®
to the
COMMON CORE STATE STANDARDS
5
Mathematics
TABLE OF CONTENTS
Introduction .......................................................................... 7
Test-Taking Tips ..................................................................... 8
Common Core
State Standards
Unit 1: Operations and Algebraic Thinking ....................... 9
Lesson 1
Write and Interpret Numerical Expressions .............. 10
5.OA.2
Lesson 2
Using the Order of Operations ................................ 13
5.OA.1
Lesson 3
Using Rules to Create Numerical Patterns .............. 16
5.OA.3
Unit 1 Practice Test ............................................................. 19
Unit 2: Number and Operations in
Base Ten: Decimals ............................................... 23
Lesson 4
Multiplying by Multiples of 10, 100, 1000 ................ 24
5.NBT.1, 5.NBT.2
Lesson 5
Multiplying Whole Numbers.................................... 27
5.NBT.5
Lesson 6
Dividing Whole Numbers ....................................... 33
5.NBT.6
Lesson 7
Writing Quotients as Equations .............................. 39
5.NBT.6
Lesson 8
Reading and Writing Decimals ............................... 43
5.NBT.3
Lesson 9
Comparing and Ordering Decimals ......................... 48
5.NBT.3
Lesson 10 Rounding Decimals ............................................... 53
5.NBT.4
Lesson 11 Adding Decimals ................................................... 56
5.NBT.7
Lesson 12 Subtracting Decimals ............................................ 61
5.NBT.7
Lesson 13 Multiplying Decimals.............................................. 66
5.NBT.1, 5.NBT.2,
Lesson 14 Dividing Decimals ................................................. 71
5.NBT.7
Unit 2 Practice Test ............................................................. 76
Unit 3: Number and Operations – Fractions..................... 83
Lesson 15 Equivalent Fractions .............................................. 84
5.NF.1
Lesson 16 Mixed Numbers and Improper Fractions.................. 88
5.NF.1
Lesson 17 Adding Fractions and Mixed Numbers .................... 92
5.NF.1, 5.NF.2
4
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5.NBT.7
Table of Contents
Common Core
State Standards
Lesson 18 Subtracting Fractions and Mixed Numbers .............. 98
5.NF.1, 5.NF.2
Lesson 19 Multiplying Fractions and Mixed Numbers ............. 104
5.NF.4, 5.NF.5, 5.NF.6
Lesson 20 Dividing Fractions ............................................... 110
5.NF.3, 5.NF.7
Unit 3 Practice Test ........................................................... 116
Unit 4: Measurement and Data ........................................ 123
Lesson 21 Converting Customary Units ................................ 124
5.MD.1
Lesson 22 Converting Metric Units ....................................... 128
5.MD.1
Lesson 23 Line Plots ........................................................... 132
5.MD.2
Lesson 24 Understanding Volume ........................................ 136
5.MD.3, 5.MD.4
Lesson 25 Finding Volume ................................................... 140
5.MD.5
Unit 4 Practice Test ........................................................... 145
Unit 5: Geometry................................................................ 151
Lesson 26 Coordinate System.............................................. 152
5.G.1 , 5.G.2 , 5.OA.3
Lesson 27 Two-Dimensional Figures .................................... 157
5.G.3, 5.G.4
Lesson 28 Triangles ............................................................ 162
5.G.3, 5.G.4
Lesson 29 Quadrilaterals ..................................................... 166
5.G.3, 5.G.4
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Unit 5 Practice Test ........................................................... 170
Math Tools ......................................................................... 177
Unit 3
Standards: A1, B2, C3
To the Teacher:
Standards Name numbers are listed for each lesson in the table of
contents. The numbers in the shaded gray bar that runs across the
tops of the pages in the workbook indicate the Standards Name for a
given page (see example to the left).
100
5
Unit 1 – Operations and Algebraic Thinking
CCSS: 5.OA.2
Lesson 1: Write and Interpret Numerical
Expressions
Write Numerical Expressions
A numerical expression combines numbers and operations. You can use numerical
expressions to show calculations with numbers. When you write numerical expressions,
it is important to match a word or phrase with its corresponding operation.
