The MathScience Innovation Center Presents That’s Sum Quilt! Written by Susan L. Cerruti.

The MathScienceInnovation Center

Presents

That’s Sum Quilt!

Written by Susan L. Cerruti

That’s Sum Quilt!

Open your tub of pattern blocks.

Select ONE block.

Find other smaller blocks to cover your block.

As an example:

Finding Fractions

Two red pieces will cover one yellow piece.

Explore and find as many possible combinations as you can. You have 2 minutes.

Let’s List Them All

Let’s make a list of all of the possible combinations we found.

Parts of a Whole

We already know 2 red pieces will cover 1 yellow piece.

Let’s focus on the pieces that will cover the large yellow block.

What other pieces will cover the yellow block?

How many green pieces will cover the yellow block?How many brown pieces will cover the yellow block?How many purple pieces will cover the yellow block?How many blue pieces will cover the yellow block?

Parts of a Whole

Let’s Talk Fraction!

Let the yellow hexagon equal the whole, or one.

Let’s find out what FRACTION of the yellow block the other pieces are?

What is a fraction?

Fractions are written as a

numerator

over a

denominator

A FRACTION is one way to show a part of a whole.

What is a fraction?

A FRACTION is one way to show a part of a whole.

It takes 2 red pieces to cover one yellow block.2

This decides the denominator of our fraction.

Our numerator for each individual block, is always 1because 1 smaller pattern block is being used. 1

What is a Fraction?

Therefore, the red piece is of the yellow block.2

1

If the yellow block has a value of 1,

then the red block has a value of2

1

Finding Fractions

Using the yellow block as the whole, or one:

• What fraction of the whole is each block?

• Let’s give each block a value.

Finding Fractions

We know the yellow block has a value of 1.

2

11

3

1

4

16

1

12

1

Equations

Can we show the relationship between the blocks in an equation?

An equation is a math sentence that contains an equal sign.

2 + 2 = 4

Equations

To show our relationships in an equation, we need to use variables.

A variable is a letter or symbol that represents a number in mathematics.

2 + = 4x2

Variables

Let’s give each pattern block a variable (or letter) so we can tell each one apart from the others.

yellowhexagon

What would be a good letter to stand for yellow hexagon?

y

What would be a good letter to stand for brown half trapezoid?

brownhalf trapezoidbr

What would be a good letter to stand for red trapezoid?

redtrapezoidr

What would be a good letter to stand for green equilateral triangle?

greenequilateral

trianglegWhat would be a good letter to stand for purple right triangle?

purpleright

trianglep

What would be a good letter to stand for blue diamond?

bluediamondbl

Using variables to write equations

The red trapezoid is of the yellow hexagon. 2

1

We replace the variables in the correct places:

The red trapezoid is2

1 of the yellow hexagonr = y

All the equations

Can you help me find the equation for the brown half trapezoid?

The brown half trapezoid is of the yellow hexagon. 4

1

We replace the variables in the correct places:

The brown half trapezoid4

1of the yellow hexagonbr = yis

All the equations

Can you help me find the equation for the green equilateral triangle?

The green triangle is of the yellow hexagon. 6

1

We replace the variables in the correct places:

The green triangle6

1of the yellow hexagong= yis

All the equations

Can you help me find the equation for the purple right triangle?

The purple triangle is of the yellow hexagon. 12

1

We replace the variables in the correct places:

The purple triangle12

1of the yellow hexagonp= yis

All the equations

Can you help me find the equation for the blue triangle?

The blue triangle is of the yellow hexagon. 3

1

We replace the variables in the correct places:

The blue triangle3

1of the yellow hexagonbl = yis

All the equations

So we have the following 5 equations:

r = y br = y

g = y p = y bl = y12

1

2

1

6

1

4

1

3

1

Framing Fractions

What would be the value of this design?

2

1

1

2

1

We add up each value:

2

6

1

6

4

6

1

6

1

6

1

+ + + + + + =

1 1+ +6

4=

or if you reduce 23

2

Framing Fractions

Write your name at the top of your paper.

Use your blocks to make a design that fits into the rectangular frame.

Framing Fractions

You must create a design that has a value of 2 inside of the first frame. 2

1

2

12

Write your number sentence for your design.6

1

2

1

3

1

3

1

6

11+ 2

1+ + + + = 2

Framing FractionsYou may not use my design.

When you have your design, trace around each block.

Framing Fractions

Do the second frame.

Your total value for the second design must equal 1 32

3

21

That’s Sum Quilt!

Put your red and brown blocks back into the tub.

You will only be using the yellow, green, blue and purple blocks for our last activity.

That’s Sum Quilt!

Make a design using only the four kinds of blocks.

It must fit on the black paper square.

Slide your design off your paper.

Glue paper blocks to the black rectangle to copy your design.

That’s Sum Quilt!

That’s Sum Quilt!

Add up the value of your quilt design.

Use a white crayon or pencil to write your name and your value on the back of your black paper.

Put the pattern blocks back into the tub.

Clean up your area. Be sure to put all unused paper pattern block into the correct container.

Questions?

Let’s Play!