Fractions, Decimals and Percents Mini-course

Session Two

Session 2 of 8

Objectives

• To promote conversation and success with mathematical endeavors.

• To use color tiles as a manipulative for illustrating fraction concepts.

• To explore the fraction concepts of equivalence, simplest form, and common denominators.

• To introduce NCTM`s Problem Solving Standard.

Session 2 of 8

Tangram Follow-up•Share at tables•Volunteers to share with large group.

Fractions – Decimals - Percents•Any new ideas to share – go ahead and post•Keep watching and listening for uses in your everyday world!

Using objects & pictures to represent fractions

• If you were going to explain the fraction

½ to a child, how might you do it?

• What objects or pictures might you use?

• What words would you use in your explanation?

Session 2 of 8

Session 2 of 8

Colored Tiles Activity• Make a collection of

the following tiles:

–1 Red

–1 Blue

–6 Green

–4 Yellow

Compare the number of RED tiles to the total number. What fraction do the RED represent?

BLUE?

GREEN?

YELLOW?

What is a Fraction?

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Names for GREEN tiles:• Based on this picture, what fraction name

would you assign to Green?

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G

Y

G G G G G

Y Y Y B R

Names for GREEN tiles:• Do you see another fraction name for

Green?

Session 2 of 8

G

Y

G G G G G

Y Y Y B R

Names for GREEN tiles:• And yet another name for Green?

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G

Y

G G G G G

Y Y Y B R

Equivalent Fractions

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Let’s do same for Yellow at your tables.

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New Set of Tiles• Make a collection of

the following tiles:

–4 Red

–5 Blue

–3 Green

–8 Yellow

Find new fractional names for each color.

BLUE?

GREEN?

YELLOW?

RED?

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Simplest form• Why is it that some fractions (like 3/20

in the previous example) have no equivalent names that can be demonstrated in this tile collection?

• When a color has several equivalent names (like red in the previous example), which fraction do you think is the easiest to work with or might be considered the “simplest” name?

Equivalent Fraction Activity• Suppose you were told that a collection of

tiles has – 1/2 Red– 1/5 Blue– 3/10 Yellow

• How many tiles should we use?

• Is there another collection that would also work?

• How can you prove that another collection also works?

Session 2 of 8

Equivalent Fraction Activity• Suppose you were told that a collection of

tiles has – 1/2 Red– 1/5 Blue– 3/10 Yellow

• Answer:

5 Red, 2 Blue, 3 Yellow

What equivalent fractions did you discover?

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Color Tile Collections (worksheet received tonight)

• Work in small groups to solve problems.

• Write equivalent fraction names for each color using the total number of tiles as the denominator.

• OK if you don’t finish all – go a pace for good discovery! Can finish at home.

• Will be looking for volunteers to share solutions and explain thinking.

Session 2 of 8

Color Tile Mysteries (worksheet received tonight)

• Work in small groups to solve problems.

• OK if you don’t finish all – go a pace for good discovery! Can finish at home.

• Will be looking for volunteers to share solutions and explain thinking.

Session 2 of 8

Session 2 of 8

NCTM Problem Solving Standard

•Build new mathematical knowledge through problem solving.

•Apply and adapt a variety of appropriate strategies to solve problems.

Session 2 of 8

Reflection & Closing

• Think about the problem solving standard.• How do the activities of this session and

the previous class promote this standard?• How have the color tiles helped your

understanding of fractions?• Bringing Mathematics Home 2 – Complete

the three problems on Fraction Problems I, using color tiles or other objects and share your solutions in session three.