
Rectangle Fractions
Years 4  8

Preparation
 Collect about 20 small objects that are more or less the same. You can use plastic screw caps, pebbles, pasta, small toy people.
 Collect straws or pencils or other thin sticks to use like the children in the photos.
 Write the title of this challenge and today's date on a fresh page in your maths journal.
Rows, Columns & Boxes
Rows
Arrange your objects in three (3) rows of four (4) like the yellow plugs in the photo.
Rows go across your tummy.
Straws are being used to show that the rows divide the whole rectangle into three equal parts.
 We know what the whole is.
 The whole is divided into 3 equal parts by the rows.
When one (1) whole is divided into 3 equal parts each part is called one third.


Objects arranged in
equal rows like this
make a rectangle shape.
You have made
one whole rectangle of objects.


one row = one third (of the rectangle)
Slide one straw down from the top and count by thirds as you go...
One third

Two thirds

Three thirds
or 1 whole rectangle. 
Do you notice that if there is one third on one side of the straw, then there must be two thirds on the other side.
1 third + 2 thirds = 3 thirds (which is 1 whole)
and
2 thirds + 1 third = 3 thirds (which is 1 whole)
Arrange fifteen (15) objects into three equal rows. Sketch them in your journal.
Explain why each row is 1 third of the rectangle.

Columns
Arrange your objects in three (3) rows of four (4) again.
Rows go across your tummy. Columns go the other way.
Straws are being used to show that the columns divide the whole rectangle into four equal parts.
 We know what the whole is.
 The whole is divided into 4 equal parts by the columns.
When one (1) whole is divided into 4 equal parts each part is called one quarter (or one fourth).


Objects arranged in
equal rows like this
make a rectangle shape.
You have made
one whole rectangle of objects.


one column = one quarter (of the rectangle)
Slide one straw across from the left and count by quarters as you go...
This is an equation from the first picture.
1 quarter + 3 quarters = 4 quarters (which is 1 whole)
Copy it into your journal.
Write an equation for each of the next two pictures.
Arrange fifteen (15) objects into three equal rows. Sketch them in your journal.
Explain why each column is 1 fifth of the rectangle.

Boxes
Arrange your objects in three (3) rows of four (4) again.
Rows go across your tummy. Columns go the other way.
Straws are being used to show that the boxes divide the whole rectangle into twelve (12) equal parts. Each part is called one twelfth (of the rectangle).

one object = one twelfth (of the rectangle)
 Start at the top left and go across the rows.
 Touch each of your objects as you count by twelfths.
 Example:
1 twelfth, 2 twelfths, 3 twelfths, 4 twelfths (or 1 third)
5 twelfths ... (keep going)
 What happens if you start from the top left and count down the columns?
Arrange fifteen (15) objects into three equal rows.
Sketch them in your journal.
Explain why each object is 1 fifteenth of the rectangle.
Have fun exploring Rectangle Fractions

Fraction Equations

Jojo and Marta were working together with this whole rectangle.
They were asked to find (10) equations. Check their work.
 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth + 1 twelfth
+ 1 twelfth + 1 twelfth = 1 whole
 12 x 1 twelfth = 1
 1  5 twelfths = 7 twelfths
 4 x 1 quarter = 1
 2 x 1 third = 2 thirds
 2 quarters + 1 quarter = 3 quarters
 1 half + 1 quarter = 3 quarters
 1 quarter + 1 third
= 1 column + 1 row
= 3 twelfths + 4 twelfths
= 7 twelfths
 2 quarters + 1 third = 6 twelfths + 4 twelfths = 10 twelfths (or 5 sixths  Jojo)
 1 half + 2 thirds
= 2 columns + 2 rows
= 6 twelfths + 8 twelfths
= 14 twelfths (Huh?)
Your challenge is to use your 15 objects in 3 rows (or your drawing) to write ten equations in your journal.

Doing It With Rectangles
 Print this Rectangle Fractions Board. You will also need a piece of paper to cover some of the rows or columns.
 Open this Rectangle Fractions Starter. You can read it on screen or print it.
 The Starter will guide you into investigating more Rectangle Fractions.
 When you get to the Challenge, figure out the first part then do lots more exploring on your own.
When you think you are pretty good at doing these try imagining the rectangle instead of drawing it.
Anytime you are ready you can write the fractions in number shorthand.
For example:
two thirds = ^{2}/_{3}
1 quarter = ^{1}/_{4}
7 tenths = ^{7}/_{10}
14 twelfths = ^{14}/_{12} = 1^{2}/_{12} (= 1^{1}/_{6})
Just Before You Finish
 Explain in your journal what you know now about fractions.
 What else would you like to know about fractions?
These notes were originally written for teachers. We have included them to support parents to help their child learn from Rectangle Fractions.
Send any comments or photos about this activity and we can start a gallery here.
Maths At Home is a division of Mathematics Centre
