Partitioning Shapes into Equal Parts
Basics on the topic Partitioning Shapes into Equal Parts
Fractions: Halves, Thirds, Quarters
We can partition shapes such as circles, squares, and rectangles into equal parts. They can have two, three, four, and more equal parts! When we have one of these parts we can answer, what are unit fractions. In this video the items are cut into halves, quarters and thirds.
Describing Fractions
You can describe each separate equal part of the partitioned shape as a half of, a third of, and a quarter of.
When we describe the equal parts that make up the whole, we would describe them as two halves, three thirds, and four quarters.
Fractions – Summary
When you partition shapes into equal parts, the individual parts are described as fractions or unit fractions. The names of the fraction depend on how many parts you partition the shape into. The table below shows the fractions’ names as well as how of parts the shape was partitioned into:
Fraction  # of parts 

halves  2 
thirds  3 
quarters  4 
After watching the video, have a go at the halves, thirds and quarters worksheets.
Transcript Partitioning Shapes into Equal Parts
Nico and Nia have arrived with all the party food ready for Axel and Tank to share them into equal parts. Let's join in as Axel and Tank teach Nico and Nia all about partitioning shapes into equal parts. Shapes such as circles, squares and rectangles can be partitioned into equal parts. Partition means to divide into parts. When partitioning shapes equally we are dividing a shape into parts of the same size. Let's look at the doughnut Nico and Nia brought! Axel and Tank have decided to partition this into two equal parts right down the middle, like this. When a shape is divided into two equal parts, each part is called onehalf. Since they have been partitioned into two equal parts, we call the parts halves. These two halves make up the whole. If Nico ate one part of the doughnut we would say there is half of the doughnut left. Now that they have partitioned, or divided, the doughnut into equal parts, let's look at the sandwich! This time, Axel and Tank decided to partition this into three equal parts, like this. When anything is divided into three equal parts, each part is onethird. How many thirds make up a whole? Threethirds make up the whole. Let's suppose Axel ate two parts of the sandwich, how much would you say is left? You would say there is a third of the sandwich left! Now that the sandwich has been partitioned, let's take a look at the sushi Nico and Nia brought! Axel and Tank have decided to partition the sushi into four equal parts, like this. When a shape is divided into four equal parts, each part is one quarter. How many quarters make up a whole? Fourquarters make up the whole. Let's suppose Tank ate three parts of the sushi, how much sushi is left? You would say there is a quarter of the sushi left! Now that the food has successfully been partitioned for the party, let's review! Remember, partition means to divide into parts. You can partition shapes such as circles, squares and rectangles into equal parts such as halves, thirds and quarters. You can also say a half of, a third of or a quarter of when talking about each equal part. Two halves make up a whole. Threethirds make up a whole and fourquarters make up a whole. All their hard work partitioning the food into equal parts has paid off and now everyone is having fun dancing the night away!
Partitioning Shapes into Equal Parts exercise

How many equal parts make a whole?
HintsThink about how many equal parts you need to make one whole.
This image shows halves. How many make one whole circle?
Solution2 halves make a whole.
3 thirds make a whole.
4 quarters make a whole.

How many equal shares?
HintsLook at how many equal parts the food is partitioned into.
Make sure the food is partitioned into equal parts.
If the food isn't partitioned, then it is a whole.
Solution The pie is 1 whole.
 The strawberry cake is divided into 2 halves.
 The chocolate brownie is divided into 3 thirds.
 The pizza is divided into 4 quarters.

How many equal shares are there?
HintsLook at how many equal parts the shape is partitioned into.
Remember:
 2 equal shares = 2 halves
 3 equal shares = 3 thirds
 4 equal shares = 4 quarters
Make sure the shape is partitioned into equal parts. If the pieces aren't equal, then it will be assigned to the none category.
SolutionLooking at the image:
 The rectangle is partitioned into halves, because there are 2 equal parts.
 This circle and square are partitioned into thirds, because there are 3 equal parts.
 This circle is partitioned into quarters, because there are 4 equal parts.
 This circle and square are none of these, because they are partitioned into unequal parts.

Equal shares.
HintsRemember:
 3 equal shares = 3 thirds
 4 equal shares = 4 quarters
To work out how many pieces are left, subtract the amount eaten from how many equal parts make the whole.
For example, if there are 2 equal parts and 1 piece was eaten, then 21 = 1.
SolutionAxel, Tank and Nia decide to divide their brownie into 3 equal parts, which means each part is one third or a third of the whole brownie.
They know that 3 thirds make up one whole.
If Tank ate 1 equal part of the brownie, then 2 thirds are left.
Axel, Tank, Nia, and Nico decide to divide their cake into 4 equal parts, which means each part is one quarter or a quarter of the whole cake.
They know that 4 quarters make up one whole.
If Nico ate 1 equal part of the cake, then 3 quarters are left.

Which shape is partitioned into three equal shares?
HintsLook for a shape partitioned into 3 pieces.
Make sure all 3 pieces are equal in size and take up the same amount of space.
SolutionThis square is partitioned into 3 equal shares, because there are 3 pieces of equal size and shape.

Ordering equal shares.
HintsThe more you partition a shape, the smaller your piece will be.
Which is larger?
 a whole piece.
 a piece of the whole that has been partitioned equally into 6 parts.
Look at the image. A piece from which cake is larger?
SolutionThe more you partition the shape, the smaller the piece becomes.
The order from largest to smallest is:
 whole
 half of
 a third of
 a quarter of
 a sixth of
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