Objectives
To review the meanings of number sentences; and
to provide practice determining whether number sentences are
true or false.
1
materials
Teaching the Lesson
Key Activities
Students 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.
Math Journal 1, pp. 56 and 69
Study Link 3 8
, / Fact Triangles
slate
calculator (optional)
[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]
2
materials
Ongoing Learning & Practice
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.
.
3
materials
Differentiation Options
READINESS
Students review
symbols for greater
than (>) and less
than (<).
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
ENRICHMENT
ELL SUPPORT
Students solve a
number-sentence
puzzle.
Students add true and
false to their Math
Word Banks.
Teaching Masters (Math Masters, pp. 95 and 96)
Differentiation Handbook
scissors; tape
Technology
Assessment Management System
Journal page 69, Problem 9
See the iTLG.
Lesson 3 9
203
Getting Started
Mental Math and Reflexes
Math Message
Students use their Multiplication/Division Fact Triangles
to practice the facts in the Try Again pile. They transfer
appropriate triangles to the OK pile and color the OK facts in the
table on journal page 56, fasten their new piles with paper clips,
and store them.
Write a sentence that is true. Write a sentence
that is false.
Study Link 3 8 Follow-Up
Students compare answers and number models.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Have a student read a sentence without saying whether it is true
or false. Ask the class to indicate thumbs-up if the sentence is
true. Repeat the procedure for other sentences. Some of these
sentences may be opinions that are neither true nor false, so you
may need to discuss fact versus opinion.
Tell students that in this lesson the class will discuss number
sentences. Number sentences, like word sentences, can also be
true or false.
Exploring the Meaning of
WHOLE-CLASS
DISCUSSION
Number Sentence
Write 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 one
suggests it, write 5 8 13 under the sentence.
Now write 5 7 on the board, and ask someone to read it. Then
write the sentence in words. Five is less than seven.
Repeat with 25 15 3. Twenty-five minus fifteen is greater
than three.
Point out that number models or number sentences, such as
5 8 13, 5 7, and 25 15 3, are shorthand for sentences
written in words. Words are replaced by mathematical symbols:
numerals consisting of the digits 0 through 9; operation symbols
such as , , (or ), and / (or ); and other symbols such as the
relation symbols , , and . Mathematical symbols are easier to
write and can be easier to understand than words.
204
Unit 3 Multiplication and Division; Number Sentences and Algebra
Ongoing Assessment: Informing Instruction
Watch for English language learners who have difficulty representing a word
sentence as a number sentence due to how phrases or words are translated
from one language to another. Some English words translate into a single word
in another language. Less and minus are examples of such words. Keep in mind
that English language learners may, for example, hear “1 less than 570” and
write “1 570.”
Determining Whether a
WHOLE-CLASS
ACTIVITY
Number Sentence Is True or False
Write the number sentence 4 5 20 on the board, and ask
whether this sentence is correct. yes Tell the class that another
way to talk about the number sentence is to say that 4 5 20 is
a true number sentence. Write the word true next to 4 5 20.
Point out that multiplying the expression 4 5 on the left side of
the equals sign and the number 20 on the right side of the equals
sign by the same number will result in another true number
sentence. For example, (4 5) 8 20 8 is also a true number
sentence. Note that this will work for any true number sentence
involving an equal sign. Have students summarize by stating that
if 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.
NOTE A number sentence has three parts:
the left side, the relation symbol, and the
right side. In 5 10 3, for example, the
left side is 5, the relation symbol is , and
the right side is 10 3. (Note that the
sentence 5 10 3 is false.) Numbers and
operation symbols (, , , /, and so on) can
appear on either side of the relation symbol.
Now write the number sentence 12 / 4 4 on the board, and ask
whether 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 on
their slates if they think the sentence is true, F if they think it is
false, and ? if they can’t tell. Discuss their answers. Repeat with
other examples (not all number sentences) such as the following:
15 13 28 T
Adjusting
the Activity
853F
42 12 20 F
17 27 T
3 18 / 6 T
The focus of this activity is to determine
whether a number sentence is true or false.
Encourage students to use calculators as
appropriate.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
716 487 616 487 F Ask: Can you tell whether it is true
or false before doing the subtractions?
4,684 182 4,694 482 F Ask: Can you tell whether it is
true or false before doing the additions?
42 50 ? (can’t tell) Ask: Why can’t you tell? How
would you change this to make it into a true sentence? A false
sentence?
8 6 ? (can’t tell) It is not a number sentence. Ask: How would
you change this to make it into a true number sentence? A false
number sentence?
Lesson 3 9
205
Student Page
Date
Practicing with Number
Time
LESSON
Number Sentences
3 9
148
Sentences
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.
F
?
F
F
1. 7 3 1
3. 80 ? 40
5. 0 4 / 4
7. 14 3 19 2
T
T
?
T
2. 6 36 6
4. 28 16 12
6. 2 7
8. 144 76 880 4
(Math Journal 1, p. 69)
9. Make up two true number sentences and two false number sentences.
Answers vary.
a. true
PARTNER
ACTIVITY
b. true
c. false
d. false
Partners identify number sentences in Problems 1–8 as true, false,
or “can’t tell.” Then have students work independently to complete
Problems 9 and 10. When they are finished, have students ask
their partners to decide which number sentences in Problem 10
are true.
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:
T
4 7 34 6
Answers vary.
