Star Wars Fractions: Halving

We used Ioan’s Star Wars Lego characters to work on halving. We set up a beach a tent in the garden, because he always seems to think more clearly outside.

Resources

Whiteboard and pen
Lego characters

Method

Ioan explained how to write fractions. The top number is called the numerator. The numerator is the number of equal parts we have.

The denominator is the bottom number and it shows the total number of parts the whole is divided in to.

A half is one of two equal parts of an object, shape or quantity. Ioan drew lots of shapes and split them in half in different ways. They can all look different, but as long as the shape is split in to two equal parts, they are all halves.

Then he moved on to working out halves of his Star Wars characters. Ioan started off with 18 characters, so knew 18 was his denominator.

To work out the numerator, he sorted his 18 characters into an array, with two rows. Then he could count how many characters were in each row. For more on using arrays for multiplication and division, see ‘Making Chocolate Arrays‘.

After some trial and error, Ioan explained why he couldn’t use odd numbers for the denominator, because he couldn’t split them in half equally without a remainder of one. Now he knew that all his denominators had to be even, he decided to work methodically to find half of all the even numbers up to 20. He started with 10/20 and worked down.

Next, he used his arrays to work out how many sixteenths he’d need for a half.

He worked out what his numerator would be, with a denominator of 14, then went on to take two characters away to start the next sum. He took two characters from the top row, meaning he no longer had arrays. The top line had 5 characters and the bottom had 7. I encouraged him to set it back out in arrays, then take one from each row away. His arrays were now ready for the next sum.