Bits and Pieces

This activity encourages students to develop mental strategies for solving fraction problems.
For example, question 2 may be solved by working out that 1/4 of 28 is 7 and then multiplying 7 by 3 to find 3/4 of 28. Alternatively, the 7 (which is 1/4 ) could be taken away from 28, leaving 3/4 . Ensure that the students connect the way that the fractions are used with the quantities of the set involved. In this case, 28 is 4/4 of the cars, so 1/4 of the cars is 7. As 4/4 – 1/4 is 3/4 , then 28 – 7 = 21 white vehicles.
Students who cannot develop a mental strategy for solving the problems might find a double number line useful. For question 3, the number line could look like this:

In question 4, the students need to explore the equivalence between 6/10 = "/50 . Again, a double number line may help those who find it hard to form a mental strategy:

Some students will choose to work out 1/10 of the lollipops first and then multiply this by 6 to find 6/10, while others may find 5/10 of the lollipops and add this amount to 1/10 to make the 6/10 .
Question 6 uses the ratio idea to find the proportion of the marbles. The students may find this question difficult unless they understand how to visualise all the marbles. They will need to see that Mike has one part and Gloria has the rest and together this makes the whole set.

Answers to Activity

Answers and some possible strategies include:
1. 15. (30 ÷ 2 = 15. Half of 30 is 15.)
2. 21. (1/4 of 28 is 7, so 3/4 is 3 x 7 = 21.
Or: 28 ÷ 4 = 7. 3 x 7 = 21)
3. 10/15 , which is 2/3 .
4. 30. (50 = 5 x 10, so 5 x 6 are liquorice. 5 x 6 = 30)
5. a. 7. (35 ÷ 5 = 7)
b. 2/5 (the same proportion as in one packet)
6. 2/3 . (12 + 6 = 18. 12/18 = 2/3 )