Numbers written in symbols, calculations that make a target, and addition grids.
OftenIn many papers, especially GL AssessmentAbout 35 seconds a question in the test
The big idea
Some verbal reasoning questions are really about numbers: a made up system where symbols stand for numbers, or a list of numbers and signs that must make a target.
Both reward slow, careful working: one symbol miscounted or one step done in the wrong order gives a wrong answer that is often one of the choices.
Tips that save marks
Symbols: use the smallest example to find the simplest symbol first.
Count each kind of symbol separately, then multiply by what it is worth.
Targets: work the brackets first and write the result above them.
Addition grids: a sum take away the edge number you know gives the one you do not.
A worked example
Three dots stand for 3, and a circle with two dots stands for 7. What do two circles and one dot stand for?
Three dots are 3, so one dot is 1.
A circle and two dots are 7, so a circle is 5.
Two circles and a dot are 5, 5 and 1 more: 11.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 35 seconds
In this addition grid, each box is the number at the start of its row added to the number at the top of its column. What number goes in the box marked ?
+
27
9
Row
24
51
33
54
25
52
34
55
15
42
24
?
Show the worked answer
Answer: A, 45
How to work it out
The missing top number is 30, found by taking a row number away from a sum in its column.
The box is 15 + 30 = 45.
Why the other options are wrong
B (44): This is one too few; add the two edge numbers again.
C (46): This is one too many; add the two edge numbers again.
D (42): This uses the number at the top of the wrong column.
E (15): This takes the numbers away; the grid adds them.
Question 2Aim for about 35 seconds
In a secret number system, 2 is written <<; 6 is written =<; 16 is written #=<. What number is ###<<?
Show the worked answer
Answer: B, 32
How to work it out
From the examples, # is 10, = is 5, < is 1. ###<< is 3 × 10 + 2 × 1 = 32.
Why the other options are wrong
A (17): 17 swaps what # and = are worth; check them against the examples.
C (31): Count the < symbols again: 31 has one < too few.
D (33): Count the < symbols again: 33 has one < too many.
E (5): 5 is the number of symbols, but they are not all worth 1.
Question 3Aim for about 35 seconds
In a secret number system, 3 is written +++; 6 is written O+; 16 is written =O+. How is 18 written?
Show the worked answer
Answer: C, =O+++
How to work it out
From the examples, = is 10, O is 5, + is 1.
18 is 1 × 10 + 1 × 5 + 3 × 1, so it is written =O+++.
Why the other options are wrong
A (O+++): O+++ is 8, 10 less than 18.
B (==+++): ==+++ is 23, 5 more than 18.
D (=O++++): =O++++ is 19, one more than 18.
E (==O+++): ==O+++ is 28, 10 more than 18.
Question 4Aim for about 35 seconds
In this addition grid, each box is the number at the start of its row added to the number at the top of its column. What number goes in the box marked ?
+
12
Row
30
20
32
?
50
11
23
38
41
31
43
58
61
Show the worked answer
Answer: B, 47
How to work it out
The missing top number is 27, found by taking a row number away from a sum in its column.
The box is 20 + 27 = 47.
Why the other options are wrong
A (48): This is one too many; add the two edge numbers again.
C (7): This takes the numbers away; the grid adds them.
D (50): This uses the number at the top of the wrong column.
E (46): This is one too few; add the two edge numbers again.
Question 5Aim for about 35 seconds
In this addition grid, each box is the number at the start of its row added to the number at the top of its column. What number goes in the box marked ?
+
16
Row
25
28
44
?
53
32
48
35
57
21
37
24
46
Show the worked answer
Answer: C, 31
How to work it out
The missing top number is 3, found by taking a row number away from a sum in its column.
The box is 28 + 3 = 31.
Why the other options are wrong
A (53): This uses the number at the top of the wrong column.
B (25): This takes the numbers away; the grid adds them.
D (30): This is one too few; add the two edge numbers again.
E (32): This is one too many; add the two edge numbers again.
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