# Lesson 6

Per Each

### Lesson Narrative

This lesson introduces students to the idea of unit price. Students use the word “per” to refer to the cost of one item or unit, as in “$6 per pound” or “$1.50 per avocado.” The phrase “at this rate” is used to indicate that the ratios of price to quantity are equivalent. (For example, “Pizza costs \$1.25 per slice. At this rate, how much for 6 slices?”) They find unit prices in different situations, and notice that unit prices are useful in computing prices for other amounts (MP7).

Students choose whether to draw double number lines or other representations to support their reasoning. They continue to use precision in stating the units that go with the numbers in a ratio in both verbal statements and diagrams (MP6).

Students also explore equivalent ratios using constant speed. They measure the time it takes them to travel a predetermined distance—first by moving slowly, then quickly—and use it to calculate and compare the speed they traveled in meters per second.

Here, double number lines are used to represent the association between distance and time, and to convey the idea of constant speed as a set of equivalent ratios (for example, 10 meters traveled in 20 seconds at a constant speed means that 0.5 meters is traveled in 1 second, and 5 meters is traveled in 10 seconds). Students come to understand that, like price, speed can be described using the terms per and at this rate.

The idea of a constant speed relating the quantities of distance and time is foundational for the later, more abstract idea of a constant rate, and is important in the development of students’ ability to reason abstractly about quantities (MP2).

Note that students are not expected to use or understand the term “unit rate” in this lesson.

### Learning Goals

Teacher Facing

• Calculate equivalent ratios between prices and quantities and present the solution method (using words and other representations).
• Calculate the distance an object travels in 1 unit of time and express it using a phrase like “meters per second” (orally and in writing).
• Calculate unit price and express it using the word “per” (orally and in writing).
• For an object moving at a constant speed, use a double number line diagram to represent equivalent ratios between the distance traveled and elapsed time.

### Student Facing

Let's use ratios to describe cost and speed.

### Required Preparation

Before class, set up 4 paths with a 1-meter warm-up zone and a 10-meter measuring zone.

### Student Facing

• I can choose and create diagrams to help me reason about constant speed.
• If I know the price of multiple things, I can find the price per thing.

Building On