4 Mathematics Instruction
2015
Florida MAFS
Table of Contents
Unit 1: Number and Operations in Base Ten, Part 1 . . . . . . . 1
Lesson 1 Understand Place Value . . . . . . . . . . . . . . . . . . . . . . 2
MAFS
4.NBT.1.1, 4.NBT.1.2
Lesson 2 Compare Whole Numbers . . . . . . . . . . . . . . . . . . . . 84.NBT.1.2
Lesson 3 Add and Subtract Whole Numbers . . . . . . . . . . . . . . 164.NBT.2.4
Lesson 4 Round Whole Numbers . . . . . . . . . . . . . . . . . . . . . 264.NBT.1.3
Unit 1 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 34
Unit 2: Operations and Algebraic Thinking . . . . . . . . . . . . 37
Lesson 5 Understand Multiplication . . . . . . . . . . . . . . . . . . . 384.OA.1.1
Lesson 6 Multiplication and Division in Word Problems . . . . . . . 444.OA.1.2
Lesson 7 Multiples and Factors . . . . . . . . . . . . . . . . . . . . . . . 544.OA.2.4
Lesson 8AWorking with Equations . . . . . . . . . . . . . . . . . . . . . 66
4.OA.1.a, 4.OA.1.b
Lesson 8B Number and Shape Patterns . . . . . . . . . . . . . . . . . . 764.OA.3.5
Lesson 9 Model Multi-Step Problems . . . . . . . . . . . . . . . . . . . 864.OA.1.3
Lesson 10 Solve Multi-Step Problems . . . . . . . . . . . . . . . . . . . 944.OA.1.3
Unit 2 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . 102
Unit 3: Number and Operations in Base Ten, Part 2 . . . . . .105
Lesson 11 Multiply Whole Numbers . . . . . . . . . . . . . . . . . . . .1064.NBT.2.5
Lesson 12 Divide Whole Numbers . . . . . . . . . . . . . . . . . . . . . 1164.NBT.2.6
Unit 3 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . 126
Unit 4: Number and Operations—Fractions . . . . . . . . . . . 129
Lesson 13 Understand Equivalent Fractions . . . . . . . . . . . . . . .1304.NF.1.1
Lesson 14 Compare Fractions . . . . . . . . . . . . . . . . . . . . . . . .1364.NF.1.2
Lesson 15 Understand Fraction Addition and Subtraction . . . . . .146
4.NF.2.3a, 4.NF.2.3b
Lesson 16 Add and Subtract Fractions . . . . . . . . . . . . . . . . . . 152
4.NF.2.3a, 4.NF.2.3d
Lesson 17 Add and Subtract Mixed Numbers . . . . . . . . . . . . . .1624.NF.2.3b, 4.NF.2.3c,
4.NF.2.3d
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Table of Contents
Unit 4: Number and Operations—Fractions (continued)
Lesson 18 Understand Fraction Multiplication . . . . . . . . . . . . . 172
MAFS
4.NF.2.4a, 4.NF.2.4b
Lesson 19 Multiply Fractions . . . . . . . . . . . . . . . . . . . . . . . . .1784.NF.2.4c
Lesson 20 Fractions as Tenths and Hundredths . . . . . . . . . . . . .1864.NF.3.5
Lesson 21 Relate Decimals and Fractions . . . . . . . . . . . . . . . . .1944.NF.3.6
Lesson 22 Compare Decimals . . . . . . . . . . . . . . . . . . . . . . . 2044.NF.3.7
Unit 4 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 214
Unit 5: Measurement and Data . . . . . . . . . . . . . . . . . . . . . 217
Lesson 23 Convert Measurements . . . . . . . . . . . . . . . . . . . . .2184.MD.1.1
Lesson 24 Time and Money . . . . . . . . . . . . . . . . . . . . . . . . . 2284.MD.1.2
Lesson 25 Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2384.MD.1.2
Lesson 26 Perimeter and Area . . . . . . . . . . . . . . . . . . . . . . . .2464.MD.1.3
Lesson 27 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2564.MD.2.4
Lesson 28 Understand Angles . . . . . . . . . . . . . . . . . . . . . . . 268
4.MD.3.5a, 4.MD.3.5b
Lesson 29 Measure and Draw Angles . . . . . . . . . . . . . . . . . . . 2744.MD.3.6
Lesson 30 Add and Subtract With Angles . . . . . . . . . . . . . . . . 2844.MD.3.7
Unit 5 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 294
Unit 6: Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297
Lesson 31 Points, Lines, Rays, and Angles . . . . . . . . . . . . . . . . 2984.G.1.1
Lesson 32 Classify Two-Dimensional Figures . . . . . . . . . . . . . . .3104.G.1.2
Lesson 33 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3224.G.1.3
Unit 6 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 332
Florida MAFS Coverage by Ready Instruction, Grade 4 . . . . . . . 335
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Develop Skills and Strategies
Lesson 8A
Part 1: Introduction
MAFS
4.OA.1.a
4.OA.1.b
Working with Equations
You have used an equation to record the answer to a problem. Now you will
learn how to use equations in a different way. Take a look at this problem.
