Grade Three: Fractions Unit 7 Finding Fair Shares

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

Solve It’s easy….right? Just change both to common denominators and then compare them. Are they equivalent or not? Which one is greater? Explain how you know? Draw a representation and write a short story (scenario) to go with it. 5 / 6 (= > <) 7 / 8

How challenging was it to…? …Solve the problem? …Draw a picture/representatio n? …Write a word problem? 5 / 6 (= > <) 7 / 8

Most of us were taught to solve fraction problems using a procedure. What learning did that take from us? Stolen Opportunity !

When the math gets harder.. Are we preparing our students to develop the mathematical content knowledge they need to be successful in middle school? High school? In College? In Life?

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

"5 out of 4 people have trouble with fractions."

Contents Investigation 1: Sharing Brownies Investigation 2: Many Ways to Make a Share Investigation 3: Introduction to Decimals

Investigation 1: Sharing Brownies Making Fair Shares Making Fraction Sets More Than One Piece Sharing Many Things Sharing Several Brownies Assessment: Sharing Four Brownies

Making Equal Shares Divide one of your brownies to show that two people get an equal share.

SAB 1-2

Making Fair Shares – Key Discussion Are your shares equal? How do you know? How could you prove it?  Cut  fold

Making Fair Shares Discuss what a fraction is Discuss meaning of numerator and denominator Divide large brownies into halves and thirds and talk about “fair shares” or “equal shares”

Key Discussion Here is a brownie that has been cut up to share among three people. Would each person get an equal share? How would you prove that the shares are equal or not equal?

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 1 st sheet: 2 equal pieces 2 nd sheet: 4 equal pieces 3 rd sheet: 8 equal pieces 4 th sheet: 3 equal pieces 5 th sheet: 6 equal pieces discuss the difference between the two ways to make sixths and how to prove they are equal

Smallest to Largest Take one of each fraction: ½, ¼, 1/8, 1/3 and 1/6 and put them in order from greatest to least- (left to right)

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

Sharing Seven Brownies- How would you share?

Sharing Brownies Are These Shares Equal?

Fractions of a Set Read P.44 math note  How is a fraction of a region different from a fraction of a set?

BREAK!

Make a new set of fraction cards with one piece missing You will need 5 sheets of paper. 1. Fold one paper into fourths. 2. Cut away 1 piece. Label it ¼. 3. Label the remaining piece ¾. 4. Continue until you have made representations for all of these fractions:

More Than One Piece Discuss “what is left” when one piece is removed

Which is greater? 3/4 or 5/6 What could you do to figure this out? (this is a great task for Standard for Practice #3: Construct viable arguments and critique the reasoning of others) 3/45/6

One Piece Missing

Reasoning with Fractions…. Is 1/2 + 1/3 more or less than 1? How do you know? Use a representation and words to defend your answer (this is great way to demonstrate Standard for Practice #3- construct viable arguments and critique the reasoning of others)

Something to think about…. Can ¼ be greater than ½ ? ??????

Welcome Back! How’s it going?

Different Shapes, Equal Pieces?

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 1/31/3 1/31/3 1/31/3

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. 1. 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. 2. 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. 3. Take turns and collect cookies until you have filled in the sheet. The player who finishes first wins..

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

Fractions on the Number Line 2/8 4/8 3/6 2/48/ /2 6/8 4/4 1/43/4

Number Line Connections How can we help students connect their cookie/brownie work to the number line?

How Do We Know if Students REALLY Understand?

Which is Greater? 3 OR 5 5 8

When Procedure Trumps Reasoning easoning-fractions.aspx easoning-fractions.aspx

Questions and Concerns????