Quick Way
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Approach:  One to one
ACCESS
Level: Year 4 and year 8
Focus: Patterns; computation strategies  
Resources:
4 pictures [simulated resources shown below.]
434kb
Questions/instructions:  

I’m going to show you some pictures of different objects.
Try to think of a quick way to work out how many objects there are without counting each one.
Here is the first page of objects.
Hand student picture 1. Allow time.

 
 
% responses
2009 ('05)
y4
y8

1. How many lizards are there?
15
87 (81)
95 (97)
2. How did you work out your answer?
solution involved multiplication
(5 × 3 or 3 × 5)
34 (35)
82 (83)
solution involving addition (5 + 5 + 5)
43 (39)
11 (12)
other sound approach not involving counting one by one
5 (9)
2 (0)
any other response, including counting one by one/counting in twos
18 (17)
5 (5)
Hand student picture 2. Allow time.  

3. Use a quick way for working out the number of ants. 22
53 (49)
75 (80)
4. How did you work out your answer?  
solution involving multiplication (5 × 2 + 3 × 4 or 5 × 5 – 3)
8 (14)
45 (51)
solution involving equivalent groupings (e.g. 9 + 9 + 4) 7 (8) 8 (8)
solution involving just addition (5 + 4 + 4 + 5 + 4) 34 (27) 21 (18)
other sound approach not involving counting one by one 10 (5) 5 (6)
any other response, including counting one by one/counting in twos 41 (46) 21 (17)
Hand student picture 3. Allow time.    
5. Use a quick way for working out the number of frogs. 16 63 (55) 74 (76)
6. How did you work out your answer?    
solution involving multiplication (4 × 4) 1 (1)  6 (8) 
solution involving recognising top and bottom have equivalent groupings
(e.g. 6 + 4 + 6; 2 + 4 + 6 + 4)
21 (23) 47 (46)
solution involving row by row addition (4 + 4 + 4 + 4 or 1 + 2 + 3 + 4 + 3 + 2 + 1) 29 (29) 20 (22)
other sound approach not involving counting one by one 10 (7) 7 (6)
any other response, including counting one by one/counting in twos 39 (40) 20 (17)
Hand student picture 4. Allow time.      
7. Use a quick way for working out the number of cherries. 50 29 (26) 52 (48)
8. How did you work out your answer?    
solution involving multiplication (7 × 5 + 5 × 3 or [3 + 7] × 5) 6 (8) 38 (36)
solution involving addition (of 5 tens or of 5 sevens and 5 threes) 21 (30) 18 (23)
other sound approach not involving counting one by one 21 (12) 18 (18)
any other response, including counting one by one/counting in twos 52 (50) 26 (23)

Total score:
11–12
4 (0) 30 (28)
9–10 11 (16) 27 (33)
7–8 25 (18) 19 (19)
4–6 37 (44) 18 (16)
0–3 23 (22)
6 (4)
Subgroup Analysis [Click on charts to enlarge] :
Year 4


Year 8


Commentary:
There was little change in performance at both year levels from 2005 to 2009. Year 4 Pasifika students performed similarly to Pakeha students.