Chapter 1 – Overview and Support Place Value, Multiplication, and Expressions

Standards: Grade-Five Chapter of the Mathematics Framework

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.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and

two-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.

Write and interpret numerical expressions.

5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Suggested Routines: Daily, 10 – 15 minutes

This time may begin or end your math time/period or it may be a separate time within your school day.

● Number Talks by Sherry Parrish (several books available at site) ○ “Number Talks” : Landmark and Friendly Numbers pgs. 190-192; Doubles and Near

Doubles pgs. 194-196; Breaking Each Number into Place Value pgs.198-200; Adding Up in Chunks pgs. 202-204

○ pg 232 - 236 (multiplication strategies - array model) ● “Which One Doesn’t Belong” Talk Routine ● Number Sense building with benchmark numbers ● Personal Math Trainer: Think Central

PD for Instructional Routines ● Core Strategies (EGUSD Math Gen Blog)

○ Choose 3 Ways ○ Number Talks / Talk Routines

● Teacher Education by Design ○ Quick Images, Counting Collections, Choral Countings, Number Strings, Three Act Tasks

What’s My Place? What’s My Value? (5.NBT.1, 2 ,5, 6)

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● Work on numbers from 100,000 to 100,000,000. ● Introduce the number of the day in different ways (different starting points). For example, display a

number on the doc camera built using base ten blocks. Have students complete the WMP?WMV? prompts starting from the built number. Other ways to start would be from word form, expanded form, etc.

● Build and sketch today’s number. ● Write the number in standard form and word form. ● Identify the place value of each place. ● Write in expanded form. ● Round to the nearest _______. ● Compare ________ to _________. ● Draw a number line. Plot two friendly numbers and today’s number on the number line. ● Add today’s number with ________. Subtract today’s number from _________. ● For rounding: Number Line, 5,000 < 5 ,725 < 6,000, Discuss whether the number is: halfway between,

less than or more than halfway between ● Create a number with the same numeral in two locations. Have a conversation about the difference

in sizes between these numerals based on their location within the number (4.NBT.1). For example, today’s #: 856, 618

● Have conversations about the size of each piece. ● Sample #s: 43,158; 71,435; 101,298; 56,804; 999,999; 375,081; 943,268; 427,593; 151,894, two

hundred seventeen thousand; eight hundred four thousand, sixty-two; sixty-five thousand fifty-eight, etc.

Counting Circles Have students stand and form a circle facing each other or stand up and count around the room. Select a counting sequence to be practiced with 8-10 numbers in the sequence. Have the students start counting around the circle one by one until the last number in the sequence is reached. When the last number is reached all students clap and that student sits down. Continue for several rounds. Number sequences should reflect the grade level standards. Sample sequences: 157,389 – 157,395; 48,906 – 48,914; 304,212 – 304,223; 718,998 – 719,007; 999,992 – 1,000,005 After students have learned how to play this game with the whole class, they can self-monitor the game within their small groups. Choral Counting Determine what you will have the class count by, as well as the number where you will start (e.g. count by 200s starting at 5,000). As students count chorally, record the numbers in rows and columns in such a way that students can clearly notice patterns in the structure. Ask questions and annotate the written count to highlight student thinking. Ask questions such as:

● What do you notice? ● Perhaps a student notices each column

increases by 1000 - Ask why is that? ● Can you predict what this number (see red box)

will be? How do you know? ● If we keep counting, will we say 9,300?

Why/Why not?

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Place Value Games ● Number Scramble

○ Materials: Index Cards Labeled 0 – 9 ■ Prompt ideas below:

● “Use your number cards to make 56,430.” ● “Create the smallest number you can with 4 digits.” Pair Share ● “Create a number with 4 digits, with a 9 in the tens place.” ● “Create any number that you would like. On your whiteboard, write it in

standard form, expanded form, and word form.” ● “Create a number with 8 in the thousands place & a 3 in the ones place.” ● “Add ten to the number we just created. Show me the new number.” ● “Create a number with 5 digits, with a 7 in the tens place and a 3 in the ten

thousands place.” ● “Create any number that you would like. On your whiteboard, write it in

standard form, expanded form, and word form.” ● Corn Shucks (Comparing multi-digit numbers)

○ Materials: recording sheet, digit cards (or 0-9 die), Players: 2-4 1. The first player selects 6 digit cards and makes the largest possible six-digit number

with those digits. Example: cards show these digits: 6, 4, 3, 3, 2, 1, this order makes the largest possible number for those digits.

