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### Bits and Pieces 2.1

Equivalent Fractions and Equal Shares

Quick Review

- Two different classes reached 3/5 of their goal. Did the two classes raise the same amount of money? Explain your thinking.
- What doe the numerator and the denominator of a fraction tell you?
- If a class goes over its goal, what can you say about the fraction of their goal they have reached?

Today’s Problem

Sid and Susan are going hiking on the Appalachian Trail in Virginia with a group of friends. They are packing snack foods that are easy to carry and to eat. Their favorite is licorice lace, a rope candy that looks like a long, round shoelace. Sid packs a licorice lace to share on the hike.

The licorice lace is 48 inches long and difficult to break into pieces. Sid can mark the licorice lace by cutting partway through. Then, it will be easy to break and share later.

Question A

There are four people going on the hike. How should Sid mark the licorice lace so that each person can have a fair share? Draw a picture and label one hiker’s share of the lace.

Question B

Two more friends join the hike! Each wants a fair share of the licorice lace. Sid has to add more marks to the lace. He is stuck with the marks he has already made. Sid makes new marks so that the new marks together with the old marks make equal-sized pieces. Draw a picture to show how Sid can add more marks to the licorice lace so it has equal-size pieces and can be broken to serve six people. Label one hiker’s share.

Question C

Well, you’ve probably guessed what happens next! Two more join the hike. Poor Sid has to re-mark the licorice lace he made for six people with additional marks. The new marks along with the old marks must form equal-size pieces to break off and share equally among eight friends. How should he re-mark the lace?

Draw a picture and label one hiker’s share.

How many inches of lace will each of the eight hikers get?

Question D

Were there any marks that could be labeled as more than one fraction?

Question E

Carlotta bought a 48 inches blueberry lace. She cut off a part for her friend Brianna.

What fraction of the blueberry lace did she give to Brianna?

How many inches of the blueberry lace did Brianna get?

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