Teaching the Lesson materials

Key ActivitiesStudents review the meanings of number sentences and determine, whenever possible, whether number sentences are true or false.

Key Concepts and Skills• Compare whole numbers. [Number and Numeration Goal 6]• Add, subtract, multiply, and divide to solve expressions.

[Operations and Computation Goals 1–4]• Use conventional notation to write number sentences.

[Patterns, Functions, and Algebra Goal 2]• Determine whether a number sentence is true or false.

[Patterns, Functions, and Algebra Goal 2]

Key Vocabulary number sentence • true number sentence • false number sentence

Ongoing Assessment: Informing Instruction See page 205.

Ongoing Assessment: Recognizing Student Achievement Use journal page 69. [Patterns, Functions, and Algebra Goal 2]

Ongoing Learning & Practice materials

Students take a 50-facts test. They use a line graph to record individual and class scores.Then students find the median and calculate the mean of class scores.

Students practice and maintain skills through Math Boxes and Study Link activities.

. Differentiation Options materials

Students review symbols for greater than (>) and less than (<).

Students solve a number-sentence puzzle.

Students add true andfalse to their Math Word Banks.

� Teaching Masters (Math Masters, pp. 95 and 96)� Differentiation Handbook� scissors; tape

ELL SUPPORTENRICHMENTREADINESS

3

� Math Journal 1, p. 70� Study Link Master (Math Masters, p. 94)� Teaching Aid Masters (Math Masters, pp. 412,

414, and 416)� pen or colored pencil

2

� Math Journal 1, pp. 56 and 69� Study Link 3�8� �, / Fact Triangles� slate � calculator (optional)

1

Lesson 3�9 203

Objectives To review the meanings of number sentences; and

to provide practice determining whether number sentences are

true or false.

Technology Assessment Management System

Journal page 69, Problem 9 See the iTLG.

204 Unit 3 Multiplication and Division; Number Sentences and Algebra

� Math Message Follow-UpHave a student read a sentence without saying whether it is trueor false. Ask the class to indicate thumbs-up if the sentence istrue. Repeat the procedure for other sentences. Some of thesesentences may be opinions that are neither true nor false, so youmay need to discuss fact versus opinion.

Tell students that in this lesson the class will discuss numbersentences. Number sentences, like word sentences, can also betrue or false.

� Exploring the Meaning of Number SentenceWrite the following sentence on the board:

The sum of five and eight is equal to thirteen.

Ask whether there is another way to write this sentence. If no onesuggests it, write 5 � 8 � 13 under the sentence.

Now write 5 � 7 on the board, and ask someone to read it. Thenwrite the sentence in words. Five is less than seven.

Repeat with 25 � 15 � 3. Twenty-five minus fifteen is greaterthan three.

Point out that number models or number sentences, such as 5 � 8 � 13, 5 � 7, and 25 � 15 � 3, are shorthand for sentenceswritten in words. Words are replaced by mathematical symbols:numerals consisting of the digits 0 through 9; operation symbolssuch as �, �, � (or ), and / (or ); and other symbols such as therelation symbols �, �, and �. Mathematical symbols are easier towrite and can be easier to understand than words.

WHOLE-CLASS

DISCUSSION

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

Getting Started

Math Message Write a sentence that is true. Write a sentence that is false.

Study Link 3�8 Follow-Up Students compare answers and number models.

Mental Math and ReflexesStudents use their Multiplication/Division Fact Trianglesto practice the facts in the Try Again pile. They transferappropriate triangles to the OK pile and color the OK facts in thetable on journal page 56, fasten their new piles with paper clips,and store them.

Lesson 3�9 205

NOTE A number sentence has three parts:the left side, the relation symbol, and theright side. In 5 � 10 � 3, for example, theleft side is 5, the relation symbol is �, andthe right side is 10 � 3. (Note that the sentence 5 � 10 � 3 is false.) Numbers andoperation symbols (�, �, �, /, and so on) canappear on either side of the relation symbol.

Ongoing Assessment: Informing InstructionWatch for English language learners who have difficulty representing a wordsentence as a number sentence due to how phrases or words are translatedfrom one language to another. Some English words translate into a single wordin another language. Less and minus are examples of such words. Keep in mindthat English language learners may, for example, hear “1 less than 570” andwrite “1 � 570.”

� Determining Whether a Number Sentence Is True or FalseWrite the number sentence 4 � 5 � 20 on the board, and askwhether this sentence is correct. yes Tell the class that anotherway to talk about the number sentence is to say that 4 � 5 � 20 isa true number sentence. Write the word true next to 4 � 5 � 20.Point out that multiplying the expression 4 � 5 on the left side ofthe equals sign and the number 20 on the right side of the equalssign by the same number will result in another true numbersentence. For example, (4 � 5) � 8 � 20 � 8 is also a true numbersentence. Note that this will work for any true number sentenceinvolving an equal sign. Have students summarize by stating thatif you multiply equals by equals you get equal quantities. Similarly,if you add equals to equals you get equal quantities. For example,(4 � 5) � 10 � 20 � 10 is also a true number sentence.

