Mathematics
Mathematics
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310NASE
Performance Coach
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CONTENTS
Standards
Letter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
DOMAIN 1: OPERATIONS AND ALGEBRAIC THINKING . . . 5
Introducing Multiplication . . . . . . . . . . . . . . . . . . . . . . 6
Lesson 1
3.OA.1
Lesson 2
Introducing Division . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.OA.2
Lesson 3
Solving Multiplication Problems . . . . . . . . . . . . . . . 24
3.OA.3
Lesson 4
Solving Division Problems . . . . . . . . . . . . . . . . . . . . 33
3.OA.3
Lesson 5
Finding Unknown Values . . . . . . . . . . . . . . . . . . . . . . 41
3.OA.4, 3.OA.6
Lesson 6
Multiplication Properties . . . . . . . . . . . . . . . . . . . . . . 51
3.OA.5
Lesson 7
Multiplication and Division Facts . . . . . . . . . . . . . . . 59
3.OA.7
Lesson 8
Solving Two-Step Word Problems . . . . . . . . . . . . . 67
3.OA.8
Lesson 9
Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.OA.9
Domain 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
DOMAIN 2: NUMBER AND OPERATIONS IN BASE TEN . . . 93
Lesson 10 Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.NBT.1
Lesson 11
Rounding Whole Numbers . . . . . . . . . . . . . . . . . . 102
3.NBT.1
Lesson 12
Addition Properties . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.NBT.2
Lesson 13
Adding 2- and 3-Digit Numbers to 1,000 . . . . . . . . 119
3.NBT.2
Lesson 14
Subtracting 2- and 3-Digit Numbers
Within 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.NBT.2
Multiplying by Multiples of 10 . . . . . . . . . . . . . . . . . 141
3.NBT.3
Lesson 15
Domain 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
DOMAIN 3: NUMBER AND OPERATIONS – FRACTIONS . . . . . 157
Lesson 16 Understanding Fractions . . . . . . . . . . . . . . . . . . . . 158
3.NF.1
Lesson 17
Fractions on a Number Line . . . . . . . . . . . . . . . . . . 167
3.NF.2.a, 3.NF.2.b
Lesson 18
Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . 177
3.NF.3.a, 3.NF.3.b
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Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
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Standards
Lesson 19
Whole Numbers as Fractions . . . . . . . . . . . . . . . . . 187
3.NF.3.c
Lesson 20
Comparing Fractions . . . . . . . . . . . . . . . . . . . . . . . 196
3.NF.3.d
Domain 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
DOMAIN 4: MEASUREMENT AND DATA . . . . . . . . . . . . . . . . 211
Lesson 21 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
3.MD.1
Lesson 22
Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
3.MD.2
Lesson 23
Liquid Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
3.MD.2
Lesson 24
Picture Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
3.MD.3
Lesson 25
Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
3.MD.3
Lesson 26
Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
3.MD.4
Lesson 27
Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
3.MD.8
Lesson 28
Understanding Area . . . . . . . . . . . . . . . . . . . . . . . . 283
3.MD.5.a, 3.MD.5.b, 3.MD.6, 3.MD.7.a
Lesson 29
Area of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
3.MD.7.a, 3.MD.7.b, 3.MD.7.c, 3.MD.7.d
Lesson 30
Perimeter and Area of Rectangles . . . . . . . . . . . . . 304
3.MD.7.b, 3.MD.8
Domain 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
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Duplicating any part of this book is prohibited by law. © 2015 Triumph Learning, LLC
Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
DOMAIN 5: GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Lesson 31 Two-Dimensional Shapes . . . . . . . . . . . . . . . . . . . . 322
3.G.1
Lesson 32
3.G.2
Equal Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
Domain 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
Math Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
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LESSON
10
3.NBT.1
Whole Numbers
1 GETTING THE IDEA
You can write whole numbers in different ways.
Standard form: 1,348
Word Form: one thousand, three hundred forty-eight
Expanded Form: 1,000 1 300 1 40 1 8
94
Thousands
Hundreds
Tens
Ones
1,
3
4
8
Domain 2: Number and Operations in Base Ten
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Place value can help you determine how to write numbers correctly.
Place value is the value of a digit based on its position in that number.
A place-value chart breaks a number down into individual digits to show their value.
This is 1,348 in a place value chart.
Example 1
What is the value of each digit in 3,256?
Strategy
Step 1
Use place-value models and a place-value chart.
Model 3,256.
Show thousands, hundreds, tens, and ones.
There are 3 thousands, 2 hundreds, 5 tens, and 6 ones.
Step 2
Write 3,256 in a place-value chart.
Use the place-value models in Step 1 to help.
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Write a comma after the number in the thousands place.
Step 3
Thousands
Hundreds
Tens
Ones
3,
2
5
6
Find the value of each digit.
The digit 3 has a value of 3,000.
The digit 2 has the value of 200.
The digit 5 has a value of 50.
The digit 6 has a value of 6.
