nd (10 days)

TEKS 3.2A: compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate (Expanded notation will be taught during Bundle 3. Expanded form should be taught during the current bundle.) 3.2B: describe the mathematical relationships found in the base-10 place value system through the hundred thousands place (Multiplicative relationships between place values will be introduced during Bundle 3.) 3.2C: represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers 3.2D: compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary

Unit Vocabulary: Base 10 place value system Digit Hundred thousands Number line Sum Compare Equal to (=) Hundreds Ones Ten thousands Compose Expanded form Hundreds period Order Tens Consecutive multiples Greater than (>) Least to greatest Period Thousands Decompose Greatest to least Less than (<) Place value Thousands period Round Whole numbers

Cognitive Complexity Verbs: compose, decompose, use, represent, describe Academic Vocabulary by Standard: 3.2A: compose, decompose, sum, place value, period, hundreds period, thousands period, thousands, hundreds, tens, ones, expanded form 3.2B: base-10 place value system, hundred thousands, ten thousands, thousands, hundreds, tens, ones, digit 3.2C: number line, consecutive multiples, place value (tens, hundreds, thousands, ten thousands), round 3.2D: place value, compare, order, whole numbers, less than (<), greater than (>), equal to (=), digit, greatest to least, least to greatest

Suggested Math Manipulatives

Base 10 Blocks Money Place Value Charts Place Value Disks Number Lines Cuisenaire Rods Dice Place Value Dice Hundreds Chart

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Bundle 1: Vertical Alignment

1.2B use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones 1.2C use objects, pictures, and expanded and standard forms to represent numbers up to 120 2.2A use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones 2.2B use standard, word, and expanded forms to represent numbers up to 1,200

3.2A: compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals

3.2B: describe the mathematical relationships found in the base-10 place value system through the hundred thousands place

4.2A interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals

1.2F order whole numbers up to 120 using place value and open number lines 2.2E locate the position of a given whole number on an open number line

3.2C: represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers

4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

1.2E use place value to compare whole numbers up to 120 using comparative language 1.2F order whole numbers up to 120 using place value and open number lines 1.2G represent the comparison of two numbers to 100 using the symbols >, <, = 2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, =)

3.2D: compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

4.2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, = 5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, =

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Bundle 1: Teacher Notes

TEKS/Student Expectations

Instructional Implications Distractor Factors Supporting Readiness Standards

TEA Supporting Information


As students represent numbers using base ten blocks, their understanding should also be associated with writing numbers in expanded form. This type of representation will allow students to focus on the value of each digit and support the understanding of the place value system (i.e. one thousand cube represents the value of 1,000; eight hundred flats represent the value of 800; two ten rods represent the value of 20; seven unit cubes represent the value of 7; 1,000 + 800+ 20 + 7= 1,827). Students need to understand that the digit in the number represents its place value which is different from the value of the number (i.e. 52,184; the digit two is in the thousands place represented by two thousand cubes, but is valued at 2,000). It will be essential to explain the use of the comma to separate the periods (i.e.; 52,184; the comma separates the hundreds period from the thousands period). Encourage students to represent a number in more than one way (i.e. 582 can be represented as 5 hundreds, 8 tens, 2 ones or 4 hundreds, 18 tens, and 2 ones or 5 hundreds, 7 tens, and 12 ones). This understanding will lend itself to regrouping in subtraction. (I.e. 582-193 = ___; 582 would have to be regrouped into 4 hundreds, 17 tens, and 12 ones).

* Students confuse the place value a digit is in with its value (i.e. 345; the digit 4 is in the tens place value but it is valued at 40). * Students may incorrectly use the word “and” to represent numbers in words (i.e. 345 is represented as “three hundred forty-five” not “three hundred and forty-five). The use of the word “and” is applied in the representation of whole number and decimal/fraction values (i.e. 3.45 is represented as “three and forty-five hundredths). * Students may not use the hyphen appropriately when representing numbers in words (i.e. 345 is represented as three hundred forty-five).

Composing and decomposing whole numbers may focus on place value such as the relationship between standard notation and expanded notation. The number 789 may be decomposed into the sum of 500, 200, 50, 30, and 9 to prepare for work with compatible numbers when adding whole numbers with fluency. Please note: Expanded notation for 12,905 is (1 x 10,000) + (2 x 1,000) + (9 x 100) + (5 x 1), while expanded form is 10,000 + 2,000 + 900 + 5. Decomposition of whole numbers does not involve carrying digits to the next place holder. Each addend of the decomposition should only have one nonzero digit. For example; 789 may not be decomposed into the sum of 600, 90, 90, and 9 or the sum of 600, 180, and 9.

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Through the use of base ten blocks, students will visually understand the magnitude of numbers (i.e. the thousand cube is ten times more than the hundred flat, the hundred flat is ten times more than the ten rod, the hundred flat is ten times smaller than the thousand cube, the ten rod is ten times smaller than the hundred flat, etc.,). Students should understand that each time you move one place to the left, the value of the numbers become ten times larger and each time you move right, the value of the numbers become ten times smaller.

This standard describes the mathematical relationship found in the base-10 place value system; this understanding will support students in identifying the value of each digit in a number in order to represent numbers in expanded notation and to effectively compare/order numbers. 3.2A: compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate 3.2D: compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

The mathematical relationships include interpreting the value of each place-value position as ten times the position to the right.

3.2C: represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers

Instruction should begin with skip counting by tens, hundreds, thousands, and ten-thousands for students to understand consecutive multiples. Students should represent these landmark values through the use of an open number line. As students are given a specific number to locate on an open number line, you will begin to assess students’ understanding of place value (i.e. students place the number 1,387 between 1,300 and 1,400), the relative position of numbers (i.e. the number 1,300 would be indicated first and the number 1,400 would be indicated second on the open number line), and the magnitude of numbers (i.e. students physically place the number 1,387 closer to 1,400 than 1,300). Students will apply this

As students will be asked to solve problems using all four operations, it will be important to estimate solutions prior to solving. As rounding is one way of estimating values, students will be able to evaluate if their solutions are reasonable. 3.2D: compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or = 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.4K: solve one-step and two-step problems involving

Words may include phrases such as “closer to,” “is about,” or “is nearly.”

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understanding to the rounding of whole numbers to the nearest 10; 100; 1,000; 10,000.

multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

3.2D: compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

As students compare the value of numbers, they need to be able to relate their understanding of place value (i.e. the number 5,342 is greater than 3,226 because the digit 5 in 5,432 means there are 5 thousands which is a value of 5,000; however, the digit 3 in 3,226 means there are only 3 thousands which is a value of 3,000). Students will compare two numbers using the correct academic vocabulary (i.e. 5,342 is greater than 3,226). It is important for students to recognize the inverse comparison statement as well (i.e. 3,226 is less than 5,342). Instruction should connect the comparative language to the symbols (>, <, =). It is critical that students do not learn how to read each of the symbols using a trick to remember directionality of the symbols (i.e. the alligator’s mouth eats the bigger number). Encourage students to write and articulate two comparison statements during activities (i.e. 5,342 > 3,226 and 3,226 < 5,342). The standard also has students ordering three or more numbers from least to greatest or greatest to least. The use of open number lines (see 3.2C) will allow students to order more efficiently as numbers increase from left to right on a number line can be associated to ordering from least

* Students may not be able to read comparison symbols correctly as they rely on a trick to determine directionality. * Students may view a comparison statement and its inverse as two different comparison statements (i.e. 456>412 is the same as 412<456). * Students may confuse the place value a digit is in with its value (i.e. 345; the digit 4 is in the tens place value but is valued at 40).

Specificity regarding notation has been included with the inclusion of the symbols >, <, or =.

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to greatest; numbers decrease from right to left on a number line can be associated as ordering from greatest to least.

