Problem-Solving
Pupils’ Version
Bridging the Gap
Note to Pupils





Do you know how to work out money totals?
- or change from £10?
- or the cost of 6 cakes when you know the price of 1?
- the cost of 1 cake when you know the total for 6?
Do you have problems knowing how to get started on tricky
maths problems?
This resource will help you to…
-
Learn about money calculations
-
and become an expert at cracking problems!
-
Using a simple 4-step guide to problem-solving
Contents
A.
Learning Area
(Start here to revise your learning)
B.
Test Yourself: Now It’s Your Turn!
(Start here if you just want to test yourself)
C.
Where To Next?
(Suggestions for main menu)
(TO GO TO LINK, HOLD DOWN CONTROL AND CLICK ON YOUR CHOICE)
How to use this resource
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Slide Show > View Show
Which One Are You ???
R U a Problem-Coward ?
… or …
PROBLEM!
R U a Problem-Cracker?
R U PC?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
How to become a
PROBLEM-CRACKER
in 4 Easy Steps!
RU PC?
Read it! … what’s it about?
HOW?
Underline it! … find the clues
Picture it! … add? subtract? multiply? divide?
Let’s try
… use a number line to help
Calculate it! … work it out !
it and
see …
Step 1
STEP 1
Read it !
- What do
I know?
- What do
I want to
find out?
… I’ll read this again
so I’m sure I get it …
Step 2
STEP 1
Read it !
STEP 2
Underline it !
Crunch Bar 50p
KEY NUMBER!
Jaz Juice
20p
KEY NUMBER!
WORD CLUE! add
WORD CLUE! subtract
KEY NUMBER!
How much
altogether?
How much
change from £1?
… and …
LOOK FOR
KEY
NUMBERS!
LOOK FOR
WORD
CLUES!
sum
fewer plus
less total divided
each altogether
lots of difference
times share all left
groups of
increase
sets of
leave
more
Some word clues
to watch out for…
+ CLUES
sum
total
- CLUES
altogether
difference
x CLUES
all
leave
lots of
÷ CLUES
more
left
Sets of
divided
plus
fewer
Groups of
share
increase
less
times
each
Step 3
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Crunch Bar 50p
Jaz Juice
20p
How much
altogether?
How much change
from £1?
0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1
This means ADD:
2 Steps so far …
50 + 20 = cost
CLICK for Step 3!
… and this means
SUBTRACT:
100 – cost = change
Step 4
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Crunch Bar 50p
Jaz Juice
20p
0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1
STEP 4 Calculate It !
How much
altogether?
How much change
from £1?
Start at 50p and
count on 20p …
60, 70,
So 50+ 20 = 70
Total cost is 70p
3 steps
done
Count
back from
100p1toto70p…
go …
90, 80, 70 = 30
So there
is 30p
CLICK
for
change !
Step 4!
The 4 Steps
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
The School Canteen Example 1
STEP 1 Read it !
STEP 2 Underline It !
KEY NUMBER!
Monday
Paul buys a 70p salad
and a 20p peach.
KEY NUMBER!
How much did he pay
altogether?
WORD CLUE! add
The School Canteen Example 1
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Monday
Paul buys a 70p salad
and a 20p peach.
0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1
This means ADD:
How much did he pay
altogether?
70 + 20
The School Canteen Example 1
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Monday
Paul buys a 70p salad
and a 20p peach.
0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1
STEP 4 Calculate It !
Start at 70p and count on 20p …
80, 90,
How much did he pay
altogether?
So 70+ 20 = 90
Total cost is 90p
(Remember! Put your answer into a sentence!)
Easy Problem-Solving in 4 Steps!
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
The School Canteen Example 2
STEP 1 Read it !
STEP 2 Underline It !
Tuesday
Paul buys a 40p
potato and leek soup,
the 90p mushroom
curry and a
10p pear.
What was his
total cost?
KEY NUMBER!
KEY NUMBER!
KEY NUMBER!
WORD CLUE! add
The School Canteen Example 2
STEP 1 Read it !
STEP 2 Underline It !
Tuesday
STEP 3 Picture It! !
Paul buys a 40p
potato and leek soup,
70p
80p
90p
£1
£1.10 £1.20 £1.30 £1.40
the 90p mushroom
curry and a
This means ADD:
10p pear.
90 + 40 + 10
What was his
total cost?
