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Fourth Grade Mathematics Curriculum Resource

for the Maryland College and Career Ready Standards

2014-2015

Fourth Grade Overview

Fourth Grade Mathematics Curriculum Guide for theMaryland College and Career Ready Standards

Operations and Algebraic Thinking (OA)

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Number and Operations in Base Ten (NBT)

Generalize place value understanding for multi-digit whole numbers.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number and Operations—Fractions (NF)

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Understand decimal notation for fractions, and compare decimal fractions.

Measurement and Data (MD)

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Represent and interpret data.

Geometric measurement: understand concepts of angle and measure angles.

Geometry (G)

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Major Cluster Supporting Cluster Additional Cluster

Grade 4 Wicomico County Public Schools Revised 2014-2015 2



Standards for Mathematical PracticeStandards Explanations and Examples1. Make sense of problems and persevere in solving them.

In fourth grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.

2. Reason abstractly and quantitatively.

Fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.

3. Construct viable arguments and critique the reasoning of others.

In fourth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain their thinking and make connections between models and equations. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.

4. Model with mathematics.

Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense.

5. Use appropriate tools strategically.

Fourth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size of units within a system and express measurements given in larger units in terms of smaller units.

6. Attend to precision. As fourth graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line plot.

7. Look for and make use of structure.

In fourth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations to explain calculations (partial products model). They relate representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting. They generate number or shape patterns that follow a given rule.

8. Look for and express regularity in repeated reasoning.

Students in fourth grade should notice repetitive actions in computation to make generalizations Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent fractions.


GRADE 4 COMMON CORE INTRODUCTION

In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

1. Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.

2. Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.

3. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.



Fourth Grade Math At-A-Glance2014-2015 Important Dates

Unit 1: Applying Place Value Concepts inWhole Number Addition and Subtraction (14 days)

September 1 Labor Day

Unit 2: Efficiency with Multiplication and Understanding Division(20 days)

September 26 Professional Day

Unit 3: Solving Problems Using Multiplicative Comparison(10 days)

October 17 MSEA ConventionOctober 21 Interim Assessment #1This day is not counted as an instructional day.

Unit 4: Understanding & Comparing Fractions (22 days)

November 3 Professional DayNovember 4 Election DayNovember 26-28 Thanksgiving

Unit 5: Fraction Operations (23 days)

December 10 Interim Assessment #2This day is not counted as an instructional day.December 22-January 2 Winter Holiday

Unit 6: Understanding & Comparing Decimals (13 days)

January 19 MLK DayJanuary 26 Professional Day

Spiral Review(8 days)

February 13 Professional DayFebruary 16 President’s DayFebruary 19 Interim Assessment #3This day is not counted as an instructional day.

PARCC PBA/MYA Testing Window March 2-27 (2 days within this window)Unit 7: Measurement Conversions & Problem Solving(12 days)

April 1-6 Spring HolidayApril 7 Professional Day

Unit 8: Geometry(16 days)

PARCC EOY Testing Window April 20- May 15 (2 days within this window)Unit 9: Fluency with Problem SolvingFollows EOY PARCC (32 days or remainder of year)

May 25 Memorial Day



Unit One – Applying Place Value Concepts in Whole Number Addition and Subtraction (14 days)

The focus of this unit is to provide students time to develop and practice efficient addition and subtraction of multi-digit whole numbers while developing place value concepts.

Unit One Standards

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. This standard will be revisited in unit 7 connected to conversions within the metric system of measurement.

4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. This standard will be revisited in unit 3 with multiplication and division as a context.

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. This standard will be revisited in unit 7 and finalized in unit 9 for fluency in addition and subtraction of multi‐digit whole numbers.

Math Language The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use these math terms in explanations or justifications.

addend algorithm compare decompose differencedigits equation estimation expanded form expressionminuend place value rounding subtrahend sum

Essential QuestionsHow does our base-10 number system work? How does understanding base-10 number system help us add and subtract? How do digit values change as they are moved around in large numbers? What determines the value of a digit? What conclusions can I make about the places within our base ten number system? What happens to a digit when multiplied and divided by 10? What effect does the location of a digit have on the value of the digit?



How does the value of digits in a number help me compare two numbers? How can we tell which number among many large numbers is the largest or smallest?Why is it important for me to be able to compare numbers? How can we compare large numbers? What determines the value of a number? Why is it important for me to be able to compare numbers?

What information is needed in order to round whole numbers to any place? How are large numbers estimated? How does understanding place value help me explain my method for rounding a number to any place? How can I round to help me find a reasonable answer to a problem? How does estimation keep us from having to count large numbers individually? How are large numbers estimated? What information is needed in order to round whole number to any place? How can rounding help me compute numbers?

What strategies can I use to help me make sense of a written algorithm? What strategies help me add and subtract multi-digit numbers? How can I ensure my answer is reasonable? What is a sensible answer to a real problem? How does knowing and using algorithms help us to be efficient problem solvers?

Common Misconceptions

NBT.4 - Often students mix up when to “carry” and when to “borrow/regroup”. Also students often do not notice the need of borrowing/regrouping and just take the smaller digit from the larger one. Emphasize place value and the meaning of the digits. If students are having difficulty with linking up similar place values in numbers as they are adding and subtracting, it is sometimes helpful to have them write their calculations on the grid paper. This assists the student with lining up the numbers more accurately. If students are having a difficult time with a standard addition algorithm, a possible modification to the algorithm might be helpful. Instead of the “shorthand” of “carrying,” students could add by place value, moving left to right placing the answers down below the “equals” line.

For example: 249 + 372 500 (Start with 200 + 300 to get the 500 110 then 40 + 70 to get 110 11 and 9 + 2 to get 11.) 621



Grade 4 Unit One – Applying Place Value Concepts in Whole Number Addition & Subtraction (14 days)

Connections/Notes Resources4.NBT.A.1Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Students use the structure of the base‐ten system to generalize their strategies and to discuss reasonableness of their computations and work towards fluency. (MP.6, MP.8).

Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.Generalize place value understanding for multi-digit whole numbers.

Students generalize their previous understanding of place value for multi-digit whole numbersThis supports their work in multi-digit multiplication and division, carrying forward into grade 5, when students will extend place value to decimals.

Students should be familiar with and use place value as they work with numbers. Some activities that will help students develop understanding of this standard are:

Investigate the product of 10 and any number, then justify why the number now has a 0 at the end. (7 x 10 = 70 because 70 represents 7 tens and no ones, 10 x 35 = 350 because the 3 in 350 represents 3 hundreds, which is 10 times as much as 3 tens, and the 5 represents 5 tens, which is 10 times as much as 5 ones.) While students can easily see the pattern of adding a 0 at the end of a number when multiplying by 10, they need to be able to justify why this works.

Investigate the pattern, 6, 60, 600, 6,000, 60,000, and 600,000 by dividing each number by the previous number.

Example: Recognize that 700 ÷ 70 = 10 applying concepts of place value and division.

In the number 85,254, how many times greater is the 5 in the thousands place than the 5 in the tens place?

Teaching Student-Centered Mathematics pg. 48 Figure 2.7 What Comes Next Activity 2.8

Lessons:Recognize a Digit Represents 10 Times the Value as the Digit to Its Right

Activities and Tasks:Place Value ProblemsPlace Value Task CardsPractice/Assessment Sheet

Videos:Understanding Multi-Digit Whole Number Place Value Concepts

Use a Place Value Chart and Arrow Cards to Understand Large Numbers

Model Numbers Using Base Ten Blocks

Understand Relationships Between Digits and Their Place Value

Multiply by Powers of Ten

Divide by Powers of 10

Online:Place Value Number Line NLVMPlace Value Calculator


http://www.crickweb.co.uk/ks2numeracy-tools.html

http://nlvm.usu.edu/en/nav/frames_asid_334_g_1_t_1.html?from=topic_t_1.html

http://learnzillion.com/lessons/806-divide-by-powers-of-10

http://learnzillion.com/lessons/805-multiply-by-powers-of-10

http://learnzillion.com/lessons/516-understand-relationships-between-digits-and-their-place-value

http://learnzillion.com/lessons/516-understand-relationships-between-digits-and-their-place-value

http://learnzillion.com/lessons/515-model-numbers-using-base-ten-blocks

http://learnzillion.com/lessons/514-use-place-value-chart-and-arrow-cards-to-understand-large-numbers

http://learnzillion.com/lessons/514-use-place-value-chart-and-arrow-cards-to-understand-large-numbers

https://www.youtube.com/watch?v=etvngj812Cg

https://www.youtube.com/watch?v=etvngj812Cg



Connections/Notes Resources4.NBT.A.1 Continued

Templates and VisualsPlace Value ChartPlace Value Arrow Cards

4.NBT.A.2Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of the comparisons.

The expanded form of 275 is 200 + 70 + 5. Students use place value to compare numbers. For example, in comparing 34,570 and 34,192, a student might say, both numbers have the same value of 10,000s and the same value of 1000s however, the value in the 100s place is different so that is where I would compare the two numbers.

Examples:

Which number makes this sentence true? 701 < 717 - x

Which number makes this sentence true? 381 + x > 830

I can rewrite the numbers as (300 + 80 + 1) + x > (800 + 30).This way I can see how many hundreds, tens, and ones I can add to make the inequality sentence true.

Connections: 4.NBT.A.1

Teaching Student-Centered Mathematicspgs. 47-51 (Numbers Beyond 1000)

Lessons:Expand That Number! IlluminationsRead and Write Numbers Using Base Ten Numerals, Number Names, and Expanded Form

Activities and Tasks:Place Value ProblemsPlace Value TriangleNumeral, Word and Expanded FormFrayer ModelOrdering 4-Digit NumbersPlace Value QR Code Task CardsIn Between Game

Videos:Read and Write Numbers in Numeric Form

Read and Write Numbers in Word Form

Creating Numbers Based on Given Conditions by Comparing Digits


http://learnzillion.com/lessons/522-creating-numbers-based-on-given-conditions-by-comparing-digits

http://learnzillion.com/lessons/522-creating-numbers-based-on-given-conditions-by-comparing-digits

http://learnzillion.com/lessons/518-read-and-write-numbers-in-word-form

http://learnzillion.com/lessons/517-read-and-write-numbers-in-numeric-form

http://illuminations.nctm.org/Lesson.aspx?id=3691




Read and Write Numbers in Expanded Form

Templates and Visuals:Place Value Arrow Cards

4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.

The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should have number experiences using a number line and hundreds chart as tools to support their work with rounding.

When students are asked to round large numbers, they first need to identify which digit is in the appropriate place.

Examples:

Round 76,398 to the nearest 1000. Step 1: Since I need to round to the nearest 1000, then the answer is either 76,000 or 77,000. Step 2: I know that the halfway point between these two numbers is 76,500. Step 3: I see that 76,398 is between 76,000 and 76,500. Step 4: Therefore, the rounded number would be 76,000.

Round 368 to the nearest hundred. This will be either 300 or 400, since those are the two hundreds before and after 368. Draw a number line, subdivide it as much as necessary and determine whether 368 is closer to 300 or 400. Since 368 is closer to 400, this number should be rounded to 400.

Teaching Student-Centered Mathematicspg. 47, Approximate Numbers & Rounding, Figure 2.6 (Number line)

Lessons:Round Numbers to the Thousands Place Using the Vertical Number LineRound Numbers to Any Place Using the Vertical Number LineUse Place Value Understanding to Round Numbers to Any PlaceUse Place Value to Round Numbers Using Real World Applications

Activities and Tasks:Rounding to Nearest Ten Number LineRounding

Videos:Locate Benchmark Numbers on a Number LineRound Numbers to the Leading Digit Using a Number LineRound Numbers to a Specified Place on a Number LineRound in Real-Life Situations


https://learnzillion.com/lessons/527-round-in-reallife-situations

https://learnzillion.com/lessons/525-round-numbers-to-a-specified-place-on-a-number-line

https://learnzillion.com/lessons/525-round-numbers-to-a-specified-place-on-a-number-line

https://learnzillion.com/lessons/524-round-numbers-to-the-leading-digit-using-a-number-line

https://learnzillion.com/lessons/524-round-numbers-to-the-leading-digit-using-a-number-line

http://learnzillion.com/lessons/523-locate-benchmark-numbers-on-a-number-line

http://learnzillion.com/lessons/519-read-and-write-numbers-in-expanded-form




Templates and Visuals:Estimating ChartHundreds Chart for Rounding

4.NBT.B.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Students build on their understanding of addition and subtraction, their use of place value and their flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place value in describing and justifying the processes they use to add and subtract.

When students begin using the standard algorithm their explanation may be quite lengthy. After much practice with using place value to justify their steps, they will develop fluency with the algorithm. Students should be able to explain why the algorithm works.

