Unit 5 Plan - Grade 3

Title	Assessment
Lesson 1 Name the Parts	Partition a Rectangle Partition the rectangle into eighths. Show Solution Any drawing that shows 8 equal parts is acceptable. Sample responses:
Lesson 2 Name Parts as Fractions	Label the Parts Label each part with the correct fraction. Partition and shade the rectangle to show $\frac{1}{4}$ . Show Solution Students label each part with $\frac{1}{8}$ . Any drawing that shows 4 equal parts, with 1 shaded part, is acceptable. Sample responses:
Lesson 3 Non-unit Fractions	Shaded Fraction The rectangle represents 1 whole. What fraction is shaded? Explain your reasoning. Show Solution $\frac{5}{6}$ . Sample response: The rectangle is split into 6 equal parts and 5 one-sixth parts are shaded.
Lesson 4 Build Fractions from Unit Fractions	Represent a Fraction This strip represents 1 whole. Partition the diagram and shade it to represent $\frac{6}{8}$ . Show Solution
Section A Check Section A Checkpoint	Problem 1 Select all diagrams that show $\frac{3}{4}$ of each whole is shaded. A. B. C. D. E. Show Solution A, E Problem 2 Shade $\frac{5}{6}$ of the rectangle. Show Solution Sample response:

Lesson 5 To the Number Line	Reflection Describe something you really understand well after today’s lesson, or describe something that was confusing or challenging. Show Solution Sample responses: I understand that fractions show up on the number line in between whole numbers. I am confused about where to label fractions on the number line.
Lesson 6 Locate Unit Fractions on the Number Line	Locate and Label Locate and label $\frac{1}{8}$ on the number line. Explain your reasoning. Show Solution Sample response: I know that 8 one-eighths are in 1, so I partitioned the number line from 0 to 1 into 8 equal parts and labeled the end of the first eighth.
Lesson 7 Non-unit Fractions on the Number Line	Where is $\frac{5}{3}$? Locate and label $\frac{2}{3}$ and $\frac{5}{3}$ on the number line. Explain your reasoning. Show Solution Sample response: I partitioned the number line into thirds, and then I counted 2 thirds and 5 thirds.
Lesson 8 Fractions and Whole Numbers	Where Is 1? Locate and label 1 on the number line. Explain your reasoning. Show Solution Sample response: I repeated the $\frac{1}{3}$ space 3 times since there are 3 one-thirds in 1.
Lesson 9 All Kinds of Numbers on the Number Line	Where Is 1 Now? Locate and label 1 on the number line. Explain your reasoning. Show Solution Sample response: I know there are 7 one-sixths in $\frac{7}{6}$ , so I split the space into 7 equal parts. I counted 6 of the parts to get to 1.
Section B Check Section B Checkpoint	Problem 1 What fraction is marked on the number line? Show Solution $\frac{1}{6}$ Problem 2 Locate and label $\frac{3}{4}$ and $\frac{5}{4}$ on the number line: Show Solution Problem 3 Locate and label the number 1 on the number line. Explain or show your reasoning. Show Solution Sample response: First I found $\frac{1}{4}$ , knowing that $\frac{3}{4}$ is three $\frac{1}{4}$ s, and then I kept going to get to $\frac{4}{4}$ or 1.

