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Level Four > Number and Algebra

Bits and Pieces

Purpose: 

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

Achievement Objectives:

Achievement Objective: NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
AO elaboration and other teaching resources

Specific Learning Outcomes: 

find fractions of a number

Required Resource Materials: 
FIO, Link, Number, Book One, Bits and Pieces, page 24
Activity: 

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:
number line.
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:
number line.

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.
number line.

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 )