Student explanation for this problem:

1. Two ones plus seven ones is nine ones.2. Nine tens plus six tens is 15 tens.3. I am going to write down five tens and think of the10 tens as one more hundred. (notates with

a 1 above the hundreds column)4. Eight hundreds plus five hundreds plus the extra hundred from adding the tens is 14

hundreds.5. I am going to write the four hundreds and think of the 10 hundreds as one more 1000. (notates

with a 1 above the thousands column)6. Three thousands plus one thousand plus the extra thousand from the hundreds is five

thousand.

Teaching Student-Centered Mathematicspg. 113 Figure 4.7, refer to top bullets

Lessons:Add with Standard AlgorithmMulti-Step Word Problems with Bar ModelsSolve Multi-Step Problems Using the Standard Addition Algorithm2-Step Subtraction

Activities and Tasks:Making Sense of the AlgorithmTo Regroup or Not to RegroupAdding and Subtracting Word ProblemsAddition and Subtraction Number Stories

Videos:Add Using Partial SumsAdd Using an Open Number LineAdd Using the Standard AlgorithmSubtract Using an Open Number LineSubtract Using the Standard Algorithm


3892+ 1567

https://learnzillion.com/lessons/3160-subtract-using-the-standard-subtraction-algorithm

https://learnzillion.com/lessons/3123-subtract-using-an-open-number-line

https://learnzillion.com/lessons/3122-add-using-the-standard-addition-algorithm

https://learnzillion.com/lessons/3057-add-using-an-open-number-line

http://learnzillion.com/lessons/3121-add-using-partial-sums

http://wcboe.mrooms.org/file.php/14/4th_Grade/Math/0-County_Curriculum_Documents/Common_Core_Resources/Number_and_Operations_in_Base_Ten/4.NBT.A.3/Hundreds_Chart-Rounding.pdf



Connections/Notes Resources

4.NBT.B.4 Continued

Student explanation for this problem:

1. There are not enough ones to take 8 ones from 6 ones so I have to use one ten as 10 ones. Now I have 3 tens and 16 ones. (Marks through the 4 and notates with a 3 above the 4 and writes a 1 above the ones column to be represented as 16 ones.)

2. Sixteen ones minus 8 ones is 8 ones. (Writes an 8 in the ones column of answer.)3. Three tens minus 2 tens is one ten. (Writes a 1 in the tens column of answer.)4. There are not enough hundreds to take 9 hundreds from 5 hundreds so I have to use one

thousand as 10 hundreds. (Marks through the 3 and notates with a 2 above it. (Writes down a 1 above the hundreds column.)

5. Now I have 2 thousand and 15 hundreds.6. Fifteen hundreds minus 9 hundreds is 6 hundreds.7. (Writes a 6 in the hundreds column of the answer).8. I have 2 thousands left since I did not have to take away any thousands. (Writes 2 in the

thousands place of answer.)

Students use the structure of the base-‐ten system to generalize their strategies and to discuss reasonableness of their computations and work towards fluency (MP.6, MP.8).

Note: Students should know that it is mathematically possible to subtract a larger number from a smaller number but that their work with whole numbers does not allow this as the difference would result in a negative number.

Connections: 4.NBT.A.2

4.NBT.B.4 Continued

Online:Circle 99 NLVMDiffy NLVMAddition with Base Ten Blocks NLVMSubtraction with Base Ten Blocks NLVMDicey Operations NRICH Math


3546 - 928

http://nrich.maths.org/6606




http://nlvm.usu.edu/en/nav/frames_asid_269_g_1_t_1.html?open=instructions&from=category_g_1_t_1.html


Unit Two – Efficiency with Multiplication and Understanding Division (20 days)In this unit students develop understanding of multiples and factors, applying their understanding of multiplication from the previous year. This understanding lays a strong foundation for generalizing strategies learned in previous grades to develop, discuss, and use efficient, accurate, and generalizable computational strategies involving multi-‐digit numbers. These concepts and the terms “prime” and “composite” are new to Grade 4, so they are introduced early in the year to give students ample time to develop and apply this understanding. Students continue using computational and problem‐solving strategies, with a focus on building conceptual understanding of multiplication of larger numbers and division with remainders. Area and perimeter of rectangles provide one context for developing such understanding. Students will continue to evaluate expressions using the conventional order or operations that was introduced in grade 3.

Unit Two Standards

4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.



Math LanguageThe terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use these math terms in explanations or justifications.area model array associative property bar model/tape diagram base tencommutative property compatible numbers composite decompose distributive property divide dividend divisor division (repeated subtraction) equation estimate expanded form expression factors inverse operation measurement division multiples multiplier multiplicand multiply number bond partial product place value prime product properties quotient remainder represent symbol variable

Essential QuestionsHow do I identify prime numbers? How do I identify composite numbers? What is the difference between a prime and a composite number? How is skip counting related to identifying multiples? What is the difference between a factor and product? How do we know if a number is prime or composite? How are factors and multiples defined? How will diagrams help us determine and show the products of two-digit numbers? How can I effectively explain my mathematical thinking and reasoning to others? What real life situations require the use of multiplication? What effect does a remainder have on my rounded answer? How can I mentally compute a division problem? What are compatible numbers and how do they aid in dividing whole numbers? How are multiplication and division related to each other? What patterns of multiplication and division can assist us in problem solving? What happens in division when there are zeroes in both the divisor and the dividend? What is the meaning of a remainder in a division problem? How do multiplication, division, and estimation help us solve real world problems? How can we organize our work when solving a multi-step word problem? How can a remainder affect the answer in a division problem? How are area and perimeter related? How are the units used to measure perimeter different/alike from the units used to measure area? How do we find the area/perimeter of a rectangle? How does the area change as the rectangle’s dimensions change (with a fixed perimeter)? What is the relationship between area and perimeter when the area is fixed?



What is the relationship between area and perimeter when the perimeter is fixed?

Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division (20 days) Connections/Notes Resources

4.OA.B.4Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.Students should understand the process of finding factor pairs so they can do this for any number 1 -100.Divisibility rules can be used as a strategy for determining if a number is prime or composite.Example:

Factor pairs for 96: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12. Multiples can be thought of as the result of skip counting by each of the factors. When skip

counting, students should be able to identify the number of factors counted e.g., 5, 10, 15, 20 (there are 4 fives in 20).

Example: Factors of 24: 1, 2, 3, 4, 6, 8,12, 24 Multiples of 1: 1,2,3,4,5…24

of 2: 2,4,6,8,10,12,14,16,18,20,22,24 of 3: 3,6,9,12,15,18,21,24 of 4: 4,8,12,16,20,24 of 5: 8,16,24 of 6: 12,24 of 24: 24

To determine if a number between1-100 is a multiple of a given one-digit number, some helpful hints include the following: all even numbers are multiples of 2 all even numbers that can be halved twice (with a whole number result) are multiples of 4 all numbers ending in 0 or 5 are multiples of 5

When listing multiples of numbers, students may not list the number itself. Emphasize that the smallest multiple is the number itself. Some students may think that larger numbers have more factors. Having students share all factor pairs and how they found them will clear up this misconception. Some students may need to start with numbers that only have one pair of factors, then those with two pairs of factors before finding factors of numbers with several factor pairs.

Teaching Student Centered Mathematicspg. 63, Finding Factors - 2.22pg. 64,Factor Patterns -2.23

Lessons:Times Square Reinforcing Multiplication SkillsUsing Factors and StrategyThe Venn FactorFactor FindingsFind Factor Pairs

Activities and Tasks:Factor Practice SheetsInvestigating Prime and Composite NumbersPrime Number PPTA Remainder of OneHow Many Tables?Finding MultiplesCommon MultiplesPrime Number HuntIdentifying MultiplesMultiples and Factors Fun with QR CodesCross the Board GameFactor Flip Prime/Composite GameFactor Race GameHead to One Hundred GameFactors and Multiples Roll GameFactors and Multiples Venn DiagramLeast Common Multiples


http://wcboe.mrooms.org/file.php/14/4th_Grade/Math/0-County_Curriculum_Documents/Common_Core_Resources/Operations_and_Algebraic_Thinking/4.OA.B.4/How-Many-Tables_Factors.pdf

http://wcboe.mrooms.org/file.php/14/4th_Grade/Math/0-County_Curriculum_Documents/Common_Core_Resources/Operations_and_Algebraic_Thinking/4.OA.B.4/A_Remainder_of_One_GR4_OA_Factors.pdf







4.OA.B.4 Continued

Prime vs. Composite: A prime number is a number greater than 1 that has only 2 factors, 1 and itself. Composite numbers have more than 2 factors.

Students investigate whether numbers are prime or composite by building rectangles (arrays) with the given area and finding which numbers have more than two rectangles (e.g. 7 can be made into only 2 rectangles, 1 x 7 and 7 x 1, therefore it is a prime number)

A common misconception is that the number 1 is prime, when in fact; it is neither prime nor composite. Another common misconception is that all prime numbers are odd numbers. This is not true, since the number 2 has only 2 factors, 1 and 2, and is also an even number.

The focus of this unit is not necessarily to become fluent in finding all factor pairs, but to use student’s understanding of the concept and language to discuss the structure of multiples and factors (MP.3, MP.7).

4.OA.B.4 Continued

Videos:Find All the Factor Pairs of a Number Using Area ModelsDetermine Multiples of a Number Using Area ModelsFind All Factor Pairs Using a Rainbow Factor LineDetermine Multiples of a Number Using Number BondsUse Divisibility Rules to Determine MultiplesUse Divisibility Rules to Determine Multiples 2

OnlineFactor Trail Game IlluminationsFactorize IlluminationsFactor Game IlluminationsFactor Track NRICH MathFactor Lines NRICH MathInteractive Hundred ChartFactor Tree NLVMSieve of Eratosthenes NLVM100 Board Splat

Templates and Visuals:Frayer ModelExample/Non-Example TemplateHundred Twenty Chart

4.OA.C.5Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Patterns involving numbers or symbols either repeat or grow. Students need multiple opportunities creating and extending number and shape patterns. Numerical patterns allow students to reinforce facts and develop fluency with operations.

Teaching Student-Centered Mathematicspg. 291 Predict Down The Line - Activity 10.1pg. 293 Grid Patterns Activity & Figure 10.2pg. 294 Extend & Explain Activity 10.3 & Predict How Many 10.4


http://www.oswego.org/ocsd-web/games/splatsquares/splatsq100.html

http://nlvm.usu.edu/en/nav/frames_asid_158_g_2_t_1.html?open=instructions&from=grade_g_2.html

http://nlvm.usu.edu/en/nav/frames_asid_202_g_2_t_1.html?from=grade_g_2.html

http://www.crickweb.co.uk/ks2numeracy-tools.html



http://illuminations.nctm.org/Activity.aspx?id=4134

http://illuminations.nctm.org/ActivityDetail.aspx?ID=64

http://illuminations.nctm.org/LessonDetail.aspx?id=L719

https://learnzillion.com/lessons/788-use-divisibility-rules-to-determine-if-a-number-is-a-multiple-of-4-or-7

https://learnzillion.com/lessons/787-use-divisibility-rules-to-determine-if-a-number-is-a-multiple-of-2-3-or-6

http://learnzillion.com/lessons/783-determine-multiples-of-a-number-using-number-bonds

http://learnzillion.com/lessons/783-determine-multiples-of-a-number-using-number-bonds

http://learnzillion.com/lessons/782-find-all-factor-pairs-using-a-rainbow-factor-line

http://learnzillion.com/lessons/781-determine-multiples-of-a-number-using-area-models

http://learnzillion.com/lessons/781-determine-multiples-of-a-number-using-area-models

http://learnzillion.com/lessons/780-find-all-the-factor-pairs-of-a-number-using-area-models

http://learnzillion.com/lessons/780-find-all-the-factor-pairs-of-a-number-using-area-models



4.OA.C.5 ContinuedPatterns and rules are related. A pattern is a sequence that repeats the same process over and over. A rule dictates what that process will look like. Students investigate different patterns to find rules, identify features in the patterns, and justify the reason for those features.

Example:

After students have identified rules and features from patterns, they need to generate a numerical pattern from a given rule.

Example: Rule: Starting at 1, create a pattern that starts at 1 and multiplies each number by 3. Stop when

you have 6 numbers.

Students write 1, 3, 9, 27, 81, 243. Students notice that all the numbers are odd and that the sums of the digits of the 2 digit numbers are each 9. Some students might investigate this beyond 6 numbers. Another feature to investigate is the patterns in the differences of the numbers (3 - 1 = 2, 9 - 3 = 6, 27 - 9 = 18, etc.)

