1
The fraction wall
Discover Mathematics P2: Term 2, Lessons 101–110
GoalUse a fraction wall to compare halves, thirds and fourths and to see equal fractions.
New words
fraction wall · bars of the same length cut into different equal partsequal fractions · different fractions that cover the same amountcompare · say which is bigger or smaller
Explanation
A fraction wall has bars that are all the same length. The top bar is 1 whole. Below it the bars are cut into halves, thirds and fourths. Look at the wall. One half is longer than one third, and one third is longer than one fourth. More equal parts means smaller parts. Some fractions are equal: on the wall 2/4 is exactly as long as 1/2.
Worked examples
Halves and fourths. One half and 2/4 are the same length, so 1/2 = 2/4.
Thirds and fourths. One third is longer than one fourth, so 1/3 is more than 1/4.
When all the parts are shaded we get the whole. 2/2, 3/3 and 4/4 are all the same length as 1 whole.
Class activity
Build your own wall. Cut four paper strips of the same length. Leave one whole. Fold the second into halves, the third into thirds, and the fourth into fourths, and cut along the folds. Lay the pieces under the whole strip and find which pieces are the same length.
Practice
1
Which is longer: 1/2 or 1/4?
1/2 is longer.
2
Find the fraction with fourths that is as long as 1/2.
2/4.
3
Is 3/4 more than a whole or less than a whole?
Less than a whole, because 4/4 is the whole.
4
Put these from the smallest piece to the biggest piece: 1/2, 1/4, 1/3.
1/4, 1/3, 1/2.
5
How many fourths make one half?
2 fourths make one half.