2. The player writes that number on line 1. 3. The second player selects 6 digit cards and makes the smallest possible number for

those digits. 4. The player writes that number on line 10. 5. The next player selects 6 digit cards and must make a number that falls between the

other two. They can place that number on any line. 6. The next player selects 6 digit cards and makes a number using those digits that could

be placed on an empty line between any two existing numbers. 7. Game continues until a number is correctly placed on each line. (All 10 lines contain a

number and they are in the correct order), OR players cannot place a number correctly on any of the empty lines.

Take Your Medicine

● Students take turns shaking weekly pill dispenser to create numbers

○ Can be used to practice writing numbers (all forms) ○ Can be used to practice reading the number ○ Can be used to compare numbers when two or more students each have a dispenser ○ Can be used to order numbers

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Numbers in a Cup

● Students take turns shaking dice in the cups to create numbers ○ Can be used to practice writing numbers (all forms) ○ Can be used to practice reading the number ○ Can be used to compare numbers

Place Value Accordion

● Using strips of paper write a number in expanded form ● Fold the paper to show the number in standard form

Manipulatives: Base 10 blocks, Place Value Chart (TR14), Graph Paper (TR34)

Vocabulary:

base Distributive Property evaluate exponent inverse operations

numerical expression order of operation period

Color Coding: Green (G )- The lesson accurately reflects the Framework standard(s). Yellow (Y) - This lesson includes notes to refer to while planning the lesson. Red (R) - This lesson does not accurately reflect the Framework standard(s). Skip the lesson.

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Essential Question: How can you use place value, multiplication, and expressions to represent and solve problems?

Lesson-by-Lesson Overview: Lesson #, Standard

Title Materials Vocab Notes

Chapter 1 Show What You Know

1.1 Y

5.NBT.1

Investigate Place Value and Patterns

Base ten blocks, MathBoard, Place Value Chart (TR 14)

Note “Common Errors” Go Math TE pg. 6 Send home the School-Home Letter located in the Standards Practice Book Pages P1-2

Assessing Prior Knowledge pages 3-4 may be used at your discretion to assess prior knowledge Read “Grade-Five Chapter of the Mathematics Framework” pg. 10 Place Value Template Blackline Master found in Teacher Resources Blackline Masters, page TR 14 Use array to model multiplication

1.2 Y

5.NBT.1

Place Value of Whole Numbers

MathBoard, Place Value Chart (TR 14)

period

Note “Common Errors” Go Math TE pg. 10 Read “Grade-Five Chapter of the Mathematics Framework” pg. 10 “Example 5.OA.3”

Be sure to include both versions of word form and both versions of expanded form:

● Two hundred sixty-two thousand,

four hundred AND

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● 2 hundred thousands, 6 ten-thousands, 2 thousands, 4 hundreds

● 200,000 + 60,000 + 2,000 + 400 AND

● (2 x100,000) + (6 x 10,000) + (2 x 1,000) + ( 4 x 100)

Use Place Value Template from 1.1 Go Math Animated Math Models - Skill 1

1.3 Y

5.OA.1

Algebra – Properties

Math Board (white

boards)

Review Vocab: Associative, Identity, and Commutative Properties Property of Addition & Multiplication Introduce New Vocab: Distributive Property

Note “Common Errors” Go Math TE pg. 14 Read “Grade-Five Chapter of the Mathematics Framework” pg.” 7 Note both “Examples 5.OA.1” and “Common Misconceptions”

1.4 Y

5.NBT.2

Algebra – Powers of 10 and Exponents

Math Board (white

boards)

Base Ten Blocks

Base, exponent Note “Common Errors” Go Math TE pg. 18 Read “Grade-Five Chapter of the Mathematics Framework” pg. 11 “Example 5.NBT.2”

1.5 G

5.NBT.2

Algebra – Multiplication Patterns

MathBoard (white board)

Note “Common Errors” Go Math TE pg. 22

Mid-Chapter Checkpoint

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1.6 G

5.NBT.5

Multiply by 1-Digit Numbers

MathBoard (white board) Graph paper TR7 - Printable Graph paper

Note “Common Errors” Go Math TE pg. 28

Use area model, partial products, and place value model to connect to the standard algorithm. Read “Grade-Five Chapter of the Mathematics Framework” pg. 14 and note “Example 5.NBT.5” “Note that the method of recording the algorithm is not the same as the algorithm itself, in the sense that the “partial products” method, which lists every digit-by-digit product separately, is a completely valid recording method for the standard algorithm. Ultimately, the standards call for understanding the standard algorithm in terms of place value, and this should be the most important goal for instruction.” *For students who are ready and have the conceptual understanding, they can be moved toward the standard algorithm .