Lesson 10 Equivalent Fractions	Find Equivalent Fractions Each diagram represents 1. Select all the diagrams whose shaded parts represent equivalent fractions. Explain your reasoning. A B C D E Show Solution C and E. Sample responses: They show different fractions, but are the same size. They are partitioned into different numbers of parts, but the shaded portions are the same size.
Lesson 11 Generate Equivalent Fractions	Two Fraction Names for Each Diagram Write two fractions that the shaded part of this diagram represents. Show that the shaded part of this diagram represents both $\frac{5}{4}$ and $\frac{10}{8}$ . Show Solution $\frac{3}{6}, \frac{1}{2}$ Sample response: Each 1 whole is partitioned into fourths. Five fourths are shaded, which represents $\frac{5}{4}$ . Each fourth can be split into two equal parts, which makes 8 eighths in 1 whole. Ten eighths are shaded, so that’s $\frac{10}{8}$ .
Lesson 12 Equivalent Fractions on a Number Line	Equivalence on the Number Line Use the number line(s) to decide whether $\frac{3}{4}$ and $\frac{6}{8}$ are equivalent. Explain your reasoning. Show Solution $\frac{3}{4}$ and $\frac{6}{8}$ are equivalent because they are at the same point on the number line. Sample responses: or
Lesson 13 Whole Numbers and Fractions	Fraction to Whole Number and Whole Number to Fraction Is $\frac{18}{4}$ a whole number? Explain or show your reasoning. Write 2 as a fraction. Explain or show your reasoning. Show Solution No. Sample response: The fractions that are whole numbers have numbers in the numerator that count by 4, like $\frac{4}{4}$ , $\frac{8}{4}$ , $\frac{12}{4}$ , and 18 isn’t in the count. Sample response: $\frac{6}{3}$ . I know 3 thirds make 1, so 6 thirds make 2.
Section C Check Section C Checkpoint	Problem 1 Select all the true equations. A. $\frac{7}{8}=\frac{3}{4}$ B. $\frac{2}{6} = \frac{1}{3}$ C. $\frac{4}{8}=\frac{3}{6}$ D. $\frac{1}{6} = \frac{2}{8}$ E. $\frac{1}{2}=\frac{2}{3}$ Show Solution B, C Problem 2 Find a fraction that is equivalent to $\frac{4}{6}$ . Use the number lines if they are helpful. Show Solution Sample response: $\frac{2}{3}$ Problem 3 Circle the fraction that is equal to a whole number: $\quad \frac{1}{4} \quad \frac{3}{4} \quad \frac{11}{4} \quad \frac{12}{4}$ Write three different fractions that are equal to 2. Show Solution Students circle $\frac{12}{4}$ . Sample response: $\frac{4}{2}$ , $\frac{6}{3}$ , $\frac{8}{4}$

Lesson 14 How Do You Compare Fractions?	How Would You Decide? How would you decide if $\frac{6}{4}$ is equivalent to $\frac{3}{4}$ ? Explain or show your reasoning. Show Solution Sample responses: I know $\frac{6}{4}$ is not equivalent to $\frac{3}{4}$ because they are not at the same location on the number line. I know $\frac{6}{4}$ is not equivalent to $\frac{3}{4}$ because they aren't the same size. I know $\frac{6}{4}$ is not equivalent to $\frac{3}{4}$ because it means 6 fourths, which is more than 3 fourths.
Lesson 15 Compare Fractions with the Same Denominator	Same Denominator Which is the greater fraction: $\frac{7}{8}$ or $\frac{6}{8}$ ? Explain or show your reasoning. Use the symbol > or < to make the statement true. $\frac{7}{8} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{6}{8}$ Show Solution $\frac{7}{8}$ is greater. Sample response: 7 one-eighth parts are more than 6 one-eighth parts. >
Lesson 16 Compare Fractions with the Same Numerator	Same Numerator Use the symbol > or < to make the statement true. Explain or show your reasoning. $\frac{4}{3} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{4}{6}$ Show Solution >. Sample response: Thirds are larger than sixths, so 4 thirds is greater than 4 sixths.
Lesson 17 Compare Fractions	All Kinds of Comparisons Use the symbol >, <, or = to make each statement true. $\frac{4}{6} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{2}{6}$ $\frac{8}{8} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{4}{4}$ An ant crawled $\frac{3}{6}$ of the length of a bench. A spider crawled $\frac{3}{4}$ of the length of the same bench. Which animal crawled farther? Explain or show your reasoning. Write a statement, using the symbol >, <, or = to represent your answer. Show Solution > = The spider crawled farther. Sample response: Fourths are larger than sixths, so 3 fourths is greater than 3 sixths. $\frac{3}{4} > \frac{3}{6}$
Lesson 18 Plan a Fun Run	No cool-down
Section D Check Section D Checkpoint	Problem 1 Use $>$ , $<$ , or $=$ to make each statement true. $\frac{1}{3}\, \underline{\hspace{1cm}} \,\frac{1}{2}$ $\frac{5}{8} \,\underline{\hspace{1cm}}\, \frac{4}{8}$ $\frac{2}{6}\, \underline{\hspace{1cm}}\, \frac{1}{3}$ $\frac{3}{2}\, \underline{\hspace{1cm}} \,\frac{3}{4}$ Show Solution $\frac{1}{3} < \frac{1}{2}$ $\frac{5}{8} > \frac{4}{8}$ $\frac{2}{6} = \frac{1}{3}$ $\frac{3}{2} > \frac{3}{4}$ Problem 2 Elena ate $\frac{1}{3}$ of a loaf of bread while Clare ate $\frac{1}{4}$ of the same loaf of bread. Clare says that she ate more of the bread because 4 is greater than 3. Do you agree with Clare? Explain or show your reasoning. Show Solution No. Sample response: Clare is not correct, Elena ate more of the bread. Thirds are bigger than fourths since the whole is split into fewer parts.