To translate a phrase into a numerical expression, you need to identify the “main”
operation or operations—addition, subtraction, multiplication, or division. Here are the
four basic operations and some related words or phrases for each.
Addition: add, sum, more, more than, plus, increased by, gain
Subtraction: subtract, difference, less, less than, minus, decreased by, loss
Multiplication: multiply, product, multiplied by, times, double, triple
Division: divide, quotient, divided by, ratio, half, third, fourth, into, equal groups
Example
Write the following phrases as numerical expressions.
Phrase
2 more than 9
the product of 8 and 5
3 less than 7
12 divided by 3
Operation
“more than” means add
“product” means multiply
“less than” means subtract
“divided by” means divide
Numerical expression
2⫹9
8⫻5
7⫺3
12 ⫼ 3
A numerical expression may include more than one operation.
Example
Write the following phrase as a numerical expression.
Subtract 4 from 9, then multiply by 5.
First, write an expression for “subtract 4 from 9”: 9 ⫺ 4
Next, multiply the first expression by 5. Use parentheses around the first
expression: 5 ⫻ (9 ⫺ 4)
A numerical expression for “Subtract 4 from 9; then multiply by 5” is 5 ⫻ (9 ⫺ 4).
10
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TIP: Order is important in subtraction and division. The numerical expression for
3 less than 7 is 7 ⫺ 3. The numerical expression for 7 less 3 is also 7 ⫺ 3.
Lesson 1: Write and Interpret Numerical Expressions
CCSS: 5.OA.2
Interpret Numerical Expressions
You can interpret a numerical expression to understand what it means.
Example
Interpret the following numerical expression.
6 ⫻ (2500 ⫹ 340)
The parentheses in the expression mean that you must first add 2500 and 340.
Then multiply the sum by 6.
The numerical expression 6 ⫻ (2500 ⫹ 340) means 6 times the sum of
2500 and 340.
Practice
Directions: For questions 1 through 12, write each phrase as a numerical expression.
1. the total of 6 and 7
9. add 7 and 5, then multiply
by 3
2. 15 minus 8
3. the sum of 4 and 12
10. subtract 6 from 9, then multiply
by 4
4. the product of 5 and 3
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5. 20 less 6
11. add 8 plus 2, then multiply by 5
6. 9 times 2
7. 40 divided by 8
12. decrease 7 by 3, then multiply
by 2
8. 6 less than 12
11
Unit 1 – Operations and Algebraic Thinking
CCSS: 5.OA.2
13. Which numerical expression means
9 less 3?
16. Which numerical expression means
21 divided by 7?
A. 9 ⫹ 3
C. 3 ⫺ 9
A. 21 ⫹ 7
C. 21 ⫻ 7
B. 9 ⫺ 3
D. 9 ⫼ 3
B. 21 ⫺ 7
D. 21 ⫼ 7
14. Which numerical expression means
8 more than 4?
17. Which numerical expression means
add 3 and 2, then multiply by 4?
A. 8 ⫹ 4
C. 8 ⫻ 4
A. 4 ⫻ (3 ⫹ 2)
C. 4 ⫹ (3 ⫻ 2)
B. 8 ⫺ 4
D. 8 ⫼ 4
B. 4 ⫻ (3 ⫺ 2)
D. 4 ⫺ (3 ⫻ 2)
15. Which numerical expression means
the product of 6 and 5?
A. 6 ⫹ 5
C. 6 ⫻ 5
B. 6 ⫺ 5
D. 6 ⫼ 5
18. Which phrase is the same as the
following numerical expression?
3 ⫻ (10 ⫺ 2)
A. 3 more than 10 minus 2
B. 3 times 10 plus 2
C. 3 times 10 minus 2
D. 3 less than 10 minus 2
Directions: For questions 19 through 22, write a numerical expression for each phrase.
19. 5 times the sum of 17 and 24
21. twice the difference of 40 minus 15
22. 4 more than 3 less than 6
12
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20. 8 times the total of 35 and 21