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Course: Grade 3 Math Bundle 2: Addition and Subtraction of Whole Numbers

Dates: September 6th- September 30th (19 days)

TEKS 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.4B: round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems 3.4C determine the value of a collection of coins and bills 3.5A: represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations 3.5E: represent real-world relationships using number pairs in a table and verbal descriptions (addition and subtraction only)

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary

Unit Vocabulary Addition Difference Nickels Properties of operations Subtraction Associative property Dimes Number lines Quarters Sum Bills Equations/ number sentences Number pairs Relationships Table Coins Estimate Patterns Round Value Commutative property Inverse operations Pennies Solutions Verbal description Compatible numbers Nearest 10 or 100 Place value Strategies Whole numbers

Cognitive Complexity Verbs: round, use, estimate, determine, solve, represent Academic Vocabulary by Standard: 3.4A: addition, difference, place value, properties of operations (associative property, commutative property, inverse properties), relationships, subtraction, strategies, sum 3.4B: addition, compatible numbers, difference, estimate, nearest 10 or 100, round, solutions, subtraction, sum 3.4C: bills, coins, dimes, nickels, pennies, quarters, value 3.5A: addition, difference, equations/ number sentences, number lines, subtraction, sum, whole numbers 3.5E: number pairs, patterns, table, verbal description


Number Lines Base 10 Blocks Snap Cubes Part/ Whole Mat Balance Scales Strip Diagrams Money

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Bundle 2 Vertical Alignment

2.4A recall basic facts to add and subtract within 20 with automaticity 2.4B add up to four two-digit numbers and subtract two digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations 2.4C solve one-step and multistep word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms 2.4D generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000

3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

4.3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations 4.3F evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm 5.3A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division 5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations 5.3K add and subtract positive rational numbers fluently

3.4B: round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems

4.2D round whole numbers to a given place value through the hundred thousands place 4.2G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers 5.2C round decimals to tenths or hundredths

1.4A identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them 1.4B write a number with the cent symbol to describe the value of a coin. 1.4C use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes 2.5A determine the value of a collection of coins up to one dollar 2.5B use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

3.4C: determine the value of a collection of coins and bills

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1.5D represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences 1.5E understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s) 2.7C represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

3.5A: represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity 5.4B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity

3.5E: represent real-world relationships using number pairs in a table and verbal descriptions

4.4B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence 5.4C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph. 5.4D recognize the difference between additive and multiplicative numerical patterns given in a table or graph

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Students will employ their understanding of place value and expanded notation to develop strategies to add and subtract. Properties of operations include the commutative, associative, and inverse properties. Although instruction may model the names of the properties, students will only be asked to employ the underlying concepts in order to solve addition and subtraction problems. Commutative & Associative Property: 134 + 517=___; (100 + 30 + 4) + (500 + 10 + 7)=___; (100+500) + (30 + 10) + (4 + 7)=___); (600 + 40 + 11=651) Inverse Property: 262-48=____ or 48 + ___ =262 48 + (2 + 50 + 162) = 262 48 + 214 = 262 or 262 – 48 = 214 As students become more fluent with numbers, the traditional algorithm can be introduced relating the steps they took with their understanding of expanded notation. As the standard requires students to solve one and two-step word problems, instruction should include samples of two-step addition, subtraction, and a mixture of addition and subtraction. In conjunction with 3.5A, students may need a visual to represent their understanding (i.e. use of a strip diagram or part-part-whole mat). Word problems should include a variety of contexts. Joining: Sarah had 43 pencils. Juan gave her 18 more pencils. How many pencils does Sarah have now? Sarah

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem. * Students may not recognize a number sentence and its inverse as being equivalent (i.e. 42 – 18 =___ is the same thing as 18 + ___=42).

Two- step problems may include addition, subtraction, or a combination of the two. The SE specifies that the numbers to be added or subtracted must be whole numbers within 1,000. The SE includes specific approaches to solving one-step and two-step problems: strategies based on place value, properties of operations, and the relationship between addition and subtraction. The one-step problem prompts students to add numbers such as 237 and 547. If using strategies based on place value, a student might add the hundreds to get 700, the tens to get 70, and the ones to get 14 and then combine 700, 70, and 14 to have a sum of 784. If using a strategy based on properties of operations, a student may consider that 237 + 547 is equivalent to 237 + (5-- + 47) = (237 + 500) + 47 = 737 + 47 = 784. If using a strategy based on the relationship between addition and subtraction, a

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had 25 pencils. Juan gave her some more pencils. Now Sarah has 43 pencils. How many pencils did Juan give her? Sarah had some pencils. Juan gave her 18 pencils. Now Sarah has a total of 43 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 43 pencils. She gave 18 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 43 pencils. She gave some to Juan. Now she only has 25 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave 18 to Juan. Now Sarah has 25 pencils left. How many pencils did Sarah have before? Comparing: Juan has 43 pencils and Sarah has 25 pencils. How many more pencils does Juan have than Sarah? Sarah has 18 fewer pencils than Juan. If Sarah has 25 pencils, how many pencils does Juan have? Juan has 18 more pencils than Sarah. If Juan has 43 pencils, how many pencils does Sarah have? Juan has 43 pencils and Sarah has 25 pencils. How many more pencils does Sarah need to have the same amount as Juan? Be sure that students represent the associated number sentences in different ways (i.e. one step: 42-18 = ___ or ___=42-18 or 18 + ___=42) (i.e. two-step: 18 + ___ + 6 = 42 or ___ = 42 – 6 – 18).

student might subtract 63 from 547 and add it to 237 to have 300 and 484, which add to 784. “Procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently” (National Research Council, 2001, pg. 121).

3.4B: round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems

In conjunction with 3.4A, students will estimate solutions to addition and subtraction problems prior to solving for the exact answer. Students will employ the understanding of representing a number on a number line between two consecutive multiples of 10 or 100 (see 3.2C) as means of estimating sums and differences (i.e.

As students will be asked to solve addition and subtraction problems, it will be important to estimate solutions prior to solving. Rounding and the use of compatible numbers will support students in estimating solutions and evaluating reasonableness of solutions.

The choice of rounding or using compatible numbers belongs to the student.

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679-344=____; 700-300=400 or 680-340=340). In adherence to the standard, the intent of rounding is to estimate a solution; therefore, employing a specific rounding rule is not necessary. Compatible numbers is another means for estimating solutions (i.e. 679-344=___; 675-350=325).


3.4C: determine the value of a collection of coins and bills

Students are to apply their knowledge of skip counting to determine the value of a collection of bills and/or coins (i.e. given four dollar bills, 3 dimes, 4 nickels, and 6 pennies students will skip count by tens to add the value of the dimes 10,20,30; continuing skip counting by fives to add the value of the nickels 35,40,45,50; then skip count by twos to add the value of the pennies; 52, 54, 56 yielding a total of $4.56).

Solving addition and subtraction of problems may include determining the value of a collection of coins and bills. 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

Students may be asked to record the value of a collection of coins using a cent symbol or a dollar sign with a decimal.

3.5A: represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

In conjunction with 3.4A, students will represent addition/subtraction problems with pictorial models (base ten representations), number lines (movement of tens and one on a number line), and equations (number sentences to represent problems) in order to solve one- and two-step problems. The use of strip diagrams (part-part-whole mat) may support the understanding of how to represent such equations (i.e. The Wildcats basketball team scored 75 points. Michael scored 35 of the points, Damon scored 20 points, and the remaining points were scored by Rayshawn. How many points were scored by Rayshawn?)

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem. * Students may not recognize a number sentence and its inverse as being equivalent (i.e. 42 – 18 =___ is the same thing as 18 + ___=42).

Pictorial models such as strip diagrams build to the use of number lines.

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Total Number of Points Scored by Wildcat’s Team (whole)

75 Michael’s

Points (part) Damon’s

Points (part) Rayshawn’s Points (part)

35 20 ? 75 = 35 + 20 + ___ Encourage students to write more than one equation for every problem. (i.e. 75 – 35 – 20 = ___)


In accordance to the standard, students should be given a real world situation (i.e. number of wheels on a tricycle) and asked to represent the number pattern in a table and a verbal description (i.e. for every tricycle there are three times as many wheels). Table representations should be both vertical and horizontal. Verbal descriptions should relate patterns to the real world situation not just identifying “what’s my rule” (i.e. “There are three times as many wheels for the number of tricycles”; not “ x 3). Students should verbalize the inverse verbal description as it applies to the number pattern in the table (i.e. number of tricycles times 3 equals the total number of wheels or the number of wheels divided by 3 equals the total number of tricycles).

* Students may identify a pattern comparing input to input values and/or output values instead of input to output values. * Students may confuse a multiplicative pattern for a numeric pattern as they view multiplication as repeated addition. * Students may not recognize the equivalency of a verbal description and tis inverse (i.e. number of tricycles times 3 equals the total number of wheels or the number of wheels divided by 3 equals the total number of tricycles).

The expectation is that students apply this skill in a problem arising in everyday life, society, and the workplace. The expectation is that students extend the relationship represented in a table to explore and communicate the implications of the relationship. Real-world relationships include situations such as the following: 1 insect has 6 legs, 2 insects have 12 legs, 3 insects have 18 legs, 4 insects have 24 legs, etc.