Ongoing Assessment:
Recognizing Student Achievement
a.
b.
c.
d.
e.
f.
69
Math Journal 1, p. 69
Journal
page 69
Problem 9
Use journal page 69, Problem 9 to assess students’ ability to determine
whether number sentences are true or false. Students are making adequate
progress 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 students
may 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]
2 Ongoing Learning & Practice
Taking a 50-Facts Test
WHOLE-CLASS
ACTIVITY
(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 and
class results.
Student Page
Date
Time
LESSON
3 9
Math Boxes
1. If 1 inch on a map represents 30 miles,
what would 3 inches represent? Circle
the best answer.
and state the rule.
Rule:
A
10 miles
B
60 miles
C
90 miles
D
300 miles
9
in
out
45
5
81
9
27
36
3
4
162–166
4. Solve the riddle. Then use your Geometry
South Dakota is 563 feet tall. The Statue
of Liberty is 151 feet tall. What is the
difference in height of the two statues?
Template to trace the shape.
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 3-7. The skills in Problems 5 and 6
preview Unit 4 content.
I am a polygon.
All my angles have the
same measure.
feet
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 70)
145
412
8
72
3. The Statue of Chief Crazy Horse in
Math Boxes 3 9
2. Complete the “What’s My Rule?” table
Study Link 3 9
Each of my 5 sides has the
same measure.
What am I?
regular pentagon
INDEPENDENT
ACTIVITY
(Math Masters, p. 94)
97
5. Make a ballpark estimate. Write a number
6. Complete.
model to show your strategy.
a. 5.05, 5.06, 5.07,
$2.50 $0.75 $3.85 $12.70
Rule:
Sample answer:
$2.50 $1 $4
$13 $20.50
b. 4, 3.8, 3.6,
Rule:
3.4
3.2
,
3.0
,
0.2
c. 2.7, 3.2, 3.7,
181
5.08 , 5.09 , 5.10
0.01
Rule: 0.5
4.2
,
4.7
,
5.2
160 161
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.
70
Math Journal 1, p. 70
206
Unit 3 Multiplication and Division; Number Sentences and Algebra
Study Link Master
Name
3 Differentiation Options
39
Reviewing > and < Symbols
Time
Number Sentences
Next to each number sentence, write T if it is true, F if it is false,
or ? if you can’t tell.
SMALL-GROUP
ACTIVITY
READINESS
Date
STUDY LINK
5–15 Min
F
T
F
T
1.
20 12 8 º 3
3.
497 500
5.
15 10 5
7.
100 5 95
9.
Write two true number sentences.
2.
4.
6.
8.
148
F
7 14 º 2
T
16 / 4 4
24 11 11 T
?
33 4
Answers vary.
(Math Masters, p. 95)
To provide experience using relation symbols, have students solve
comparison problems using analogies and mnemonic devices.
11. a.
b.
Solving a Puzzle
Explain why 7 º 8 is not a number sentence.
Sample answer: There is not a relation
symbol, such as , , or .
How could you change 7 º 8 to make a true number sentence?
Sample answers: 7 º 8 56;
24 7 º 8; 9 º 9 7 º 8
INDEPENDENT
ACTIVITY
ENRICHMENT
Answers vary.
Write two false number sentences.
10.
c.
5–15 Min
How could you change 7 º 8 to make a false number sentence?
Sample answers: 7 º 8 13;
65 7 º 8; 22 7 º 8
(Math Masters, p. 96)
Practice
To apply students’ understanding of true number sentences, have
them arrange digits in a puzzle grid to make three number
sentences. Students may not repeat a digit in any row or column.
36 , 48, 60 , 72, 84
54 , 108, 162, 216 , 270, 324
24,
12.
13.
Rule:
Rule:
12
54
Math Masters, p. 94
SMALL-GROUP
ACTIVITY
ELL SUPPORT
Building a Math Word Bank
5–15 Min
(Differentiation Handbook)
To provide language support for number sentences, have students
use 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.
Teaching Master
Name
Date
LESSON
3 9
Teaching Master
Time
Name
> and < Symbols
3 9
Different symbols are used to show that numbers and amounts are not equal.
means “is less than”
Below are some ways to help you remember
these symbols. Try each one.
3,896
2. 7 6 9 8
3. 600 900 700 300
4. 7 6 5 8
5. 13,009 13,053
6. 8 8 9 6
7. 500 800 700 700
8. 5 10 9 7
9. 34,783 34,239
10. 11 6 12 8
11. 12,000 7,000 18,000 9,000
12. 36 / 9 25 / 5
1.
The alligator eats the bigger number.
The less-than symbol looks like the
fingers and thumb on your left hand.
The words left and less start with the
same letter. The less-than symbol
points to the lesser number.
2<5
5>2
Mark two dots next to the greater
number. Mark one dot next to the
lesser number. Connect each of the
two dots to the single dot, and the
symbol will be correct.
13.
1.
6
Example:
means “is greater than”
Math Masters, p. 95
Time
A Number-Sentence Puzzle
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.
3,568
What is your favorite way to remember the and symbols?
Pick one from above, or tell about your own idea.
Answers vary.
Date
LESSON
2.
149
Sample answers:
2
º
6
3
º
4
6
º
4
2
º
3
3
º
2
4
º
6
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.
2
2
2
3
3
3
4
4
4
6
6
6
Math Masters, p. 96
Lesson 3 9
207