SFUSD Mathematics Core Curriculum Development Project › ... › 4 › 0 ›...

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SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.2: Decimal Number System, 2014−2015

SFUSD Mathematics Core Curriculum Development Project

2014−2015

Creating meaningful transformation in mathematics education

Developing learners who are independent, assertive constructors of their own understanding

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Grade 5

Unit 5.2: Decimal Number System

Number of Days

Lesson Reproducibles Number of Copies

Materials

1 Entry Task Name a Decimal HW: Name a Decimal

1 per student 1 per student

2 Lesson Series 1 Engage NY 5.1.1 Place Value Patterns (3 pages) Engage NY 5.1.1 Place Value Patterns Exit Ticket EM Student Reference Book p. 327 – Number Top-It HW: Place Value Decimals (3 pages)

1 per student 1 per student EM SRB 1 per student

EM number cards Place-value mats Counters Personal white boards and markers

1 Apprentice Task Where Does the Decimal Point Belong? (3 pages) Rounding and Number Lines


2 Lesson Series 2 EM 4th Grade 4.7 Journal pp. 93-95 (3 pages) EM 4th Grade Base Ten Exchange Board EM 4th Grade Modeling Decimals HW: EM 4th Grade 4.7 Study Link EM Masters p 399-402 (4 pages) Engage NY 5.1.B.5 Name Dec Fractions (2 pages) Engage NY 5.1.B.5 Name Dec Fractions Exit Ticket HW: EngageNY 5.1.B.5 Name Dec Fracs (2 pages)

1 per student 1 per student 1 per pair 1 per student 1 per student 1 per student 1 per student

Base Ten Blocks Place-value mats Personal white boards and markers EM number cards

1 Expert Task Gymnasts and Players (2 pages) EM Student Reference Book p. 321 HW: SF Giants

1 per student EM SRB 1 per student

2 Lesson Series 3 Engage NY 5.1.C.7 Student Pages (2 pages) Engage NY 5.1.C.7 Exit Ticket HW: Engage NY 5.1.C.7 (2 pages) Engage NY 5.1.C.8 Student Pages (2 pages) Engage NY 5.1.C.8 Exit Ticket HW: Engage NY 5.1.C.8 (2 pages)

1 per student 1 per student 1 per student 1 per student 1 per student 1 per student

Base Ten Blocks Personal white boards and markers

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1 Milestone Task Decimals – MARS Performance Assessment Decimals Constructed Response


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Unit Overview

Big Idea

• Decimal place value is an extension of whole number place value, where each place value to the left of another is ten times greater than the one to the right (e.g., 1.0 = 0.1 x 10.)

• The base-ten numeration system extends infinitely to very large and very small numbers.

Unit Objectives

• Students will understand that the value of one digit in one place is 10 times the value of the digit to its right and is 10 times less the value of the digit to the left.

• Students will apply whole number understanding to reading, writing, rounding, and comparing decimals using the place value system.

Unit Description

The unit starts with students demonstrating prior knowledge with fourth grade standards including tenths and hundredths; this first day also includes some fun extensions with videos and games. The first lesson series applies prior knowledge with the base-ten system. Students will engage in real world discussion about the density of decimals (the concept that any two numbers in base 10 have infinite numbers between them). They will then apply this understanding in paper and pencil format on number lines and on grids to help them conceptualize that any digit to the right of a place is ten times less and any digit to the left of that place is ten times more. Our apprentice task checks in on how far students have come with this concept of base ten; this task also provides a diagnostic for upcoming lessons with rounding. Our second lesson series guides students through model using base ten blocks. The lessons are designed to move from manipulatives to expanded notation that expresses numbers in each place as multiples of ten. Students also compare decimals using <, >, and = symbols to record their results of comparisons. Our expert task uses the real world examples of statistics in gymnastics and baseball. Students rank athletes from either the San Francisco Giants or the US Women’s Gymnastics team, and make posters to describe their reasoning; the recommendation is that they do this task in teams. This task also includes a set of short answer questions that assess all the standards previously taught in this unit. Our third lesson series is focused on rounding. It is designed to make use of prior skills with whole number rounding, and to bring that in to their work with decimals. Our milestone task includes both a performance assessment with open number lines as well as short answer questions that assess all of the standards taught. It is important to note that this unit is fundamental to all of the future decimal work done in fifth grade and beyond. It is essential that students have a deep understanding of decimal number system, place value, relative place value and base ten. Use your professional judgment to determine how long you need to spend on each lesson. Additional days may be required. Math talks and math games are interwoven throughout the unit and may be used at the discretion of the classroom teacher.