Solution
The value of each digit is shown in Step 3.
Lesson 10: Whole Numbers 95
Example 2
Pia took a plane trip. It was 2,594 miles. Write 2,594 in word form.
Strategy
Step 1
Step 2
Use a place-value chart.
Write 2,594 in a place-value chart.
Thousands
Hundreds
Tens
Ones
2,
5
9
4
Write the value and the word name of the digit before the comma.
The digit before the comma is the 2 in the thousands place.
2 thousands  2,000
Write a comma after the word thousand.
two thousand,
Step 3
Write the value and the word name for the digits after the comma.
The digits after the comma are 594.
5 hundreds  500
9 tens  90
4 ones  4
five hundred ninety-four
Step 4
Write the word name for the whole number.
Solution
The word form of 2,594 is two thousand, five hundred ninety-four.
Example 3
A stadium holds 47,903 people. What is 47,903 in expanded form?
Strategy
Step 1
Use a place-value chart to find the value of each digit.
Write 47,903 in a place-value chart.
Write each digit in the chart. Write a comma after the thousands place.
96
Ten Thousands
Thousands
Hundreds
Tens
Ones
4
7,
9
0
3
Domain 2: Number and Operations in Base Ten
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two thousand, five hundred ninety-four
Step 2
Write the value of each digit.
40,000
Step 3
7,000
900
3
Write the number in expanded form.
Write a 1 sign between the values of each digit.
Since the tens digit has a 0, you do not have to list the value.
40,000 1 7,000 1 900 1 3
Solution
The expanded form of 47,903 is 40,000 1 7,000 1 900 1 3.
2 COACHED EXAMPLE
A park had 85,012 visitors. Write 85,012 in word form.
Write the number in a place-value chart.
Ten Thousands
Thousands
Hundreds
Tens
Ones
Write the word name for the value of the digits before the comma.
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Write a comma after the word thousand.
Next, write the word name for the value of the digits after the comma.
Write the word name for the whole number.
The word form of 85,012 is
.
Lesson 10: Whole Numbers 97
3 LESSON PRACTICE
1
A movie theater sold 31,809 tickets. Read each statement about the
number of tickets. Select True or False.
A. The word form is thirty-one thousand, eighty-nine. ○ True
B. The value of the digit 3 is 30,000.
○ False
○ True ○ False
C. The expanded form is 30,000 1 1,000 1 800 1 9. ○ True ○ False
98
○ True ○ False
E. The tens place has a value of 0.
○ True ○ False
F. The value of the digit 9 is 90.
○ True ○ False
Draw a line from each place-value model to the number it represents.
A.
•
• 1,032
B.
•
• 1,230
C.
•
• 1,302
D.
•
• 1,320
Domain 2: Number and Operations in Base Ten
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2
D. The value of the digit 8 is 80.
3
An elephant has a mass of 6,145 kilograms. Write the number of
kilograms in word form. Explain how you wrote the number.
4
For each number, write an “X” to show the value of the digit 7.
Number of Letters
70,000
7,000
700
70
57,400
40,704
86,973
73,090
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91,740
5
A pet shelter received bags of dog food. It received four thousand,
eighty-eight bags. Select True or False for each statement.
A. The shelter received 4,088 bags.
○ True
○ False
B. The number of bags can be written as ○ True
4,000 1 800 1 8.
○ False
C. The value of both 8s in the number of ○ True
bags is the same.
○ False
D. The expanded form for the number of ○ True
bags has no hundreds.
○ False
Lesson 10: Whole Numbers 99
6
Complete the expanded form for each number.
Standard Form
Expanded Form
1 400 1
40,404
40,444
40,000 1
1
44,004
40,000 1
1
44,040
7
14
1 40
1
Felipe and Ava wrote the word form for the number 9,000 + 100 + 1.
Felipe
Ava
nine thousand, one hundred one
nine thousand, one hundred ten
Part A
Who wrote the number in correct word form?
Part B
Part C
What error did the other student make?
100 Domain 2: Number and Operations in Base Ten
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How do you know who wrote the correct word form?
8
A ballpark has 50,287 seats. Is the word form or expanded form correct?
Select Yes or No.
A. fifty thousand, two hundred eighty-seven ○ Yes ○ No
B. 50,000 1 2,000 1 80 1 7
○ Yes ○ No
C. fifty thousand, twenty-eight hundred seven ○ Yes ○ No
D. 50,000 1 200 1 80 1 7
9
○ Yes ○ No
Cody used models to represent the length of the Missouri River.
Write the length of the Missouri River in standard form.
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miles
10 Mr. Diaz drove his car a certain number of miles. Read the clues to find
how many miles he drove.
• There is a 2 in the hundreds place.
• The value of the digit in the ten thousands place is 20,000.
• The digit in the tens place has a value of 60.
• The digit 8 is used twice in the number.
It has a value of 8,000 and a value of 8.
Mr. Diaz drove
miles.
Lesson 10: Whole Numbers 101