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Unit 02 · Fraction Operations and ModelsLesson

Day 018Equal Groups in Fraction Bars

LearnClassworkAnswer keyPDF packet ↗
Standards 6.NS.A.1
LEARNING TARGET

I can model fraction division as equal-sized groups.

01 · LEARN

Build the idea

A quotient asks how many groups of the divisor fit in the dividend. Rename both fractions with a common denominator, draw equal parts, and count groups. A partial group is a fraction of the divisor, not of the original whole.

WORKED EXAMPLE 1

Draw a bar partitioned into 10 equal parts. Shade 6 parts. Circle groups of 4 parts. Use the model to find 3/5 ÷ 2/5.

3/2

Each small part is 1/10; 6 shaded parts divided into groups of 4 gives 6/4 = 3/2 groups.

WORKED EXAMPLE 2

Draw a bar partitioned into 8 equal parts. Shade 7 parts. Circle groups of 1 parts. Use the model to find 7/8 ÷ 1/8. Explain the partial group.

7

Each small part is 1/8; 7 shaded parts divided into groups of 1 gives 7/1 = 7 groups.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Draw a bar partitioned into 6 equal parts. Shade 3 parts. Circle groups of 3 parts. Use the model to find 1/2 ÷ 1/2.

  2. Draw a bar partitioned into 8 equal parts. Shade 3 parts. Circle groups of 3 parts. Use the model to find 3/8 ÷ 3/8.

  3. Draw a bar partitioned into 12 equal parts. Shade 7 parts. Circle groups of 2 parts. Use the model to find 7/12 ÷ 1/6.

  4. Draw a bar partitioned into 10 equal parts. Shade 7 parts. Circle groups of 4 parts. Use the model to find 7/10 ÷ 2/5.

  5. Draw a bar partitioned into 10 equal parts. Shade 4 parts. Circle groups of 3 parts. Use the model to find 2/5 ÷ 3/10.

  6. Draw a bar partitioned into 10 equal parts. Shade 5 parts. Circle groups of 5 parts. Use the model to find 1/2 ÷ 1/2.

  7. Draw a bar partitioned into 10 equal parts. Shade 5 parts. Circle groups of 5 parts. Use the model to find 1/2 ÷ 1/2. Explain the partial group.

  8. Draw a bar partitioned into 10 equal parts. Shade 6 parts. Circle groups of 2 parts. Use the model to find 3/5 ÷ 1/5. Explain the partial group.

  9. Draw a bar partitioned into 8 equal parts. Shade 7 parts. Circle groups of 6 parts. Use the model to find 7/8 ÷ 3/4. Explain the partial group.

  10. Draw a bar partitioned into 12 equal parts. Shade 9 parts. Circle groups of 7 parts. Use the model to find 3/4 ÷ 7/12. Explain the partial group.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 1

    Each small part is 1/6; 3 shaded parts divided into groups of 3 gives 3/3 = 1 groups.

  2. 1

    Each small part is 1/8; 3 shaded parts divided into groups of 3 gives 3/3 = 1 groups.

  3. 7/2

    Each small part is 1/12; 7 shaded parts divided into groups of 2 gives 7/2 = 7/2 groups.

  4. 7/4

    Each small part is 1/10; 7 shaded parts divided into groups of 4 gives 7/4 = 7/4 groups.

  5. 4/3

    Each small part is 1/10; 4 shaded parts divided into groups of 3 gives 4/3 = 4/3 groups.

  6. 1

    Each small part is 1/10; 5 shaded parts divided into groups of 5 gives 5/5 = 1 groups.

  7. 1

    Each small part is 1/10; 5 shaded parts divided into groups of 5 gives 5/5 = 1 groups.

  8. 3

    Each small part is 1/10; 6 shaded parts divided into groups of 2 gives 6/2 = 3 groups.

  9. 7/6

    Each small part is 1/8; 7 shaded parts divided into groups of 6 gives 7/6 = 7/6 groups.

  10. 9/7

    Each small part is 1/12; 9 shaded parts divided into groups of 7 gives 9/7 = 9/7 groups.

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