Unit 2 Plan - Grade 5

Lesson 1

Share Sandwiches

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How Much? (1 problem)

Draw a diagram to show how much sandwich each person will get.

3 sandwiches are equally shared by 4 people.
Explain or show how you know that each person gets the same amount of sandwich.

Show Solution

Sample responses:
Sample responses:
- Each person gets one fourth of each sandwich.
- Each person gets one half plus one fourth of a sandwich.
- Each person gets $\frac{3}{4}$ of a sandwich.

Lesson 2

Share More Sandwiches

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How Much Sandwich? (1 problem)

4 sandwiches are equally shared by 5 students. How much sandwich does each student get? Explain or show your reasoning.
Write a division expression to represent the situation.

Show Solution

$\frac{4}{5}$ sandwich. Sample response: Student draws 4 shapes to represent the sandwiches and partitions them. $4\div5=\frac{4}{5}$
$4\div5$

Lesson 3

Interpret Equations

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Share Water (1 problem)

3 liters of water are shared equally by 5 people. How much water does each person get? Write a division equation to represent the situation. Draw a diagram if it is helpful.

Show Solution

$\frac{3}{5}$ liters of water, $3 \div 5 = \frac{3}{5}$ . Sample response:

Lesson 4

Division Situations

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How Much Milk? (1 problem)

Complete the table below.

Equation	Situation
	5 children share 4 cups of milk so each child gets the same amount of milk. How many cups of milk will each child get?
Diagram

Show Solution

$4 \div 5 = \frac {4}{5}$

Lesson 5

Relate Division and Fractions

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Explain It. (1 problem)

Explain why $8 \div 5 = \frac{8}{5}$ .

Show Solution

Sample response: I can divide 8 into 5 equal parts. This is

8 \div 5

. Each of the parts is

\frac{1}{5}

of one whole and since there are 8 wholes,

8\div5=\frac{8}{5}

.

Section A Check

Section A Checkpoint

Problem 1

Five friends equally share 3 liters of water. How many liters of water does each person get? Explain or show your reasoning.

Show Solution

$\frac{3}{5}$ liter. Sample response:

<p>3 diagrams of equal length. 5 parts. 1 part shaded. Total length, 1 liter.</p>

Problem 2

Write a division equation that matches the diagram. Explain or show your reasoning.

4 diagrams of equal length. 3 equal parts. 1 part shaded. Total length, 1.

Show Solution

4 \div 3 = \frac{4}{3}

. Sample response: There are 4 wholes and they are divided into three equal shares. One of those shares is shaded and that’s

\frac{4}{3}

total shaded.

Problem 3

Explain why $10 \div 4 = \frac{10}{4}$ .

Show Solution

Sample response: If I divide 10 things each into 4 equal shares and take one of each, it is $10 \div 4$ since there are 4 equal shares in 10. Since each share is $\frac{1}{4}$ and there are 10 of those shares, one for each thing, that’s also $\frac{10}{4}$ .

Lesson 6

Relate Division and Multiplication

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A Different Relay Race (1 problem)

Lin and Han ran a 5 mile relay race as a team. They each ran the same distance. Draw a diagram to represent the situation.
How far did each student run?

Show Solution

Sample response:
$2\frac{1}{2}$ miles or $\frac{5}{2}$ mile. Sample response: The diagram shows 2 whole miles and $\frac{1}{2}$ of another mile.

Lesson 7

Divide to Multiply Unit Fractions

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Another Race (1 problem)

Together, 6 children run a 5 mile relay race. They each run the same distance.

Select all the expressions that represent this situation.

$\frac{1}{6} \times 5$
$\frac{1}{5} \times 6$
$5 \div 6$
$\frac{5}{6}$

Show Solution

A, C, D

Lesson 8

Divide to Multiply Non-Unit Fractions

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Two Thirds (1 problem)

Find the value of each expression. Explain or show your reasoning.

$\frac{1}{3}\times 4$
$\frac{2}{3}\times 4$

Show Solution

$\frac{4}{3}$ (or equivalent). Sample response: $4\div3=\frac{4}{3}$
$\frac{8}{3}$ (or equivalent). Sample response: I doubled the answer to the first question.

Section B Check

Section B Checkpoint

Problem 1

3 diagrams of equal length. 5 equal parts. 1 part shaded. Total length, 1.

Explain how the diagram shows $3 \div 5$ .
Explain how the diagram shows $3 \times \frac{1}{5}$ .
What is the value of $3 \div 5$ ? Explain or show your reasoning.

Show Solution

Sample response: There are 3 whole rectangles and 1 out of 5 equal shares of the rectangles is shaded. So, that’s $3 \div 5$ .
Sample response: There are 3 shaded parts and each is $\frac{1}{5}$ of a whole rectangle. So, that's $3 \times \frac{1}{5}$ .
$\frac{3}{5}$ . Sample response: There are 3 shaded pieces and each is $\frac{1}{5}$ of a whole rectangle.

Problem 2

Explain or show how each expression represents the shaded parts of the diagram.

$2 \times (4 \div 3)$
$4 \times \frac{2}{3}$
$4 \times 2 \times \frac{1}{3}$

Show Solution

Sample responses:

Each rectangle is divided into 3 equal parts and 2 of them are shaded. So, that’s $2 \times (4 \div 3)$ .
There are 4 groups of $\frac{2}{3}$ of a rectangle. So, that’s $4 \times \frac{2}{3}$ .
There are 4 groups of 2 small parts and each one is $\frac{1}{3}$ of a rectangle. So, that’s $4 \times 2 \times \frac{1}{3}$ .

