Lesson 1

Relationships between Quantities

Let’s try to solve some new kinds of problems.

Problem 1

A sandwich store charges $20 to have 3 turkey subs delivered and $26 to have 4 delivered.

  1. Is the relationship between number of turkey subs delivered and amount charged proportional? Explain how you know.
  2. How much does the store charge for 1 additional turkey sub?
  3. Describe a rule for determining how much the store charges based on the number of turkey subs delivered.

Problem 2

Which question cannot be answered by the solution to the equation \(3x=27\)?


Elena read three times as many pages as Noah. She read 27 pages. How many pages did Noah read?


Lin has 27 stickers. She gives 3 stickers to each of her friends. With how many friends did Lin share her stickers?


Diego paid $27 to have 3 pizzas delivered and $35 to have 4 pizzas delivered. What is the price of one pizza?


The coach splits a team of 27 students into 3 groups to practice skills. How many students are in each group?

Problem 3

The area of the Mojave desert is 25,000 square miles. A scale drawing of the Mojave desert has an area of 10 square inches. What is the scale of the map?

(From Unit 2, Lesson 7.)

Problem 4

Each picture shows two polygons, one labeled Polygon A and one labeled Polygon B. Describe how to move Polygon A into the position of Polygon B using a transformation.

    Two quadrilaterals, polygon A and polygon B on a grid. Every point of polygon B is a reflection of polygon A.
    Two triangles, polygon A and polygon B on a grid. Every point of polygon B is a rotation of polygon A.
    Two figures A and B on a grid. Every point of figure B is 1 unit up and 3 units to the right of figure A.
(From Unit 1, Lesson 3.)