In this equation, n represents an unknown number. Find the value of n that
makes the equation true.
83 1 12 5 84 1 n
83 1 12
5
84 1 n
Explore It
Use the math you already know to solve the problem.
You can think of an equation as you would a balance scale.
Imagine there are 83 1 12 grapes in the left pan. There are 84 grapes in the right
pan and Jenn adds some more. Will the scale balance if Jenn adds 20 grapes to
the right pan? How do you know?
Jill thinks that n is 10. She replaces the n in the question with 10.
83 1 12 5 84 1 10. Is Jill’s equation true? How do you know?
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L8A: Working with Equations
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Part 1: Introduction
Lesson 8A
Find Out More
An equation compares two quantities. An equation can be true or false.
True Equations
False Equations
2 5 10 2 89 5 5 1 1
3 1 5 5 2 3 4
8 1 1 5 20 4 2
The left and right sides of a true equation must be equal. You can adjust the numbers
on both sides, or compensate, to find an unknown number. With this strategy, you
compare the left and right sides to find relationships.
11
83
1
12
84
5
1
n
21
84 is 1 more than 83, so the unknown number, n, must be 1 less than 12. The diagram
helps you see that n must be 11.
83 1 12 5 84 1 11
95 5 95
The equation is true.
Reflect
1 Make a diagram to compare the two sides of this equation.
42 1 58 5 n 1 60
2 What is the value of n? Explain how you know.
L8A: Working with Equations
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Part 2: Modeled Instruction
Lesson 8A
Read the problem below. Then explore different ways to compare the left and
right sides of an equation.
Decide if this equation is true or false without computing.
46 2 23 5 40 2 29
Model It
Make a diagram to compare the values on both sides of the equation.
27
0
10
20
2 10
30
26
46
40
50
2 9 2 10 2 10
Compare the starting points. 40 is 6 less than 46.
Break up the subtraction to make it easy to compare.
Is the equation true?
Model It
You can use a bar model to visualize the equation.
46
2 23
2 29
40
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L8A: Working with Equations
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Part 2: Guided Instruction
Lesson 8A
Connect It
Now you will further explore the problem from the previous page.
3 How are the two sides of a true equation related?
4 Explain how the first model shows the equation is true or false.
5 Explain how the second model shows the equation is true or false.
6 Simplify both sides of the equation and explain how this proves that the equation
is false.
Try It
Use what you just learned to solve these problems.
7 Are these equations true or false? Explain how you know.
a.58 1 30 5 88 2 5
b.21 1 38 5 35 1 24
L8A: Working with Equations
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Part 3: Modeled Instruction
Lesson 8A
Read the problem below. Then explore different ways to represent the
relationships.
Find the unknown number in this equation.
4 3 n 5 16 1 20
Picture It
The left side shows groups of 4. So, make a bar model to show groups of 4.
16
4
4
20
4
4
4
4
4
4
4
4 3 n 5 16 1 20
The number of groups of 4 on the left side of the equation is unknown.
But, the bar model helps you find the number of groups of 4.
Model It
You can also use factors. Break apart each number on the right to show factors
of 4.
43n5
16
1
20
4 3 n 5 (4 3 4) 1 (4 3 5)
Now you can use the distributive property on the right side to find the number of
groups of 4.
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L8A: Working with Equations
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Part 3: Guided Instruction
Lesson 8A
Connect It
Now you will solve the problem from the previous page using each of the
two models.
8 How many groups of 4 does the bar model show? How does this help you solve the problem?
9 Why do the two equations shown in the Model It section have the same value?
10 Complete this equation using the distributive property.
(4 3 4) 1 (4 3 5) 5 4 3 ( 1 )
How does the distributive property help you solve the problem?
Try It
Use what you just learned to solve these problems. Explain your strategies.
11 Decide if this equation is true or false without multiplying.
21 3 5 5 3 3 28
12 Find the unknown number n in this equation without dividing.
5 3 n 5 45 4 3
L8A: Working with Equations
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Part 4: Guided Practice
Lesson 8A
Study the model below. Then solve problems 13–15.
Student Model
Look for relationships
between the numbers in
the equation.
Decide if this equation is true or false without adding.
20 1 52 5 14 1 60
Look at how you could show your thinking with a diagram.
18
20
1
60
The equation is false.
13 Decide if this equation is true or false without multiplying.
Explain how you know.
32
3
6
5
8
3
3
42
72
14
added to compensate. The two sides are not equal.
4
How could you use a
bar model to solve this
problem?