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Course: Grade 3 Math Bundle 3: Multiplication and Division of Whole Numbers (Understanding Multiplication and Division)

Dates: October 4th- November 18th (34 days)

TEKS

3.2A: compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate (Expanded notation should be introduced in this bundle.) 3.2B: describe the mathematical relationships found in the base-10 place value system through the hundred thousands place (Multiplicative relationships are introduced in this bundle.) 3.4D: determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10 3.4E: represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting 3.4H: determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally 3.4I: determine if a number is even or odd using divisibility rules 3.4J: determine a quotient using the relationship between multiplication and division 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts 3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations 3.5C: describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24 3.5D: determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product 3.5E represent real-world relationships using number pairs in a table and verbal descriptions (Multiplication and Division) 3.6C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

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ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1B: monitor oral and written language production and employ self-corrective techniques or other resources Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3E: share information in cooperative learning interactions 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Vocabulary

Unit Vocabulary Area models Division Hundreds period Period Strategies Array Divisor Inverse operations Place value Strip diagrams Associative property Equal groups Length Product Sum Base-10 place value system Equal shares Multiplication Properties of

operations Table

Columns Equal-sized groups Multiplication facts Quotient Tens Commutative property Equations Number line Rectangles Then thousands Compose Even Number pairs Repeated addition Thousands Decompose Expanded notation Number sentence Repeated subtraction Thousands period Digit Expression Odd Rows Unknown number Distributive property Factors Ones Skip counting Verbal description Dividend Hundred thousands Patterns Square unit Divisibility rules Hundreds

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Cognitive Complexity Verbs: solve, use, compose, decompose, describe, represent, determine Academic Vocabulary by Standard: 3.2A: compose, decompose, sum, place value, period, hundreds period, thousands period, thousands, hundreds, tens, ones, expanded notation 3.2B: base-10 place value system, hundred thousands, ten thousands, thousands, hundreds, tens, ones, digit: 3.4D: array, columns, equal-sized groups, factor, multiplication, product, rows 3.4E: area models, arrays, equal-sized groups, factor, multiplication facts, number line, product, repeated addition, skip counting 3.4H: dividend, division, divisor, equal groups, equal shares, quotient, repeated subtraction 3.4I: divisibility rules, even, odd 3.4J: division, quotient, dividend, divisor, multiplication, product, factor 3.4K: area model, array, equal groups, division, quotient, divisor, dividend, multiplication, product, factor, properties of operations (associative property, commutative property, distributive property, inverse operations), strategies 3.5B: arrays, division, equations, multiplication, product, quotient, strip diagrams 3.5C: arrays, equal-sized groups, expression, multiplication, number line, repeated addition, skip counting 3.5D: division, quotient, divisor, dividend, multiplication, product, factor, number sentence/ equation, unknown number 3.5E: number pairs, patterns, table, verbal description 3.6C: array, area, factor, length, multiplication, product, rectangles, row, square unit


Color Tiles Grid Paper Number Line Pattern Blocks Dice Dominoes Hundreds Chart Strip Diagrams Base 10 Blocks Counters

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1.2B use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones 1.2C use objects, pictures, and expanded and standard forms to represent numbers up to 120 2.2A use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones 2.2B use standard, word, and expanded forms to represent numbers up to 1,200


4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals


4.2A interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left 5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals

2.6A model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined

3.4D: determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10

3.4E: represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings 5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm

3.4H: determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally

3.4I: determine if a number is even or odd using divisibility rules

3.4J: determine a quotient using the relationship between multiplication and division

3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

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3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations


3.5C: describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24

1.5G apply properties of operations to add and subtract two or three numbers

3.5D: determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product



4.4B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence 5.4C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph. 5.4D recognize the difference between additive and multiplicative numerical patterns given in a table or graph

2.9F use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit

3.6C: determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

4.5C use models to determine the formulas for the perimeter of a rectangle (l + w +l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w) 4.5D solve problems related to perimeter and area of rectangles where dimensions are whole numbers 5.4H represent and solve problems related to perimeter and/or area and related to volume

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As students represent numbers using base ten blocks, their understanding should also be associated with writing numbers in expanded form. This type of representation will allow students to focus on the value of each digit and support the understanding of the place value system (i.e. one thousand cube represents the value of 1,000; eight hundred flats represent the value of 800; two ten rods represent the value of 20; seven unit cubes represent the value of 7; 1,000 + 800+ 20 + 7= 1,827). Students need to understand that the digit in the number represents its place value which is different from the value of the number (i.e. 52,184; the digit two is in the thousands place represented by two thousand cubes, but is valued at 2,000). It will be essential to explain the use of the comma to separate the periods (i.e.; 52,184; the comma separates the hundreds period from the thousands period). Encourage students to represent a number in more than one way (i.e. 582 can be represented as 5 hundreds, 8 tens, 2 ones or 4 hundreds, 18 tens, and 2 ones or 5 hundreds, 7 tens, and 12 ones). This understanding will lend itself to regrouping in subtraction. (I.e. 582-193 = ___; 582 would have to be regrouped into 4 hundreds, 17 tens, and 12 ones).

* Students confuse the place value a digit is in with its value (i.e. 345; the digit 4 is in the tens place value but it is valued at 40). * Students may incorrectly use the word “and” to represent numbers in words (i.e. 345 is represented as “three hundred forty-five” not “three hundred and forty-five). The use of the word “and” is applied in the representation of whole number and decimal/fraction values (i.e. 3.45 is represented as “three and forty-five hundredths). * Students may not use the hyphen appropriately when representing numbers in words (i.e. 345 is represented as three hundred forty-five).

Composing and decomposing whole numbers may focus on place value such as the relationship between standard notation and expanded notation. The number 789 may be decomposed into the sum of 500, 200, 50, 30, and 9 to prepare for work with compatible numbers when adding whole numbers with fluency. Please note: Expanded notation for 12,905 is (1 x 10,000) + (2 x 1,000) + (9 x 100) + (5 x 1), while expanded form is 10,000 + 2,000 + 900 + 5. Decomposition of whole numbers does not involve carrying digits to the next place holder. Each addend of the decomposition should only have one nonzero digit. For example; 789 may not be decomposed into the sum of 600, 90, 90, and 9 or the sum of 600, 180, and 9.


Through the use of base ten blocks, students will visually understand the magnitude of numbers (i.e. the thousand cube is ten times more than the hundred flat, the hundred flat is ten times more than the ten rod, the hundred flat is ten times smaller than the

This standard describes the mathematical relationship found in the base-10 place value system; this understanding will support students in identifying the

The mathematical relationships include interpreting the value of each place-value position as ten times the position to the right.

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thousand cube, the ten rod is ten times smaller than the hundred flat, etc.,). Students should understand that each time you move one place to the left, the value of the numbers become ten times larger and each time you move right, the value of the numbers become ten times smaller.

value of each digit in a number in order to represent numbers in expanded notation and to effectively compare/order numbers. 3.2A: compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate 3.2D: compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

3.4D: determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10

Students should be provided with a variety of examples of equally-sized groups of objects to determine the total (i.e. a picture of 4 tricycles yields 12 tires). Instruction should include the use of arrays (i.e. a rectangular array with 5 rows and 3 columns yields a total of 15 units). In adherence to the standard, examples are limited to 10 x 10. In conjunction with 3.4E, instruction should relate the visual representations to its associated multiplication sentence (i.e. a rectangular array with 5 rows and 3 columns yields a total of 15 units; 5 x 3=15). Students should also relate the term factor and product to the pictorial and number sentence (i.e. a rectangular array with 5 rows and 3 columns yields a total of 15 units; 5 x 3 = 15; the 5 and 3 are factors of the product 15).

It is critical for students to develop the conceptual understanding of multiplication before moving to the abstract understanding of the standard algorithm and solving problems involving multiplication. This supporting standard provides that developmental progression. 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

Arrays should reflect the combination of equally-sized groups of objects. For example, 2 groups of pizza slices with 7 slices in each. Students may be expected to represent the solution using a number sentence. For example, 2 x 7 = 14.

3.4E: represent multiplication facts by using a variety of approaches such as repeated

The intent of this standard is to build the conceptual understanding of multiplication. Students will use a variety of methods to

It is critical for students to develop the conceptual understanding of

Examples of 5 x 4 using the listed strategies: Repeated addition:

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addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

understand the meaning of multiplication. Be sure the actions of each strategy is related to the number sentence (i.e. 3 x 6 = 18; the 3 represents the three tires on a tricycle and the 6 represents the number of tricycles and 18 represents the total number of tires; the 3 represents the number of spaces hopped in between each number on a number line and the 6 represents how many times we hopped by three and 18 represents the total number of hops; 18 represents the total number of “spaces” hopped; the 3 represents the number of rows in the array and the 6 represents the number of columns and the 18 represents the total number of units). Instruction should also associate the terms factor and product to the pictorial and numeric representation.

multiplication before moving to the abstract understanding of the standard algorithm and solving problems involving multiplication. This supporting standard provides that developmental progression. 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

4 + 4 + 4 + 4 + 4 = 20 Skip counting: 4, 8, 12, 16, 20 Equal sized- groups:

Arrays:

Area Models:

Equal Jumps on a Number Line:

3.4H: determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally

In accordance with the standard, instruction of division should include the use of manipulatives to model fair-sharing and the understanding of repeated subtraction to build conceptual understanding of the operation. Instruction should relate the manipulation of the objects to its associated division sentence (i.e. 15 lollipops shared among 5 friends can be modeled with 15 colored tiles divided into five equal groups, 15 ÷ 5 = 3). Students should also relate the terms quotient, dividend, and divisor to the actions and values in the number sentence (i.e. 15 color tiles represents the dividend,

It is critical for students to develop the conceptual understanding of multiplication before moving to the abstract understanding of the standard algorithm and solving problems involving multiplication. This supporting standard provides that developmental progression. 3.4K: solve one-step and two-step problems involving multiplication and division

Students are expected to think with both forms of division: partitioning into equal shares (determining the number of groups with a given number of objects in each group) and sharing equally (determining the number of items in each group when the objects are shared equally among a given number). Students may be asked to

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the 5 friends represent the divisor and the 3 lollipops in each group represent the quotient; dividend ÷ divisor = quotient).

within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

use number sentences to record the solutions.