Lesson 1

Name the Parts

Partition a Rectangle

Partition the rectangle into eighths.

Show Solution

Any drawing that shows 8 equal parts is acceptable.

Sample responses:

Diagram. Rectangle partitioned into 8 equal parts.

Lesson 2

Name Parts as Fractions

Label the Parts

Label each part with the correct fraction.
Partition and shade the rectangle to show $\frac{1}{4}$ .

Show Solution

Students label each part with $\frac{1}{8}$ .
Any drawing that shows 4 equal parts, with 1 shaded part, is acceptable. Sample responses:

Lesson 3

Non-unit Fractions

Shaded Fraction

The rectangle represents 1 whole. What fraction is shaded? Explain your reasoning.

Diagram. Rectangle partitioned into 6 equal parts, 5 of them shaded.

Show Solution

\frac{5}{6}

. Sample response: The rectangle is split into 6 equal parts and 5 one-sixth parts are shaded.

Lesson 4

Build Fractions from Unit Fractions

Represent a Fraction

This strip represents 1 whole. Partition the diagram and shade it to represent $\frac{6}{8}$ .

Show Solution

Section A Check

Section A Checkpoint

Problem 1

Select all diagrams that show $\frac{3}{4}$ of each whole is shaded.

A.

<p>Diagram. One rectangle partitioned into 4 parts. 3 parts shaded. Total length, 1.</p>

B.

Diagram. Circle partitioned into 4 unequal parts, 3 of them shaded.

C.

Diagram. One rectangle partitioned into 2 parts. Both parts shaded. Total length, 1.

D.

Diagram. 2 rectangles partitioned into 2 parts. First one, half shaded. Second one, all shaded. Total length, 1.

E.

Diagram. Circle partitioned into 4 equal parts, 3 of them shaded.

Show Solution

A, E

Problem 2

Shade $\frac{5}{6}$ of the rectangle.

Show Solution

Sample response:

Lesson 5

To the Number Line

Reflection

Describe something you really understand well after today’s lesson, or describe something that was confusing or challenging.

Show Solution

Sample responses:

I understand that fractions show up on the number line in between whole numbers.
I am confused about where to label fractions on the number line.

Lesson 6

Locate Unit Fractions on the Number Line

Locate and Label

Locate and label $\frac{1}{8}$ on the number line. Explain your reasoning.

Number line. Evenly spaced tick marks labeled zero, one, and two.

Show Solution

Sample response: I know that 8 one-eighths are in 1, so I partitioned the number line from 0 to 1 into 8 equal parts and labeled the end of the first eighth.

Lesson 7

Non-unit Fractions on the Number Line

Where is $\frac{5}{3}$?

Locate and label $\frac{2}{3}$ and $\frac{5}{3}$ on the number line. Explain your reasoning.

Number line. 0 to 2 by ones. Evenly spaced tick marks. First tick mark, 0. Last tick mark, 2.

Show Solution

Sample response: I partitioned the number line into thirds, and then I counted 2 thirds and 5 thirds.