Example: Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and

observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. (1, 4, 7, 10, 13)

While working on 4.OA.C.5, students use manipulatives to determine whether a number is prime or composite. Although there are shape patterns in arrays, the focus of this unit is number patterns.

p. 299 What's Next & Why Activity 10.6 & 10.74.OA.C.5 Continued

Lessons:Patterns on Charts IlluminationsGrowing Patterns IlluminationsPolygons, Perimeter, and Patterns IlluminationsExploring Other Number Patterns IlluminationsCalendar Capers AIMSA Banquet at Tony’s AIMS

Activities and Tasks:Numeric Patterns Practice SheetDouble Plus OneExtending PatternsDoubling DimesPiecing Together Patterns

Videos:Find the Rule for a Function Machine Using a Vertical table

Find Missing Elements in Growing Patterns

Determine the Rule in Patterns that Decrease

Generate a Pattern Sequence Using a T-Chart

Chessboard Algebra and Function Machines

On Line:Number Patterns NLVMHundreds Chart NLVM100 Board Splat


http://www.oswego.org/ocsd-web/games/splatsquares/splatsq100.html


http://nlvm.usu.edu/en/nav/frames_asid_185_g_2_t_1.html

https://www.teachingchannel.org/videos/algebra-lesson-planning

http://learnzillion.com/lessons/797-generate-a-pattern-sequence-using-a-tchart

http://learnzillion.com/lessons/794-determine-the-rule-in-patterns-that-decrease

http://learnzillion.com/lessons/792-find-missing-elements-in-growing-patterns

http://learnzillion.com/lessons/790-find-the-rule-for-a-function-machine-using-a-vertical-table

http://learnzillion.com/lessons/790-find-the-rule-for-a-function-machine-using-a-vertical-table







4.OA.C.5 is repeated in unit 8, where the focus will be on identifying shape patterns.Connections: 4.OA.B.44.OA.A.3Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Focus should NOT be on finding KEY WORDS to indicate the four operations!

Students need many opportunities solving multistep story problems using all four operations.

This is the f i rs t t i m e student s ar e expecte d t o i nterpre t re m a i nder s base d upo n the context . All four operations will be addressed in unit 7, and the standard will be finalized in unit 9.

Example: Chris bought clothes for school. She bought 3 shirts for $12 each and a skirt for $15. How much

money did Chris spend on her new school clothes?

3 x $12 + $15 = a

In division problems, the remainder is the whole number left over when as large a multiple of the divisor as possible has been subtracted.

Example: Kim is making candy bags. There will be 5 pieces of candy in each bag. She had 53 pieces of

candy. She ate 14 pieces of candy. How many candy bags can Kim make now?(7 bags with 4 pieces left over)

There are 29 students in one class and 28 students in another class going on a field trip. Each car can hold 5 students. How many cars are needed to get all the students to the field trip?(12 cars, one possible explanation is 11 cars holding 5 students and the 12th holding the remaining 2 students) 29 + 28 = 11 x 5 + 2

Lessons:How to Bag It IlluminationsGet the Picture, Get the Story IlluminationsA Squadron of Bugs: Introducing Division with Remainders IlluminationsArea & Perimeter Multistep Word problems

Activities and Tasks:Multistep Word ProblemsMultistep Problems Add-SubtractMultistep Problems Add-MultiplyMultistep Mixed PracticeCarnival TicketsAt the CircusKickoff Prep Interpreting Remainders

Videos:Estimate to Assess Whether an Answer is ReasonableSolve Word Problems Using ObjectsSolve Word Problems by Drawing PicturesSolve Word Problems by Writing an EquationSolve Multi-Step Word Problems by Writing an Equation

Online:Multi-Step Word Problem Resource


http://www.mathplayground.com/wp_videos.html

http://learnzillion.com/lessons/3079-solve-multistep-word-problems-by-writing-an-equation

http://learnzillion.com/lessons/3079-solve-multistep-word-problems-by-writing-an-equation

http://learnzillion.com/lessons/2944-solve-word-problems-by-writing-an-equation

http://learnzillion.com/lessons/2943-solve-word-problems-by-drawing-pictures

http://learnzillion.com/lessons/2998-solve-word-problems-using-objects

http://learnzillion.com/lessons/3049-estimate-to-assess-whether-an-answer-is-reasonable

http://learnzillion.com/lessons/3049-estimate-to-assess-whether-an-answer-is-reasonable




http://illuminations.nctm.org/LessonDetail.aspx?ID=L209



4.OA.A.3 ContinuedEstimation skills include identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, and verifying solutions or determining the reasonableness of situations using various estimation strategies. Estimation strategies include, but are not limited to:

front-end estimation with adjusting (using the highest place value and estimating from the front end, making adjustments to the estimate by taking into account the remaining amounts)

clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate)

rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values)

using friendly or compatible numbers such as factors (students seek to fit numbers together-e.g., rounding to factors and grouping numbers together that have round sums like 100 or 1,000)

using benchmark numbers that are easy to compute (students select close whole numbers for fractions or decimals to determine an estimate)

4.NBT.B.5Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.The focus of instruction should be on strategies other than the algorithm.

Students who develop flexibility in breaking numbers apart have a better understanding of the importance of place value and the distributive property in multi-digit multiplication. Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying whole numbers and use words and diagrams to explain their thinking. They use the terms factor and product when communicating their reasoning. Multiple strategies enable students to develop fluency with multiplication and transfer that understanding to division. Use of the standard algorithm for multiplication is an expectation in the 5 th grade.

Base Ten Blocks and Drawings:To illustrate 154 x 6 students use base 10 blocks or use drawings to show 154 six times. Seeing 154 six times will lead them to understand the distributive property,154 x 6 = (100 + 50 + 4) x 6 = (100 x 6) + (50 x 6) + (4 x 6) = 600 + 300 + 24 = 924

Teaching Student-Centered Mathematicspg. 113-118, Figures 4.8, 4.10, 4.11, 4.12, pg. 129 Expanded Area Lesson

Lessons:Multiply and ConquerNumber Line DancingAll About Multiplication: Modeling Multiplication with Streets and AvenuesConnect Area Models and Partial ProductsFrame Filling AIMSMultiplying with Tens AIMSMultiplication Stretch AIMS








4.NBT.B.5 Continued

Partial Products:

Rectangular Array:

Bar Model

4.NBT.B.5 Continued

Activities and Tasks:Multiplication Using the Area Model Teaching Pkt.Partial Products TemplateMultiplication Area Model PPTArea Model for Multiplication ProblemsMultiply 2-digit x 2-digit PracticeMultiplication Strategy: Partial Products 1Multiplication Strategy: Partial Products 2Multiplication Strategy: Doubling & HalvingMake the Smallest ProductMake the Largest ProductMultiplication BumpFrench FriesClosest to One ThousandTarget 300 GameBreaking Apart a Factor

Videos:

Use an Array to Multiply a Two-Digit Number by a One-Digit NumberUse Area Models to Show Multiplication of Whole NumbersUse Place Value Understanding to Multiply Three and Four Digit NumbersUse an Area Model for Multiplication of Two-Digit NumbersUse an Area Model to Multiply a Three Digit NumberReady for Two Steps?

Online:


http://www.mathplayground.com/TB_MD/tb_md2_iFrame.html

https://learnzillion.com/lessons/1877-use-an-area-model-to-multiply-a-three-digit-number-by-a-one-digit-number

https://learnzillion.com/lessons/1879-use-an-area-model-for-multiplication-of-twodigit-numbers-by-twodigit-numbers

https://learnzillion.com/lessons/1879-use-an-area-model-for-multiplication-of-twodigit-numbers-by-twodigit-numbers

https://learnzillion.com/lessons/1878-use-place-value-understanding-to-multiply-three-and-four-digit-numbers

https://learnzillion.com/lessons/1878-use-place-value-understanding-to-multiply-three-and-four-digit-numbers

https://learnzillion.com/lessons/1876-use-area-models-to-show-multiplication-of-whole-numbers

https://learnzillion.com/lessons/1876-use-area-models-to-show-multiplication-of-whole-numbers

http://learnzillion.com/lessons/1875-use-an-array-to-multiply-a-two-digit-number-by-a-one-digit-number

http://learnzillion.com/lessons/1875-use-an-array-to-multiply-a-two-digit-number-by-a-one-digit-number

http://www.google.com/url?sa=i&rct=j&q=compensation%20multiplication&source=images&cd=&cad=rja&uact=8&docid=O-b7ajU3p-lTUM&tbnid=Rs6TD4eIAGNTKM:&ved=0CAUQjRw&url=http://www.youtube.com/watch?v%3DSIXKT8CWirM&ei=ixabU9imIfTKsQTr3IGQAQ&bvm=bv.68911936,d.cWc&psig=AFQjCNGwtrtft8owemgbZRHaHzcI4ARwGg&ust=1402758960629455

http://www.google.com/url?sa=i&rct=j&q=grade+4+bar+model+multiplication+examples&source=images&cd=&cad=rja&uact=8&docid=XstdiTCB-ibI5M&tbnid=U5mxJkdM4DJEwM:&ved=0CAUQjRw&url=http://mathcoachscorner.blogspot.com/2013_09_01_archive.html&ei=yBCbU7qoGdi0yATDsYG4Dg&bvm=bv.68911936,d.cWc&psig=AFQjCNH84nv60EkQV-cK-cSMhiIKrCe7Hg&ust=1402757145208549

http://www.google.com/url?sa=i&rct=j&q=grade+4+bar+model+multiplication+examples&source=images&cd=&cad=rja&uact=8&docid=DG_4yqmjcMwsyM&tbnid=_imBm6rtIKv09M:&ved=0CAUQjRw&url=http://mathcoachscorner.blogspot.com/2013/09/alternate-strategies-for-multi-digit.html&ei=Zw-bU-nHCszgsATF0IGwDQ&bvm=bv.68911936,d.cWc&psig=AFQjCNH84nv60EkQV-cK-cSMhiIKrCe7Hg&ust=1402757145208549

http://www.google.com/url?sa=i&rct=j&q=grade+4+bar+model+examples&source=images&cd=&cad=rja&uact=8&docid=Abnv9AgcDMPrkM&tbnid=n0qRQdUFaZWzmM:&ved=0CAUQjRw&url=http://en.wikipedia.org/wiki/Singapore_math&ei=8gqbU8ruA5WhsATy04Bo&bvm=bv.68911936,d.cWc&psig=AFQjCNFlHMeUXhwIMx6w4pMt5k-d7aVUmA&ust=1402756126447464



Area Models: 14 x 16 = 224

Rectangle Measurement: Virtual Manipulative


http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html?from=category_g_2_t_1.html



Area Models Continued:

Place Value Disks:

Connections:


http://www.google.com/url?sa=i&rct=j&q=compensation%20multiplication&source=images&cd=&cad=rja&uact=8&docid=xVFoERJSlDoqKM&tbnid=rr-77pEMtD0xYM:&ved=0CAUQjRw&url=http://teacher.scholastic.com/products/math180/esampler/demo/block2_topic3_lesson_1.html&ei=yxWbU9L9GIiYyAS6oICwCQ&bvm=bv.68911936,d.cWc&psig=AFQjCNGwtrtft8owemgbZRHaHzcI4ARwGg&ust=1402758960629455

http://www.google.com/url?sa=i&rct=j&q=grade+4+bar+model+multiplication+examples&source=images&cd=&cad=rja&uact=8&docid=XstdiTCB-ibI5M&tbnid=U5mxJkdM4DJEwM:&ved=0CAUQjRw&url=http://icsdk5math.wikispaces.com/Multiplication%2B%26%2BDiv%2BStrategies&ei=gRCbU-KPBdWeyATF04DYBQ&bvm=bv.68911936,d.cWc&psig=AFQjCNH84nv60EkQV-cK-cSMhiIKrCe7Hg&ust=1402757145208549



4.OA.A.2; 4.OA.A.3; 4.NBT.A.1

4.NBT.B.6Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and or area models.The focus of instruction should be on strategies and models before the algorithm.In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context.

Examples:A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the boxes so that each box has the same number of pencils. How many pencils will there be in each box?

Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups. Some students may need to trade the 2 hundreds for tens but others may easily recognize that 200 divided by 4 is 50.

Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4)

Using Multiplication:4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65

Using an Open Array or Area Model:After developing an understanding of using arrays to divide, students begin to use a more abstract model for division. This model connects to a recording process that will be formalized in the 5 th grade.

1: 150 ÷ 6

Students make a rectangle and write 6 on one of its sides. Theyexpress their understanding that they need to think of the rectangleas representing a total of 150.