3.4I: determine if a number is even or odd using divisibility rules

Instruction should allow students to use concrete objects to create equal pairs to determine if a number is even or odd (i.e. the number 17 has eight pairs with one left over reflecting an odd number). In accordance with the standard, instruction should relate the divisibility of two to even numbers (i.e. the number 14 had seven pairs reflecting an even number; 14 is divisible by two). If a whole number has in its ones place a 2,4,6,8, or 0, the number is even as it is divisible by two (e.g. the number 356 is divisible by two; therefore it is even because of the 6 in the ones place).

As students solve problems using all operations, developing patterns with even and odd solutions can support students with their computational efficiency and accuracy. 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

To determine if a number is even, one may apply the divisibility rule for 2: A number is divisible by 2 if the ones digit is even (0, 2, 4, 6, 8).

3.4J: determine a quotient using the relationship between multiplication and division

In accordance with the standard, students should relate the product from a multiplication number sentence to that of a quotient in a division number sentence. Factor x factor = product (i.e. 8 x 6 = 48) Product ÷ factor = factor (i.e. 48 ÷ 6 = 8) Dividend (product) ÷ Divisor (factor) = quotient (factor)

Relating multiplication to division supports a student’s ability to represent and solve multiplication and division problems. 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups;

The identification of the relationship between multiplication and division lays the foundation for determining a quotient based on this relationship. For example, the quotient of 40 ÷ 8 can be found by determining what factor makes 40 when multiplied by 8.

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properties of operations; or recall of facts 3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

In conjunction with 3.4G, students build on their flexibility of numbers to solve one- and two-step multiplication and/or division problems. Instruction should include the use of manipulatives for equal grouping, base ten blocks to build arrays and the use of rectangular area models to build the concrete understanding of the operation. Pictorial models (i.e. arrays and area models) should be related to the use of partial products/partial quotients and the traditional algorithm. Both strategies yield the same product, however, the partial products method models the value of each digit being multiplied and the traditional algorithm models the digits in each place value being multiplied. Encourage students to demonstrate their understanding in more than one way.

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem.

The focus of this standard is developing number-based strategies to solve multiplication and division problems within 100. This may include multiplying a two-digit number by a one-digit number. The product and dividend may be less than 100, but no operand is limited to the multiplication/ division facts.

3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

In conjunction with 3.4K, students will represent multiplication/division problems with arrays, strip diagrams (similar to part-part-whole mat), and equations in order to solve one- and two-step problems. The use of strip diagrams may support the understanding of how to represent such equations (i.e. Michael scored three times as many baskets as Rayshawn. If Rayshawn scored 5 baskets, how many baskets did Michael make?)

Michael’s Baskets ?

Rayshawn’s Baskets



5 5 5 Encourage students to write more than one equation for every problem (i.e. ___=5+5+5; ___=3x5).

* Students who do not have an understanding of the context of the problem may incorrectly represent the expression/equation (i.e. if Michael scored three times as many baskets as Rayshawn; that means that the number of baskets Michael scored should be higher than Rayshawn). * Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem.

This standard is an extension of 3.4K. The focus is on developing representations that build to numeric equations for multiplication and division situations by connecting arrays to strip diagrams.

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3.5C: describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24

In conjunction with 3.4D/E, this standard extends the concrete understanding of basic multiplication facts to two-digit by one-digit multiplication. Students relate the multiplicative expression to repeated addition (24 + 24 + 24), equal-sized groups (three groups of 24), arrays (represent two ten rods and four unit cubes three times), area models (represent a 20 + 4 rectangles three times yielding 20 + 20 + 20 + 4 + 4 + 4), equal jumps on a number line (jump 24 spaces three times on a number line), skip counting, (24, 48, 72).

Describing multiplicative expressions as a comparison will support the strategies of arrays, area models, and equal groups for solving multiplicative and/or division problems. 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts 3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

Building on 2.6A where multiplication is represented as repeated addition, 3 x 24 may be described as 3 groups of 24. The focus of this SE is on the numerical relationship between 24 and the product 3 x 24. The product of 3 x 24 will be 3 times as much as 24. This lays the foundation for future work in grade 5 with fraction multiplication and determining part of a number.

3.5D: determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product

In accordance with the standard, instruction should vary the unknown of a multiplication or division equation (i.e. ___ x 3 = 24; 3 x ___ = 24; 24 ÷ ___ = 3; 24 ÷ 3 = ___). In conjunction with 3.4J, students should relate the multiplicative terms (factor and product) to the division terms (quotient, dividend, and divisor) to further develop the relationship between multiplication and division.

Relating multiplication and division equations supports a student’s ability to represent and solve multiplication and division problems. 3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

If the multiplication or division equation relates to multiplication facts up to 10 x 10, students may apply their knowledge of facts and the relationship between multiplication and division to determine the unknown number. Students may be expected to use the relationship between multiplication and division for a problem such as 12 = ___ ÷ 6. The student knows that if 12 = ___ ÷ 6, then 12 x 6 = ___, so ___ = 72. Students may also be expected to solve problems where they state that the value 4 makes 3 x ___ = 12 a true equation.

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In accordance to the standard, students should be given a real world situation (i.e. number of wheels on a tricycle) and asked to represent the number pattern in a table and a verbal description (i.e. for every tricycle there are three times as many wheels). Table representations should be both vertical and horizontal. Verbal descriptions should relate patterns to the real world situation not just identifying “what’s my rule” (i.e. “There are three times as many wheels for the number of tricycles”; not “ x 3). Students should verbalize the inverse verbal description as it applies to the number pattern in the table (i.e. number of tricycles times 3 equals the total number of wheels or the number of wheels divided by 3 equals the total number of tricycles).

* Students may identify a pattern comparing input to input values and/or output values instead of input to output values. * Students may confuse a multiplicative pattern for a numeric pattern as they view multiplication as repeated addition. * Students may not recognize the equivalency of a verbal description and tis inverse (i.e. number of tricycles times 3 equals the total number of wheels or the number of wheels divided by 3 equals the total number of tricycles).

The expectation is that students apply this skill in a problem arising in everyday life, society, and the workplace. The expectation is that students extend the relationship represented in a table to explore and communicate the implications of the relationship. Real-world relationships include situations such as the following: 1 insect has 6 legs, 2 insects have 12 legs, 3 insects have 18 legs, 4 insects have 24 legs, etc.


Instruction should connect the visual of an array to area to a related multiplication fact (i.e. There are four rows with two unit squares in each row for a total of square units; 4 x 2 = 8; the area of this rectangle is 8 square units).

Students should also connect the appropriate vocabulary to the arrays (i.e. the number of rows and columns represent the factors and the total number of square units represents the product) and number sentence (i.e. 4 x 2 = 8; the 4 and the 2 represent the factors and 8 represents the product).

* Students confuse the concept of area with perimeter. * Students who just count up the number of square units to determine the area may not connect how multiplication relates to area. * Students may think that a 4 by 2 array yields a different area than a 2 by 4 array.

The SE limits the two-dimensional surfaces to rectangles with whole-number side lengths. Students may use concrete or pictorial models of square units to represent the number of rows and the number of unit squares in each row. Units of area may be square inches, square centimeters, square feet, square meters, etc. Students may be expected to use multiplication to determine the area of a rectangle instead of counting squares.

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Course: Grade 3 Math Bundle 4: Multiplication and Division of Whole Numbers (Expanding and Mastering Multiplication and Division)

Dates: November 28th-December 16th (15 days)

TEKS 3.4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts 3.4G: use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Algorithm Dividend Factor Partial products Properties of operations Associative property Division Mental math Product Quotient Commutative property Division fact Multiplication Properties Strategies Distributive property Divisor Multiplication fact

Cognitive Complexity Verbs: recall, use Academic Vocabulary by Standard: 3.4F: division fact, division, quotient, dividend, divisor, multiplication fact, multiplication, factor, product 3.4G: algorithm, factor, multiplication, product, properties of operations (associative property, commutative property, distributive property), strategies (mental math, partial products, properties)


Color Tiles Grid Paper Number Line Pattern Blocks Dice Dominoes Hundreds Chart Strip Diagrams Base 10 Blocks Counters

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3.4F: recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings 5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm

3.4G: use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings 4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15 4.4D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties 5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm

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3.4F: recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

As students begin developing their understanding of multiplication through a variety of approaches, instruction must move to the recalling of these facts with automaticity. It is critical that students have enough time developing the contextual meaning of multiplication before moving to the abstract. Students may need additional time to experience real world examples of determining the total number of objects in an equal grouping set (a picture of six tricycles reflects 3 x 6 = 18) and taking the total number of objects and putting them into equal groups (taking 18 wheels and placing into groups of 3; 18 ÷ 3 = 6) in order to understand how multiplication and division are related. Instruction should relate how the terms factor/product/ quotient relate to multiplication and division.