Lesson 8

Fractions and Whole Numbers

Where Is 1?

Locate and label 1 on the number line. Explain your reasoning.

Number line. Two tick marks, 0 and one third.

Show Solution

Sample response: I repeated the $\frac{1}{3}$ space 3 times since there are 3 one-thirds in 1.

Lesson 9

All Kinds of Numbers on the Number Line

Where Is 1 Now?

Locate and label 1 on the number line. Explain your reasoning.

Number line. One tick mark labeled 0, one labeled seven sixths.

Show Solution

Sample response: I know there are 7 one-sixths in

\frac{7}{6}

, so I split the space into 7 equal parts. I counted 6 of the parts to get to 1.

Section B Check

Section B Checkpoint

Problem 1

What fraction is marked on the number line?

<p>Number line. 0 to 1. Evenly spaced tick marks. First tick mark, 0. Second tick mark has a point plotted. 4 unlabeled tick marks. Last tick mark, 1.</p>

Show Solution

$\frac{1}{6}$

Problem 2

Locate and label $\frac{3}{4}$ and $\frac{5}{4}$ on the number line:

Number line. Evenly spaced tick marks labeled 0, 1, and 2.

Show Solution

Problem 3

Locate and label the number 1 on the number line. Explain or show your reasoning.

Number line. Two tick marks labeled 0 and 3 fourths.

Show Solution

Sample response:

First I found

\frac{1}{4}

, knowing that

\frac{3}{4}

is three

\frac{1}{4}

s, and then I kept going to get to

\frac{4}{4}

or 1.

Lesson 10

Equivalent Fractions

Find Equivalent Fractions

Each diagram represents 1.

Select all the diagrams whose shaded parts represent equivalent fractions. Explain your reasoning.

Diagram. Rectangle partitioned into 4 equal parts, 3 parts shaded. — A

Diagram. Rectangle partitioned into 2 parts, 1 part shaded. — B

Diagram. Rectangle partitioned into 3 equal parts, 2 parts shaded. — C

Diagram. Rectangle partitioned into 4 equal parts, 1 part shaded. — D

Diagram. Rectangle partitioned into 6 equal parts, 4 of them shaded. — E

Show Solution

C and E. Sample responses: They show different fractions, but are the same size. They are partitioned into different numbers of parts, but the shaded portions are the same size.

Lesson 11

Generate Equivalent Fractions

Two Fraction Names for Each Diagram

Write two fractions that the shaded part of this diagram represents.
Show that the shaded part of this diagram represents both $\frac{5}{4}$ and $\frac{10}{8}$ .

Show Solution

$\frac{3}{6}, \frac{1}{2}$
Sample response: Each 1 whole is partitioned into fourths. Five fourths are shaded, which represents $\frac{5}{4}$ . Each fourth can be split into two equal parts, which makes 8 eighths in 1 whole. Ten eighths are shaded, so that’s $\frac{10}{8}$ .

Lesson 12

Equivalent Fractions on a Number Line

Equivalence on the Number Line

Use the number line(s) to decide whether $\frac{3}{4}$ and $\frac{6}{8}$ are equivalent. Explain your reasoning.

Number line. Tick marks labeled 0 and 1.

Show Solution

\frac{3}{4}

and

\frac{6}{8}

are equivalent because they are at the same point on the number line. Sample responses:

or

Lesson 13

Whole Numbers and Fractions

Fraction to Whole Number and Whole Number to Fraction

Is $\frac{18}{4}$ a whole number? Explain or show your reasoning.
Write 2 as a fraction. Explain or show your reasoning.

Show Solution

No. Sample response: The fractions that are whole numbers have numbers in the numerator that count by 4, like $\frac{4}{4}$ , $\frac{8}{4}$ , $\frac{12}{4}$ , and 18 isn’t in the count.
Sample response: $\frac{6}{3}$ . I know 3 thirds make 1, so 6 thirds make 2.

Section C Check

Section C Checkpoint

Problem 1

Select all the true equations.

A.

\frac{7}{8}=\frac{3}{4}

B.

\frac{2}{6} = \frac{1}{3}

C.