5
6 is subtracted from 20 to get 14, but 6 is not
Solution:
How can you change
one number on the
right side to make the
equation true?
Pair/Share
52
26
Pair/Share
If you multiply 4 by 2,
what must you do to the
6 to compensate?
1
Solution: L8A: Working with Equations
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Part 4: Guided Practice
14 Use these four numbers to create a true addition equation.
29, 30, 61, 60
Explain how to use compensation to show your equation is true.
Show your work.
Lesson 8A
Include one of the
smaller numbers and
one of the larger
numbers on each side of
your equation.
Possible work:
Pair/Share
Solution: 15 Which statement is NOT true about the following equation?
8 1 57 5 n 1 60
Circle the letter of the correct answer.
How can you make a
true equation with these
numbers that shows
subtraction on both
sides of the equal sign?
Mark each answer
statement true or false.
Then pick the false one.
A The value of n must be less than 8.
B You can find n by adding 8 1 57.
C Both sides of the equation must equal 65.
D 57 is 3 less than 60, so 8 is 3 more than n.
Garam chose B as the correct answer. How did he get that
answer?
L8A: Working with Equations
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Pair/Share
Why can you eliminate
answer C?
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Part 5: MAFS Practice
Lesson 8A
Solve the problems.
1 Use this equation.
33 1 n 5 23 1 15
Circle the letter of the statement that completes this argument.
33 is 10 more than 23, so the number n must be .
A
10 more than 15
B
10 less than 15
C
equal to 23 1 15
D
equal to 33 1 15
2 Which side of a true equation is greater?
A
the left side
B
the right side
C
The two sides have the same value.
D
It depends on the equation.
3 Tell whether each equation is True or False.
74
a.3 3 2 5 6 2 1
True
False
b.14 1 6 5 15 1 7
True
False
c.12 3 5 5 30 1 30
True
False
d.52 2 20 5 30 1 2
True
False
L8A: Working with Equations
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Part 5: MAFS Practice
Lesson 8A
4 Decide if this equation is true or false without adding. Explain your reasoning.
51 1 17 5 50 1 16
Answer 5 Use compensation to find the unknown number n in this equation. Include a diagram
in your work. Explain your reasoning.
84 1 52 5 n 1 50
Show your work.
Answer 6 Use a factoring strategy to show this equation is true. Draw a diagram and explain
your reasoning.
77 3 5 5 7 3 55
Answer Self Check Go back and see what you can check off on the Self Check on page 37.
L8A: Working with Equations
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75
Develop Skills and Strategies
Lesson 8B
Part 1: Introduction
MAFS
4.OA.3.5
Number and Shape Patterns
You have used rules to describe patterns in numbers. In this lesson, you will
explore patterns further. Take a look at this problem.
What are the next two numbers in the pattern below?
5, 10, 15, 20, 25, , Explore It
Use the math you already know to solve the problem.
What are two ways to get from 5 to 10? How do you get from 10 to 15? What rule works for all of the numbers in the pattern? How can you find the number that comes after 25? What are the next two numbers in the pattern? 76
L8B: Number and Shape Patterns
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Part 1: Introduction
Lesson 8B
Find Out More
Is “add 5” the only relationship between the numbers in the pattern? Look at the
numbers, along with the model of the numbers, and try to find a different pattern.
5, 10, 15, 20, 25
If you look only at the ones digits, you see that they alternate between 5 and 0. From
the model, you can see that the number of dots alternates between odd and even.
The pattern below also follows the rule “add 5.”
22, 27, 32, 37, 42
Do the other relationships you found in the first pattern apply to this pattern, too?
The numbers in this pattern also alternate between odd and even, but the ones digits
alternate between 2 and 7 instead of between 5 and 0. So, sets of numbers can share
some patterns or rules, but have others that are different.
Reflect
1 Describe a pattern that you have noticed in the real world.
L8B: Number and Shape Patterns
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Part 2: Modeled Instruction
Lesson 8B
Read the problem below. Then explore different ways to understand it.
Orlando does push-ups every day. Each day, he wants to do 4 more push-ups
than the day before. Find out how many push-ups Orlando will do each day
this week if he does 20 on Monday.
Picture It
You can use a table to help understand the problem.
Day
Number of
Push-ups
Monday
Tuesday
Wednesday
Thursday
Friday
20
+4
+4
+4
+4
Model It
You can also use a number line to help understand the problem.
14
20
Monday
14
14
14
24
28
32
Tuesday Wednesday Thursday
36
Friday
Start at 20, the number of push-ups done on Monday, and then count 4 more for
each day.
78
L8B: Number and Shape Patterns
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Part 2: Guided Instruction
Lesson 8B
Connect It
Now you will explore the problem from the previous page further.