The recalling of multiplication facts will allow students to solve multiplication and division problems with efficiency. 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

The level of skill with “automaticity” requires recall of basic multiplication facts up to 10 x 10 with speed and accuracy at an unconscious level. Automaticity is part of procedural fluency. As such, it should not be overly emphasized as an isolated skill. Students may be asked to recall these facts when solving problems. The unknown may be determined using the relationship between multiplication and division.

3.4G: use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

In accordance with the standard, students are to use strategies to develop their conceptual understanding of two-digit times one-digit multiplication. The use of mental math, partial products, and operational properties will allow students to build their flexibility in the use of numbers (i.e. 24 x 5 = (20 + 4) x 5 = (20 x 5) + (4 x 5) = 100 + 20 = 120). It is imperative to relate those actions to the steps found in the traditional algorithm. In the partial products strategy, the tens place was multiplied by 5 first and then the ones place value was multiplied by 5 second. The two values were added together yielding a product of 120. In the traditional algorithm, the ones place value was multiplied by five first and the tens place value was multiplied by five

It is critical for students to develop the conceptual understanding of multiplication before moving to the abstract understanding of the standard algorithm and solving problems involving multiplication. This supporting standard provides that developmental progression. 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

Strategies and algorithms include mental math; partial products; the commutative, associative, and distributive properties; and the standard algorithm. For example, when prompted to multiply 97 x 3, a student may determine the product by multiplying 90 x 3 and 7 x 3 and adding 270 and 21 for an answer of 291. A student may also think of 97 x 3 as (100 – 3) x 3, multiplying 100 x 3 to get 300 and then subtracting 3 x 3 or 9 for an answer of 291.

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second. The two values were added together yielding a product of 120. Both strategies yield the same product; however, the partial products method models the value of each digit being multiplied and the traditional algorithm models the digits within each place value being multiplied. Encourage students to demonstrate their understanding in more than one way.

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Course: Grade 3 Math Bundle 5: Fractions

Dates: January 2nd- January 27th (18 days)

TEKS 3.3A: represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines 3.3B: determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line 3.3C: explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number 3.3D: compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b 3.3E: solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines 3.3G: explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model 3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models 3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical whole need not have the same shape 3.7A: represent fractions of halves, fourths, and eighths as distances from zero on a number line

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ELPS Learning Strategies 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

Vocabulary

Unit Vocabulary Area Distance Fractional units Part of a whole Strip diagram Area model Eighths Fraction Point Sum of the parts Comparison symbol Equal parts Greater than (>) Polygon Thirds Compose Equal parts of a whole Half/ halves Portion Two-dimensional Congruent Equivalent fractions Less than (<) Shape Unit fraction Decompose Fourths Number line Sixths Whole Denominator Fractional part Numerator Size Zero

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Cognitive Complexity Verbs: represent, use, determine, explain, compose, decompose, solve, explain, recognize, compare Academic Vocabulary by Standard: 3.3A: denominator, equal parts, fractions, fractional part, number line, numerator, part of a whole, strip diagram, whole 3.3B: denominator, equal parts, fraction, numerator, number line, part of a whole, point, whole 3.3C: equal parts, fractional units, part of a whole, unit fraction, whole 3.3D: compose, decompose, denominator, equal parts, fraction, numerator, part of a whole, sum of the parts, whole 3.3E: denominator, equal parts, fractions, numerator, part of a whole, whole 3.3F: area, denominator, distance, equivalent fractions, equal parts of a whole, number lines, numerator, whole 3.3G: area model, distance, equal parts, equivalent fractions, number line, part of a whole, point, portion, whole 3.3H: comparison symbol, denominator, equal parts, fractions, greater than (>), less than (<), numerator, part of a whole, size, whole 3.6E: area, congruent, equal shares, polygon, shape, two-dimensional, unit fraction, whole 3.7A: distance, fractions (halves, fourths, eighths), number line, zero


Fraction Bars Fraction Circles Cuisenaire Rods Pattern Blocks Snap Cubes 2-Color Counters Power Polygons Color Tiles Number Lines Rulers (STAAR Math Chart) Geoboards

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2.3A partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words 2.3B explain that the more fractional parts used to make a whole, the smaller the part. the fewer the fractional parts, the larger the part 2.3C use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole 2.3D identify examples and non-examples of halves, fourths, and eighths

3.3A: represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines 3.3C: explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number 3.3E: solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8

4.2G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

2.2F name the whole number that corresponds to a specific point on a number line

3.3B: determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line


3.3D: compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b

4.3A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b 4.3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations

3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

4.3C determine if two given fractions are equivalent using a variety of methods

3.3G: explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model

4.3C determine if two given fractions are equivalent using a variety of methods

3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

4.3D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <

1.6G partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words 1.6H identify examples and non-examples of halves and fourths

3.6E: decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

2.9C represent whole numbers as distances from any given location on a number line

3.7A: represent fractions of halves, fourths, and eighths as distances from zero on a number line


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3.3A: represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

In adherence to the standard, fractions are limited to those equal to or less than one whole and include denominators of 2, 3, 4, 6, and 8 equal parts. Students will utilize manipulatives (i.e. pattern blocks, geoboards, etc.); pictorial models (i.e. circles, rectangles, etc.). strip diagrams (i.e. rectangular strips of folded paper), and number lines (i.e. lines containing intervals that are divided equally between zero and one whole to represent a fraction.

This supporting standard develops the conceptual understanding of fractional parts of a whole. Being able to represent fractions using concrete objects, pictorial models, strip diagrams, and number lines will provide a strategy for comparing and determining equivalency of fractions. 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines 3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

Specificity is included for the fractions that students are expected to model. Fractions are greater than zero and less than or equal to one. The denominators may be 2, 3, 4, 6, or 8. The limitation of denominators in this SE does not limit denominators in other SEs. Concrete models may include linear models to build to the use of strip diagrams and number lines. Students are expected to represent fractions using pictorial models, including strip diagrams and number lines.

3.3B: determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line

In adherence to the standard, instruction is limited to fractions greater than zero but less than one whole and will limit fractions to 2, 3, 4, 6, and 8 equal parts. Students will utilize number lines containing intervals that are divided equally between zero and one whole. Students will be asked to identify the fractional point represented on a given number line. Students will need to determine the number of parts that make up the whole (the total number of intervals) and the distance a specific fractional point is away from zero in order to

Locating a fraction as a specific point on a number line will provide students a strategy for comparing and determining equivalency of fractions. 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines 3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using

The limitations placed on denominators in this SE do not limit the denominators in other SEs. The focus of this standard is on the part to whole representations using tick marks on a number line.

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appropriately name the fractional value. Instruction should relate to how to read increments on a ruler (i.e. half, fourth, and eighths) to that of a number line.

symbols, words, objects, and pictorial models

3.3C: explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

All fraction lessons should begin with identifying how many parts it takes to equal one whole (i.e. the square has been divided into four equal parts diagonally, so it takes 4 triangles to make up the whole square). In adherence to the standard, it is not possible to have a whole divided into zero equal parts (i.e. 6/0 is not a fractional unit). A unit fraction identifies one part of the whole (i.e. one triangle represents ¼ of the whole square).

In conjunction with 3.3D, students will have to understand the term “unit fraction” in order to write an appropriate number sentence for a given fraction. This understanding will support students when adding and subtracting fractions with equal denominators in grade 4. 4.3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

This SE focuses on unit fractions. Fractions may have denominators of 2, 3, 4, 6, or 8 and are not limited to these values. Students are expected to describe or explain the fraction 1/b. For example, ¼ is the quantity formed by one part of a whole that has been partitioned into 4 equal parts. A fraction may be part of a whole object or part of a whole set of objects.

3.3D: compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b

In conjunction with 3.3C, as students identify the unit fraction for a given whole (i.e. one triangle represents ¼ of the whole square), instruction will extend to using unit fractions to represent the sum of the parts of an a/b fraction (i.e. as three of the four triangles are shaded its value can be represented as ¼ + ¼ + ¼ = 3/4). Encourage students to write more than one number sentence (i.e. ¼ + ¼ + ¼ = ¾; 2/4 + ¼ = ¾). To support students with transitioning from the concrete to abstract learning of fractions, students should associate the pictorial representation to the values in the number sentence (i.e. 2/4 + ¼ = ¾; students shade each portion of the area model a different color to represent the different addends of

In conjunction with 3.3C, as students begin to write an appropriate number sentence with unit fractions for a given fraction. This understanding will support students when adding and subtracting fractions with equal denominators in grade 4. 4.3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

This SE focuses on non-unit fractions greater than zero and less than or equivalent to one. Students may be expected to describe fractional parts of whole objects. Students are expected to compose and decompose fractions. For example, 3/5 = 1/5 + 1/5 + 1/5. Fractions may have denominators of 2, 3, 4, 6, or 8 and are not limited to these values. A fraction may be part of a whole object or part of a set of objects to build to 3.3E.

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the equation). 1/4

1/4

1/4 1/4

The standard limits number sentences to those with common denominators (i.e. students would not represent ¾ as ½ + ¼ = ¾). In adherence to the standard, sums of fractions are limited to those greater than zero and less than or equal to one whole (i.e. students would not be expected to represent 6/4, but would be expected to represent 4/4).

