goMath2.7.notebook

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September20,2013

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1 4/61/6=

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Amultiplicativeinverseisareciprocalofanumberthatismultipliedbythatnumberresultinginaproductof1.

goMath2.7.notebook

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September20,2013

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2 Kristenwantstocutladderrungsfroma6ftboard.Howmanyladderrungscanshecut?

goMath2.7.notebook

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3 Halhas3/4yardofstring.Howmany1/12yardpiecesofstringcanhecutfrom3/4yard?

A 3

B 6

C 9

D 12

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2

Divide Fractions

Using the Whiteboard Use the table of contents to go to specific sections of the lesson, or, tap Next to go to the first section of the lesson.

Teaching the Math Discuss the Essential Question with students: How do you divide fractions?

Common Core Standards for Mathematical Content CC.6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving

division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Common Core Standards for Mathematical Practice CC.K12.MP.4 Model with mathematics.

CC.K12.MP.5 Use appropriate tools strategically.

Navigating the SMART Notebook file

Home Return to the Main Menu. Example View a sample problem.

Teacher Notes Open the Teacher Notes PDF. Answer Show the correct answer to a problem.

Previous Go to the previous page. Try Another Generate another problem for extra practice.

Next Go to the next page.SMART Response Question

Indicates the question is compatible with a SMART Response interactive Response system.Action Arrow Reveal hidden content.

Try This Reveal additional problems. Tap again to return to the previous page. WorkspaceReveal additional content for the activity. Tap again to return to the previous page.

TipsClear or reset the screen To reset the screen, tap Edit > Reset Page or tap the Reset Page button if it is on

the toolbar.

Add tools and functions to your SMART Notebook toolbar or floating palette Tap the Customize button in the toolbar or floating palette, and then drag the tool to

the toolbar or floating palette.

3

Unlock the Problem

Using the Whiteboard Have the class read the problem aloud. Then read the One Way instruction. Tap the first Action Arrow and read the Step 1. Tap Think to reveal helpful text. Guide a volunteer to use the Highlighter Tool to make a horizontal strip along the

number line that represents the total length of the original board.

Tap the second Action Arrow to reveal Step 2. Tap Think to reveal helpful text. Guide a volunteer to use the Pen to make vertical tick marks along the number line

that represent the size of the pieces into which the board will be cut.

Guide a different volunteer to use the Pen to make and label horizontal brackets over the number line that represent the individual pieces into which the board will be cut.

Instruct a volunteer to use the Pen to fill in the missing number in the statement.

Teaching the Math Ask: What does represent on the number line? the total length of the original board

Ask: What are you asked to find? How many groups of are in .

Ask: What does a group of represent? one piece of the board

Ask: Now how does the number line show the groups of ? Possible answer: is half

of , so there are 2 groups of between 0 and and 2 groups of between and .

Answer Key

So, there are yard pieces in yard.

4

Unlock the Problem: Another Way

Using the Whiteboard Pull out the Problem tab and review the problem with students. Read the instructions and Step 1. Tap Think to reveal helpful text. Instruct a volunteer to use the Pen to fill in the blank spaces in the equation. Tap the Action Arrow and read Step 2 aloud. Tap Think to reveal helpful text. Ask students to solve the problem. If available, have students use their SMART Response remotes to answer. If installed, click the SMART Response tab, and then start the question to

begin voting. Guide the volunteer to use the Pen to write the answers on the lines. A volunteer may use the Pen to show his or her work. Tap Math Talk to reveal a discussion question.

Teaching the Math Ask: Why is 6 a common denominator of ? Because 3 is a factor of 6. Ask: Why did you multiply the numerator and denominator of by 2? To write an equivalent fraction with a denominator of 6.Ask: Why was not rewritten as an equivalent fraction? Because the denominator

in is already 6.Ask: Once you have a common denominator, how do you find the quotient? Divide the numerators.

Answer Key

So, . Toby and his dad can cut yard pieces.