2 How many push-ups did Orlando do each day?
Monday: Tuesday: Wednesday: Thursday: Friday: 3 What is the rule for the pattern? 4 What does the pattern tell you about what happens when you start with an even
number and add an even number? 5 What other pattern(s) do you see in this set of numbers? 6 Explain how you found the additional pattern(s). Try It
Use what you just learned to solve these problems.
7 Lori scored 100 points in a game, then doubled her score each of the next 3 times
she played. What were Lori’s scores the first 4 times she played the game?
8 What is one additional pattern in Lori’s scores? L8B: Number and Shape Patterns
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Part 3: Modeled Instruction
Lesson 8B
Read the problem below. Then explore different ways to understand it.
Camille made a shape pattern with pattern blocks that goes back and forth
between a triangle and a square. Draw the pattern that Camille made.
Picture It
You can use models to help understand the problem.
Start by describing the pattern with words. Repeat the pattern at least 3 times.
triangle square triangle square triangle square
Now draw the shapes in the order you named them.
Model It
You can also use pattern blocks to help understand the problem.
Use pattern blocks in the shapes Camille used to create her pattern.
80
L8B: Number and Shape Patterns
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Part 3: Guided Instruction
Lesson 8B
Connect It
Now you will explore the shape pattern from the previous page further.
9 How many sides does a triangle have? 10 How many sides does a square have? 11 How could you describe the pattern using the number of sides the shapes have?
12 What would the 10th shape in the pattern be? 13 Explain how you can figure out what the 85th number in the pattern would be
without drawing all 85 shapes. Try It
Use what you just learned to solve this problem.
14 Describe any rules you see in the shape pattern below.
L8B: Number and Shape Patterns
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81
Part 4: Guided Practice
Lesson 8B
Study the model below. Then solve problems 15–17.
Student Model
The student used the rule
“add 2” because each
sandwich is $2 more
than the one before.
Hungry Heath’s sells four different sizes of sandwiches: small,
medium, large, and jumbo. The small sandwich costs $3. Each
size after that costs $2 more than the size before it. How much
does each sandwich cost?
Look at how you could show your work using a picture.
small
medium
12
jumbo
large
12
12
Pair/Share
Are there any other
patterns in this set of
numbers?
There is more than one
pattern in these shapes!
Solution: small: $3, medium: $5, large: $7, jumbo: $9
15 Draw the next two shapes in the shape pattern shown below.
Pair/Share
Are your shapes the
same as your partner’s?
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Solution: L8B: Number and Shape Patterns
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Part 4: Guided Practice
16 Eva drew a shape pattern that goes back and forth between
rectangles and ovals.
Lesson 8B
There are several ways to
describe a pattern!
What are two other patterns shown in this set of shapes?
Solution: Did you partner
describe the pattern in
the same way you did?
17 Lana wrote the pattern below.
Pair/Share
7, 14, 21, 28, 35
If the pattern continues, what would be the next number in the
pattern? Circle the letter of the correct answer.
You can check your
answer by working
backward!
A40
B42
C49
D70
Diego chose D as the correct answer. How did he get that answer?
Solution: L8B: Number and Shape Patterns
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Pair/Share
What would the next
3 numbers in the
pattern be?
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Part 5: MAFS Practice
Lesson 8B
Solve the problems.
1 What would be the 99th number in the pattern shown below?
10, 20, 30, 40, 50
A99
B900
C909
D990
2 Nia used pattern blocks to make the shape pattern shown below.
Which does NOT describe Nia’s shape pattern?
A
Each shape has one more side than the shape before it.
B
The shapes in the odd numbered spots have an odd number of sides.
C
The sides in a shape are all the same length.
D
The hexagon only appears in spots that are multiples of 4.
3 Choose Yes or No to tell whether the pattern follows the rule: 17.
84
a. 7, 17, 27, 37
Yes
No
b. 1, 7, 49, 343
Yes
No
c.
3, 10, 17, 24
Yes
No
d. 7, 77, 777, 7777
Yes
No
e. 7, 14, 21, 28
Yes
No
L8B: Number and Shape Patterns
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Part 5: MAFS Practice
Lesson 8B
4 Tell whether each sentence is True or False.
a. A number pattern that follows the rule “add 3”
True
False
the number 3.
True
False
The number pattern that follows the rule “start
at 20 and subtract 4” has only even numbers.
True
False
True
False
has both odd and even numbers.
b. A number pattern starts with 5 cannot include
c.
d. A number pattern that follows the rule “multiply
by 2” must have even numbers only.
5 Draw a shape pattern that follows the rule that the shapes go back and forth between
four sides and five sides.
Show your work.
Answer 6 Write a number pattern that follows the rule “subtract 6” and also has all odd
numbers.
Show your work.
Answer Self Check Go back and see what you can check off on the Self Check on page 37.
L8B: Number and Shape Patterns
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