Lesson 19
Compare to 1
Lesson Narrative
In previous lessons, students have compared the size of a product to the size of one factor by reasoning about the size of the other factor. They have done this using calculation, area diagrams, and number line diagrams. The goal of this lesson is to use the distributive property to explain why the comparisons work in all cases without calculating. The key observation is that a number greater than 1, such as \(\frac{5}{4}\), can be written as \(1 + \frac{1}{4}\) so multiplying by \(\frac{5}{4}\) increases any number by \(\frac{1}{4}\) of that number. In the same way multiplying by \(\frac{3}{4}\) or \(1 - \frac{1}{4}\) decreases any number by \(\frac{1}{4}\) of that number.
- Engagement
- MLR8
Activity 1: Compare Fraction Products on the Number Line
Learning Goals
Teacher Facing
- Explain what happens to a given fraction when multiplied by a fraction greater than or less than 1.
Student Facing
- Let’s explain what happens when we multiply a fraction by a fraction greater than, less than, or equal to 1.
Required Preparation
CCSS Standards
Lesson Timeline
| Warm-up | 10 min |
| Activity 1 | 15 min |
| Activity 2 | 20 min |
| Lesson Synthesis | 10 min |
| Cool-down | 5 min |
Teacher Reflection Questions
Suggested Centers
- Rectangle Rumble (3–5), Stage 5: Fraction Factors (Addressing)
- Rolling for Fractions (3–5), Stage 4: Multiply Fractions (Supporting)