Math Talk Write equivalent fractions with 9 as a common denominator: and .

Then find . There are 3 groups of in , so .

5

Activity

Using the Whiteboard Read the introductory text. Pull out the Definition tabs to view the definitions of reciprocals and

multiplicative inverses. Review the table with students. Point out the places in which numbers are

missing. Guide a volunteer to use the Pen to fill in the missing answers in the table. Tap the first Action Arrow to reveal a question. Instruct a volunteer to use the Pen to write an answer to the question on the

blank lines. Tap the second Action Arrow to reveal another question. Instruct a volunteer to use the Pen to write an answer to the question on the

blank lines.

Teaching the Math Direct students attention to the first row of the table.Ask: What is ? 2

Ask: What is the same about the two problems in the first row of the table? Possible answer: The first number is the same and the answer in the same.Ask: What is different about the two problems? Possible answer: In the first

problem, is divided by . In the second problem, is multiplied by .

Ask: What are and ? Explain. Possible answer: and are reciprocals.

.

After students finish the activity, have them work through a similar pair of problems,

such as , and .

Answer Key

How are each pair of division and multiplication problems the same, and how are they different? The first fractions and the answers in each pair are the same. The second fractions in each pair are reciprocals of each other.

How could you use the pattern in the table to rewrite a division problem involving fractions as a multiplication problem? Rewrite the division as multiplication by the reciprocal of the divisor.

6

Example

Using the Whiteboard Read the instructions and the problem to students. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap first Action Arrow. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap second Action Arrow. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap thrid Action Arrow. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap Math Talk to reveal a discussion question.

Teaching the Math Ask: How do you know that is the dividend and is the divisor? The original piece is yd long, and it is being cut into pieces that are yd long.

Common ErrorsError: Students may not take the time to check their answers using inverse operations.

Example:

Springboard to Learning: Remind students of the importance of checking their work. Point out that checks will not be time-consuming because, in the end, students will become more proficient at them. Checking their work will also improve their fluency in multiplying fractions.

Answer Key Estimate: 1 = 12

Since the estimate is 12, the answer is reasonable.So, Winnie can cut 9 yd pieces of string.

Math Talk Multiplication and division are inverse operations. Multiplying the quotient by the divisor should result in the dividend.

7

Share and Show

Using the Whiteboard Read the instructions and the problem to students. Have a volunteer use the Pen to write the estimates on the blank lines. Tap the first Action Arrow and read the instructions to students. Instruct a volunteer to use the Pen to fill in the missing denominator. Tap second Action Arrow and read the instructions to students. Instruct a volunteer to use the Pen to fill in the blank spaces in the equation.

Answer Key Possible Estimate: 1 3 =

8

Share and Show

Using the Whiteboard Read the instructions and the problem to students. Guide a volunteer to use the HIghlighter Tool and Pen to draw on and label the

number line in order to solve the problem. Tap Try Another to replace the problem with a different type of problem. Read the new instructions and the problem to students. Guide a volunteer to use the Pen to write an estimate and the actual quotient. Tap Math Talk to reveal a discussion question.

Teaching the Math Use Math Talk to focus on students understanding of lesson concepts. Students will compare their estimate to the answer to determine if the estimate is reasonable.

Answer Key First problem:

Second problem:Possible Estimate: 3Quotient: 4

Math Talk Possible answer: is close to 1. . Since , or , 4 is a reasonable estimate.

9

On Your Own

Using the Whiteboard Read the instructions to students. Then read the first problem to the class. Have a student use the Pen to make an estimate and write it on the

blank line. Have a volunteer use the Pen to find the quotient and write the answer on the

blank line. Tap the Action Arrow to reveal another problem. Have a student use the Pen to make an estimate and write it on the blank line Use the Eraser to erase any writing on the page. Have a volunteer use the Pen to find the quotient and write the answer on the

blank line.

