Fair Share: Fraction Story Problems

CCSS Context:

This lesson builds on students' concepts they have gotten throughout this unit about halves and fourths and puts it into a real life situation. One of the shifts in the Common Core is contextualizing problems into real life scenarios. First graders, particularly those with siblings, often encounter having to share something fairly. This lesson challenges them to do so and make sure there are the correct number of fair shares. 

Read Aloud: 

This lesson is all about the idea of sharing something equally among a group of people. To help kids connect to this idea, we will chorally read the story Two for Me, One for You. This is available on Reading A-Z (login required) and is a F&P leveled F book. Reading the book chorally will help kids practice reading for fluency, which is part of CCSS RF1.4b, "Read grade-level text orally with accuracy, appropriate rate, and expression on successive readings."

Objective:

 Justin would have been happy if he had made 2 equal piles! Then he and his brother would have had fair shares, or fractions, of the set. Your thinking job today is: How will I divide a shape to make sure everyone gets an equal share?

Materials needed: chart paper, paper plates (or paper circles)

Present Problem: My best friend and I are sharing an apple pie. Show how we could share it so we both have equal shares.

• How many people are sharing this pie? 
• What shape should I draw to match the pie?
• Partner talk: What are 2 different ways I could divide this pie into 2 equal shares? Students are practicing planning how to make the shape in the abstract, then they will prove or disprove their guess in a minute! This gives kids an opportunity to critique their own reasoning and the reasoning of others (MP3).

I will pass out a paper plate to each partner group to represent the pie. One partner will get to hold this pie and fold it to show how they could share it equally between me and my best friend. 

• Partner talk: Which piece will be mine? Would we call that amount one half or one fourth? Why?

Present new problem: My best friend, my mom, my brother and I are sharing an apple pie. Show how we could share it so we each have an equal share.

• How are these problems the same and different?
• How many people are sharing this pie? 
• Partner talk: How could you divide the pie into 4 equal shares? 

I will pass out a second paper plate to the partner groups to represent the new pie. The other partner will fold this pie to show how it could be shared equally between the four people.

• Partner talk: Which piece will be mine? Would we call that amount one half or one fourth? Why?

One counterintuitive part of teaching fractions to young children is the idea of a shape divided into 2 pieces has larger pieces than one divided into 3 or 4. When asked what way gets the bigger pieces, the shape divided into 2 or 4, many children will say the 4 because 4 is a greater number. This middle portion of the lesson is designed so students have to reason about the relative size of the portions.

Present Problem: I am wondering who get the bigger pieces of pie, the 2 people in the first problem, or the 4 people in the second problem. The pie is the same size in both problems. But I want to know: Which group of people got to eat more pie?

• Partner Work: Look at your two pies. Which one is divided into halves? How do you know? Which one is divided into fourths? How do you know?
• Which pieces of pie are bigger? 

I'll feign confusion: I'm confused. The number 4 is bigger so I think those 4 people must have gotten more pie. Do you agree or disagree? Why or why not?

• Partner talk: Why are the slices smaller on the pie divided into fourths?
• Potential answers: More people have to share the pie; The pie has to be cut into 4 pieces rather than 2 pieces; etc.

End with a challenge!

My chart paper will have multiple squares drawn on it. Some will be divided into halves, some fourths, but all will show halves and fourths in different ways. My challenge will be to shade half of each shape, even if it is divided into fourths.

• This helps students start to think about equivalent fractions, which sets students up for the 3rd grade standard they will encounter, where they use models to show equivalent fractions (3.NF.A.3).