Composing/Decomposing Mixed Numbers and Improper Fractions

Learning objective:

Students will be able to represent and decompose fractions, including improper fractions, as sums of fractions with the same denominator, using multiple methods such as concrete, pictorial, and symbolic representations. 4.3A/B

K.6(A) identify two‐dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles

TEKS 4.3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and
recording results with symbolic representations (S)

Ways to Express Fractions

Fraction

Improper Fraction

Mixed Number

7

Fractions

Image created by HISD Curriculum using Google Docs

Image created by HISD Curriculum using Google Docs

Image created by HISD Curriculum using Google Docs

3

4

7

4

1

3

4

Fraction

Numerator

Denominator

Unit Fraction

6

Vocabulary Lesson

Image created by HISD Curriculum using Google Docs

Image created by HISD Curriculum using Google Docs

Image created by HISD Curriculum using Google Docs

Image created by HISD Curriculum using Google Docs

3

4

3

4

3

4

1

4

Open Ended

What is an improper fraction?

Multiple Select

Select all the improper fractions.

• 
  

  $$\frac{3}{4}$$
  

• $$\frac{18}{9}$$

• $$\frac{7}{7}$$

• $$\frac{9}{10}$$

• $$\frac{109}{100}$$

Open Ended

What is a mixed number?

Multiple Select

Select all the mixed numbers.

• 
  

  $$8\ \frac{1}{2}$$
  

• $$\frac{43}{40}$$

• $$6\ \frac{2}{5}$$

• $$12\ \frac{4}{7}$$

• $$\frac{12}{10}$$

10

Let’s represent.

10

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Fill in the Blanks

What is the denominator for this mixed number/improper fraction?

12

The model is shaded to represent a mixed number with a value greater than 1 whole.

12

Which equation shows two different ways to represent this mixed number as a
sum?

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• Label your model

• Label the answer choices

• Eliminate

• Choose

13

White Board Work

13

The blank model shown can be shaded to represent .

Write at least 4 expressions to represent 7/10 as a sum of fractions.

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7

10

15

15

The blank model shown can be shaded to represent .

Which expression does NOT show a way to represent as a sum of
fractions?

Image by HISD Curriculum using Google Slides

7

10

7

10

Multiple Choice

Which expression does NOT show a way to represent 7/10  as a sum of fractions?

Multiple Choice

Daphne made fruit punch. She mixed $$\frac{2}{3}$$ cup cherry juice, $$\frac{1}{3}$$ cup grape juice, $$\frac{2}{3}$$ cup ginger ale, and $$\frac{1}{3}$$ cup lime juice. Which fraction equation can be used to find the amount of punch Daphne made?

Multiple Choice

How would you write this model as an improper fraction?

• 3 1/5

• 16/5

• 2 6/5

• 15/5

Multiple Choice

How would you write this model as a mixed number?

• 3 1/5

• 2 1/5

• 16/5

• 15/5

Let's learn ways to convert (change) from one to another using math!

Multiple Choice

Write 15/4 as a mixed number.

• 3 3/4

• 3 1/4

• 4 1/4

• 4 1/5

Multiple Choice

Write 8/3 as a mixed number.

• 6 1/3

• 2 1/3

• 2 2/3

• 3 2/3

Multiple Choice

Write 34/8 as a mixed number.

• 4 2/8

• 4 1/8

• 3 2/8

• 2 4/8

Mixed Numbers to Improper Fractions

MAD

Multiply the Denominator and the Whole Number

Add the Numerator

Denominator stays the same

Fill in the Blanks

What improper fraction is equal to $2\frac{2}{5}$  ?

Fill in the Blanks

What improper fraction is equal to $1\frac{2}{3}$  ?

Fill in the Blanks

What improper fraction is equal to $5\frac{4}{6}$  ?

Fill in the Blanks

What improper fraction is equal to $2\frac{3}{8}$  ?