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CCSS-M Content Standards

Numbers and Operations in Base Ten Understand the place value system. 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 5.NBT.3 Read, write, and compare decimals to thousandths.

5.NBT.3a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). 5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.4 Use place value understanding to round decimals to any place.

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Progression of Mathematical Ideas

Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

“Students in Grade 4 work with fractions having denominators 10 and 100.4.NF.5 Because it involves partitioning into 10 equal parts and treating the parts as numbers called one tenth and one hundredth, work with these fractions can be used as preparation to extend the base-ten system to non-whole numbers.” K-5, Number and Operations in Base Ten The Common Core Standards Writing Team http://ime.math.arizona.edu/progressions/ In fourth grade, students learn to read decimals to the hundredths. Most importantly, they begin to understand that rules that govern whole numbers also apply to numbers less than one. As a practical application, fourth graders write the expanded form for such numbers as thirty-four and seven tenths: for example 34= 34.7, also described as (3 x 10) + (4 x 1) + (7 x ) and (3 x 10) + (4 x 1) + (7 x 0.1).

“Students extend their understanding of the base-ten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths.... New at grade 5 is the use of whole number exponents to denote powers of 10.” K-5, Number and Operations in Base Ten The Common Core Standards Writing Team http://ime.math.arizona.edu/progressions/ Students must be fluent with the uniformity of the base-ten system to proficiently add, subtract, multiply, and divide decimals, using the same place value understanding as they have with whole numbers. The core learning of this unit has to do with building out prior learning (whole numbers and decimals to the hundredths) to the thousandths, with a clear understanding that places to the right are ten times less than places to the left. Rounding, comparing, and notating numbers to the thousandths depends both upon conceptual understanding of base ten and fluency with reading and writing numbers.

In future units, fifth grade students will perform operations with decimals to hundredths. Sixth grade students will extend their computational fluency to include negative numbers and numbers much larger and smaller than place values described by standards at the earlier grades.

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Unit Design All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both formative and summative assessments of student learning. The tasks are designed to address four central questions: Entry Task: What do you already know? Apprentice Task: What sense are you making of what you are learning? Expert Task: How can you apply what you have learned so far to a new situation? Milestone Task: Did you learn what was expected of you from this unit?

1 day 2 days 1 day 2 days 1 day 2 days 1 day Total: 10 days

Lesson Series 1

Lesson Series 2

Lesson Series 3

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Task

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Entry Task Name a decimal

Apprentice Task A: Where does the decimal point

belong? B: Rounding and Number Lines

Expert Task Gymnasts and Baseball Players

Milestone Task Constructed Response: Decimals (MARS) Performance: Number Lines & Expanded

Notations

CCSS-M Standards

5 NBT.1, 5 NBT.2 5 NBT.1, 5 NBT.2 5 NBT.3a, 5 NBT.3b 5 NBT.1, 5 NBT.2, 5 NBT.3a, 5 NBT.3b, 5 NBT.4

Brief Description of task

Students will be asked to name a number that falls between two given benchmarks.

Students will be asked to place a decimal point into a number based on the desired place value. Students will also round decimals and locate numbers on a number line as a diagnostic for Lesson Series 2.

Students analyze different sports data using decimals to the thousandths. They round numbers, compare numbers to benchmarks, name numbers between two given benchmarks, and describe their thinking about decimals.

Students will be asked to complete MARS task on decimals. They also answer other questions based on decimal number line, expansion using decimal fractions, and rounding.

Sources Adapted from Lessons for Decimals and Percents by Burns and De Francisco SFUSD Teacher Created

Adapted from Lessons for Decimals and Percents by Burns and De Francisco SFUSD Teacher Created

SFUSD Teacher Created MARS SFUSD Teacher Created

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

5 NBT.1, 5 NBT.2

5 NBT.1, 5 NBT.2, 5 NBT.3a, 5 NBT.3b 5 NBT.1, 5 NBT.2, 5 NBT.3a, 5 NBT.3b, 5 NBT.4

Brief Description of Lessons

Students will be reviewing and exploring the concepts of decimals using various real world situations.