Teaching Student-Centered Mathematicspg. 93 How Close Can You Get? Activity 3.10, pg. 121-124, pg. 121 Figure 4.16, pg. 124 Figure 4.17

Lessons:Pack 10 Trading AIMSLeftovers with 100Division Requiring Decomposing a RemainderDivision with remainders Using Arrays and Area ModelsDivision Word Problems with RemaindersExplain Remainders Using Place Value UnderstandingWhole Number Quotients and RemaindersTwo-Digit Dividends with Number DisksSolve Division Problems Without Remainders Using Area ModelsSolve Division Problems With Remainders Using Area Models

Activities and Tasks:Division Using the Area Model Teacher PacketDivision of the DayDivision Strategy: Partial Quotients 1Division Strategy: Partial Quotients 2Division Strategy: Partition the DividendEstimate the Quotient




4.NBT.B.6 Continued

1. Students think, 6 times what number is a number close to 150? They recognize that 6 x 10 is 60 sothey record 10 as a factor and partition the rectangle into 2 rectangles and label the area aligned to the factor of 10 with 60. They express that they have only used 60 of the 150 so they have 90 left.

2. Recognizing that there is another 60 in what is left they repeat the process above. They express that they have used 120 of the 150 so they have 30 left.

3. Knowing that 6 x 5 is 30. They write 30 in the bottom area of the rectangle and record 5 as a factor.4. Students express their calculations in various ways:

Example 1:

Example 2: 1,917 ÷ 9

A student’s description of his or her thinking may be:

I need to find out how many 9s are in 1917. I know that 200 x 9 is 1800.So if I use 1800 of the 1917, I have 117 left. I know that 9 x 10 is 90.So if I have 10 more 9s, I will have 27 left. I can make 3 more 9s.

Group Activity for DivisionRemainders Game4.NBT.B.6 Continued

Videos:Divide Two-Digit Dividends Using Friendly MultiplesReport Remainders as FractionsReport Remainders as Whole Numbers by Drawing Pictures to Decide Whether to Round Up or DownDivide Three-Digit DividendsDivide Four-Digit Dividends

Online:The Quotient Cafe IlluminationsRemainders CountModels for Division Video from Math PlaygroundTime for Remainders Video from Math PlaygroundArea Model Division with Single Digit Divisors Video form YouTubeRectangle Division NLVM

Templates and Visuals:Division Anchor Chart Samples



http://www.youtube.com/watch?v=I2o5O3abFJw



http://www.curriculumsupport.education.nsw.gov.au/countmein/children_remainders_count.html

http://illuminations.nctm.org/ActivityDetail.aspx?ID=224

https://learnzillion.com/lessons/1484-divide-fourdigit-dividends

https://learnzillion.com/lessons/1483-divide-threedigit-dividends

https://learnzillion.com/lessons/1481-report-remainders-as-whole-numbers-by-drawing-pictures-to-decide-whether-to-round-up-or-down

https://learnzillion.com/lessons/1481-report-remainders-as-whole-numbers-by-drawing-pictures-to-decide-whether-to-round-up-or-down

https://learnzillion.com/lessons/1480-report-remainders-as-fractions

http://learnzillion.com/lessons/1482-divide-twodigit-dividends-using-friendly-multiples



I have 200 nines, 10 nines and 3 nines. So I made 213 nines. 1917 ÷ 9 = 213

4.MD.A.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Students developed understanding of area and perimeter in 3rd grade by using visual models.

While students are expected to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work.

The formula for area is I x w and the answer will always be in square units.

The formula for perimeter can be 2 l + 2 w or 2 (l + w) and the answer will be in linear units.

This standard provides the context of area and perimeter of rectangles to use for problem solving. Students are first introduced to formulas in this unit and make sense of the formulas using their prior work with area and perimeter.

Example:

Find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Teaching Student-Centered MathematicsPg. 265 Fixed Perimeters & Areas Activities 9.7 & 9.8 pg. 288-289 Fixed Areas Expanded Lesson

Lessons:What's My Area? IlluminationsChairs IlluminationsFiguring Areas Math SolutionsArea in Metric (Unit)Conversions (Unit)

Activities and Tasks:Area & Perimeter Word ProblemsArea and Perimeter of ShapesUsing Equations to Find Area of ShapesFinding Area of Rod DesignsArea with Cuisenaire RodsDetermining the Missing Side with PerimeterArea and Perimeter with Cheese CrackersDesigning a Zoo Enclosure (Area)Fencing a Garden (Perimeter)Sammy’s Sport Complex Area PracticeGoing to the DogsHorsing AroundHow Many TablesPerimeter and Area Practice

Videos:Use Area Models to Find the Area of RectanglesFind Missing Side Lengths Using the Formula for AreaFind Perimeter Using the Standard Formula


https://learnzillion.com/lessons/3047-find-perimeter-using-the-standard-formula

https://learnzillion.com/lessons/2425-find-missing-side-lengths-using-the-formula-for-area

https://learnzillion.com/lessons/2425-find-missing-side-lengths-using-the-formula-for-area

http://learnzillion.com/lessons/2374-use-area-models-to-find-the-area-of-rectangles





Find Missing Side Lengths Using the Formula for Perimeter

Unit Three – Solving Problems Using Multiplicative Comparison (10 days)

In this unit students are introduced to multiplicative compare problems, extending their conceptual work with multiplicative comparison. For students to develop this concept, they must be provided rich problem situations that encourage them to make sense of the relationships among the quantities involved, model the situation, and check their solution using a different method. These problems ar e ne w t o G rad e 4 students .

The comparison is based on one set being a particular multiplier of the other. In an additive comparison problem, the underlying question is what amount would be added to one quantity in order to result in the other. The underlying question for multiplicative comparison problems is what factor would multiply one quantity in order to result in the other.

It is important to introduce multiplicative comparison problems to our grade 4 students as these problems can be extended in later years to include multiplication and division of fractions. Thus, including these problems with whole numbers in grade 4 lays the groundwork for developing an understanding of multiplication and division of fractions and decimals in later grades.

Multiplicative comparison problems involve a comparison of two quantities in which one is described as a multiple of the other. The relation between quantities is described in terms of how many times larger one is than the other. The number quantifying this relationship is not an identifiable quantity. In the following problem, the animals’ weights are measurable quantities, but the other quantity (three times as much) simply describes the relationship between the measurable quantities:

The first grade class has a hamster and a gerbil. The hamster weighs 3 times as much as the gerbil. The gerbil weighs 9 ounces. How much does the hamster weigh?

The table on the following page is an important resource for writing multiplicative comparison problems.


https://learnzillion.com/lessons/3048-find-missing-side-lengths-using-the-formula-for-perimeter

https://learnzillion.com/lessons/3048-find-missing-side-lengths-using-the-formula-for-perimeter


Multiplicative Comparison problems can also be constructed for any of the three basic problem types, as seen below. Multiplicative compare problems appear first in the CCSSM in fourth grade, with whole number values. In Grade 5, unit fractions language such as “one third as much” may be used.

Unit Three Standards

4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.


Multiplicative

Comparison

Smaller Unknown: Larger Unknown: Multiplier Unknown:

4th Grade

4.OA.2

The giraffe is 18 feet tall. She is 3 times as tall as the kangaroo. How tall is the kangaroo?

Measurement Example:A rubber band is stretched to be 18 centimeters long and that is 3 times as long as it was at first. How long was the rubber band at first?

The giraffe in the zoo is 3 times as tall as the kangaroo. The kangaroo is 6 feet tall. How tall is the giraffe?

Measurement Example:A rubber band is 6 centimeters long. How long will the rubber band be when it is stretched to be 3 times as long?

The giraffe is 18 feet tall. The kangaroo is 6 feet tall. The giraffe is how many times taller than the kangaroo?

Measurement Example:A rubber band was 6 centimeters long at first. Now it is stretched to be 18 centimeters long. How many times as long is the rubber band now as it was at first?

5th GradeThe giraffe is 18 feet tall. The kangaroo is 1/3 as tall as the giraffe. How tall is the kangaroo?

The kangaroo is 6 feet tall. She is 1/3 as tall as the giraffe. How tall is the giraffe?

The giraffe is 18 feet tall. The kangaroo is 6 feet tall. What fraction of the height of the giraffe is the height of the kangaroo?


4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Math Language The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use these math terms in explanations or justifications.additive comparison area model associative property bar model/tape diagram base ten commutative property compatible numbers composite decompose distributive property equation estimate expanded form expression factors inverse operation multiplicand multiplier multiples multiplicative comparison multiply number bond partial product place value prime product properties represent symbol variable

Essential Questions

How can multiplication be used to answer questions? How do you express a multiplication comparison equation as a written statement?What is the difference between a multiplicative comparison and an additive comparison?How do we solve multiplication word problems involving multiplicative comparison using drawings and equations?


Use of Key Words 1. Key words are misleading. Some key words typically mean addition or subtraction. This is not always true. Consider: There were 4 jackets left on the playground on Monday and 5 jackets left on the playground on Tuesday. How many jackets were left on the playground? "Left" in this problem does not mean subtract.

2. Many problems have no key words. Example: How many legs do 7 elephants have? There is no key word. However, any 1st grader should be able to solve the problem by thinking and drawing a picture or building a model.

3. It sends a bad message. The most important strategy when solving a problem is to make sense of the problem and to think. Key words encourage students to ignore meaning and look for a formula. Mathematics is about meaning (Van de Walle, 2012). Avoid Key Words



Grade 4 Unit Three - Solving Problems Using Multiplicative Comparison (10 days)

Connections/Notes Resources4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.

In multiplicative comparison problems, there are two different sets being compared. The first set contains a certain number of items. The second set contains multiple copies of the first set. Any two factors and their product can be read as a comparison. Let’s look at a basic multiplication equation:4 x 2 = 8.

Students should be given opportunities to write and identify equations and statements for multiplicative comparisons.Example:5 x 8 = 40.Sally is five years old. Her mom is eight times older. How old is Sally’s Mom?

5 x 5 = 25Sally has five times as many pencils as Mary. If Sally has 5 pencils, how many does Mary have?

Teaching Student-Centered Mathematics:pg. 63 Figure 2.15, pg. 65 The broken Multiplication Key Activity 2.25

Lessons:Multiplicative Comparison (Unit)

Activities and Tasks:Representing Multiplicative Comparison ProblemsComparing Growth Variation1Comparing Growth Variation 2Task Cards Multiplication as a ComparisonMeasuring MammalsInterpreting Multiplicative ComparisonInterpreting Multiplicative Comparison 2

Videos:Comparing Numbers Using Bar ModelsSee Multiplication As a Comparison Using Number Sentences

Online:Multiplicative Comparison Samples

4.OA.A.2


https://www.khanacademy.org/commoncore/#grade-4-OA

https://learnzillion.com/lessons/2543-see-multiplication-as-a-comparison-using-number-sentences

https://learnzillion.com/lessons/2543-see-multiplication-as-a-comparison-using-number-sentences

https://learnzillion.com/lessons/2569-comparing-numbers-using-bar-models



Connections/Notes ResourcesMultiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Students need many opportunities to solve contextual problems.

A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?In solving this problem, the student should identify $6 as the quantity that is being multiplied by 3. The student should write the problem using a symbol to represent the unknown. ($6 x 3 = )

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?In solving this problem, the student should identify $18 as the quantity being divided into shares of $6.The student should write the problem using a symbol to represent the unknown. ($18 ÷ $6 = )

When distinguishing multiplicative comparison from additive comparison, students should note that: Additive comparisons focus on the difference between two quantities (e.g., Deb has 3 apples

and Karen has 5 apples. How many more apples does Karen have?) A simple way to remember this is, “How many more?”

Multiplicative comparisons focus on comparing two quantities by showing that one quantity is a specified number of times larger or smaller than the other. (e.g., Deb ran 3 miles. Karen ran 5 times as many miles as Deb. How many miles did Karen run?) A simple way to remember this is “How many times as much?” or “How many times as many?”

Teaching Student Centered Mathematicspg.304 - 307, Story Translations - Activity 10.10

Lessons:Multiply and ConquerMultiplicative Comparison Word Problems2-Step Multiplicative ComparisonMultiplicative Comparison (Unit)

Activities and Tasks:Representing Multiplicative Comparison ProblemsMultiplicative Comparison ProblemsComparing Money RaisedAt the CircusMultiplication Story Structures Fall Themed PPTPractice TaskMultiplicative Comparison Task CardsMultiplicative Comparison Word Problems Within 100Multiplicative Comparison Word Problems 2Task Cards Multiplication as a Comparison

Online:Thinking Blocks (virtual manipulatives)

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including


http://www.mathplayground.com/NewThinkingBlocks/thinking_blocks_multiplication_division.html

http://illuminations.nctm.org/LessonDetail.aspx?id=L858



Connections/Notes Resourcesproblems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Work should be specifically with word problems using multiplicative comparison with distances, time, money, and measurements.

