Stern Structural Arithmetic and Fractions

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Stern Structural Arithmetic and Fractions. Temple Ary Lois Feldman. www.sternmath.com International Dyslexia Association Conference March 9, 2010. Agenda. Discuss: What’s hard about teaching fractions?

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Stern Structural Arithmetic and Fractions

Temple Ary Lois Feldman

www.sternmath.com

International Dyslexia Association Conference March 9, 2010

Agenda
• Discuss: What’s hard about teaching fractions?
• Fraction story where each pair will cut fractions.
• Play 2 fraction games.
• Discuss what you learn about fractions from the games.
• Show you a preview of a new fraction book.
• Show you a money game that connects fractions, decimals and percents.
Candy Bars
• Imagine your favorite candy bar
• I have a candy bar and I’m about to take a bite….

One Whole

One Whole

one half

one half

What is another name for a whole?

I have a candy bar and I’m about to take a bite….

Fourths

One Whole

• What is another name for a whole?
• What is another name for a half?
• Which is bigger – a fourth or a half?

I have candy bar and I’m about to take a bite….

Eighths

One Whole

1

2

1

2

1

4

1

4

1

4

1

4

1

8

1

8

1

8

1

8

1

8

1

8

1

8

1

8

Hiding Game

What piece is missing?

Variation: Hide two pieces

Hiding Game
• What does one think about when figuring out which piece is hidden?
• What row?
• How many pieces is the whole cut into?

8

8

8

4

2

4

Fraction Lotto Game

Fraction Pieces

Fraction Lotto Box

Numerators

1

1

1

2

2

3

Denominators

Putting Away Game
• When the one student wins, play the putting away game.
• The students whose board is not full have a head start

When removing the pieces, you are, in fact, subtracting:

4

1=

4

1

4

• Draw two denominator cards
• Draw two numerator cards

2

1

Where do I want to put the numerators?

4

8

At the end of the game (so I can fill the game board),

allow them to pick just pick one numerator & denominator

Double or Half

Put 3 on sides of a die:

Put 3 on sides of a die:

1 x

2

2 x

¼, ¼, ½,2/4, 3/4, 1

Make 6 cards

• Each person has an empty Lotto Board
• Roll the die (1/2 x)
• Pick a card (1/4)
• “½ of ¼ equals 1/8”
• Student puts a 1/8 size piece on the lotto board
• Students may exchange pieces at any time
• Need exact amount to fill board
Division of Fractions

How many fourths are in a whole?

1

2

3

4

Fractions are smaller than a whole…so there are 4.

Division of Fractions
• Division of Whole Numbers
• 30 divided by 6
• Easy to demonstrate in the number track as containment
• How many 6s are going to fit into 30?
• Able to show that five 6-blocks fit into this space
• Division of Fractions
• ½ divided by ¼
• How can we demonstrate containment?
• How many 1/4s are going to fit into 1/2

1/2

1/4

1/4

Another Example

How many 1/8 yard pieces are in ¾ yard of material?

.

3

1

.

4

8

¾ yard of material and cut into 1/8 yard pieces

.

3

3

3

\$3 divided by

.

4

4

What do I have to do?

1. Makeinto quarters

2. Chunk into

groups of 3

.

3

3

.

4

12

3

Multiply 3 x 4

Total # of parts

How many groups?