Math Coach Lesson index ↗
Unit 02 · Fraction Operations and ModelsLesson

Day 019Partial 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 4 equal parts. Shade 2 parts. Circle groups of 1 parts. Use the model to find 1/2 ÷ 1/4.

2

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

WORKED EXAMPLE 2

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

1

Each small part is 1/8; 7 shaded parts divided into groups of 7 gives 7/7 = 1 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 6 parts. Circle groups of 3 parts. Use the model to find 1 ÷ 1/2.

  2. Draw a bar partitioned into 10 equal parts. Shade 8 parts. Circle groups of 3 parts. Use the model to find 4/5 ÷ 3/10.

  3. Draw a bar partitioned into 10 equal parts. Shade 7 parts. Circle groups of 3 parts. Use the model to find 7/10 ÷ 3/10.

  4. Draw a bar partitioned into 8 equal parts. Shade 8 parts. Circle groups of 4 parts. Use the model to find 1 ÷ 1/2.

  5. Draw a bar partitioned into 8 equal parts. Shade 2 parts. Circle groups of 1 parts. Use the model to find 1/4 ÷ 1/8.

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

  7. 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. Explain the partial group.

  8. Draw a bar partitioned into 8 equal parts. Shade 2 parts. Circle groups of 2 parts. Use the model to find 1/4 ÷ 1/4. Explain the partial group.

  9. Draw a bar partitioned into 10 equal parts. Shade 4 parts. Circle groups of 2 parts. Use the model to find 2/5 ÷ 1/5. Explain the partial group.

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

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 2

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

  2. 8/3

    Each small part is 1/10; 8 shaded parts divided into groups of 3 gives 8/3 = 8/3 groups.

  3. 7/3

    Each small part is 1/10; 7 shaded parts divided into groups of 3 gives 7/3 = 7/3 groups.

  4. 2

    Each small part is 1/8; 8 shaded parts divided into groups of 4 gives 8/4 = 2 groups.

  5. 2

    Each small part is 1/8; 2 shaded parts divided into groups of 1 gives 2/1 = 2 groups.

  6. 3/2

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

  7. 1

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

  8. 1

    Each small part is 1/8; 2 shaded parts divided into groups of 2 gives 2/2 = 1 groups.

  9. 2

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

  10. 1

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

← Lesson indexBack to top ↑Day 020 →