Activities and Tasks:Word Problems



Unit 4 – Understanding and Comparing Fractions (22 days)

In this unit students extend their prior knowledge of unit fractions with denominators of 2, 3, 4, 6, and 8 from Grade 3 to include denominators of 5, 10, 12, and 100. In Grade 4, they use their understanding of partitioning to find unit fractions to compose and decompose fractions in order to add fractions with like denominators. This is foundational for other work with fractions, such as comparing fractions and multiplying fractions by a whole number. Students will also develop an understanding of fraction equivalence and various methods for comparing fractions. Students should understand that when comparing fractions, it is not always necessary to generate equivalent fractions. Other methods, such as comparing fractions to a benchmark, can be used to discuss relative sizes. The justification of comparing or generating equivalent fractions using visual models is an emphasis of this unit.

Unit Four Standards

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principal to recognize and generate equivalent fractions.

4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <, =, or >, and justify the conclusions, e.g., by using a visual fraction model.

Math Language The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use these math terms in explanations or justifications.

benchmark fractions compare decompose denominator equation equivalent fractions fraction increment mixed number multiple number line numerator parts partition unit fraction visual fraction model whole whole number



Essential Questions

What is a fraction and how can it be represented? How can equivalent fractions be identified? How can we find equivalent fractions? How can a fraction represent parts of a set? What do the parts of a fraction tell about its numerator and denominator? What is a fraction and how can it be represented? What is a fraction and what does it represent? What is a mixed number and how can it be represented? What is an improper fraction and how can it be represented? What is the relationship between a mixed number and an improper fraction? Why is it important to identify, label, and compare fractions (halves, thirds, fourths, sixths, eighths, tenths) as representations of equal parts of a whole or set? In what ways can we model equivalent fractions? How can identifying factors and multiples of denominators help to identify equivalent fractions?

How can we find equivalent fractions? In what ways can we model equivalent fractions?

How can we find equivalent fractions and simplify fractions? How can benchmark fractions be used to compare fractions? What are benchmark fractions? How are benchmark fractions helpful when comparing fractions? How do we know fractional parts are equivalent? What happens to the value of a fraction when the numerator and denominator are multiplied or divided by the same number? How are equivalent fractions related? How can you compare and order fractions? How are benchmark fractions helpful when comparing fractions? How do I compare fractions with unlike denominators? How do you know fractions are equivalent? What can you do to decide whether your answer is reasonable? How can identifying factors and multiples of denominators help to identify equivalent fractions? How do we represent a fraction that is greater than one? How do we locate fractions on a number line? How do we make a line plot to display a data set? How do we apply our understanding of fractions in everyday life?



Grade 4 Unit Four – Understanding & Comparing Fractions (22 days)

Connections/Notes Resources4.NF.B.3Understand a fraction a/b with a > 1 as a sum of fractions 1/b.a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. Justify decompositions, e.g., by using a visual fraction model.

A fraction with a numerator of one is called a unit fraction.

When students investigate fractions other than unit fractions, such as 2/3, they should be able to decompose the non-unit fraction into a combination of several unit fractions.

Fraction Example 1:

Being able to visualize this decomposition into unit fractions helps students when adding or subtracting fractions. Students need multiple opportunities to work with mixed numbers and be able to decompose them in more than one way. Students may use visual models to help develop this understanding.

Teaching Student Centered Mathematicspg. 150 First Estimates Activity 5.13

Lessons:Decompose Fractions as a Sum of Unit Fractions 1Decompose Fractions as a Sum of Unit Fractions 2Decompose Fractions Using Tape DiagramsDecompose Fractions into Sums of Smaller Fractions

Activities and Tasks:Adding Fractions Using Pattern BlocksPizza SharePicture PieDecomposing FractionsComparing Sums of Unit FractionsMaking 22 Seventeenths in Different WaysPlastic Building BlocksWriting a Mixed Number as an Equivalent FractionAdding and Subtracting Like FractionsFraction Field EventFraction Missing AddendsPizza ParlorChocolate Bar ProblemSense or NonsenseSense or Nonsense 2




Connections/Notes Resources4.NF.B.3 Continued

Fraction Example 2:

Word Problem Example 1:

Mary and Lacey decide to share a pizza. Mary ate 3/6 and Lacey ate 2/6 of the pizza. How much of the pizza did the girls eat together?

Solution: The amount of pizza Mary ate can be thought of a 3/6 or 1/6 and 1/6 and 1/6. The amount of pizza Lacey ate can be thought of a 1/6 and 1/6. The total amount of pizza they ate is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 or 5/6 of the whole pizza.

4.NF.B.3 Continued

Videos:Add Fractions by Joining Parts

Online:Number Line Bars - Fractions NLVM

Suggested manipulatives to develop this concept: fraction strips, Cuisenaire rods, fraction towers, fraction fringes (AIMS), fraction squares, fraction circles, and pattern blocks.

Visual fraction models include tape diagrams, area models, number line diagrams, set diagrams (See Van de Walle pgs.162-166).

4.NF.A.1Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principal to recognize and generate equivalent fractions.

This standard extends the work in third grade by using additional denominators (5, 10, 12, and 100).

Students can use visual models or applets to generate equivalent fractions.

Teaching Student-Centered Mathematics:pgs. 144-146 Activities 5.7, 5.8, and 5.9pgs. 151-156 Activities 5.14 - 5.19, Figure 5.20pgs. 140-141 activities 5.4 and 5.5

Lessons:MSDE Unit: Equivalent FractionsInvestigating Fractions with Pattern BlocksInvestigating Equivalent Fractions with Relationship Rods





http://nlvm.usu.edu/en/nav/frames_asid_265_g_2_t_1.html?open=activities&from=grade_g_2.html

http://learnzillion.com/lessons/1421-add-fractions-by-joining-parts




4.NF.A.1 Continued

All the models above show 1/2. The second model shows 2/4 but also shows that 1/2 and 2/4 are equivalent fractions because their areas are equivalent. When a horizontal line is drawn through the center of the model, the number of equal parts doubles and size of the parts is halved.

Students will begin to notice connections between the models and fractions in the way both the parts and wholes are counted and begin to generate a rule for writing equivalent fractions.

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.

4.NF.A.1 Continued

Lessons Continued :Eggsactly EquivalentFraction ClotheslineBlack Wholes AIMSFraction Fringe AIMSFractions with Pattern Blocks AIMSFraction Time AIMSFraction DominoesPicture Parts AIMSSame Name Frame AIMSShady Fractions AIMSFraction Equivalence Using a Tape DiagramHalf Track AIMS

Activities and Tasks:Equal Fractions PPTGeoboard Activity 1One-Color Rod TrainsCreating Equivalent FractionsMoney in the Piggy BankExplaining Fraction Equivalence with PicturesEqual Fraction Pairs with Cuisenaire RodsFraction Wall GamePattern Block PuzzlesUsing Benchmarks to Compare FractionsChoose a DenominatorMSDE Unit Equivalent FractionsRunning Laps TaskSugar in Six Cans of Soda Task






4.NF.A.1 Continued

Videos:Recognize Equivalent Fractions Using Area Models

Online:Fraction Bars Virtual Manipulative NLVMEquivalent Fractions Virtual Manipulative NLVM12 Fraction Activity ToolsFraction Models Tool IlluminationsEquivalent Fractions Illuminations

Templates and Visuals:Fraction SquaresEquivalent Fraction CardsEquivalent Fractions Display

4.NF.A.2Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <, =, or >, and justify the conclusions, e.g., by using a visual fraction model.

Benchmark fractions include common fractions between 0 and 1 such as halves, thirds, fourths, fifths, sixths, eighths, tenths, twelfths, and hundredths.

Fractions can be compared using benchmarks, common denominators, or common numerators.

Symbols used to describe comparisons include <, >, =.

Fractions may be compared using as a benchmark.

Teaching Student Centered Mathematicspgs. 144-146 Activities 5.7, 5.8, and 5.9pgs. 146-148 Activities 5.10, 5.11, and 5.12

Lessons:Fractional Clothesline IlluminationsBenchmark FractionsFraction SortHalf Track AIMSUsing Benchmarks to Compare FractionsExtend Understanding of Fraction Equivalence and Ordering





http://learnzillion.com/lessons/616-recognize-equivalent-fractions-using-area-models




4.NF.A.2 Continued

Possible student thinking by using benchmarks:

o is smaller than because when1 whole is cut into 8 pieces, the piecesare much smaller than when 1 whole is cut into 2 pieces.

Possible student thinking by creating common denominators:

o

56 > because

36 = and

56 >

36

Fractions with common denominators may be compared using the numerators as a guide.

o

26 <

36 <

56

Fractions with common numerators may be compared and ordered using the denominators as a guide.

o

310 <

38 <

34

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

4.NF.A.2 Continued

Activities and Tasks:Birthday FractionsSpin to Win GamePattern Block FractionsWho Ate More?Which is Larger?How to Find a Fraction on a Number Line PPTSnack TimeDetermining Fraction Value on a Number LineFraction Card GamesFraction CompareListing Fractions in Increasing SizeCompare Fraction StrategiesWrite About FractionsFraction Card GamesBetween 0 and 1 Fair Pairs AIMS

Videos:Compare Fractions Using the Benchmark Fraction 1/2Compare Fractions to a Benchmark of One Half Using Number Lines

Online:Fun with Fractions Illuminations LessonsPlaying Fraction Tracks NCTM GameLocating & Ordering Equivalent Fractions on a Number Line PBIS LessonFraction Monkeys GameFraction Models Tool Illuminations

Templates and Visuals:Fraction Squares



http://learnzillion.com/lessons/1321-compare-fractions-to-a-benchmark-of-one-half-using-number-lines

http://learnzillion.com/lessons/1321-compare-fractions-to-a-benchmark-of-one-half-using-number-lines

http://learnzillion.com/lessons/1431-compare-fractions-using-the-benchmark-fraction-12




Unit Five – Fraction Operations (23 days)

In this unit students will use their understanding of adding and subtracting fractions and generating equivalent fractions to solve problems involving fractions and mixed numbers. Students rely on their previous work with whole numbers as fractions to compose and decompose whole numbers

into fractional quantities. Data is used in this unit to support students’ understanding of fractional quantities both smaller and larger than 1. Students also apply their understanding of composing and decomposing fractions to develop a conceptual understanding of multiplication of a fraction by a whole number. Students use and extend their previous understandings of operations with whole numbers and relate that understanding to fractions.

Unit Five Standards

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)


http://www.corestandards.org/Math/Content/4/NF/B/4

http://www.corestandards.org/Math/Content/4/MD/B/4

http://www.corestandards.org/Math/Content/4/NF/B/3/d

http://www.corestandards.org/Math/Content/4/NF/B/3/c



c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Math LanguageThe terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use these math terms in explanations or justifications.

benchmark fractions compare decompose denominator equation equivalent fractions fraction increment line plot mixed number multiple multiplicative comparison number line numerator parts partition unit fraction visual fraction model whole

Essential Questions

How are fractions used in problem-solving situations? How can I find equivalent fractions? How can I represent fractions in different ways? How can improper fractions and mixed numbers be used interchangeably? How can I add and subtract fractions of a given set? How can you use fractions to solve addition and subtraction problems? How do we add fractions with like denominators?

What happens to the denominator when I add fractions with like denominators? Why does the denominator remain the same when I add fractions with like denominators?

How can I be sure fractional parts are equal in size? How can I model the multiplication of a whole number by a fraction? How can I multiply a set by a fraction? How can I multiply a whole number by a fraction?

How can I represent multiplication of a whole number? How can we model answers to fraction problems? How can we use fractions to help us solve problems?

How can we write equations to represent our answers when solving word problems? How do we determine a fractional value when given the whole number? How do we determine the whole amount when given a fractional value of the whole? How does the number of equal pieces affect the fraction name? How is multiplication of fractions similar to division of whole numbers?



How is multiplication of fractions similar to repeated addition of fraction? What does it mean to take a fractional portion of a whole number? What is the relationship between multiplication by a fraction and division? What is the relationship between the size of the denominator and the size of each fractional piece (i.e. the numerator)? What strategies can be used for finding products when multiplying a whole number by a fraction?

Grade 4 Unit Five – Fraction Operations (23 days)

Connections/Notes Resources4.NF.B.3Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Mixed numbers are introduced for the first time in 4 grade. Students should have ample experience subtracting and adding mixed numbers where they work with mixed numbers or convert mixed numbers to improper fractions.

A separate algorithm for mixed numbers in addition and subtraction is not necessary. Students will tend to add or subtract the whole numbers first and then work with the fractions using the same strategies they have applied to problems that contained only fractions.

Students use visual and concrete models to represent a fractional situation in order to add and subtract fractions (MP.4).

