Grade Three: Fractions Unit 7 Finding Fair Shares

Let’s Start with some MATH! If the whole square is equal to 1, label each part with the appropriate fraction

What makes work with fractions so difficult for students? (p. 109)

Overview of our Sessions Investigation 1: Sharing Brownies Investigation 2: Many Ways to Make a Share CMS Unit: Fractions on a Number Line

One Brownie to Share Take 1 brownie. How can you cut the brownie so that two people can have equal shares?

Fraction Notation What would you call the share of the brownie that one person gets? This piece is _____ of the whole. What does the number on the top stand for? What does the number on the bottom stand for?

Fraction Notation Read Math Note 3: Vocabulary on page 25 Turn and Talk: What is most important here?

Sharing Brownies Using the sheet of large brownies, create the “fair shares” on the activity sheet. SAB 1-2

Key Discussion: Are your shares equal?

Making Fair Shares – Key Discussion Are these shares equal? How do you know? How could you prove it?

Why focus on “fair” shares? 1/3 ¼

Common Core State Standards What standards are evident in this lesson? How can I ensure that this lesson is about mathematics and not about coloring?

Making Fraction Sets -Get with a partner and take 5 sheets of the same color paper -Fold into equal pieces, then draw lines to separate them -Label each piece with the fraction name -Cut into equal pieces 1st sheet: 2 equal pieces 2nd sheet: 4 equal pieces 3rd sheet: 8 equal pieces 4th sheet: 3 equal pieces 5th sheet: 6 equal pieces discuss the difference between the two ways to make sixths and how to prove they are equal

Aarrgghh, I know some of my students… What challenges may arise as students create fraction sets? What can you do that will not interfere with student learning?

Smallest to Largest 14 ½ Take one of each fraction set. Order them from least to greatest (left to right). Switch to Doc cam for discussion

True or False? “The Smaller the Denominator, the _________ the fraction” 1 or 1 7 5 3 Or 4 7 5 This generalization is only true if referring to UNIT fractions

A student’s fraction models What do you know about Billy’s understanding of fractions based on his models?

Common Core State Standards What standards are evident in this lesson? How can I ensure that this lesson is about mathematics and not about coloring?

Make a new set of fraction cards with one piece missing You will need 5 sheets of paper. Fold one paper into fourths. Cut away 1 piece. Label it ¼. Label the remaining piece ¾. Continue until you have made representations for all of these fractions: 1 8 7 Have participants get in groups of 2 and create these according to directions. Discuss all of the ways students used this representation; to compare, to add, to order, etc. 1 2 1 4 3 4 1 6 5 6 2 3 1 20

NO Common Denominators! Which is larger 5/6 or 7/8

NO Common Denominators! Which is larger, 5/6 or 7/8

Many Ways to Make a Whole With your partner, find different ways to make a whole. Record on FRACTION FACTS Chart

Common Core State Standards Do 3rd Graders need to add fractions with unlike denominators in the Common Core? Do they need to add fractions at all? Why keep this lesson?

Sharing Seven Brownies Imagine there are seven brownies to share equally among four people. About how many brownies do you think each person will get? Work with a partner to find out exactly how many brownies each person will get. Record your work on a sheet of paper. Use small brownies. Have participants glue

Gallery Walk What do you notice about our solutions?

Common Core State Standards Do students need to consider quantities greater than one? 3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Wrap Up

Exit Ticket

Welcome Back! How’s it going?

Investigation 2: Many Ways To Make a Share Making Cookie Shares The Fraction Cookie Game Assessment: Many Ways to Make a Share Making Half-Yellow Designs

Fraction Equations 1/3 1/3 1/3

What’s it Worth? Using the hexagon “cookies” and pattern blocks, create as many equations = 1 as you can.

Fraction Equations

How Many Ways can we Make a Half?

Fraction Cookie Game You need: Pattern Blocks Fraction number cubes (2 in one color and 1 in a different color) Hexagon Cookie recording sheet Play with a partner. Each player rolls one fraction number cube and takes that amount in pattern blocks, or “cookies.” Record the cookies you collect on Hexagon Cookie recording sheet. At the end of a turn, each player must have the fewest number of pieces possible. For example, if you have 2 and ½ cookies altogether, you should have 2 yellows and 1 red in front of you. Trade in smaller fraction pieces for larger ones, and check each other’s cookie shares as you play. Take turns and collect cookies until you have filled in the sheet. The player who finishes first wins..

Playing once doesn’t cut it! Big Ideas: Fraction Cookie Game Key Ideas: Playing once doesn’t cut it! Big Ideas: Discussion is most important!

How much of this design is Yellow?

Make Your Own Half-Yellow Design

Share Designs Read p.83 “Equivalent Fractions”

Fractions on a Number Line Around the room there are 6 lines. With your group… Place the cards in the appropriate place on the number line Equivalent fractions should be place UNDER (not next to) each other Create your own number line