Lesson 14

Solving Problems with Rational Numbers

Lesson Narrative

In this lesson students put together what they have learned about rational number arithmetic and the interpretation of negative quantities, such as negative time or negative rates of change. They solve problems with rational numbers in the context of a negative flow rate from a tank and negative charges on an electricity bill or a bank account. The problems in this section are designed so that it is natural to solve them by filling in tables or making numerical calculations. In the next lesson, students will move towards solving algebraic equations.

As students reason about the meaning of negative quantities, they engage in MP2.

Learning Goals

Teacher Facing

• Apply operations with rational numbers to solve problems involving repeated gains or losses, and present (orally, in writing, and using other representations) the solution method.

Student Facing

Let’s use all four operations with signed numbers to solve problems.

Student Facing

• I can represent situations with expressions that include rational numbers.
• I can solve problems using the four operations with rational numbers.

Building On

Building Towards

Glossary Entries

• rational number

A rational number is a fraction or the opposite of a fraction.

For example, 8 and -8 are rational numbers because they can be written as $$\frac81$$ and $$\text-\frac81$$.

Also, 0.75 and -0.75 are rational numbers because they can be written as $$\frac{75}{100}$$ and $$\text-\frac{75}{100}$$.