Solve problems that involve adding and subtracting fractions with related denominators.
Find equivalent fractions and order fractions.
Number Framework Stage 7
An important part of number sense is to have a concept of the size of fractions independent of doing calculations. For example, a student with a good sense of number will know immediately that 11/21 is more than 1/2 because 11 is over half the available 21 pieces.
Problem: Show 4/9 using the two different-coloured circle pieces and discuss whether it is more or less than 1/2.
Each student rotates the circles until one colour circle shows as near to 4/9 as they can. Discuss why it is 4/9.Look at the other colour and discuss what fraction it is.
(Answer: 5/9 because there are 9/9 in 1 whole.)
Examples: Show these fractions on the circles and work out the other fraction that adds up to 1 whole: 3/7 4/5 5/9 5/11 11/21...
Problem: “I have made 15/31, but you cannot see it. Describe in words what this fraction looks like.”
(Possible answer: the fraction is just a little bit less than 1/2.)
“What is the other fraction?” (Answer: 16/31.)
Examples: Describe these fractions without using the circles and work out the other fraction that adds up to 1 whole: 5/11 2/5 4/7 8/17 6/13
Problem: “Maurice eats 2/5 of a cake, and Norris eats 3/7 of a same sized cake. In total, do they eat more or less than 1 cake?”
Discuss the answer. (Answer: Both are a little less than 1/2 so the total is less than 1 whole.)
Examples: Without calculating, determine whether these are more or less than 1:
2/5 + 12/23 17/33 + 6/11 51/100 + 6/12 24/48 + 29/60 24/47 + 61/120 ...
Examples: Is 1 – 21/43 more or less than 1/2? Is 11/45 more or less than 1/4? Is 3/4 – 11/40 more or less than 1/2? Is 3/4 + 15/62 more or less than 1?
Hard example: Is 3/7 + 14/27 more or less than 1? (Answer: Here the gap between 3/7 and 1/2 is more than the gap between 14/27 and 1/2. So 3/7 + 14/27 < 1.)
Make up two fractions that both have denominators greater than 30 and that add up to just a little bit less than 1.
Printed from https://nzmaths.co.nz/resource/estimating-fractions at 3:54am on the 22nd May 2024