Students will use base-ten blocks to compare decimals. They then use this information to write decimals in expanded notation.

In this series, students apply place value understanding to rounding to the thousandths place. They also locate decimals on number lines and use number lines to round.

Sources

Lessons for Decimals and Percents by Carrie De Francisco and Marilyn Burns Engage NY Everyday Mathematics http://www.youtube.com/watch?v=cfmscdOHoaE

Everyday Mathematics Lessons for Decimals and Percents by Carrie De Francisco & Marilyn Burns Engage NY

Engage NY http://www.youtube.com/watch?v=ZbBmEKfL9K0

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Entry Task Name a Decimal

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will identify decimal numbers between two numbers, as well

as name decimals greater than and less than benchmarks. ● Students will identify decimals up to the thousandths place. ● Students will describe their thinking.

CCSS-M Standards Addressed: 5 NBT.1, 5 NBT.2 Potential Misconceptions:

● Students may not yet know that there are infinite decimal numbers between any two numbers.

● Students may have some basic confusion with the base-ten system. ● Before work to the thousandths, all decimal experience can be used

with the real world context of money. Students may have no prior exposure to thousandths.

Launch: Students will be asked to take a 15-minute pre-assessment test individually. During: Students will work on the task. Students will make sure to show their work, and explain their thinking using words or drawings. Closure/Extension: As this is a quick task, when students are finished with their pre-assessment, they will have opportunity to watch video clips that will begin to activate their prior knowledge about decimals. Use discretion about what order to use these in. The students will also have the opportunity to play a game that activates and extends prior knowledge about decimals.

1. http://www.youtube.com/watch?v=0JB3bNfLqEM warmup/review: This is a catchy song about decimals, framed as a rap. Quick pace but good visuals. Three minutes long.

2. www.youtube.com/watch?v=iLw9OBV7HYA . This is a video clip from Superman 3 in which Richard Pryor hacks a computer program to steal fractions of pennies. The video could be a good jumping off place for discussion: What is he planning to steal? What are halves of pennies? Computer technology potentially funny for kids, as the film is from 1983. The clip is 3 minutes long.

3. Number Top-It to the thousandths. 5th grade Everyday Mathematics, SRB 327.

Homework included.

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Name a Decimal

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 7. Look for and make use of structure.

Structures for Student Learning: Academic Language Support:

Vocabulary: decimal, between, greater than, less than Sentence frames: We showed our work by _____. This shows _____, because _____.

Differentiation Strategies:

● Allow extra time for students who might need it. Participation Structures:

● Diagnostic test – Individually ● (For closure and extension activities):

○ Watching Video Clips & discussion that follows: Whole group ○ Number Top-It: small groups or partners

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Lesson Series #1

Lesson Series Overview: Students will be reviewing and exploring the concepts of decimals using various real work situations. CCSS-M Standards Addressed: 5 NBT.1, 5 NBT.2 Time: 2 days

Lesson Overview – Day 1 Resources

Description of Lesson: This lesson introduces students to thousandths by asking students to predict the possible weight of a lobster that weighed between 2.56 and 2.57 pounds. Using this concept and the context of money, students learn about extending beyond decimals to the hundredths.

The Lobster Problem from Lessons for Decimals and Percents by Carrie De Francisco and Marilyn Burns, Chapter 6, pp.42−48.


Description of Lesson: This lesson introduces students to the concept of the base-ten system where in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and of what it represent in the place to its left. This lesson can be a bit challenging to teach. We suggest that you read the entire lesson through prior to teaching. We have included a video for your reference that explains how to use the place value charts for addition. Extension: Students can play Number Top-It to reinforce place-value concept. Notes: Model for students by using place-value chart and going through the procedure of actually multiplying by 10 when moving to the left and dividing by 10 when moving to the right.