Word Problem Example: Susan and Maria need 8 3/8 feet of ribbon to package gift baskets. Susan has 3 1/8 feet of ribbon and

Maria has 5 3/8 feet of ribbon. How much ribbon do they have altogether? Will it be enough to complete the project? Explain why or why not.

The student thinks: I can add the ribbon Susan has to the ribbon Maria has to find out how much ribbon they have altogether. Susan has 3 1/8 feet of ribbon and Maria has 5 3/8 feet of ribbon. I can write this as 3 1/8 + 5 3/8. I know they have 8 feet of ribbon by adding the 3 and 5. They also have

Lessons:Add Mixed NumbersSubtract Mixed NumbersAdd a Mixed Number and a FractionSubtract a Fraction from a Mixed NumberSubtract a Mixed Number from a Mixed NumberEstimate Sums and Differences of FractionsAdd and Subtract Fractions (Unit)Adding Fractions on a Number Line (Unit)Lesson Use Visual Models to Add and Subtract Two Fractions with the Same UnitsLesson Use Visual Models to Add Two Fractions with Related Units

Activities and Tasks:Adding Mixed NumbersAdding Fractions Using Pattern Blocks




Connections/Notes Resources1/8 and 3/8 which makes a total of 4/8 more. Altogether they have 8 4/8 feet of ribbon. 8 4/8 is larger than 8 3/8 so they will have enough ribbon to complete the project. They will even have a little extra ribbon left, 1/8 foot.

Additional Example:

Trevor has 4 1/8 pizzas left over from his soccer party. After giving some pizza to his friend, he has 2 4/8 of a pizza left. How much pizza did Trevor give to his friend?

4.NF.B.3 Continued

Solution: Trevor had 4 1/8 pizzas to start. This is 33/8 of a pizza. The x’s show the pizza he has left which is 2 4/8 pizzas or 20/8 pizzas. The shaded rectangles without the x’s are the pizza he gave to his friend which is 13/8 or 1 5/8 pizzas.

A cake recipe calls for you to use ¾ cup milk, ¼ cup of oil, and 2/4 cup of water. How much liquid is needed to make the cake?

Adding and Subtracting Like FractionsGeoboard Add Like DenominatorsMaking GranolaMixed Number Word ProblemsSense or NonsenseSense or Nonsense 2The Chocolate Bar ProblemI Have…Who Has Fraction Game4.NF.B.3 Continued

Activities and Tasks Continued:Writing a Mixed Number as an Equivalent Fraction Word ProblemsChoose a DenominatorMaking 22 Seventeenths in Different WaysWho Has Fraction GameSubtracting Fractions Using a Number Line

Videos:Adding Mixed Numbers by Creating Equivalent FractionsAdd Fractions with Like Denominators by Decomposing Into Unit Fractions

Online:Adding Fractions e-tool NLVMFraction Models Tool IlluminationsThinking Blocks - Fractions


http://www.mathplayground.com/tb_fractions/thinking_blocks_fractions.html


http://learnzillion.com/lessons/2777-add-fractions-with-like-denominators-by-decomposing-into-unit-fractions

http://learnzillion.com/lessons/2777-add-fractions-with-like-denominators-by-decomposing-into-unit-fractions

http://learnzillion.com/lessons/850-adding-mixed-numbers-by-creating-equivalent-fractions

http://learnzillion.com/lessons/850-adding-mixed-numbers-by-creating-equivalent-fractions




Often students think that it does not matter which model to use when finding the sum or difference of fractions. They may represent one fraction with a rectangle and the other fraction with a circle. They need to know that the models need to represent the same whole. In addition students have a tendency to add both the numerator and denominator when using different operations with fractions as opposed to just adding numerators.

4.MD.B.4Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Example:Ten students in Room 31 measured their pencils at the end of the day. They recorded their results on the line plot below.

4.MD.B.4 extends students’ work from Grade 3 with simple fractions on a line plot (3.MD.B.4) to include eighths and to now solve addition and subtraction problems using the data.

Students reason about fractions by using abstract models to represent both the data and the fractional quantities (MP.2, MP.4).

Teaching Student Centered Mathematicspg. 333

Lessons:Line PlotsMeasurement in Fraction UnitsMeasurement and Data Line Plots (Unit)Fraction Line Plot Word ProblemsFraction Word Problems with Line PlotsLine Plot Lesson

Activities and Tasks:Measuring & ShowingLength of AntsObjects in My DeskPulling a Few StringsMeasurement Line PlotsMeasure in Fractional Units Word Problems

Videos:Create a Line Plot Using a Data Set of Fractional Measures


http://learnzillion.com/lessons/3303-create-a-line-plot-using-a-data-set-of-fractional-measures

http://learnzillion.com/lessons/3303-create-a-line-plot-using-a-data-set-of-fractional-measures

http://www.corestandards.org/Math/Content/4/MD/B/4



Connections/Notes ResourcesCreate a Line Plot Using Fractions

Online:Ruler Game

Templates and Visuals:Line Plot Template

4.OA.A.1Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.OA.A.1 is readdressed in this unit to include m u l t i p li cat i o n o f f ract i on s and apply the understanding of “times as much” (i.e. multiplication as comparison) to multiplying a fraction by a whole number.

Lessons:Solve Multiplicative Comparison Word Problems Involving Fractions

4.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.Students need many opportunities to work with problems in context to understand the connections between models and corresponding equations. Contexts involving a whole number times a fraction lend themselves to modeling and examining patterns.

Examples: 3 x (2/5) = 6 x (1/5) = 6/5

Teaching Student Centered Mathematicspg. 167 - 169 Figure 6.6 (left side)

Lessons:Introducing Multiplication of FractionsProduct of Whole Number and a Mixed NumberMultiplying FractionsMultiply Fraction by Whole Number (Unit)Activities and Tasks:






If each person at a party eats 3/8 of a pound of roast beef, and there are 5 people at the party, how many pounds of roast beef are needed? Between what two whole numbers does your answer lie?

A student may build a fraction model to represent this problem.

4.NF.B.4 Continued

Fraction of a Whole Number QR Code ActivityModels for Fraction MultiplicationWhole Number by Fraction Word ProblemsVisual Fractions by Whole NumbersFraction as a Multiple of One GameA Bowl of BeansBirthday CakeFractions and Whole Numbers in WordsProducts of Fractions and Whole Numbers4.NF.B.4 Continued

Animal ShelterMultiplying a Whole Number by a FractionTadpoles and Frogs







Unit Six – Understanding & Comparing Decimals (13 days)

In this unit of study students use their previous work with fractions to represent special fractions in a new way. Students use their understanding of equivalent fractions to begin to use decimal notation, however, it is not the intent at this grade level to connect this notation to the base-‐ten system.

The focus is on solving word problems involving simple fractions or decimals. Work with money can support this work with decimal fractions.

Unit Six Standards

4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.





base ten system decimal decimal fraction decimal point denominator equivalent hundredths increment number line numerator tenths unit fraction visual models whole number

Essential Questions

How are decimal fractions written using decimal notation? How are decimal numbers and decimal fractions related? How are decimals and fractions related? How can I combine the decimal length of objects I measure? How can I model decimals and fractions using the base-ten and place value system? What are the benefits and drawbacks of each of these models? How can I write a decimal to represent a part of a group? How does the metric system of measurement show decimals? What are the characteristics of a decimal fraction? What is a decimal fraction and how can it be represented? What models can be used to represent decimals? What patterns occur on a number line made up of decimal fractions? What role does the decimal point play in our base-ten system? When can tenths and hundredths be used interchangeably? When is it appropriate to use decimal fractions? When you compare two decimals, how can you determine which one has the greater value? Why is the number 10 important in our number system?




NF.5, 6 & 7 - Students treat decimals as whole numbers when making comparison of two decimals. They think the longer the number, the greater the value. For example, they think that .03 is greater than 0.3. Furthermore, students do not understand how the places in decimal notation have the same correspondence (places to the left are 10 times greater than the places to their immediate right) as the places in whole numbers.

Grade 4 Unit Six – Understanding & Comparing Decimals (13 days)

Connections/Notes Resources4.NF.C.5Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

Students can use base ten blocks, graph paper, and other place value models to explore the relationship between fractions with denominators of 10 and denominators of 100.

Students may represent 3/10 with 3 longs and may also write the fraction as 30/100 with the whole in this case being the flat (the flat represents one hundred units with each unit equal to one hundredth). Students begin to make connections to the place value chart as shown in 4.NF.6.

This work in fourth grade lays the foundation for performing operations with decimal numbers in fifth grade.

Students’ work with decimals (4.NF.5–7) depends to some extent on concepts of fraction equivalence and elements of fraction arithmetic. Students express fractions with a denominator of 10 as an equivalent fraction with a denominator of 100;

Teaching Student Centered Mathematicspg. 182 Base-Ten Fraction Models, figure 7.1

Lessons:What's the (Decimal) Point?Fraction Decimal Equivalence on Place Value Chart

Activities and Tasks:Sums of OneEquivalent Fractions with Denominators of 100Adding Tenths and HundredthsExpanded Fractions and DecimalsHow Many Tenths and HundredthsPARCC Sample ItemIntroduction of Decimals with Base Ten






Example:Express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Fractions and Decimal Number LineDenominators of Tenths and HundredthsShow What You Know About Decimals

Videos:Use a Number Line to Show How Fractions with Denominators of 10 and 100 Are Equivalent

Templates and Visuals:Decimal Fraction Cards

4.NF.C.6Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Students make connections between fractions with denominators of 10 and 100 and the place value chart. By reading fraction names, students say 32/100 as thirty-two hundredths and rewrite this as 0.32 or represent it on a place value model as shown below.

Students use the representations explored in 4.NF.5 to understand 32/100 can be expanded to 3/10 and

Teaching Student Centered Mathematicspg. 183 Multiple Names & Formatspg. 186 Activity7.2 Base Ten Fractions to Decimalspg. 187 Activity 7.3 Calculator Decimal Counting, figure 7.7

Lessons:Clued Into Decimals AIMSDecimal Detectives AIMSExpress Money Amounts as Decimal NumbersModel Equivalence of Tenths and Hundredths

Activities and Tasks:Decimal Fraction DominoesEquivalence Dominoes


Hundreds Tens Ones Tenths Hundredths

3 2

http://learnzillion.com/lessons/2841-use-a-number-line-to-show-how-fractions-with-denominators-10-and-100-are-equivalent-

http://learnzillion.com/lessons/2841-use-a-number-line-to-show-how-fractions-with-denominators-10-and-100-are-equivalent-



Connections/Notes Resources2/100.

Students represent values such as 0.32 or 32/100 on a number line. 32/100 is more than 30/100 (or 3/10) and less than 40/100 (or 4/10). It is closer to 30/100 so it would be placed on the number line near that value.

Understand decimal notation for fractions, and compare decimal fractions. Extending fraction equivalence to the general case is necessary to extend arithmetic from whole numbers to fractions and decimals.

Decimal Scavenger HuntDecimals in MoneyRepresenting Decimals with Base 10 BlocksDecimal MatchDecimal Match Set 2Decimal Model Matching CardsFlag Fractions

Videos:Convert Decimals to Fractions to the Tenths

Online:Decimal SquaresTemplates and Visuals:Decimals VisualDecimal Squares Set

4.NF.C.7Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Students build area and other models to compare decimals. Through these experiences and their work with fraction models, they build the understanding that comparisons between decimals or fractions are only valid when the whole is the same for both cases.

Each of the models below shows 3/10 but the whole on the right is much bigger than the whole on the left. They are both 3/10 but the model on the right is a much larger quantity than the model on the left.

When the wholes are the same, the decimals or fractions can be compared.

Teaching Student Centered Mathematicspg. 191 Activity 7.9 Line 'Em Up, Figure 7.11pg. 202-203 Expanded Lesson Friendly Fractions to Decimals

Lessons:Compare DecimalsUse Place Value Chart and Metric Measurement to Compare DecimalsDueling Decimals AIMS

Activities and Tasks:Compare & Order Decimal PPTOrdering DecimalsComparing Decimals


http://learnzillion.com/lessons/1424-convert-decimals-to-fractions-to-the-tenths-place-using-number-lines



Connections/Notes ResourcesDraw a model to show that 0.3 < 0.5. (Students would sketch two models of approximately the same size to show the area that represents three-tenths is smaller than the area that represents five-tenths.

Decimal SortTrash Can BasketballDecimal Path GameExpanding Decimals with MoneyDismissal DutyUsing Place ValueDecimal ActivitiesCreate Your Own Decimal Number Line

Online:Decimal Squares

Templates and Visuals:Decimal RulerDecimal Cards for Comparing and Ordering

4.MD.A.2Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.Examples:

4.MD.A.2 was addressed in unit 3. It is important to note that students are not expected to do computations with quantities in decimal notation. Students can use visual fraction models to solve problems involving simple fractions or decimals.