1.7 Y

5.NBT.5

Multiply by 2-Digit Numbers

MathBoard (white board)

Note “Common Errors” Go Math TE pg. 32

Use area model, partial products, and place value model to connect to the standard algorithm. Read “Grade-Five Chapter of the Mathematics Framework” pg. 14 and note “Example 5.NBT.5” Math Framework pg. 14 “Note that the method of recording the algorithm is not the same as the algorithm itself, in the sense that the “partial products” method, which lists every digit-by-digit product separately, is a completely valid recording method for the standard algorithm. Ultimately, the standards call for understanding

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the standard algorithm in terms of place value, and this should be the most important goal for instruction.” *For students who are ready and have the conceptual understanding, they can be moved toward the standard algorithm.

1.8 Y

5.NBT.6

Relate Multiplication to Division

MathBoard(white board), Graph paper

Introduce Vocab: Inverse operations, Review Vocab: Distributive Property, quotient

Note “Common Errors” Go Math TE pg. 36 Read “Grade-Five Chapter of the Mathematics Framework” pg. 15 and note Example 1 and 2 (5.NBT.6) Use Area Model, Understanding of Distributive Property, Partial Quotients

1.9 Y

5.NBT.6

Problem Solving – Multiplication and Division

MathBoard(white board)

Note “Common Errors” Go Math TE pg. 40 Read “Grade-Five Chapter of the Mathematics Framework” pg. 15 and note Example 1 and 2 (5.NBT.6)

Multiplication/Division Fact Review will help students understand how to break apart the dividend. (Compatible numbers and use of 10 as a factor -multiples of 10)

1.10 G

5.OA.1 5.OA.2

Algebra – Numerical Expressions

MathBoard (white board)

Numerical expression

Note “Common Errors” Go Math TE pg. 44 Read “Grade-Five Chapter of the Mathematics Framework” pg. 7 and note Example 2 and Common Misconceptions (2nd bullet) This lesson builds toward the order of operations

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1.11 G

5.OA.1

Algebra – Evaluate Numerical Expressions

MathBoard (white board)

Evaluate, order of operations

Note “Common Errors” Go Math TE pg. 48 Read “Grade-Five Chapter of the Mathematics Framework” pg. 7 and note Examples 1 and 2 and Common Misconceptions (1st bullet)

1.12 G

5.0A.1

Algebra – Grouping Symbols

MathBoard (white board)

Note “Common Errors” Go Math TE pg. 52 Read “Grade-Five Chapter of the Mathematics Framework” pg. 7 and note Examples 1 and 2 and Common Misconceptions

Chapter 1 Review /Test G

● Additional chapter test available in Go Math Assessment Guide pages AG37-AG42. ● Digital Option: Personal Math Trainer (PMT) can be assigned to each student along with

modifications if needed

Reteach Options

Look over your Chapter 1 Assessment to determine standards/areas of need. Reteach standards from this unit to help meet students’ need. Some ideas for reteach activities are listed below:

● Go Math TE - P55/56 (for assessment used in student textbook) can be used for error analysis - reteach concepts for student interventions

● Go Math TE - P60A (for assessment used from Go Math Assessment Guide) can be used for error analysis - reteach concepts for student interventions

● Think Central Personal Math Trainer (PMT) - Post-Test Homework version (can be assigned to each student along with modifications if needed

● Go Math Reteach book for this chapter. ● Math centers or math games focused on unit standards ● Small group instruction focused on a single standard using the Go Math

Intensive Intervention Skill Pack materials ● Whole group instruction focused on a single standard ● My Favorite No: Learning from Mistakes (Teaching Channel-

https://www.teachingchannel.org/videos/class-warm-up-routine ) – Rewrite student work with an error and work as a class to identify positives in the work and areas that need to be revised

● Select 1 – 3 problems to resolve in their groups and discuss whole class. We want new learning to occur on this day that helps students over misconceptions.

● Complete the “Performance Task” from Go Math! In the Assessment Book in small groups. Share strategies and discuss whole class.

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