### Lesson plan

# When Having Like Denominators Isnâ€™t Enough!

#### Learning Objectives

Students will subtract mixed numbers where the larger fraction has a lesser numerator and a like denominator.

#### Introduction

*(5 minutes)*

- Write (or display) the following expressions on the board:
- 5 1/4 - 2 3/4
- 3 2/8 - 1 7/8
- 9 2/4 - 3 3/4

- Have students think, pair, and share their thoughts of a singular challenging trait these expressions have in common.
- As students share out their ideas, write down any related academic language, terms, or ideas.
- Point out how the
**Minuend**(the number being subtracted from) has a lesser numerator than the fraction in the**Subtrahend**(the number being subtracted).

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Explain that if we come across this situation, we know right away that we
*Must*Subtract from improper fractions. The subtrahend and minuend must be converted to improper fractions to solve the expression. - Demonstrate how to convert mixed numbers to improper fractions using the
*Mixed and Improper Fractions*Strategy listed in the Materials and Preparation section and solve 5 1/5 - 2 3/5. - Review converting improper fractions to mixed numbers and convert the improper differences for 5 1/4 - 2 3/4.

#### Guided practise

*(10 minutes)*

- Guide your students for each of the remaining opening exercises:
- 3 2/8 - 1 7/8
- 9 2/7 - 3 3/7

- Answer any clarifying questions.

#### Independent working time

*(15 minutes)*

- Issue the following exercises for students to solve on paper or in their maths journals:
- 4 1/5 - 1 3/5
- 3 2/5 - 2 1/5
- 6 3/4 - 2 4/4
- 4 1/6 - 1 5/6
- 7 2/7 - 2 5/7

#### Differentiation

**Support:**

- Use unifix cubes or linking blocks to demonstrate subtraction of mixed numbers.
- Demonstrate subtraction semi-concretely, using block notation to show mixed number to improper fractions conversions and subtraction.

**Enrichment:**

- Issue problems that have unlike mixed numbers and subtrahends with lesser numerators, (see resources for challenge problems.)

#### Technology Integration

- Slideshow applications are an excellent way to present exercises in succession text notation.

#### Assessment

*(5 minutes)*

- Show your students a subtraction expression with like mixed numbers and the minuend has a lesser numerator.
- Offer three possible conversions and have your students select the proper one by a show of fingers, â€œone, two, or three,â€ along with an explanation of their choice.

#### Review and closing

*(10 minutes)*

- Review the independent work time exercises by having students state their answers and explain their reasoning.
- Discuss the question, "What kind of clues do differences give us about minuends and subtrahends?â€™