LESSON PLAN

Improper Fractions and Mixed Numbers

Apothem Team

Grade 6 · Number

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Formalize

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Show 7 fraction thirds. Ask: How many whole units? How many thirds left over? Guide them to see 2⅓.

Explore

Students build improper fractions with manipulatives, then record them as mixed numbers. Reverse: Give a mixed number, build it, then write as an improper fraction.

Formalize

Record the two conversion algorithms on the board:

Improper → Mixed: Divide numerator by denominator. Quotient = whole, remainder = new numerator. Mixed → Improper: (whole × denominator) + numerator, over the same denominator.

Connect: 7 ÷ 3 = 2 R1, so 7/3 = 2⅓. Reverse: 2⅓ = (2×3+1)/3 = 7/3. Both forms work; pick the most useful.

Practice

Conversion practice set. Exit ticket: Convert one improper to mixed and one mixed to improper.

Exit ticket

Conversion practice set. Exit ticket: Convert one improper to mixed and one mixed to improper.

TIP Use visual models heavily. Fraction circles and number lines make the conversion concrete.

WORKED EXAMPLES

Convert 11/4 to a mixed number.

11 ÷ 4 = 2 R3, so 11/4 = 2¾.

Convert 3⅖ to an improper fraction.

(3 × 5) + 2 = 17, so 3⅖ = 17/5.

MATERIALS

•Fraction circles or strips

•Number lines

•Manipulatives

•Whiteboards

WATCH FOR

!Forgetting to include the remainder as the new numerator when converting.

!Reversing the steps in the conversion algorithm.

!Thinking improper fractions and mixed numbers represent different quantities.