\frac{4}{8}=\frac{3}{6}

D.

\frac{1}{6} = \frac{2}{8}

E.

\frac{1}{2}=\frac{2}{3}

Show Solution

B, C

Problem 2

Find a fraction that is equivalent to $\frac{4}{6}$ . Use the number lines if they are helpful.

Show Solution

Sample response:

$\frac{2}{3}$

Problem 3

Circle the fraction that is equal to a whole number: $\quad \frac{1}{4} \quad \frac{3}{4} \quad \frac{11}{4} \quad \frac{12}{4}$
Write three different fractions that are equal to 2.

Show Solution

Students circle $\frac{12}{4}$ .
Sample response: $\frac{4}{2}$ , $\frac{6}{3}$ , $\frac{8}{4}$

Lesson 14

How Do You Compare Fractions?

How Would You Decide?

How would you decide if $\frac{6}{4}$ is equivalent to $\frac{3}{4}$ ? Explain or show your reasoning.

Show Solution

Sample responses:

I know $\frac{6}{4}$ is not equivalent to $\frac{3}{4}$ because they are not at the same location on the number line.
I know $\frac{6}{4}$ is not equivalent to $\frac{3}{4}$ because they aren't the same size.
I know $\frac{6}{4}$ is not equivalent to $\frac{3}{4}$ because it means 6 fourths, which is more than 3 fourths.

Lesson 15

Compare Fractions with the Same Denominator

Same Denominator

Which is the greater fraction: $\frac{7}{8}$ or $\frac{6}{8}$ ? Explain or show your reasoning.
Use the symbol > or < to make the statement true.

$\frac{7}{8} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{6}{8}$

Show Solution

$\frac{7}{8}$ is greater. Sample response: 7 one-eighth parts are more than 6 one-eighth parts.
>

Lesson 16

Compare Fractions with the Same Numerator

Same Numerator

Use the symbol > or < to make the statement true. Explain or show your reasoning.

$\frac{4}{3} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{4}{6}$

Show Solution

>. Sample response: Thirds are larger than sixths, so 4 thirds is greater than 4 sixths.

Lesson 17

Compare Fractions

All Kinds of Comparisons

Use the symbol >, <, or = to make each statement true.
1. $\frac{4}{6} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{2}{6}$
2. $\frac{8}{8} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{4}{4}$
An ant crawled $\frac{3}{6}$ of the length of a bench. A spider crawled $\frac{3}{4}$ of the length of the same bench.
1. Which animal crawled farther? Explain or show your reasoning.
2. Write a statement, using the symbol >, <, or = to represent your answer.

Show Solution

1. >
2. =
1. The spider crawled farther. Sample response: Fourths are larger than sixths, so 3 fourths is greater than 3 sixths.
2. $\frac{3}{4} > \frac{3}{6}$

Lesson 18

Plan a Fun Run

No cool-down

Section D Check

Section D Checkpoint

Problem 1

Use $>$ , $<$ , or $=$ to make each statement true.

$\frac{1}{3}\, \underline{\hspace{1cm}} \,\frac{1}{2}$
$\frac{5}{8} \,\underline{\hspace{1cm}}\, \frac{4}{8}$
$\frac{2}{6}\, \underline{\hspace{1cm}}\, \frac{1}{3}$
$\frac{3}{2}\, \underline{\hspace{1cm}} \,\frac{3}{4}$

Show Solution

$\frac{1}{3} < \frac{1}{2}$
$\frac{5}{8} > \frac{4}{8}$
$\frac{2}{6} = \frac{1}{3}$
$\frac{3}{2} > \frac{3}{4}$

Problem 2

Elena ate $\frac{1}{3}$ of a loaf of bread while Clare ate $\frac{1}{4}$ of the same loaf of bread. Clare says that she ate more of the bread because 4 is greater than 3.

Do you agree with Clare? Explain or show your reasoning.

Show Solution

No. Sample response: Clare is not correct, Elena ate more of the bread. Thirds are bigger than fourths since the whole is split into fewer parts.

Unit 5 Fractions As Numbers — Unit Plan