Answer Key Mari wants to cut a yd piece of ribbon into 6 equal pieces. How long will each piece be?Estimate: yd Quotient: yd

Yee puts lb of orange slices in bags that hold lb each. How many bags does

she fill?Estimate: 8 Quotient: 6

10

Problem Solving

Using the Whiteboard Read the instructions and review the table with students. Read the problem to students. Guide a volunteer use the Pen to solve the problem. If available, have students use their SMART Response remotes to answer. If installed, click the SMART Response tab, and then start the question to

begin voting.

Answer Key 8

11

H.O.T. Problem

Using the Whiteboard Read the instructions and review the table with students. Pull out the Problem tab. Review the previous problem with students. Guide a volunteer use the Pen to write and solve a new problem on the

blank lines.

Answer Key Check students problems.

12

Test Prep

Using the Whiteboard Read the question to the students. Ask students to solve the problem. If available, have students use their SMART Response remotes to answer. If installed, click the SMART Response tab, and then start the question to

begin voting. Students may also use the Pen to circle the answer. Tap Answer to view the correct answer.

Teaching the Math Test Prep CoachIf students selected:A) They divided the numerators of the fractions or the denominators of the fractions.B) They made a computation error. D) They chose the denominator of the divisor.

Answer Key C) 9

13

Summarize

Using the Whiteboard Read aloud the Essential Question: How do you divide fractions? Instruct a volunteer to use the Pen to write his or her answer. Pull out the Answer tab to reveal the answer.

Answer Key Essential Question: Possible answer: You can use reciprocals and inverse operations. Instead of dividing by a fraction, you can multiply by its reciprocal.

Copyright 2013 by Houghton Mifflin Harcourt Publishing Company

All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, broadcasting or by any other information storage and retrieval system, without written permission of the copyright owner unless such copying is expressly permitted by federal copyright law.

Only those pages that are specifically enabled by the program and indicated by the presence of the print icon may be printed and reproduced in classroom quantities by individual teachers using the corresponding students textbook or kit as the major vehicle for regular classroom instruction.

Common Core State Standards Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

HOUGHTON MIFFLIN HARCOURT and the HMH Logo are trademarks and service marks of Houghton Mifflin Harcourt Publishing Company. You shall not display, disparage, dilute or taint Houghton Mifflin Harcourt trademarks and service marks or use any confusingly similar marks, or use Houghton Mifflin Harcourt marks in such a way that would misrepresent the identity of the owner. Any permitted use of Houghton Mifflin Harcourt trademarks and service marks inures to the benefit of Houghton Mifflin Harcourt Publishing Company.

All other trademarks, service marks or registered trademarks appearing on Houghton Mifflin Harcourt Publishing Company websites are the trademarks or service marks of their respective owners.

SMART Notebook

3

Unlock the Problem

Using the Whiteboard Have the class read the problem aloud. Then read the One Way instruction. Tap the first Action Arrow and read the Step 1. Tap Think to reveal helpful text. Guide a volunteer to use the Highlighter Tool to make a horizontal strip along the

number line that represents the total length of the original board.

Tap the second Action Arrow to reveal Step 2. Tap Think to reveal helpful text. Guide a volunteer to use the Pen to make vertical tick marks along the number line

that represent the size of the pieces into which the board will be cut.

Guide a different volunteer to use the Pen to make and label horizontal brackets over the number line that represent the individual pieces into which the board will be cut.

Instruct a volunteer to use the Pen to fill in the missing number in the statement.

Teaching the Math Ask: What does represent on the number line? the total length of the original board

Ask: What are you asked to find? How many groups of are in .

Ask: What does a group of represent? one piece of the board

Ask: Now how does the number line show the groups of ? Possible answer: is half

of , so there are 2 groups of between 0 and and 2 groups of between and .

Answer Key

So, there are yard pieces in yard.

