# Estimating with Fractions

AO elaboration and other teaching resources

AO elaboration and other teaching resources

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.

#### Using Materials

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...

#### Using Imaging

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

#### Using Number Properties

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.)*

#### Understanding Number Properties:

Make up two fractions that both have denominators greater than 30 and that add up to just a little bit less than 1.