Now write the number sentence 12 / 4 � 4 on the board, and askwhether this sentence is correct. no 12 / 4 � 4 is an example of a false number sentence. Write the word false next to 12 / 4 � 4.

To reinforce this idea, lead the class in the following slate routine:Write a number sentence on the board. Have students write T ontheir slates if they think the sentence is true, F if they think it isfalse, and ? if they can’t tell. Discuss their answers. Repeat withother examples (not all number sentences) such as the following:

� 15 � 13 � 28 T

� 8 � 5 � 3 F

� 42 � 12 � 20 F

� 17 � 27 T

� 3 � 18 / 6 T

� 716 � 487 � 616 � 487 F Ask: Can you tell whether it is trueor false before doing the subtractions?

� 4,684 � 182 � 4,694 � 482 F Ask: Can you tell whether it istrue or false before doing the additions?

� 42 � � 50 ? (can’t tell) Ask: Why can’t you tell? Howwould you change this to make it into a true sentence? A falsesentence?

� 8 � 6 ? (can’t tell) It is not a number sentence. Ask: How wouldyou change this to make it into a true number sentence? A falsenumber sentence?

WHOLE-CLASS

ACTIVITY

Adjustingthe Activity

The focus of this activity is to determinewhether a number sentence is true or false.Encourage students to use calculators asappropriate.AUDITORY � KINESTHETIC � TACTILE � VISUAL

206 Unit 3 Multiplication and Division; Number Sentences and Algebra

Math Boxes LESSON

3�9

162–166

70

Date Time

1. If 1 inch on a map represents 30 miles,what would 3 inches represent? Circle the best answer.

A 10 miles

B 60 miles

C 90 miles

D 300 miles

145

2. Complete the “What’s My Rule?” table and state the rule.

Rule: 9 in out

45 5

81 9

27 3

36 4

72 8

3. The Statue of Chief Crazy Horse in South Dakota is 563 feet tall. The Statueof Liberty is 151 feet tall. What is thedifference in height of the two statues?

feet412

4. Solve the riddle. Then use your GeometryTemplate to trace the shape.

I am a polygon.All my angles have the same measure.Each of my 5 sides has the same measure.What am I?

regular pentagon97

160 161

5. Make a ballpark estimate. Write a numbermodel to show your strategy.

$2.50 � $0.75 � $3.85 � $12.70

181

6. Complete.

a. 5.05, 5.06, 5.07, , ,

Rule:

b. 4, 3.8, 3.6, , ,

Rule:

c. 2.7, 3.2, 3.7, , ,

Rule: �0.5

�0.2

�0.015.08 5.09 5.10

3.4 3.2 3.0

4.2 4.7 5.2

$2.50 � $1 � $4 � $13 � $20.50

Sample answer:

Math Journal 1, p. 70

Student Page

� Practicing with Number Sentences(Math Journal 1, p. 69)

Partners identify number sentences in Problems 1–8 as true, false,or “can’t tell.” Then have students work independently to completeProblems 9 and 10. When they are finished, have students asktheir partners to decide which number sentences in Problem 10are true.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 69, Problem 9 to assess students’ ability to determinewhether number sentences are true or false. Students are making adequateprogress if they are able to use conventional notation to write appropriate number sentences. They may write simple number sentences involving an equals symbol, one operation symbol, and 1-digit whole numbers. Some studentsmay write more elaborate number sentences with several operations, large numbers, fractions or decimals, parentheses, and the relation symbol � or �.

[Patterns, Functions, and Algebra Goal 2]

� Taking a 50-Facts Test(Math Masters, pp. 412, 414, and 416)

See Lesson 3-4 for details regarding the administration of the 50-facts test and the recording and graphing of individual andclass results.

� Math Boxes 3�9(Math Journal 1, p. 70)

Mixed Practice Math Boxes in this lesson are paired withMath Boxes in Lesson 3-7. The skills in Problems 5 and 6preview Unit 4 content.

� Study Link 3�9(Math Masters, p. 94)

Home Connection Students tell whether sentences are true or false. They write a question mark if it is not possible to tell. Then they write true and false

number sentences and explain why a given expression is not a number sentence.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

WHOLE-CLASS

ACTIVITY

2 Ongoing Learning & Practice

PARTNER

ACTIVITY

Journal

page 69 �Problem 9

69

Date Time

Number SentencesLESSON

3� 9

Answers vary.

148

Answers vary.