SMART Notebook

4

Unlock the Problem: Another Way

Using the Whiteboard Pull out the Problem tab and review the problem with students. Read the instructions and Step 1. Tap Think to reveal helpful text. Instruct a volunteer to use the Pen to fill in the blank spaces in the equation. Tap the Action Arrow and read Step 2 aloud. Tap Think to reveal helpful text. Ask students to solve the problem. If available, have students use their SMART Response remotes to answer. If installed, click the SMART Response tab, and then start the question to

begin voting. Guide the volunteer to use the Pen to write the answers on the lines. A volunteer may use the Pen to show his or her work. Tap Math Talk to reveal a discussion question.

Teaching the Math Ask: Why is 6 a common denominator of ? Because 3 is a factor of 6. Ask: Why did you multiply the numerator and denominator of by 2? To write an equivalent fraction with a denominator of 6.Ask: Why was not rewritten as an equivalent fraction? Because the denominator

in is already 6.Ask: Once you have a common denominator, how do you find the quotient? Divide the numerators.

Answer Key

So, . Toby and his dad can cut yard pieces.

Math Talk Write equivalent fractions with 9 as a common denominator: and .

Then find . There are 3 groups of in , so .

SMART Notebook

5

Activity

Using the Whiteboard Read the introductory text. Pull out the Definition tabs to view the definitions of reciprocals and

multiplicative inverses. Review the table with students. Point out the places in which numbers are

missing. Guide a volunteer to use the Pen to fill in the missing answers in the table. Tap the first Action Arrow to reveal a question. Instruct a volunteer to use the Pen to write an answer to the question on the

blank lines. Tap the second Action Arrow to reveal another question. Instruct a volunteer to use the Pen to write an answer to the question on the

blank lines.

Teaching the Math Direct students attention to the first row of the table.Ask: What is ? 2

Ask: What is the same about the two problems in the first row of the table? Possible answer: The first number is the same and the answer in the same.Ask: What is different about the two problems? Possible answer: In the first

problem, is divided by . In the second problem, is multiplied by .

Ask: What are and ? Explain. Possible answer: and are reciprocals.

.

After students finish the activity, have them work through a similar pair of problems,

such as , and .

Answer Key

How are each pair of division and multiplication problems the same, and how are they different? The first fractions and the answers in each pair are the same. The second fractions in each pair are reciprocals of each other.

How could you use the pattern in the table to rewrite a division problem involving fractions as a multiplication problem? Rewrite the division as multiplication by the reciprocal of the divisor.

SMART Notebook

6

Example

Using the Whiteboard Read the instructions and the problem to students. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap first Action Arrow. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap second Action Arrow. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap thrid Action Arrow. Instruct a volunteer to use the Pen to write the answers in the answer spaces. Tap Math Talk to reveal a discussion question.

Teaching the Math Ask: How do you know that is the dividend and is the divisor? The original piece is yd long, and it is being cut into pieces that are yd long.

Common ErrorsError: Students may not take the time to check their answers using inverse operations.

Example:

Springboard to Learning: Remind students of the importance of checking their work. Point out that checks will not be time-consuming because, in the end, students will become more proficient at them. Checking their work will also improve their fluency in multiplying fractions.

Answer Key Estimate: 1 = 12

Since the estimate is 12, the answer is reasonable.So, Winnie can cut 9 yd pieces of string.

Math Talk Multiplication and division are inverse operations. Multiplying the quotient by the divisor should result in the dividend.

SMART Notebook

7

Share and Show

Using the Whiteboard Read the instructions and the problem to students. Have a volunteer use the Pen to write the estimates on the blank lines. Tap the first Action Arrow and read the instructions to students. Instruct a volunteer to use the Pen to fill in the missing denominator. Tap second Action Arrow and read the instructions to students. Instruct a volunteer to use the Pen to fill in the blank spaces in the equation.

