Download Y6 Algebra - Pairs of Numbers

Find pairs of numbers that satisfy an equation with two
unknowns. (mastery)
1
a and b stand for whole numbers.
a + b = 100
a is 10 more than b.
Calculate the values of a and b.
2
Toffees
Lollipops
7p each
10p each
a=
b=
Marcus spent 61p on toffees and lollipops.
How many of each did he buy?
3
toffees
lollipops
c and d stand for whole numbers.
c + d < 10
c x d = 20
c>d
4
6
d=
Write the missing numbers so that 3a + 2b = 40.
One is done for you.
5
c=
c - 2d = 10
3a + 2b = 40
when a = 10 and b =
3a + 2b = 40
when a = 6 and b =
3a + 2b = 40
when a = 12 and b =
3a + 2b = 40
when a = 0
and b =
when c = 20
d=
when d = 10
c=
a and b stand for whole numbers.
a x b = 42
a + b = 13
a=b+1
a=
b=
5
Find pairs of numbers that satisfy an equation with two
unknowns. (mastery with greater depth)
1
a and b stand for whole numbers.
a + b = 1000
a is 250 more than b.
Calculate the values of a and b.
2
a=
b=
q=
r=
c=
d=
p + q = 140
q + r = 90
p + q + r = 200
Calculate the values of p, q and r.
p=
3
c and d stand for whole numbers.
c + d = 17
c x d = 72
c + 1= d
4
Write the missing numbers so that 4a + 5b = 100.
One is done for you.
5
6
4a + 5b = 100
when a = 20 and b =
4a + 5b = 100
when a = -5 and b =
4a + 5b = 100
when a = 12.5 and b =
4a + 5b = 100
when a = 30
5c - 2d = -10
when c = 10
d=
when d = 10
c=
a stands for a whole number that is more than 5 and less than 12
b stands for a whole number that is more than 20 and less than 30
What is the smallest number that a x b could be?
What is the largest number that b - a could be?
and b =
4
Find pairs of numbers that satisfy an equation with two
unknowns.
Teacher’s notes
Useful interactive games to teach the skills needed to develop algebraic thinking.
http://mathsframe.co.uk/en/resources/resource/104/
balancing_sums
I think balancing scales are a really useful starting point to
think about algebra. This game has lots of control over
level.
http://mathsframe.co.uk/en/resources/resource/100/
balance_scales_add_move_or_remove_a_weight
Balance the scales by either adding a weight, removing a
weight or moving a weight from one side to the other.
http://mathsframe.co.uk/en/resources/resource/121/
shape_sequences
A great game to encourage generalising about sequences
and finding the nth term.
Answers:
Mastery - 1) a = 55, b = 45 2) 3 toffees, 4 lollipops
Mastery WGD
1) 625, 375
2) 110, 30, 60
3) 8, 9
3) 11, 2, 20
4) 24, 10, -4
4) 5, 30
5) a = 7, b =6
5) 30, 6
6) 121, 23