3.3E: solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8

The study of fractions will extend to real world situations in which students will have to partition a whole object (i.e. a candy bar being shared among three friends) or set of objects (i.e. a bag containing 6 pieces of candy being shared among three friends) and determine the fractional amount (i.e. each friend would receive 1/3 of the whole candy bar; each friend would receive 2/6 of the bag of candy as 1/6 + 1/6 = 2/6). Instruction should begin with identifying the whole so that students can identify if they are working with a whole object or a set of objects. In adherence to the standard, situations are limited to wholes (denominators) of 2, 3, 4, 6, and 8.

Through the partitioning of concrete objects or sets of objects, this supporting standard develops the conceptual understanding of fractions. The visual representations of fraction will support the comparing of fractions. 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines 3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

This SE focuses on solving problems with fractional parts of whole objects or sets of objects. Fractions should have denominators of 2, 3, 4, 6, or 8. The limitation of denominators in this SE does not limit denominators in other SEs. A fraction may be part of a whole object or part of a whole set of objects. Fractions are not limited to being between 0 and 1. In this way, the SE is an extension of 2.3C, where students are expected to count beyond one whole. Examples of problems include situations such as 2 children sharing 5 cookies.

3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of

It is important for the introduction of equivalent fractions to be modeled through the use of

* Students may view an equivalent fraction with a larger denominator as a bigger value

Fractions are greater than zero and less than or equal to one.

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objects and pictorial models, including number lines

concrete objects (i.e. if a hexagon pattern block represents the whole, two trapezoids could also represent one whole and so could six triangles; hence one trapezoid pattern block would cover half of the whole hexagon and so does three triangles; therefore, ½ = 3/6). Instruction can then progress to the use of pictorial models (i.e. a square has been divided into two equal parts with half of the square shaded representing ½; the same square is then divided into four equal parts now reflecting 2/4; the same square is then divided into eight equal parts reflecting 4/8; hence ½ = 2/4 = 4/8). In conjunction with 3.3B, students can use a number line as a means of representing equivalent fractions (i.e. ½ = 2/4 = 3/6 = 4/8 as they are all the same distance away from zero). In adherence to the standard, equivalent fractions are limited to denominators of 2, 3, 4, 6, and 8.

than that of a smaller denominator (i.e. ½ is smaller than 2/4 because 2 is smaller than 4). * Students may not relate area to determining equivalency of fractions (i.e. a square divided into two equal triangles is the same amount of area as a square divided into two equal rectangles; both the triangle and a rectangle would represent ½ of the square). * Students may not relate distance on a number line to determining equivalency of fractions (i.e. ½ is a shorter distance away from zero than 2/4 because 2 is smaller than 4). * Students may not understand that compared fractions must be fractions of the same whole.

The limitation of denominators in this SE does not limit denominators in other SEs. Models that are linear build to the use of strip diagrams and number lines.

3.3G: explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model

In conjunction with 3.3F, as students represent equivalent fractions with the use of objects/pictorial models (i.e. fraction circles, pattern blocks, geoboards, etc.), it is essential that they understand that in order for two fractions to be equivalent they must take up the same amount of area (i.e. if a hexagon represents one whole, then a trapezoid represents halves and triangles represent sixths; one trapezoid represents ½ of the whole and three triangles represent 3/6 of the whole; these two fractions are equivalent because they take up the same amount of area); likewise, when using number lines students need to

Students can use concrete objects and/or number lines to determine equivalency of fractions. This standard supports the understanding that equivalent fractions will be located on the same point of a number line and/or cover the same amount of area of the same whole. 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

The emphasis with this SE is on the understanding that equivalent fractions must be describing the same whole. 6/8 does not equal ¾ when the 6/8 is part of a candy bar and the ¾ is part of a pizza. While they both describe ¾ of their respective wholes, the amounts described by 6/8 and ¾ are not the same.

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understand that two fractions are equivalent if they are the exact same distance away from zero (i.e. ½, 2/4. 3/6, and 4/8 all fall on the same point on the number line representing equivalency).

3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

In adherence to the standard, the comparison of fractions are limited to those where the numerators are the same with different denominators (1/4 and 1/8) or the denominators are the same with different numerators (2/3 and 1/3). This will allow the focus to be on the size of the whole or the size of the part in order to compare fractions. Students should be able to articulate that when the denominators are the same size, the numerator will determine which is larger/smaller (i.e. 2/6 < 5/6 because both fractions were divided into the same number of parts but 2/6 had three less parts than 5/6) and when the numerators are the same, the size of the denominator will determine which is larger/smaller (i.e. 3/8<3/6 because an object divided into eight equal parts would be a smaller area than an object divided into six equal parts). Encourage students to state two comparison statements ensuring understanding (i.e. 3/8<3/6 and 3/6>3/8).

* Students may not understand that larger denominators yield smaller parts of a whole; the smaller denominators yield larger parts of a whole. * Students may not view the comparison statement 3/8<3/6 is the same as 3/6>3/8.

Fractions may have denominators of 2, 3, 4, 6, or 8 and are not limited to these values. Examples include situations such as comparing the size of one piece when sharing a candy bar equally among four people or equally among three people.

3.6E: decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

Students should divide a two-dimensional shape into equal parts in more than one way (i.e. a square can be divided into two equal parts vertically, horizontally, or diagonally). Students recognize that each equal part of the two-dimensional shape has the same amount of area and can be

The supporting standard relates fractional equivalency to area. The instructional focus is on how two fractions are equivalent if the two fractional portions have the same area and the two fractional portions/areas do not necessarily have to be the same shape.

Students may be expected to separate two congruent squares in half in two different ways.

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represented as a unit fraction (i.e. one part of the two equal parts can be represented as ½). In adherence to the standard, students must also recognize that equal shares of the same whole do not have to have the same shape but have the same amount of area (i.e. both the rectangular half of a whole square and the triangular half of the whole square represent ½).

3.6C: determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

Students may be expected to identify that the smaller parts represent one-half of each of the original squares even though the halves from one square are not congruent to the halves in the other square.


Fractional parts of a whole can be represented as the distance away from zero on a number line. Instruction should begin with the folding of paper strips to develop students’ concrete understanding. Instruction can then extend fractional distances on a number line to the use of the ruler in measuring the length of objects to the nearest ½, ¼, and 1/8 increments. This understanding will support further study of comparing fractions and determining equivalent fractions using a number line.

Locating a fraction as a specific point on a number line will allow students a strategy for comparing and determining equivalency of fractions. 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines 3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

The focus of this SE is on the length of the portion of a number between 0 and the location of the point. This SE builds to 4.3G where any fraction or decimals to the tenths or hundredths may be represented as distances from zero on a number line. This SE extends 2.3C and includes fractions greater than one.

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Course: Grade 3 Math Bundle 6: Geometry

Dates: January 30th- February 17th (15 days)

TEKS 3.6A: classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language 3.6B: use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3E: share information in cooperative learning interactions Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary

Unit Vocabulary Attribute Faces Rectangle Solid Trapezoid Cone Figure Rectangular prism Sphere Triangular prism Cube Parallelogram Rhombus Square Two-dimensional Cylinder Polygon Shape Three-dimensional Vertex/vertices Edges Quadrilateral Sides Faces

Cognitive Complexity Verbs: classify, sort, use, draw examples Academic Vocabulary by Standard: 3.6A: attribute, edges, faces, figure, polygon, shape, sides, solid, two-dimensional, parallelogram, quadrilateral, rectangle, rhombus, square, trapezoid, three-dimensional, cone, cube (special rectangular prism), cylinder, sphere, triangular prism, rectangular prism, vertex/ vertices 3.6B: attributes, vertex/ vertices, side, polygons, rhombus, parallelogram, trapezoid, rectangle, square (special type of rectangle), quadrilateral


AngLegs Geometric Solids Geoboards Dot Paper Power Polygons Translucent Geometric Shapes Geometric Shapes Building Set

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1.6A classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language 2.8C classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices 2.8B classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language

3.6A: classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

4.6D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size 5.5A classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

1.6C create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons 1.6D identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language 2.8A create two-dimensional shapes based on given attributes, including number r of sides and vertices

3.6B: use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

4.6A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines 4.6B identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure 4.6C apply knowledge of right angles to identify acute, right, and obtuse triangles

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3.6A: classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

Students must be given a variety of two- and three- dimensional figures to sort based on their attributes (i.e. number of sides/edges, number of vertices, number/types of faces, etc.). Instruction should model the language of informal deduction (i.e. all squares are rectangles, but not all rectangles are squares; all cubes are rectangular prisms, but not all rectangular prisms are cubes). In adherence to the standard, solids are limited to prisms, cones, cylinders, spheres, and cubes and do not include pyramids. Students should recognize that the shape of the base defines whether the prism is triangular or rectangular.

* Students may interchange the term side referencing two-dimensional shapes and edge referencing a three-dimensional shape. * Students may count the common vertices of a three-dimensional figure twice as they view each face independently. * Students may not view a square as a rectangle or a cube as a rectangular prism.

Formal geometric language includes terms such as vertex, edge, and face. Figures may be classified by either attributes or their names.

