Fractious Fractions (Y8)
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Approach:  One to one
ACCESS
Level: Year 8
Focus: Fractions of an amount  
Resources:
24 multilink blocks, 4 cards
184kb
Questions/instructions:

Hand students 24 multilink blocks and card 1.
Here are 24 blocks.
 
 
% responses
2009 ('05)
y4
y8
1. What is 1/4 of 24? 6   79 (85)
Tell me how you worked this out.
You can use the blocks if you want to.		      
Calculation strategy: 24 ÷ 4 = 6   26 (28)
  4 × 6 = 24   20 (21)
4 equal groups with blocks, count 1 group   13 (16)
any other appropriate strategy   20 (18)
Hand student card 2.    
2. What is 2/3 of 24? 16   56 (51)
Tell me how you worked this out.
You can use the blocks if you want to.		      
Calculation strategy: 24 ÷ 3 = 8 and 2 × 8 = 16   24 (23)
  3 × 8 = 24 and 2 × 8 = 16   14 (8)
3 equal groups with blocks, count 2 groups   14 (19)
any other appropriate strategy   5 (3)
Hand student card 3.    
3. What is 5/6 of 24? 20   56 (59)
Tell me how you worked this out.
You can use the blocks if you want to.		      
Calculation strategy: 24 ÷ 6 = 4 and 5 × 4 = 20   22 (24)
  6 × 4 = 24 and 5 × 4 = 20   12 (8)
6 equal groups with blocks, count 5 groups   17 (25)
any other appropriate strategy   5 (5)
Remove the blocks from the student but leave them in sight. Hand student card 4.    
4. If you had to find 1 1/2 lots of these blocks, how many would you need? 36   53 (48)
Tell me how you worked this out.
You can use the blocks if you want to.		      
Calculation strategy: 24 ÷ 2 = 12 and 12 + 24 = 36; OR
1/2 × 24 = 12 and 12 + 24 = 36		   46 (47)
  2 × 12 = 24 and 12 + 24 = 36   1 (0)
  found 1/2 of 24 blocks, added to 24   4 (0)
  any other appropriate strategy   4 (4)

Total score:
 11–12
  15 (11)
8–10
  18 (23)
5–7
  21 (19)
2–4
  20 (27)
0–1  
26 (20)
Subgroup Analysis [Click on charts to enlarge] :
Year 8
Commentary:
There was no meaningful change in performance from 2005 to 2009. Both Mäori and Pasifika students averaged substantially lower than Pakeha students.