�

4 � 7 � 34 � 6 T

Tell whether each number sentence below is true or false. Write T for true or F for false. If it is not possible to tell, write ? on the answer blank.

1. 7 � 3 � 1 2. 6 � 36 6

3. 80 � ? � 40 4. 28 � 16 � 12

5. 0 � 4 / 4 6. 2 � 7

7. 14 3 � 19 2 8. 144 � 76 � 880 4

9. Make up two true number sentences and two false number sentences.

a. true

b. true

c. false

d. false

10. Make up three true number sentences and three false number sentences. Mix them up. Ask your partner to write whether each sentence is true or false.

Example:

a.

b.

c.

d.

e.

f.

TF?FT?TF

Math Journal 1, p. 69

Student Page

� Reviewing > and < Symbols(Math Masters, p. 95)

To provide experience using relation symbols, have students solvecomparison problems using analogies and mnemonic devices.

� Solving a Puzzle (Math Masters, p. 96)

To apply students’ understanding of true number sentences, havethem arrange digits in a puzzle grid to make three numbersentences. Students may not repeat a digit in any row or column.

� Building a Math Word Bank(Differentiation Handbook)

To provide language support for number sentences, have studentsuse the Word Bank template found in the Differentiation Handbook.Ask students to write the terms number sentence, true, and false,draw pictures relating to each term, and write other related words.See the Differentiation Handbook for more information.

5–15 Min

SMALL-GROUP

ACTIVITYELL SUPPORT

5–15 Min

INDEPENDENT

ACTIVITYENRICHMENT

5–15 Min

SMALL-GROUP

ACTIVITYREADINESS

3 Differentiation Options

Name Date Time

LESSON

3�9 A Number-Sentence Puzzle

1. Cut out the number tiles at the bottom of the page. Tape them in the number sentences below so that

◆ each number sentence is true,

◆ the same digit appears only one time in each row, and

◆ the same digit appears only one time in each column. Sample answers:

2. Explain the strategy you used to solve this problem.

I multiplied the largest number by the smallest number and the two middle numbers together, and I checked if the products were equal. Then I multiplied the two largest numbers to make the larger product and the two smallest numbers to make the smaller product.

149

2 º

º

º

�

�

�

º

º

º

6 3 4

6 4 2 3

3 2 4 6

2

4

2

4

2

4

3

6

3

6

3

6

Math Masters, p. 96

Teaching Master

Lesson 3�9 207

Name Date Time

LESSON

3�9 > and < Symbols

Different symbols are used to show that numbers and amounts are not equal.

Example:

� means “is greater than” � means “is less than”

Below are some ways to help you remember these symbols. Try each one.

13. What is your favorite way to remember the � and � symbols? Pick one from above, or tell about your own idea.

Answers vary.

9. 34,783 34,239

10. 11 � 6 12 � 8

11. 12,000 � 7,000 18,000 � 9,000

12. 36 / 9 25 / 5�

�

�

�

5. 13,009 13,053

6. 8 � 8 9 � 6

7. 500 � 800 700 � 700

8. 5 � 10 9 � 7�

�

�

�

1. 3,568 3,896

2. 7 � 6 9 � 8

3. 600 � 900 700 � 300

4. 7 � 6 5 � 8�

�

�

�

The alligator eats the bigger number.

The less-than symbol looks like thefingers and thumb on your left hand.The words left and less start with thesame letter. The less-than symbolpoints to the lesser number.

5 > 22 < 5Mark two dots next to the greaternumber. Mark one dot next to thelesser number. Connect each of thetwo dots to the single dot, and thesymbol will be correct.

6

Math Masters, p. 95

Teaching Master

Name Date Time

STUDY LINK

3�9

148

Next to each number sentence, write T if it is true, F if it is false,or ? if you can’t tell.

1. 20 � 12 � 8 º 3 2. 7 � 14 º 2

3. 497 � 500 4. 16 / 4 � 4

5. 15 � 10 � 5 6. 24 � 11 � 11

7. 100 � 5 � 95 8. 33 � 4

9. Write two true number sentences.

10. Write two false number sentences.

11. a. Explain why 7 º 8 is not a number sentence.

b. How could you change 7 º 8 to make a true number sentence?

c. How could you change 7 º 8 to make a false number sentence?

65 � 7 º 8; 22 � 7 º 8Sample answers: 7 º 8 � 13;

24 � 7 º 8; 9 º 9 � 7 º 8Sample answers: 7 º 8 � 56;

symbol, such as �, �, or �.Sample answer: There is not a relation

Answers vary.

Answers vary.?TTFTTFF

Practice

12. 24, , 48, , 72, Rule:

13. , 108, 162, , 270, Rule: �54 32421654�12 846036

Number Sentences

Math Masters, p. 94

Study Link Master