2. Use simple formulae.
Generate and describe linear number sequences.
Express missing number problems algebraically.
Find pairs of numbers that satisfy an equation with two unknowns.
Enumerate possibilities of combinations of two variables

3. Using a Formula If a=4 b=5 c=6 d=7 Calculate the answers to these:
3c + c² =
2c + d =
d² - c² =
3a + 2b =
a³ - a² =
a² - c =
a² + b² + c² + d² =
d + b² =
b³ + a³ - d² - c = 15 54 19 13 22 48 10
126 32
134
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4. Mystery Shapes Work out what number the shape represents
in each calculation:
 ÷ 3 = 12 ÷ 2
24 -  = 16 + 
² x  = 27
3( +  + ) = 18
4 x ² = 16
5 = 3 + 10
 = 18
 = 4
 = 3
 = 2
 =2
 = 5
Click for a hint.
Work out the order of the calculation given and then work backwards using inverse operations.
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5. Number Sequences
These sequences are created using a formula including ‘n’ which means any number.
For the 1st number n = 1, for the 2nd number n = 2 and so on.
For each sequence, work out the 6th, 15th, 21st and 100th number on the sequence.
Formula
First 5 Numbers in the Sequence
6th
15th
21th
100th
n + 20
21, 22, 23, 24, 25…
n - 12
-11, -10, -9, -8, -7…
2n + 4
6, 8, 10, 12, 14…
5 + 3n
8, 11, 14, 17, 20…
8n ÷ 2
4, 8, 12, 16, 20…
7n - 17
-10, -3, 4, 11, 18…
Formula
First 5 Numbers in the Sequence
6th
15th
21th
100th
n + 20
21, 22, 23, 24, 25… 26 35 41
120
n - 12
-11, -10, -9, -8, -7… -6 3 9 88
2n + 4
6, 8, 10, 12, 14… 16 34 46
204
5 + 3n
8, 11, 14, 17, 20… 23 50 68
305
8n ÷ 2
4, 8, 12, 16, 20… 24 60 84
400
7n - 17
-10, -3, 4, 11, 18… 25
130
683 15
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6. Writing Algebra
Write the algebraic expression for each of these explanations:
p is 4 more than y
z is twice k
d is half of r
t is the square root of m
A plumber cost is 3 times the hours worked (h) plus £30 call out charge.
Gravity (g) is mass (m) multiplied by acceleration (a)
p = y + 4
2k = z
d = r ÷ 2
t = √m
3h + 30
g = ma or g = m x a
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7. Mystery Pairs
Write 4 or more possible combinations of pairs of numbers that would make these calculations correct:
a + b = 10
ca = 24
d = ½ e
y = m²
pk = 60 and k - p = 11
m x 2n = 36 and n ÷ m = 2
3f ÷ h = 9 and f + 2h = 35
0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, (and reversed)
1 x 24, 2 x 12, 3 x 8, 4 x 6 (and reversed)
Any pair of numbers where e = 2 x d
Any pair where m x m = y
Find the only pair of numbers that makes both of these calculation pairs correct:
p = 4 and k = 15
m = 3 and n = 6
f = 21 and h = 7
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8. Possibilities A B C a + m = 21 b – f = 50 ck = 60 a < m b > f
Read each of the rules carefully and write all the possible combinations for each question: A B C
a + m = 21
b – f = 50
ck = 60
a < m
b > f
c < k
10 < m < 20
69 < (b + f) < 91
(k-c) < 50
Possible answers: a 2 3 4 5 6 7 8 9 10 m 19 18 17 16 15 14 13 12 11 c 2 3 4 5 6 k 30 20 15 12 10 b 60 61 62 63 64 65 66 67 68 69 70 f 10 11 12 13 14 15 16 17 18 19 20
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