## Math Mission

## Opening

Solve word problems involving fractions.

Solve word problems involving fractions.

Denzel wants to fence in a rectangular play area for his dog. The play area will extend the entire length of his backyard, which is $8\frac{1}{3}$ yards.

- If he wants his dog to have 50 square yards to play in, how wide does he need to make the play area?

Ask yourself:

- What is the formula for the area of a rectangle?
- What measurements does the problem provide?
- What is the unknown measurement?

Martin walks $\frac{4}{5}$ of a mile to school each day. The distance Emma walks to school is $\frac{5}{6}$ of the distance Martin walks.

- How far does Emma walk?

Ask yourself:

Can you use a number line to model the situation?

The male hippopotamus at the zoo weighs 2 tons. He weighs $1\frac{1}{2}\times f=2$ times as much as the female hippopotamus weighs.

- How much does the female hippopotamus weigh?

Does the female hippopotamus weigh more or less than the male?

Choose one of the problems you solved. Prepare a solution that you can share with your classmates. Include a drawing and an explanation of what you did to solve the problem.

Write two word problems.

- Write one word problem that uses multiplication and the numbers $4\frac{2}{3}$ and $\frac{1}{3}$.
- Write a second word problem that uses division and the numbers $4\frac{2}{3}$ and $\frac{1}{3}$.
- Solve both problems.

Take notes on your classmates’ approaches to solving and writing fraction word problems.

As your classmates present, ask questions such as:

- How are the quantities in the problem related?
- What is the unknown quantity in the problem?
- How does your equation represent the problem situation?
- Is your answer reasonable? How do you know?
- Where are the known and unknown quantities in the problem you wrote?
- How do you know that your problem is a multiplication or a division situation?

**Read and Discuss**

- The fractions $\frac{a}{b}$ and $\frac{b}{a}$, with numerators and denominators inverted, are called
*reciprocals*of each other. The key property of reciprocals is that their product is always 1.

$\frac{a}{b}\times \frac{b}{a}=\frac{a\times b}{b\times a}=1$Reciprocals are also called

$\frac{3}{4}\times 5=\frac{15}{4}$*multiplicative inverses*. This name refers to the fact that if you multiply a fraction by a number, and then multiply the result by the reciprocal of the fraction, the result is “undone.” For example:

$\frac{15}{4}\times \frac{4}{3}=\frac{15}{3}=5$- You can use the properties of reciprocals to help you divide by fractions. The general rule is:
*To divide by a fraction, multiply by the reciprocal of the fraction*. Algebraically, the rule looks like this: $\frac{a}{b}\xf7\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$

Can you:

- Solve a problem that involves dividing a fraction by a fraction?
- Determine which operation is needed to solve a word problem?
- Explain what reciprocals are and how to use them to help you solve division problems involving fractions?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**An example of an everyday situation that involves fraction division is …**