Engage NY 5.5.1 Place Value Patterns • Teacher Pages • Student Pages • Exit Ticket • Homework

EM Student Reference Book p. 327 – Number Top-It (Decimals) Place-Value Chart Youtube clip http://www.youtube.com/watch?v=cfmscdOHoaE

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Apprentice Task

A: Where does the decimal point belong? B: Rounding and Number Lines



Math Objectives: ● A: Students will demonstrate understanding of place value by adding a decimal

point to a set of digits to form a number between two given numbers. ● B: Students will also answer diagnostic questions that help you understand

their prior knowledge of both rounding and number lines, which are taught in Lesson Series 2. (Note that we borrowed the A/B structure from Everyday Mathematics; all questions on the B part of this assessment test are content that has not yet been taught in fifth grade and should not figure into the score for the task.)

CCSS-M Standards Addressed: 5.NBT.1, 5.NBT.2 Potential Misconceptions TASK A:

● This task assumes that students understand the difference between “digit” and “number.” For example, the digits are “4107,” but possible answers for number include “41.07.” Preteach the vocabulary if there is confusion.

TASK B: ● Students might not be familiar with the vertical number line in part B of the

task; this will be featured in upcoming lessons. ● Similarly, students might have general confusion with rounding, or might not be

able to apply the skill of rounding in general to rounding to the thousandths place.

GENERAL MISCONCEPTIONS:

● Basic confusion with the base-ten system.

Launch: Students will be asked to complete a worksheet individually. Frame for them that some of the questions (especially in part B) might be hard for them, but students should do the best that they can. During: Students will work on the task. Have students show their work and explain their thinking using words or drawings. Closure/Extension: Students will be asked to present their work in small groups and give rationales for their answers. Use your professional discretion for the best structure for presentation. Task B on the worksheet is actually a pre-test on rounding and number lines and should not be counted as part of the apprentice task score, but might make for excellent class discussion within this extension. Homework included.

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A: Where does the decimal point belong? B: Rounding and Number Lines


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 7. Look for and make use of structure.


Vocabulary: decimal point, digit, number, between, less than, nearest, equal when rounded” Sentence frames: I know that _______ is ______ because _________. (Or if greater scaffold is needed: “I know that (number) is between (number) and (number) because______.” I chose these numbers because ______________. I know that _______.

Differentiation Strategies: Test accommodations are at your discretion; however, here are some suggested strategies:

● Provide additional time. ● Read the questions out loud. ● Provide physical manipulatives (such as base-ten blocks). ● Modify questions as necessary. Specifically, for “Where does the decimal point belong?” (Task A), the task would be easier if you prewrote the digits or

guided certain students through prewriting the digits first. Then, the student would need only to place the decimal physically. Participation Structures:

● Task assessment: Individually ● Presentation: Small Group

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Lesson Series #2

Lesson Series Overview: Students will use base-ten blocks to compare decimals. They then use this information to write decimals in expanded notation. CCSS-M Standards Addressed: 5 NBT.1, 5 NBT.2, 5 NBT.3a, 5 NBT.3b Time: 2 days


Description of Lesson: Two Options: Both choices use base-ten blocks to model numbers in the decimal range. Choose the one that you think will work best for your class. First Option: Everyday Mathematics Fourth Grade Volume 1 Lesson 4.7, Decimal Place Value

● Students use number lines to visualize the relationship between successive places in decimals.

● They review the place-value chart for whole numbers and extend it to decimals. ● They practice identifying places in decimals and the values of the digits in those

places. Second Option: Representing Decimals with Base Ten Blocks from Lessons for Decimals and Percents by Carrie De Francisco & Marilyn Burns, Chapter 1, pp. 1–8.

● In this lesson, the students use base-ten blocks to represent tenths, hundredths, and thousandths, assigning the value of one whole to the flat.

● The focus in this lesson is on having students build numbers with the blocks and represent them using common fractions with which they are familiar.

Notes: Suggested game to play if time allows: EM 4th Grade Base-10 Exchange (Thousandths) Students who need extra practice may also benefit from creating a place-value flipbook.

NOTE: For Day 1, there are two suggested lessons that provide access to this content. First Option: EM 4th Grade: 4.7

• Teacher Edition Volume 1 pp. 271-276 • Student Math Journal Volume 1 pp. 93-95 • Base-10 Exchange (Thousandths) Math Master p.459 • HW: Study Link 4.7

Second Option: Representing Decimals with Base Ten Blocks from Lessons for Decimals and Percents by Carrie De Francisco & Marilyn Burns, Chapter 1, pp. 1–8. Extra Support: EM 4th Grade Compact Place-Value Flip Book Math Master, pp. 399–402


Description of Lesson: Engage New York Grade 5 Lesson 5: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning.