3.6B: use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

Students identify four-sided polygons as quadrilaterals and sort given quadrilaterals into subcategories based on their attributes. Instruction should include how the subcategories are similar, yet different (i.e. all squares can be called a rectangle, parallelogram, and rhombus; however, a square cannot be called a trapezoid). Be sure students are exposed to both regular and right angled trapezoids. In adherence to the standard, students should also create examples of quadrilaterals that do not fall into any of the identified subcategories.

In order to classify and sort two- and three- dimensional shapes, students must identity attributes that define such figures. Determining examples and non-examples of such categories will allow students to focus on defining attributes. 3.6A: classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

This SE includes the identification or recognition of quadrilaterals as a subcategory of 2D figures. This SE builds on 2.8C where students are expected to classify and sort polygons.

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Course: Grade 3 Math Bundle 7: Measurement

Dates: February 21st- March 24th (19 days)

TEKS 3.6C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row 3.6D decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area 3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line 3.7B determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems 3.7C determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes 3.7D determine when it is appropriate to use measurements of liquid volume (capacity) or weight 3.7E determine liquid volume (capacity) or weight using appropriate units and tools

ELPS Learning Strategies 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Addition Eighths Liquid volume Number line Row Additive property Event Liter Ounce Sides Area Factor Measurement tools Perimeter Square unit Array Fourths Metric Pint Subtraction Capacity Fraction Milliliter Polygon Time intervals Composite figure Gallon Minute Product Units Cup Half/halves Multiplication Quart Weight Customary Hour Non-overlapping Rectangles Zero Distance Length

Cognitive Complexity Verbs: decompose, determine, represent, determine, use Academic Vocabulary by Standard: 3.6C: array, area, factor, length, multiplication, product, rectangles, row, square unit 3.6D: additive property, area, array, composite figure, non-overlapping, rectangle 3.7A: distance, fractions (halves, fourths, eighths), number line, zero 3.7B: length, perimeter, polygon, sides 3.7C: addition, minute, subtraction, time intervals, hour, event 3.7D: capacity, liquid volume, weight 3.7E: capacity, customary, liquid volume, measurement tools, metric, units, weight, gallon, quart, pint, cup, ounce, milliliter, liter


Measuring Tape Rulers Capacity Containers Number Lines Centimeter Cubes Weights Balance Scales Spring Scales Clocks Grid Paper Geoboards Dot Paper

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3.6D: decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area


2.9C represent whole numbers as distances from any given location on a number line



2.9E determine a solution to a problem involving length, including estimating lengths

3.7B: determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems


1.7E tell time to the hour and half hour using analog and digital clocks 2.9G read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.

3.7C: determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes

4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.

3.7D: determine when it is appropriate to use measurements of liquid volume (capacity) or weight

4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

3.7E: determine liquid volume (capacity) or weight using appropriate units and tools

4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

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Instruction should connect the visual of an array to area to a related multiplication fact (i.e. There are four rows with two unit squares in each row for a total of square units; 4 x 2 = 8; the area of this rectangle is 8 square units).

Students should also connect the appropriate vocabulary to the arrays (i.e. the number of rows and columns represent the factors and the total number of square units represents the product) and number sentence (i.e. 4 x 2 = 8; the 4 and the 2 represent the factors and 8 represents the product).

* Students confuse the concept of area with perimeter. * Students who just count up the number of square units to determine the area may not connect how multiplication relates to area. * Students may think that a 4 by 2 array yields a different area than a 2 by 4 array.

The SE limits the two-dimensional surfaces to rectangles with whole-number side lengths. Students may use concrete or pictorial models of square units to represent the number of rows and the number of unit squares in each row. Units of area may be square inches, square centimeters, square feet, square meters, etc. To build on 2.9F, students may be expected to use multiplication to determine the area of a rectangle instead of counting squares.

3.6D: decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area

Instruction should associate the decomposing of composite figures to creating two or more arrays. Encourage students to decompose composite figures into more than one way; associate a given multiplication expression to each component of the composite figures; represent an addition equation representing the area of each subsection of the figure in order to determine the area of the

Decomposing composite figures into non-overlapping rectangles will support the student’s ability to apply their understanding of multiplication to area. 3.6C: determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each

Composite figures should be comprised of rectangles, including squares as special cases of rectangles.

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composite figure.

(1 x 3) + (2 x 3) + (2 x 2) = 3 + 6 + 4 = 13

row


Fractional parts of a whole can be represented as the distance away from zero on a number line. Instruction should begin with the folding of paper strips to develop students’ concrete understanding. Instruction can then extend fractional distances on a number line to the use of the ruler in measuring the length of objects to the nearest ½, ¼, and 1/8 increments. This understanding will support further study of comparing fractions and determining equivalent fractions using a number line.

Locating a fraction as a specific point on a number line will allow students a strategy for comparing and determining equivalency of fractions. 3.3F: represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines 3.3H: compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

The focus of this SE is on the length of the portion of a number between 0 and the location of the point. This SE builds to 4.3G where any fraction or decimals to the tenths or hundredths may be represented as distances from zero on a number line. This SE extends 2.3C and includes fractions greater than one.

3.7B: determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems

Instruction should include finding the perimeter of regular and irregular shaped polygons. In adherence with the standard, problems should include where all side lengths are given and students determine the perimeter; some of the side lengths are given and students must use direct comparisons to determine unknown side lengths in order to calculate the perimeter; or the perimeter and

* Students will only add up the lengths of the sides that are given within a problem without considering side lengths that may be missing. * Students confuse the concept of area with perimeter.

For example, students may measure the side lengths of a polygon to determine its perimeter using inches or centimeters. Side lengths should be whole numbers. Students may also be expected to determine a missing side length of a polygon when given the perimeter of the polygon

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some of the side lengths are given and students must determine the missing side lengths.

and the remaining side lengths.

3.7C: determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes

In adherence with the standard, students are to use a tool (i.e. Mandy took 15 minutes to eat breakfast, 10 minutes to get dressed, and 5 minutes to make her bed. How long did it take her to get ready this morning? If Mandy wakes up at 7:10 AM every morning and she takes 30 minutes to get ready, what time is she ready for school? If Mandy must leave for school by 7:40 and she takes 30 minutes to get ready, what time should she wake up for school?)

Determining solutions to elapsed time problems within the hour will extend to solving elapsed time problems outside of the hour in grade 4. 4.8C solve problems that deal with measurement of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

Students may be asked to use tools such as analog and digital clocks to solve problems related to the addition and subtraction of intervals of time in minutes. Problems may include a start time with an interval or an end time with an interval. Intervals may be less than or greater than 1 hour. Problems may not include a start time and an end time as elapsed time is addressed in 4.8C.

3.7D: determine when it is appropriate to use measurements of liquid volume (capacity) or weight

Students need to understand the difference between the liquid volume (capacity) and the weight of an object (i.e. the number of fluid ounces in a bottle of water is a different measure than the weight of the water bottle). In conjunction with 3.7E, instruction should invoke the use of various measurement tools for students to investigate the difference between the two concepts.

Understanding the difference between liquid volume (capacity) and weight will support students in solving such problems appropriately in grade 4. 4.8C solve problems that deal with measurement of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

In addition to metric units, students are expected to distinguish between liquid ounces and ounces that measure weight. Mass is not included in this SE as mass is not the same as weight. The metric unit for weight, a Newton, is introduced in grade 8 science.

3.7E: determine liquid volume (capacity) or weight using appropriate units and tools

In conjunction with 3.7D, students should be able to select appropriate tools to measure capacity (i.e. graduated cylinders, cups, and containers)

Students will need hands on experiences with selecting and using appropriate tools and measurement units for liquid volume (capacity) and weight

Students are expected to use appropriate units and tools to determine liquid volume (capacity) in the customary and metric

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vs. weight (i.e. scales). Instruction should also include practice with metric and customary measurements.

in order to solve such problems in grade 4. 4.8C solve problems that deal with measurement of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

systems. Students may measure liquid volume (capacity). Students may measure weight. Students are expected to use appropriate units and told to determine weight in the customary system. Mass is not included in this SE as mass is not the same as weight. The metric unit for weight, a Newton, is introduced in grade 8 science.

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Course: Grade 3 Math Bundle 8: Data Analysis

Dates: March 27th- April 7th (10 days)

TEKS 3.8A: summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals 3.8B: solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

ELPS Learning Strategies 1B: monitor oral and written language production and employ self-corrective techniques or other resources Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions Speaking 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Bar graph Data Frequency table Labels Pictograph Categorical data Dot plot Graph title Numerical data Scaled intervals Categories Data

Cognitive Complexity Verbs: summarize, use, solve Academic Vocabulary by Standard: 3.8A: bar graph, categories, data, dot plot, frequency table, graph titles, labels, pictograph, scaled intervals 3.8B: bar graph, categorical data, dot plot, frequency table, pictograph, scaled intervals, numerical data


Grid Paper Color Tiles Snap Cubes Rulers

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1.8B use data to create picture and bar-type graphs 2.10B organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more

3.8A: summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

4.9A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions 5.9A represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and leaf plots.