Example:

.3 + .6 = 310 + ❑❑

Lessons:Solve Word Problems with Measurements in Decimal FormSolve Word Problems Involving Money

Activities and Tasks:Margie Buys ApplesMoney Word ProblemsDecimal Place Value Mat



Unit Seven –Measurement Conversions & Problem Solving (12 days)

In this unit students build a conceptual understanding of the relative sizes of units of measure within a single system of measurement. Measurement conversions are used to reinforce multiplication as a comparison. In this unit students combine competencies from different domains to solve

measurement problems using the four operations. Measurement, in this unit, provides a context for problem solving. A ll o f th e p r ob l e m type s in the Common Core State Standards for Mathematics Situations Tables, on pages 52 and 53, must be addressed in this unit using larger numbers than those in the table.

Unit Seven Standards

4.OA.A.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 ´ 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.NBT.A.1 Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.






capacity centimeter(cm) conversion cup (c) customary equivalents fluid ounces foot (ft) gallon (gal) gram (g) kilogram (kg) kilometer (km) liquid volume liter (L) mass measure equivalents meter (m) metric mile (mi) milliliter (mL) ounce (oz) pint (pt) pound (lb) quart (qt) relative size ton unit volume weight yard (yd)

Essential Questions

About how heavy is a kilogram? Can different size containers have the same capacity? Does volume change when you change the measurement material? Why or why not? How are fluid ounces, cups, pints, quarts, and gallons related? How are grams and kilograms related? How are the units of linear measurement within a standard system related? How are units in the same system of measurement related? How can fluid ounces, cups, pints, quarts, and gallons be used to measure capacity? How can we estimate and measure capacity? How do we compare customary measures of fluid ounces, cups, pints, quarts, and gallons? How do we compare metric measures of milliliters and liters? How do we measure volume? How do we use weight measurement? How heavy does one pound feel? What around us weighs about a gram? What around us weights about a kilogram? What connection can you make between the volumes of geometric solids? What do you do if a unit is too heavy to measure an item? What happens to a measurement when we change units? What is a unit?



What is the difference between a gram and a kilogram? What is weight? What material is the best to use when measuring capacity? What material is the best to use when measuring volume? What should you do if a unit is too heavy to measure an item? What units are appropriate to measure weight? When do we use conversion of units? When should we measure with grams? Kilograms? Why are standard units important? Why are units important in measurement? Why do we measure weight? Why do we need to be able to convert between capacity units of measurement? Why is it important to be able to measure weight?


4.MD.1 & 2 - Student believe that larger units will give larger measures. Students should be given multiple opportunities to measure the same object with different measuring units. For example, have the students measure the length of a room with one-inch tiles, with one-foot rulers, and with yard sticks. Students should notice that it takes fewer yard sticks to measure the room than the number of rulers of tiles needed.

4.MD.4 - Students use whole-number names when counting fractional parts on a number line. The fraction name should be used instead. For example, if two-fourths is represented on the line plot three times, then there would be six-fourths.

Specific strategies may include: Create number lines with the same denominator without using the equivalent form of a fraction. For example, on a number line using eighths, use 48 instead of 12. This will help students later when they are adding or subtracting fractions with unlike denominators. When representations have unlike denominators, students ignore the denominators and add the numerators only. Have students create stories to solve addition or subtraction problems with fractions to use with student created fraction bars/strips.

4.MD.5 - Students are confused as to which number to use when determining the measure of an angle using a protractor because most protractors have a double set of numbers. Students should decide first if the angle appears to be an angle that is less than the measure of a right angle (90°) or greater than the measure of a right angle (90°). If the angle appears to be less than 90°, it is an acute angle and its measure ranges from 0° to 89°. If the angle appears to be an angle that is greater than 90°, it is an obtuse angle and its measures range from 91° to 179°. Ask questions about the appearance of the angle to help students in deciding which number to use.



Grade 4 Unit Seven – Measurement Conversions & Problem Solving (12 days)

Connections/Notes Resources4.OA.A.1.Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 ´ 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

This standard was addressed in unit 3, in which the focus was on basic facts. In this unit, measurement will be the focus of the word problems.

Lessons:Multiplicative Comparison Using Measurement

Activities and Tasks:Multiplicative Comparison ProblemsMultiplicative Comparison Problems 2

4.NBT.A.1Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

This standard was addressed in unit 3, in which the focus was on addition and subtraction. In this unit, metric measurement provides an opportunity to deepen the students’ understanding of place value in relation to multiples of 10.

Lessons:Relate Metric Units to Place Value Units

Activities and Tasks:Metric Relationships





4.MD.A.1Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

The units of measure that have not been addressed in prior years are pounds, ounces, kilometers, milliliters, and seconds. Students’ prior experiences were limited to measuring length, mass, liquid volume, and elapsed time. Students did not convert measurements. Students need ample opportunities to become familiar with these new units of measure.

4.MD.A.1 Continued

Students may use a two-column chart to convert from larger to smaller units and record equivalent measurements. They make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches because there are 3 groups of 12.

Example:

kg g ft in lb oz

1 1000 1 12 1 16

2 2000 2 24 2 32

3 3000 3 36 3 48

Teaching Student Centered Mathematicspg. 275 About One Unit Activity 9.13pg. 276 Activities 9.14, 9.15pg. 277 Activity 9.16pg. 280 Activities 9.18 & 9.19

4.MD.A.1 Continued

Lessons:Counting Crocodiles Math SolutionsCreate Conversion Tables for Measurement and Use Tables to Solve Problems

Activities and Tasks:Equivalent CapacitiesCapacity CreatureTime EquivalentsMeasurement Conversion ProblemsMaking a KilogramEstimating WeightMeasurement ConcentrationRelative Sizes of Measurement UnitsEquivalent Measure TablesCapacity Equivalents FlipbookMetric RelationshipsFruit Roll Up MeasurementCustomary Measurement Foldable





Videos:Compare and Convert Customary Units of Length

Online:Measurement Games

Templates and Visuals:Equivalent GraphicMeasurement Signs


http://learnzillion.com/lessons/2316-compare-and-convert-customary-units-of-length


4.OA.A.3Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

4.OA.A.3 is repeated here to include all four operations and will be finalized in Unit 14. Repeating these standards throughout the year provides students multiple opportunities to develop these skills—which are major areas of focus for this grade level.

Lessons:Ready to take the Plunge (omit % problems or have students solve with a calculator)Multi-Step Word Problems Mixed Number Measurements to Single UnitsSolve Multi-Step Measurement Word ProblemsUse Addition and Subtraction to Solve Multi-Step Word Problems Involving Length, Mass, and Capacity

Activities and Tasks:Multi-Step Word Problems with Measurement

4.MD.A.2Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Examples:

Division/fractions: Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends so each friend gets the same amount. How much ribbon will each friend get?Students may record their solutions using fractions or inches. (The answer would be 2/3 of a foot or 8 inches. Students are able to express the answer in inches because they understand that 1/3 of a foot is 4 inches and 2/3 of a foot is 2 groups of 1/3.)

Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. What was the total number of minutes Mason ran?

Lessons:Found Pounds IlluminationsUsing a Timeline to Determine Elapsed Time IlluminationsIt’s the Last Straw AIMSFuel Filling Figures AIMSMix-Ups & Mysteries AIMSWord Problems with WeightCreate Conversion Tables for Time and Use Tables to Solve ProblemsSolve Problems Using Mixed Units of Time






4.MD.A.2 Continued

Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she gave the clerk a $5.00 bill, how much change will she get back?

Multiplication: Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters, Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys have?

Number line diagrams that feature a measurement scale can represent measurement quantities. Examples include: ruler, diagram marking off distance along a road with cities at various points, a timetable showing hours throughout the day, or a volume measure on the side of a container.

At 7 a.m., Candace wakes up to go to school. It takes her 8 minutes to shower, 9 minutes to get dressed, and 17 minutes to eat breakfast. How many minutes does she have until the bus comes at 8 a.m.? Use the number line to help solve the problem.

Some parts of this standard could be met earlier in the year (such as using whole-number multiplication to express measurements given in a larger unit in terms of a smaller unit —see also 4.MD.1), while others might be met only by the end of the year (such as word problems involving addition and subtraction of fractions or multiplication of a fraction by a whole number—see also 4.NF.3d and 4.NF.4c.

4.MD.A.2 Continued

Lessons Continued:Addition and Subtraction Word Problems Involving Metric LengthWord Problems Involving Metric MassWord Problems Involving Metric Capacity

Activities and Tasks:Elapsed Time PPT/TPTMeasurement Word ProblemsElapsed Time Practice Sheets(3)Elapsed Time Warm-UpsAnd the Winner Is…As the Clock TicksTournament TimeMetric System Problems

Videos:Convert Measurements to Solve Distance ProblemsRepresent Fractional Distance Measurement Quantities Using Diagrams

Online:Orange Drink NRICH Math

Templates and Visuals:Elapsed Time Ruler 1Elapsed Time Ruler 224 Hour Number Line


http://learnzillion.com/lessons/2847-represent-fractional-distance-measurement-quantities-using-diagrams

http://learnzillion.com/lessons/2847-represent-fractional-distance-measurement-quantities-using-diagrams

http://learnzillion.com/lessons/2542-convert-measurements-to-solve-distance-problems

http://learnzillion.com/lessons/2542-convert-measurements-to-solve-distance-problems


Unit Eight – Geometry (16 days)

This unit is an introduction to angles and angle measurement. Students start this unit drawing and naming points, lines, segments, rays and angles since it is foundational to the other standards in this unit. Students use their understanding of equal partitioning and unit measurement to understand angle and turn measure. Students also develop their spatial reasoning skills by using a wide variety of attributes to talk about 2-dimensional shapes. Students analyze geometric figures based on angle measurement, parallel and perpendicular lines, and symmetry.

Unit Eight Standards

4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of a specified measure.

4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

4.G.A.2 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. Recognize right triangles as a category, and identify right triangles.

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.




acute angle angle arc circle complimentary angledegree equiangular triangle equilateral triangle intersect isosceles triangle line line segment line of symmetry measure obtuse angleone-degree angle parallel lines parallelogram perpendicular lines plane figure polygon protractor quadrilateral ray rectangle reflex angle rhombus right angle scalene triangle side square straight angle supplementary angle symmetry triangletrapezoid vertex (of a 2-D figure)

Essential Questions

What is an angle?How are a circle and an angle related?Why do we need a standard unit with which to measure angles?How are the angles of a triangle related? How can angles be combined to create other angles?How can we measure angles using wedges of a circle? How can we use angle measures to draw reflex angles? How can we use the relationship of angle measures of a triangle to solve problems?How do we measure an angle using a protractor? How does a circle help with measurement? How does a turn relate to an angleHow is a circle like a ruler?What are benchmark angles and how can they be useful in estimating angle measures?What do we actually measure when we measure an angle? What do we know about the measurement of angles in a triangle? What does half rotation and full rotation mean?How are geometric objects different from one another? How are quadrilaterals alike and different? How are symmetrical figures created? How are symmetrical figures used in artwork? How are triangles alike and different? How can angle and side measures help us to create and classify triangles?



How can shapes be classified by their angles and lines? How can the types of sides be used to classify quadrilaterals? How can triangles be classified by the measure of their angles? How can we sort two-dimensional figures by their angles? How can you create different types of quadrilaterals? How can you create different types of triangles? How can you determine the lines of symmetry in a figure? How can you use only a right angle to classify all angles? How do you determine lines of symmetry? What do they tell us? How is symmetry used in areas such as architecture and art? In what areas is symmetry important? What are the geometric objects that make up figures? What are the mathematical conventions and symbols for the geometric objects that make up certain figures? What are the properties of quadrilaterals? What are the properties of triangles? What are triangles?What is a quadrilateral? What is symmetry? What makes an angle a right angle? What properties do geometric objects have in common? Where is geometry found in your everyday world? Which letters of the alphabet are symmetrical?



Grade 4 Unit Eight – Geometry (16 days)

Connections/Notes Resources4.MD.C.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same.

Teaching Student Centered Mathematicspg. 272 A Unit Angle Activity 9.12, Figure 9.13

Lessons:Use a Circular Protractor to Understand a One- Degree AngleCircles and Angles (Unit)

Activities and Tasks:Angles PPTAngles on the GeoboardAngles as Parts of a CircleAngle Explorer ToolAngle WebStudent Angle ExplorerAngle Flipbook

Templates and Visuals:7 x 7 Geoboard Paper

Online:Angle Explorer


http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html



Connections/Notes Resources4.MD.C.6Measure angles in whole-number degrees using a protractor. Sketch angles of a specified measure.

