1. Equal Sharing and Equivalence
Lesson 3-1
Equal Sharing and Equivalence
Overview: Students extend their understanding of fraction equivalence by solving number stories involving shared quantities.

2. Math Message
Two brothers go to lunch and share three 8-inch pizzas equally. How much pizza does each brother get? Be prepared to share a drawing you could use to solve the problem.

3. Exploring Equivalent Fractions through Equal Sharing
Math Message Follow-Up
Is there enough for each brother to get 1 whole pizza?
How many pizzas are left over?

4. Share your drawings you used to model and solve the problem.
Here are some possible strategies you could have used:
Give one whole pizza to each brother. Cut the third pizza in half. Each brother gets one whole pizza and ½ of another pizza, or 1 ½ pizzas.

5. How would you write 3 halves as a fraction?
Here are some possible strategies you could have used:
Cut each of the 3 pizzas into 2 equal parts. Each brother gets 3 parts or 3 halves.
How would you write 3 halves as a fraction?

6. How would you write 6 fourths as a fraction?
Here are some possible strategies you could have used:
Cut each of the 3 pizzas into 4 equal parts. Each brother gets 6 parts or 6 fourths.
How would you write 6 fourths as a fraction?

7. Do the fractions 1 ½, 3/2, and 6/4 all refer to the same whole?
Do 1 ½, 3/2, and 6/4 name the same amount of pizza?
How do you know?

8. Fractions that name the same amount are called equivalent fractions.
Are 1 ½, 3/2, and 6/4 examples of equivalent fractions?
How do you know?

9. In this lesson, you will have the opportunity to reason further about equivalent fractions as we discuss different ways to solve equal-sharing number stories.

10. Six hikers share 4 pounds of trail mix equally
Six hikers share 4 pounds of trail mix equally. How many pounds of trail mix does each hiker get?
Use drawings to model and solve the problem.

11. Each hiker get 4/6 of a pound.
Here are some possible strategies you could have used:
Divide each of the 4 pounds into 6 equal parts. Share the sixths so that each hiker gets 1/6 of each of the 4 pounds. How do you write 4 sixths as a fraction?
Each hiker get 4/6 of a pound.

12. Each hiker get 2/3 of a pound.
Here are some possible strategies you could have used:
Divide the pounds evenly so that each group of three hikers gets 2 pounds of trail mix. Then divide each of the 2 pounds into thirds so each hiker gets 1/3 of each of the 2 pounds. How do you write 2 thirds as a fraction?
Each hiker get 2/3 of a pound.

13. Do the fractions 4/6 and 2/3 both refer to the same whole?
How do you know?

14. Are 4/6 and 2/3 equivalent fractions?
How do you know?

15. Five campers share 3 yards of blue string equally to make bracelets
Five campers share 3 yards of blue string equally to make bracelets. How much string does each camper get?

16. Here are some possible strategies you could have used:
Cut each yard into 5 equal parts. Share the fifths so each camper gets 1/5 of each of the 3 yards. 3 fifths written as a fraction is 3/5. Each camper gets 3/5ths of a yard.

17. Here are some possible strategies you could have used:
Cut each of the yards into 10 equal parts. Share the tenths so each camper gets 2/10 of each of the 3 yards. 6 one-tenths written as a fraction is 6/10. Each camper gets 6/10ths of a yard.

18. Do the fractions 3/5, and 6/10 both refer to the same whole?
Do 1 ½, 3/2, and 6/4 name the same amount of pizza?
How do you know?

19. Are 3/5 and 6/10 equivalent fractions?
How do you know?

20. Practice
Complete math journal pages Use models to solve the problems in more than one way.

21. Summary
Let’s discuss the different solutions to the problems on math journal pages
These are equivalent fractions.
How did you use the answer to problem 2 to solve problem 3?

22. Exit Ticket
Is 3/6 equivalent to ½?