: Algebra & Logic
Trend Task
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Approach: Independent  Level: Year 4 and year 8
Focus:   Basic algebra and patterns
Resources: Answer booklet
324KB
Questions / instructions:

This is a machine that changes numbers. It multiplies the number you put in by 3, and then adds 2 more. So, if you put in 4, it puts out 14.

   
% responses
2005 ('01)
Y4
Y8
1. If you put in a 5, what number will the machine put out?
17
19 (20)
83 (75)
2. If you put in a 10, what number will the machine put out?
32
20 (18)
81 (74)
YEAR 8 ONLY:
3. If you got out a 41, what number was put in? 13 • . 43 (32)  
4 If “X” is the number put into the machine, and “Y” is the number coming out, write down a formula which will give the value of “Y” whatever the value of “X”.
y = 3x + 2
22 (3)
or equivalent
5 (21)
YEAR 4 ONLY:
3. Make the next triangle and write the number under it.
1 3 6 10
drawing and number correct
36 (28)
one correct, but other omitted
10 (12)
4. Which number is equal to 3 tens plus 5 tens?
A
8
 
B
80
76 (67)
C
180
D
1800

5. How many blocks will be needed to make the next shape in this pattern?

9
57 (52)
YEAR 4 & 8:
[question 5 for Year 8]  
6. The Jones Kids
What is the smallest number of children in the Jones family if each child has at least one brother and at least one sister?
4
23 (19)
37 (38)
Total score:
7
3 (1)
6
5 (4)
7 (1)
5
10 (8)
11 (7)
4
17 (13)
17 (17)
3
16 (18)
26 (28)
2
22 (20)
21 (22)
1
19 (21)
6 (7)
[Note: Maximum score of 6 for year 8]
0
9 (14)
12 (18)
Commentary:
Year 8 students were able to handle the calculations based on an algebraic system but had difficulty in generating the underlying equation. Year 4 students had trouble with most of the questions here. Progress was seen for both year 4 and year 8 from 2001 to 2005.
 
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