Fractions in a Whole

Doing operations with fractions helps the students understand fractions. Operations provide a purpose for using fractions and highlight key structures in the numbers.

Using Materials

Problem: “Owen makes up a packet of sweets consisting of 4 yellow sweets and 3 blue sweets. What fraction of the packet is yellow?” “blue?”

Discuss why the fractions are 4/7 and 3/7.  Write + on the board and discuss the answer. (Answer: or 1 whole.)

Examples: Repeat using cubes to work out: 4/6 + 2/6

7/10 + 3/10
8/11 + 3/11

Using Imaging

Problem: Show the students 5 yellow cubes and hide 2 blue cubes.“The yellow cubes represent of a packet of sweets. How many blue cubes am I hiding and what fraction of a packet am I hiding?”(Answer: 2 sweets and of a packet.)  Examples: Repeat to work out:

6/11 + ? = 1
1/5 + ? = 1
? + 6/11 = 1...

Using Number Properties

Problem: “Maria bought a box of envelopes for her business. After a month, she finds there is  only 5/31 of the box left. What fraction of the box has been used?”

(Answer: 31/31 = 1 box, so 31/31  – 5 = 31-5/31 = 26/31 must have been used.)

Examples: Work out: 6/17 + ? = 1

27/47 + ? = 1
?  + 57/100 = 1
1 - 12/23 = ?/23
1 – 90/101 = ?/101 ….

Understanding Number Properties:

Write down two fractions whose denominators are both 1 000 and whose numerators make the fractions add up to 1 whole.