Unit 6, Lesson 19
Compare to 1
Grade 5
Preparation
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 calculations, 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 fraction greater than 1, such as , can be written as ‘the whole part plus the fractional part,’ in our example, . So multiplying by a fraction greater than 1 increases any number by the part of the fraction greater than the whole. This means multiplying by increases any number by of that number. In the same way, a fraction less than 1, such as , can be written as 'the whole minus the difference between the whole and the fraction,' in our example, or . So multiplying by a fraction less than 1 decreases any number by the difference between the whole and the fraction. This means multiplying by decreases any number by of that number.
This lesson has a Student Section Summary.
- Engagement
- MLR8
- Justify (orally and in writing) why $A \times B > B$ if $A > 1$, and $A \times B < B$ if $A < 1$ when, $A$ and $B$ are fractions.
- Let’s explain what happens when we multiply a fraction by a fraction greater than 1, less than 1, or equal to 1.
Required Preparation
None
Teacher Reflection Questions
During the last two lessons, students have noticed and explained patterns and generalizations about multiplying by numbers greater than 1, less than 1, and equal to 1. What are some ways that you honored students’ language while strategically incorporating more precise academic language?