Lesson 9

Relate Area to Multiplication

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Fractional Pieces (1 problem)

Find the area of the shaded region. Explain or show your reasoning.

Area diagram, Length, 5. Width, 1 fourth.

Show Solution

$\frac{5}{4}$ or $1 \frac{1}{4}$ square units. Sample response: I counted the shaded pieces which are fourths. I figured out that I had enough to fill one unit square and $\frac{1}{4}$ of a second unit square.

Lesson 10

Fractional Side Lengths Less than 1

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A Fractional Side Length (1 problem)

Write a multiplication expression to represent the area of the shaded region.
Find the area of the shaded region.

Show Solution

$\frac{3}{4} \times 5$ or $5 \times \frac{3}{4}$
$\frac{15}{4}$ or $3 \frac{3}{4}$ square units

Lesson 11

Fractional Side Lengths Greater than 1

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Find the Area (1 problem)

Write a multiplication expression to represent the area of the shaded region.
What is the area of the shaded region?

Show Solution

$3 \times \frac{11}{3}$ or $\frac{11}{3} \times 3$ or $\frac{11 \times 3}{3}$ or $\frac{3 \times 11}{3}$
11 square units (or equivalent)

Lesson 12

Decompose Area

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Decompose Rectangles (1 problem)

Find the area of the shaded region.

Area diagram. Length, 3 and 1 fourth. Width, 4.

Show Solution

Sample responses:

$4 \times 3 \frac{1}{4}$ square units
13 square units

Lesson 13

Area and Properties of Operations

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Equivalent Expressions (1 problem)

Select all the expressions that represent the area of the shaded region.

Area diagram. Length, 3 and 2 fifths. Width, 2.

$(2 \times 3) + \left(2 \times \frac{2}{5}\right)$
$6\frac{2}{5}$
$2 \times \left(3 + \frac{2}{5}\right)$
$(2 \times 4) - \left(2 \times \frac{3}{5}\right)$
$(2 \times 3) + \frac{2}{5}$
$2 \times \frac{17}{5}$

Show Solution

A, C, D, F

Lesson 14

Area Situations

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Find the Values (1 problem)

Find the value of each product. Show your thinking. Organize it so it can be followed by others.

$\frac{5}{3} \times 15$
1 $\frac{3}{4} \times 8$
$\frac{10}{25} \times 10$

Show Solution

$\frac{75}{3}$ or 25 (or equivalent). Sample response: I multiplied 15 and 5 and have that many $\frac{1}{3}$ s.
14. Sample response: $8 \times 1 = 8$ and $\frac {3}{4} \times 8 = 6$ and $8 + 6 = 14$
$\frac{100}{25}$ or 4 (or equivalent). Sample response: I multiplied 10 and 10 and have that many $\frac{1}{25}$ s.

Lesson 15

Multiply More Fractions

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Mixed Number Multiplication (1 problem)

Find the value of each expression. Explain or show your reasoning.

$12 \times 9 \frac {2}{3}$
$3 \frac {5}{9} \times 18$

Show Solution

116. Sample response: $12 \times 9 + \left(12 \times \frac {2}{3}\right) = 108 + 8 = 116$
64. Sample response: $(3 \times 18) + \left(\frac {5}{9} \times 18\right) = 54 + 10 = 64$

Lesson 16

Estimate Products

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Estimate and Solve (1 problem)

Jada says the value of each product is about 20. For each problem, explain why Jada’s estimate is too high, just right, or too low.

$5\frac{5}{6} \times 4 = \underline{\hspace{0.7cm}}$

20 is…

too low

too high

about right
$3 \times 6\frac{5}{8} = \underline{\hspace{0.7cm}}$

20 is…

too low

too high

about right

Show Solution

Too low. Sample response: $5 \frac{5}{6}$ is very close to 6, and $6 \times 4 = 24$ . So, $5\frac{5}{6}\times 4 = 23 \frac{2}{6}$ .
About right. Sample response: $3 \times 6 = 18$ and $\frac{5}{8}$ is a little more than $\frac{1}{2}$ so it's a little more than $18 + \frac{3}{2}$ .

Lesson 17

Mosaic Pictures

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No cool-down

Section C Check

Section C Checkpoint

Problem 1

For each diagram, write an expression for the area of the shaded region. Then find the area.

Show Solution

Expression: $\frac{1}{3} \times 5$ or $5 \times \frac{1}{3}$ (or equivalent). Area: $\frac{5}{3}$ square units
Expression: $\frac{2}{4} \times 3$ or $\frac{1}{2} \times 3$ (or equivalent). Area: $\frac{6}{4}$ square units
Expression: $\frac{5}{3} \times 4$ (or equivalent). Area: $\frac{1}{3}$ square units

Problem 2

Clare made a flag that is 2 meters long and $\frac{3}{5}$ meter wide. What is the area of the flag? Explain or show your reasoning.

Show Solution

\frac{6}{5}

m. Sample response:

2 \times \frac{3}{5} = \frac{6}{5}

Problem 3

Find the value of each expression.

$\frac{1}{5} \times 10$
$5\frac{2}{3} \times 4$
$\frac{13}{4} \times 5$

Show Solution

$\frac{10}{5}$ or 2 (or equivalent)
$20 \frac{8}{3}$ or $\frac{68}{3}$ (or equivalent)
$\frac{65}{4}$ (or equivalent)

Unit 2 Fractions As Quotients And Fraction Multiplication — Unit Plan