1.8C draw conclusions and generate and answer questions using information from picture and bar-type graphs 2.10D draw conclusions and make predictions from information in a graph 2.10C write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

3.8B: solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

4.9B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot 5.9C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot

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3.8A: summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

According to the TEKS, students need to collect, organize, and display their own data. Personalizing such activities will allow students to make more sense of the data and summarize more appropriately. Instruction needs to include multiple categories (i.e. extend survey question of “Do you like cats and dogs?” to “What is your favorite animal?”) In accordance with the standard, data should be represented on a frequency table, dot plot, pictograph, or bar graph. Graph representations should include both vertical and horizontal formats. Pictographs should include symbolism that does not represent one-to-one correspondence (i.e. smiley face represents 4 people) and portion representations (i.e. a picture of half a smiley face yields 2 people). Bar graphs include scaled intervals (i.e. information on the x- or y-axis skip counts by tens). Extend instruction to include representing the same data set in each of the four types of displays to compare. Summarization of data should also include being able to determine the total amount of data collected by viewing a graph (i.e. the sum of each bar graph length will yield the total number of data pieces).

* Students may misinterpret pictographs in which each picture represents a value other than one. * Students may misread bar graphs that have scaled intervals. *When representing the same set of data on all four types of graphs, students may interpret the data as different because of the difference in visual representations. * When representing the same set of data vertically and horizontally, students may interpret the data as different because of the difference in the visual representations.

A frequency table shows how often an item, a number, or a range of numbers occurs. Tally marks and counts may be used to record frequencies. Students begin work with frequency tables in grade 3. A dot plot may be used to represent frequencies. A number line may be used for counts related to numbers. A line labeled with categories may be used as well if the context requires. Dots are recorded vertically above the number line to indicate frequencies. Dots may represent one count or multiple counts if so noted. A dot plot of categorical data is also called a “Cleveland” plot.

3.8B: solve one- and two-step problems using categorical data represented with a frequency

Instruction should vary the context of the problems being asked of the students (i.e. joining, separating,

This supporting standard merges the calculation of whole numbers with various graph representations.

Students begin work with pictographs in grade K and bar graphs in grade 1.

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table, dot plot, pictograph, or bar graph with scaled intervals

comparing, and distance). In conjunction with 3.8A, as students have graphed the same data set on 4 different types of graphs, students could then solve the same problem using the different graph representations to model their flexibility in moving among the different types of graphs.

Through the interpretation of data on a graph, students should be able to apply their ability to solve addition/subtraction and multiplication/division of whole numbers. 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts 3.8A: summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

Students begin work with frequency tables and dot plots in grade 3. Students solve one- and two- step problems with scaled intervals.

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Course: Grade 3 Math Bundle 9: Personal Financial Literacy

Dates: April 10th- April 13th (4 days)

TEKS 3.9A: explain the connection between human capital/labor and income 3.9B: describe the relationship between the availability or scarcity of resources and how that impacts cost 3.9C: identify the costs and benefits of planned and unplanned spending decisions 3.9D: explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest 3.9E: list reasons to save and explain the benefit of a savings plan, including for college 3.9F: identify decisions involving income, spending, saving, credit, and charitable giving

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3E: share information in cooperative learning interactions Reading 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Availability of resources Cost Interest Principle Scarcity of resources Benefits Credit Labor Resources Spending Borrower Decisions Lender Saving Unplanned spending Charitable giving Human capital Needs Savings plan Wants College Income Planned spending

Cognitive Complexity Verbs: explain, describe, identify, list Academic Vocabulary by Standard: 3.9A: human capital, income, labor 3.9B: availability of resources, scarcity or resources, cost 3.9C: benefits, costs, decisions, planned spending, unplanned spending 3.9D: resources, borrower, credit, interest, lender, needs, principle, wants 3.9E: benefit, college, saving, savings plans 3.9F: charitable giving, credit, decisions, income, saving, spending

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1.9A define money earned as income 3.9A: explain the connection between human capital/labor and income

4.10A distinguish between fixed and variable expenses 5.10A define income tax, payroll tax, sales tax, and property tax 5.10B explain the difference between gross income and net income

2.11F differentiate between producers and consumers and calculate the cost to produce a simple item

3.9B: describe the relationship between the availability or scarcity of resources and how that impacts cost

4.10B calculate profit in a given situation

2.11B explain that saving is an alternative to spending

3.9C: identify the costs and benefits of planned and unplanned spending decisions

2.11D identify examples of borrowing and distinguish between responsible and irresponsible borrowing 2.11E identify examples of lending and use concepts of benefits and costs to evaluate lending decisions

3.9D: explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest

4.10E describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending 5.10C identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments

1.9C distinguish between spending and saving 2.11A calculate how money saved can accumulate into a larger amount over time

3.9E: list reasons to save and explain the benefit of a savings plan, including for college

4.10C compare the advantages and disadvantages of various savings options

1.9D consider charitable giving 3.9F: identify decisions involving income, spending, saving, credit, and charitable giving

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3.9A: explain the connection between human capital/labor and income

Human capital (skills, knowledge, competency, and education) has a positive correlation to one’s ability to gain income. Students need to understand that the more education, experience, and abilities they have usually leads to the earning of more money. Instruction should include students researching various professions, the amount of education needed, and the average earned income for such professions.

Understanding human capital/labor and income will support one’s ability to manage their financial resources more effectively for a lifetime of financial security.

This SE relates work with income, including the relationship between effort and income on the individual level and the relationship between the number of people working together and the amount of product/ income created. Human capital can be on the individual level, including ways in which an individual can be of greater benefit to his employer of the marketplace at large.

3.9B: describe the relationship between the availability or scarcity of resources and how that impacts cost

This standard is laying the foundation for the law of supply and demand. Students need to understand that as the availability of resources is abundant, the cost of the items tends to be less; when the availability of a resource is scarce, the cost tends to be higher. Instruction should include several real world examples (i.e. release of a new game system tends to be high at first because everyone is wanting the item and there are few available in the store; however, after several months the cost of the game system goes down because there is no longer a need for such an item, game systems are available in several stores, or have been replaced by a newer game system).

Understanding how the availability or scarcity of a resource impacts costs will support one’s ability to manage their financial resources more effectively for a lifetime of financial security.

This SE relates a fundamental rule of economics: The rarer an object is, the more expensive it tends to be. The more common an object is, the less expensive it is.

3.9C: identify the costs and benefits of planned and unplanned spending decisions

In conjunction with 3.9F, students need to understand that financial decisions made will have positive

Identifying the costs and benefits of planned and unplanned spending decisions will support

This SE builds upon 2.11B.

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and negative results. In adherence with this standard, students should weigh the benefits for planning for unexpected spending versus the costs of not planning for unexpected spending.

one’s ability to manage their financial resources more effectively for a lifetime of financial security.

3.9D: explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest

In adherence with the standard, instruction should address how credit can be used when one goes beyond their ability to pay. Students will need to understand the role and responsibility of a borrower and lender. Be sure to provide students with several real world examples of how not only the principle of the loan, but also the interest, must be paid back.

Understanding the use and expectations associated with credit will support one’s ability to manage their financial resources more effectively for a lifetime of financial security.

This SE builds to 4.10C, 5.10C, and the discussion of credit in grade 6.

3.9E: list reasons to save and explain the benefit of a savings plan, including for college

In adherence to the standard, students should identify several reasons why they should save (i.e. purchase a large item, in case of emergencies, college, etc.). In conjunction with 3.9C/F, students should recognize the benefits of saving.

Listing reasons to save and explain the benefits will support one’s ability to manage their financial resources more effectively for a lifetime of financial security.

Specificity is expected through a list of reasons to save and students being able to explain the benefits of saving. Students are not expected to calculate the savings at this level.

3.9F: identify decisions involving income, spending, saving, credit, and charitable giving

In adherence with the standard, instruction should model how individuals have decisions that need to be made in regards to income (i.e. how much should I be earning for my weekly allowance?), spending (i.e. how much of my allowance do I feel comfortable enough spending each week?), saving (i.e. how much money should I save of my allowance?), credit (i.e. should I save my money for the new video game or take a loan from my dad?), and charitable giving (i.e. how much should I donate to the less fortunate?).

Understanding the concepts of income, spending, saving, credit, and charitable giving will support one’s ability to manage their financial resources more effectively for a lifetime of financial security.

This SE builds upon 1.9D where students are first asked to consider charitable giving.

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Course: Grade 3 Math Bundle 10: STAAR Review and Testing

Dates: April 18th-May 8th (15 days)

TEKS -Review previously taught skills/TEKS -Address STAAR questions STEMS at varied DOK levels

Course: Grade 3 Math Bundle 11: Extended Learning

Dates: May 9th- June 1st (17 days)

TEKS Continued Problem Solving 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.5A: represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts 3.5B: represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations Continued Number Sense 3.4A: solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 3.4K: solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts 3.4F: recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts 3.4G: use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties 3.5D: determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product Project Based Learning -Introduce project-based learning activities with strong integration of TEKS that need extended exposure for mastery.

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