Engage NY 5th Grade Module 1: Lesson 5 (1.B.2-1.B.15)

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● Students will work on naming decimals in expanded form. ● Students will work on writing decimals in word form and in unit form. ● Students will review multiplying decimals by 10,100, and 1000. ● Students will review multiplying and dividing by exponents. ● Students will review multiplying metric units.

Students use base 10 blocks and personal white boards during this lesson. Notes: This lesson may take you more than one day. Please be sure to read this entire lesson through prior to teaching. Make adjustments as you see fit. Suggested game to play if time allows: Decimal Number Top-It (see Lesson Series 1) Homework: In preparation for the Expert Task, students should bring in any statistics they know or are able to find about baseball and gymnastics.

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Expert Task

Gymnasts and Players



Math Objectives: ● Students will round decimals and notice when numbers with different

values are now equal after rounding to a specific place. ● Students will create numbers that fall between two numbers written to

the thousandths place. ● Students will say whether each value in a data set is closer to three

given benchmarks. ● Students will explain in words what they understand about

thousandths. CCSS-M Standards Addressed: 5.NBT.3 Potential Misconceptions:

● Students might believe they need to have more background knowledge about either baseball or gymnastics.

● Students might struggle with reading the charts; see note under differentiation.

● Students might still have confusion with the density of rational numbers, where every two numbers have an infinite set of numbers between them. This would show up if students are still unable to name a number between two given benchmarks.

Launch: ● Students should be able to read and interpret the data set without real

world experience of baseball or gymnastics. However, as this problem is grounded in the real world context of sports, students benefit from background knowledge about baseball or gymnastics.

● NOTE from Lesson Series 2: It might be a great homework task for the night before to bring artifacts to share. It is likely that some students in the class will have prior knowledge of at least the athletes themselves, if not the mathematical content of the scores. If students bring their own artifacts, this might be a great way to kick off the task.

● Within the context of the task itself, encourage students to persevere with the task they are about to do, especially regarding reading and understanding the data.

● Establish or remind students of any necessary routines for working in partners or groups.

During:

● Choose how to structure paired or group experiences. ● Students work together to make sense of the task and to complete

each of the five questions. Closure/Extension:

● If students have brought baseball or gymnastics artifacts, they could share those resources with the group in a presentation format.

● Students can present their thinking to the group. ● End with a game if time permits. High Number Toss Decimal Version.

Student Reference Book, p. 321. ● Homework included. ● The Additional Questions can be printed for students who need extra

practice with anything in the previous lesson series.

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Gymnasts and Players


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure.


Vocabulary ● Sports content: Note that the math task can be completed without prior content knowledge of the sports, but that any background knowledge might

make this a more accessible task. See homework at the end of Lesson Series 2 and launching the task at the beginning of the expert task itself. ○ Baseball: Giants, player, AVG/batting average, OBP/on base percentage, team, recruit ○ Gymnastics: USA Gymnastics, Olympics, vault, parallel bars, balance beam, mat

● Math content: ○ round, closer to ○ conditional language throughout the task, such as “If you rounded... to the nearest hundredth, who would have...?” and “What might her score

be?” ○ “figured to the thousandths place”

Sentence frames For group work:

I agree with _____ because _____. I disagree with _____ because _____. I heard _____ say _____. I would like to add _____.

For general math content: We showed our work by _____. This shows _____. I know that _______ is ______ because _________. (Or if greater scaffold is needed: “I know that (number) is between (number) and (number) because______.” I chose these numbers because ______________. I know that _______.

Differentiation Strategies:

● Test accommodations are at your discretion; however, here are some suggested strategies: ○ Provide additional time. ○ Read the questions out loud. ○ Provide physical manipulatives (such as base-ten blocks).

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○ Modify questions as necessary. Specifically, if the charts are difficult to understand, support individual students. Reading and interpreting data is a significant to fifth grade math, but should not get in the way of students being able to show what they know about the specific content standards. Note if future small group work is needed in this case.