Answer Key Possible Estimate: 1 3 =

SMART Notebook

8

Share and Show

Using the Whiteboard Read the instructions and the problem to students. Guide a volunteer to use the HIghlighter Tool and Pen to draw on and label the

number line in order to solve the problem. Tap Try Another to replace the problem with a different type of problem. Read the new instructions and the problem to students. Guide a volunteer to use the Pen to write an estimate and the actual quotient. Tap Math Talk to reveal a discussion question.

Teaching the Math Use Math Talk to focus on students understanding of lesson concepts. Students will compare their estimate to the answer to determine if the estimate is reasonable.

Answer Key First problem:

Second problem:Possible Estimate: 3Quotient: 4

Math Talk Possible answer: is close to 1. . Since , or , 4 is a reasonable estimate.

SMART Notebook

9

On Your Own

Using the Whiteboard Read the instructions to students. Then read the first problem to the class. Have a student use the Pen to make an estimate and write it on the

blank line. Have a volunteer use the Pen to find the quotient and write the answer on the

blank line. Tap the Action Arrow to reveal another problem. Have a student use the Pen to make an estimate and write it on the blank line Use the Eraser to erase any writing on the page. Have a volunteer use the Pen to find the quotient and write the answer on the

blank line.

Answer Key Mari wants to cut a yd piece of ribbon into 6 equal pieces. How long will each piece be?Estimate: yd Quotient: yd

Yee puts lb of orange slices in bags that hold lb each. How many bags does

she fill?Estimate: 8 Quotient: 6

SMART Notebook

10

Problem Solving

Using the Whiteboard Read the instructions and review the table with students. Read the problem to students. Guide a volunteer use the Pen to solve the problem. If available, have students use their SMART Response remotes to answer. If installed, click the SMART Response tab, and then start the question to

begin voting.

Answer Key 8

SMART Notebook

11

H.O.T. Problem

Using the Whiteboard Read the instructions and review the table with students. Pull out the Problem tab. Review the previous problem with students. Guide a volunteer use the Pen to write and solve a new problem on the

blank lines.

Answer Key Check students problems.

SMART Notebook

12

Test Prep

Using the Whiteboard Read the question to the students. Ask students to solve the problem. If available, have students use their SMART Response remotes to answer. If installed, click the SMART Response tab, and then start the question to

begin voting. Students may also use the Pen to circle the answer. Tap Answer to view the correct answer.

Teaching the Math Test Prep CoachIf students selected:A) They divided the numerators of the fractions or the denominators of the fractions.B) They made a computation error. D) They chose the denominator of the divisor.

Answer Key C) 9

SMART Notebook

13

Summarize

Using the Whiteboard Read aloud the Essential Question: How do you divide fractions? Instruct a volunteer to use the Pen to write his or her answer. Pull out the Answer tab to reveal the answer.

Answer Key Essential Question: Possible answer: You can use reciprocals and inverse operations. Instead of dividing by a fraction, you can multiply by its reciprocal.

Copyright 2013 by Houghton Mifflin Harcourt Publishing Company

All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, broadcasting or by any other information storage and retrieval system, without written permission of the copyright owner unless such copying is expressly permitted by federal copyright law.

Only those pages that are specifically enabled by the program and indicated by the presence of the print icon may be printed and reproduced in classroom quantities by individual teachers using the corresponding students textbook or kit as the major vehicle for regular classroom instruction.

Common Core State Standards Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

HOUGHTON MIFFLIN HARCOURT and the HMH Logo are trademarks and service marks of Houghton Mifflin Harcourt Publishing Company. You shall not display, disparage, dilute or taint Houghton Mifflin Harcourt trademarks and service marks or use any confusingly similar marks, or use Houghton Mifflin Harcourt marks in such a way that would misrepresent the identity of the owner. Any permitted use of Houghton Mifflin Harcourt trademarks and service marks inures to the benefit of Houghton Mifflin Harcourt Publishing Company.

All other trademarks, service marks or registered trademarks appearing on Houghton Mifflin Harcourt Publishing Company websites are the trademarks or service marks of their respective owners.

SMART Notebook

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