Before students begin measuring angles with protractors, they need to have some experiences with benchmark angles. They transfer their understanding that a 360º rotation about a point makes a complete circle to recognize and sketch angles that measure approximately 90º and 180º. They extend this understanding and recognize and sketch angles that measure approximately 45º and 30º. They use appropriate terminology (acute, right, and obtuse) to describe angles and rays (perpendicular).

What is the measure of angle m?

Ask the student to estimate the measure of theangle. Then, measure the angle with a protractorwith paying close attention to the double labeling

Teaching Student Centered Mathematicspgs. 272-274

Lessons:Flagging Down Angles AIMSFlight Paths AIMSUsing ProtractorsCircles and Angles (Unit)

Activities and Tasks:Angle Flip CardsUsing a ProtractorAngles in TrianglesAngles in QuadrilateralsPredicting and Measuring AnglesAnglesAngle Barrier GameAngles PPTDetermining 90° AnglesMeasuring AnglesMeasuring Angles 2Measuring Angles Using a ProtractorI Have…Who Has…AnglesAngles in NamesTypes of AnglesTypes of Angles 2Comparing AnglesAngle Explorer ToolStudent Angle ExplorerProtractor Golf

Videos:Read a Protractor




Connections/Notes Resourcesof the protractor. Angle & Protractor Video

Angle & Protractor ActivitiesTypes of AnglesOnline:Angle Explorer

4.G.A.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen daily. Students do not easily identify lines and rays because they are more abstract.

Students select and use a protractor to measure angles and represent the angles with drawings (MP.4, MP.5).

Students might explore line segments, lengths, perpendicularity, and parallelism on different types of grids, such as rectangular and triangular (isometric) grids.

Can you find a rectangle on a triangular grid? Can you find a non-rectangular parallelogram on a rectangular grid?

Given a segment on a rectangular grid that is not parallel to a grid line, draw a parallel segment of the

Teaching Student Centered Mathematicspg. 217 Can You Make It? Activity 8.5

Lessons:Line Segments on the Geoboard Math SolutionsParallel LinesPoints, Lines, Segments, Rays and AnglesLines, Segments, Rays UnitTypes of Lines (Unit)

Activities and Tasks:Line Flip BookTypes of Lines PPTIdentifying LinesComparing AnglesAlphabet LinesLine Segments on the GeoboardQR Code Scavenger HuntParallel and Perpendicular Pictures with QuestionsGetting Gym Equipment in LineThe Race Is On

Videos:


http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html



Connections/Notes Resourcessame length with a given endpoint. Draw Points, Lines, Segments

Draw Parallel and Perpendicular LinesLabel and Name Points, Lines, Rays and Angles Using Math Notation

Templates and Visuals:Geoboard Recording Paper

4.OA.C.5Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

In this unit, 4.OA.C.5 includes repeated and growing shap e patterns.

The concepts in this unit lend themselves to using technology applications (MP.5).

Patterns involving numbers or symbols either repeat or grow. Students need multiple opportunities creating and extending number and shape patterns.

Patterns and rules are related. A pattern is a sequence that repeats the same process over and over. A rule dictates what that process will look like.

Students investigate different patterns to find rules, identify features in the patterns, and justify the reason for those features.

After students have identified rules and features from patterns, they need to generate a numerical or shape pattern from a given rule.

Teaching Student Centered Mathematicspg. 291 Predict Down The Line - Activity 10.1pg. 293 Grid Patterns Activity & Figure 10.2pg. 294 Extend & Explain Activity 10.3 & Predict How Many 10.4p. 299 What's Next & Why Activity 10.6 & 10.7

Lessons:Looking Back and Moving Forward IlluminationsWhat's Next? IlluminationsGrowing Patterns IlluminationsShape Patterns Math Solutions

Activities and Tasks:Shape Patterns Practice SheetsSquare NumbersTriangular Numbers

Videos:





https://learnzillion.com/lessons/2416-label-and-name-points-lines-rays-and-angles-using-math-notation

https://learnzillion.com/lessons/2416-label-and-name-points-lines-rays-and-angles-using-math-notation

https://learnzillion.com/lessons/2313-draw-parallel-and-perpendicular-lines

https://learnzillion.com/lessons/2346-draw-points-lines-and-line-segments



Connections/Notes ResourcesGenerating Number/Shape Patterns That Follow a Given Rule and Identifying Pattern Features

Find the 9th Shape for a Geometric Pattern Using a Table

Online:Color Patterns NLVM

4.MD.C.7Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Examples: If the two rays are perpendicular, what is the value of m?

Joey knows that when a clock’s hands are exactly on 12 and 1,the angle formed by the clock’s hands measures 30°. What is themeasure of the angle formed when a clock’s hands are exactly on the 12 and 4?

The five sections in the diagram are the exact same size.Write an equation that will help you find the measure of the indicated angle.Find the angle measurement.

Lessons:Supplementary Angles Math is Fun Mini-LessonComplementary Angles Math is Fun Mini-LessonDecompose Angles Using Pattern Blocks

Activities and Tasks:How Many Degrees?Unknown Angle Word ProblemsFinding an Unknown AnglePattern Block AnglesAngles in a Right TriangleAdditive AnglesAdditive Angles #2Additive Angles #3Additive Angle Practice

Videos:Understand that Angle Measure is Additive by


https://learnzillion.com/lessons/3253-understand-that-angle-measure-is-additive-by-decomposing


http://learnzillion.com/lessons/793

http://learnzillion.com/lessons/793

https://www.youtube.com/watch?v=vKcXncMARu4

https://www.youtube.com/watch?v=vKcXncMARu4



Connections/Notes ResourcesDecomposingCompose and Decompose AnglesFind Unknown Angles Using Angle Properties

Online:Banana Hunt Angle GameDecomposing Angles


https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-geometry-topic/cc-4th-interpreting-angles/e/decomposing-angles

https://learnzillion.com/lessons/3254-find-unknown-angles-using-angle-properties

https://learnzillion.com/lessons/3270-compose-and-decompose-angles

https://learnzillion.com/lessons/3253-understand-that-angle-measure-is-additive-by-decomposing


4.G.A.2Classify 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. Recognize right triangles as a category, and identify right triangles.A trapezoid is a quadrilateral with at least one pair of parallel sides.

Two-dimensional figures may be classified using different characteristics such as, parallel or perpendicular lines or by angle measurement.

Parallel or Perpendicular Lines:

Students should become familiar with the concept of parallel and perpendicular lines. Two lines are parallel if they never intersect and are always equidistant. Two lines are perpendicular if they intersect in right angles (90°).

Students may use transparencies with lines to arrange two lines in different ways to determine that the 2 lines might intersect in one point or may never intersect. Further investigations may be initiated using geometry software. These types of explorations may lead to a discussion on angles.

Parallel and perpendicular lines are shown here:

Example:Identify which of these shapes have perpendicular or parallel sides and justify your selection.

A possible justification that students might give is:The square has perpendicular lines because the sidesmeet at a corner, forming right angles.

Teaching Student Centered Mathematicspg. 212 Shape Sorts Activity 8.1pg. 213 What's my Shape Activity 8.2pg. 225 Triangle Sort BLM #29

Lessons:Rectangles and ParallelogramsWhat's So Special About Triangles, Anyway?Trying Out TangramsPolygon CaptureAnalyze and Classify TrianglesClassify TrianglesQuadrilateral UnitTriangles and Quadrilaterals (Unit)

Activities and Tasks:Triangles on the GeoboardClassifying Triangles 1Classifying Triangles 2Triangle Pack for ClassifyingRight Triangles on the GeoboardIsosceles Triangles on the GeoboardConstructing QuadrilateralsAre These Right?Quadrilateral CriteriaClassifying 2-Dimensional FiguresClassifying QuadrilateralsQuadrilateral Word ProblemsQuadrilateral Mini-Lesson Power PointSpecial Quadrilateral Reference SheetMonster Munch Identifying TrianglesVideos:Know Your Quadrilaterals

Classify Various Quadrilaterals by Describing Their Properties


https://learnzillion.com/lessons/2936-classify-various-quadrilaterals-by-describing-their-properties

https://learnzillion.com/lessons/2936-classify-various-quadrilaterals-by-describing-their-properties

https://www.youtube.com/watch?v=rXZcYHVwkqI&feature=share





4.G.A.2 Continued

Angle Measurement:

This expectation is closely connected to 4.MD.5, 4.MD.6, and 4.G.1. Students’ experiences with drawing and identifying right, acute, and obtuse angles support them in classifying two-dimensional figures based on specified angle measurements. They use the benchmark angles of 90°, 180°, and 360° to approximate the measurement of angles.

Triangle Classification:

Right triangles can be a category for classification. A right triangle has one right angle. There are different types of right triangles. An isosceles right triangle has two or more congruent sides and a scalene right triangle has no congruent sides

Students will use side length to classify triangles as equilateral, equiangular, isosceles, or scalene; and can use angle size to classify them as acute, right, or obtuse. They then learn to cross-classify, for example, naming a shape as a right isosceles triangle.

4.G.A.2 Continued

Classify Two-Dimensional Figures by Examining Their Properties

Classify Triangles by Examining Their Properties

Online:Quadrilateral QuestVirtual Pinboard Create & Identify 2-Dimensional Figures

Templates and Visuals:Geoboard Recording PaperFrayer Model 2-D Shapes

*IRC has die cuts for: squares, rectangles, octagon, hexagon, pentagon, trapezoid, triangle, and rhombus. One piece of construction paper will produce 4 of each 2D figure for students to use in sorting activities. Ordering multiple figures will allow you to modify the 2D shapes. Example: Cut one trapezoid to make it a right trapezoid.

4.G.A.3Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more lines of symmetry.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

Identify line-symmetric figures and draw lines of symmetry.

Given a half of a figure and a line of symmetry, accurately draw the other half to create a symmetric figure.

Teaching Student Centered Mathematicspg. 234 Pattern Block Mirror Symmetry Activity 8.15pg. 235 Dot Grid Line Symmetry Activity 8.16

Lessons:Finding Lines of SymmetryRecognize Lines of Symmetry



https://learnzillion.com/lessons/3040-classify-triangles-by-examining-their-properties

https://learnzillion.com/lessons/2879-classify-twodimensional-figures-by-examining-their-properties

https://learnzillion.com/lessons/2879-classify-twodimensional-figures-by-examining-their-properties


4.G.A.3 ContinuedPolygons with an odd number of sides have lines of symmetry that go from a midpoint of a side through a vertex.

4.G.A.3 Continued

Activities and Tasks:Determining SymmetrySymmetry in ShapesSymmetry on the GeoboardSymmetry in Regular PolygonsSymmetrical Coin DesignsSymmetrical Coin Designs 2Lines of Symmetry for TrianglesLines of Symmetry for QuadrilateralsLines of Symmetry for CirclesPattern Block Symmetry

Videos:

Identify Line Symmetry in Regular PolygonsIdentify Line Symmetry in Irregular PolygonsIdentify Line Symmetry in a Geometric FigureUsing Imagery to Find Lines of Symmetry

Online:Symmetry GameSymmetry SortVirtual Geoboard NLVM


http://ccss4.watchknowlearn.org/Video.aspx?VideoID=16627&CategoryID=15498

https://learnzillion.com/lessons/3215-identify-line-symmetry-in-a-geometric-figure

https://learnzillion.com/lessons/3214-identify-line-symmetry-in-irregular-polygons

https://learnzillion.com/lessons/3096-identify-line-symmetry-in-regular-polygons


Unit Nine – Fluency with Problem Solving (32 days or remainder of year)

This is a culminating unit in which students focus on problem solving in order to demonstrate fluency with the standard algorithms in addition and subtraction. They demonstrate computational fluency with all problem types. All standards in this unit have been addressed in prior units. These concepts require greater emphasis due to the depth of the ideas, the time they take to master, and/or their importance to future mathematics.Students should experience rich problem solving across the standards. The problem solving should not be skill isolated. In demonstrating fluency, students explain and flexibly use properties of operations and place value to solve problems, looking for shortcuts and applying generalized strategies (MP.2, MP.8).

This unit is designed for application and review of the problem types for which your students show the least fluency. Review back to the previous units for comments, clarification, examples, and resources according to the needs of your students.

Unit Nine Standards

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.


4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.


http://www.corestandards.org/Math/Content/4/NF/B/3/d



4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Mixed Problem Solving Resources:

Lessons:

Building a Business Illuminations

Exploring with Math Trails Illuminations

Super Bowl Scores Illuminations

Activities and Tasks:

Fraction Word Problems Mixed

Karl’s Garden

Multi-Step Word Problems QR Code Task Cards

Measurement Distance, Time, Liquid Volume Word Problems

Saving Money 1 & 2






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