Participation Structures:

● This is recommended as a partner or small group task. ● Any sharing of artifacts can be done whole group.

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Lesson Series #3

Lesson Series Overview: In this series, students apply place value understanding to rounding to the thousandths place. They also locate decimals on number lines and use number lines to round. CCSS-M Standards Addressed: 5 NBT.1, 5 NBT.2, 5 NBT.3a, 5 NBT.3b, 5 NBT.4 Time: 2 days


Description of Lesson: This lesson introduces students to the concept of using place-value to round to any place. Students use a vertical number line model (drawn on personal white boards) to review rounding whole numbers. They then extend this model to round decimals to any place. The number line helps student visual relative magnitude, focusing on more or less than halfway between multiples of decimal units. Notes: It is suggested that you make one or both of the following anchor charts to support student work.

Engage NY Grade 5.1.C.7 Round a Decimal • Teacher Pages • Student Pages • Exit Ticket • HW

Youtube video for your reference that helps explain rounding on the vertical number line: http://www.youtube.com/watch?v=ZbBmEKfL9K0

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Anchor Chart 1 Rounding Numbers When you round a number, you find its approximate value. Let’s look at rounding decimals. Step 1: Underline the digit in the place to which you want to round. ex: 3.416 ; tenths Step 2: Look at the digit to the right and ask yourself: Five or higher add 1 more, Four or lower just ignore ex: 3.416 just ignore ex: 4.76 add one more Step 3: Drop The digit to the right of the underlined digit: ex: 3.416 3.4 ex: 4.76 4.8

Anchor Chart 2


Description of Lesson: This lesson has students round a given decimal to any place using place value understanding and the vertical number line.

● Students will review renaming the units and rounding to different place values. ● Students will work to develop a deeper understanding of the vertical number line

concept. ● Students will round and decompose decimals on the vertical number lines.

Notes: Game to be played if time allows: If time allows, look ahead to the Expert Task and assign suggested homework below.

Engage New York Grade 5.1 Lesson 8 • Teacher Pages • Student Pages • Exit Ticket • HW

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Milestone Task

Performance Assessment: Decimals (MARS 2009); Constructed Responses: Decimal Number Line, Extended Form, and Rounding



Math Objectives: To assess students’ progress on mathematical content through the end of the Decimal Unit.

● Students will round decimals and notice when numbers with different values are now equal after rounding to a specific place.

● Students will create numbers that fall between two numbers written to the thousandths place.

● Students will say whether each value in a data set is closer to three given benchmarks.

● Students will explain in words what they understand. CCSS-M Standards Addressed: As our milestone tasks, these two assessments together assess all four standards with the strand. 5.NBT.1, 5.NBT.2, 5.NBT.3, 5.NBT.4 Potential Misconceptions:

● Students may be unclear about any suggested additional directions regarding showing work and explaining how they solved problems.

Launch: Set expectations for how students will complete this Milestone Task which is part of the CLA 1. Make sure to go over the directions and expectations of each part of the task. Students will work individually on their Milestone Task until the work is complete. During: Students will work on both the constructed response questions and the performance assessment. Make sure students pay attention to the questions that are assigned for them to complete, show their work, and explain their thinking using words or drawings. Students who have completed the task can choose from menu of games that have been used during the unit. Closure/Extension: After completion and scoring of the Milestone Task, each student will review the task and pay close attention to why each problem was scored in a particular way. The whole class will review the test and make note of/discuss the most challenging problems.

● Note: Take note of challenge areas for use in planning any necessary re-teaching.

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Performance Assessment: Decimals (MARS 2009); Constructed Responses: Decimal Number Line, Extended Form, and Rounding


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 7. Look for and make use of structure


Vocabulary: decimals, tenths, hundredths, thousandths, nearest, bigger, smaller, biggest, smallest, order Sentence frames: I showed my work by _____. I figured this out by ____. This shows _____.

Differentiation Strategies: Test accommodations is at your discretion; however, here are some suggested strategies:

• Provide additional time. • Read the questions out loud. • Provide physical manipulatives (such as base-ten blocks). • Modify questions as necessary.

Participation Structures (group, partners, individual, other):

● Individual task (test)

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