Unit 6, Lesson 2
More than That, Less than That
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students see how to use the distributive property to write a compact expression for situations where one quantity is described in relation to another quantity in language such as “half as much again“ and “one third more than.“ If is half as much again as , then . Using the distributive property, this can be written as . Students apply this sort of reasoning to various situations and other fractional amounts of increase or decrease.
As students investigate multiple examples to recognize the relationship , they are making use of repeated reasoning (MP8). As students look for opportunities to use the distributive property to write equations in a simpler way, they are making use of structure (MP7).
The last activity is optional because it provides an opportunity for additional practice relating descriptions, tape diagrams, and equations.
If there is any additional time left in the class, it is recommended to do the optional activity so that students have an opportunity to write the equations themselves
- Apply the distributive property to generate algebraic expressions that represent a situation involving adding or subtracting a fraction of the initial value, and explain (orally) the reasoning.
- Coordinate tables, equations, tape diagrams, and verbal descriptions that represent a relationship involving adding or subtracting a fraction of the initial value.
- Generalize a process for finding the value that is “half as much again,” and justify (orally and in writing) why this can be abstracted as $\frac32 x$ or equivalent.
Let’s use fractions to describe increases and decreases.
Required Preparation
None