The School Canteen Example 2
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Tuesday
70p
Paul buys a 40p
80p
90p
£1
£1.10 £1.20 £1.30 £1.40
STEP 4 Calculate It !
potato and leek soup,
the 90p mushroom
curry and a
Start at 90p and count on 40p …
£1, £1.10, £1.20, £1.30
10p pear.
Then count on 10p … £1.40
What was his
total cost?
Total cost is £1.40
Which is easier –
Start at 90p and count on 40p
or+ 40 + 10 = £1.40
So 90
Start at 40p and count on 90p ?
Easy Problem-Solving in 4 Steps!
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
The School Canteen Example 3
STEP 1 Read it !
STEP 2 Underline It !
Wednesday
Paul buys a 68p
KEY NUMBER!
chicken salad bagel.
WORD CLUE! subtract
How much change did
he get back from £1?
KEY NUMBER!
The School Canteen Example 3
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Wednesday
Paul buys a 68p
chicken salad bagel.
How much change did
he get back from £1?
30p
40p
50p
60p
70p
80p
90p
This means
SUBTRACT:
£1 – 68p
OR 100 - 68
£1
The School Canteen Example 3
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Wednesday
30p
40p
50p
70p
80p
90p
£1
STEP 4 Calculate It !
Paul buys a 68p
chicken salad bagel.
60p
You can
subtract
£170p
in lots of
Count
back 68p
fromfrom
£1 by
different
ways:…
instead
of 68p:
OR
90p…80p…70p…60p…50p…40p…30p
80p of
then
to £1
trytoone
the
How much change did - Count on from 72p up
or £1 – 60p –
2p8ptooother
much!ways
8p count
– 60p back by 2p …
he get back from £1? or £1 –So
or
£1 – 70p + 2p
(Easier. Why?)
…31p…32p
See way which
Let’s tryPaul
one out
…32p
gets
you change
prefer!
Easy Problem-Solving in 4 Steps!
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
The School Canteen Example 4
STEP 1 Read it !
STEP 2 Underline It !
Thursday
KEY NUMBER!
Paul buys a 54p
tomato soup and an
apple pie.
Altogether he spends
£1.32.
How much was the
pie?
WORD CLUE! total
KEY NUMBER!
WORD CLUE!
Missing number
The School Canteen Example 4
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Thursday
70p
80p
90p
£1
£1.10 £1.20 £1.30 £1.40
Paul buys a 54p
tomato soup and an
apple pie.
Altogether he spends
£1.32.
How much was the
pie?
This means
SUBTRACT:
£1.32 – 54P
OR 132 - 54
The School Canteen Example 4
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Thursday
Paul buys a 54p
tomato soup and an
apple pie.
70p
80p
90p
£1
£1.10 £1.20 £1.30 £1.40
STEP 4 Calculate It !
You can subtract 54p from £1.32 in
Count back
£1.32 by
2p to the 1st
lots from
of different
ways:
friendly number: £1.30
Altogether he spends £1.32 – 50p – 4p
Then
count
back by 50p …
£1.32
–
4p
–
50p
£1.32.
How much was the
pie?
£1.20
… £1.10
90p Why?)
… 80p
£1.32
– 52p
– 2p… £1 …
(Easier.
£1.32 – 2p – 50p – 2p (Even easier! Why?)
Then count back by 2p more … 78p
Take a look …
The pie cost is 78p
Easy Problem-Solving in 4 Steps!
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
The School Canteen Example 5
STEP 1 Read it !
STEP 2 Underline It !
Thursday
Paul buys 6 mini
cheese ‘n tomato
pizzas at 15p each.
How much did he
spend altogether?
KEY NUMBER!
KEY NUMBER!
WORD CLUE!
multiply
WORD CLUE!
total
The School Canteen Example 5
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Thursday
This means ADD:
6 groups of 15
Paul buys 6 mini
cheese ‘n tomato
pizzas at 15p each.
BUT EASIER TO …
How much did he
spend altogether?
MULTIPLY !
15 + 15 + 15 + 15 + 15
6 X 15p
6 x 19
OR USE NEAREST TENS
6 x 19
OR DOUBLE and HALVE
The School Canteen Example 5
= 6 xSTEP
20 -3 6
x 1 It! !
Picture
= 120
- 6
= 114
STEP 1 Read it !
=
=
=
=
3 x 38
3 x 30 +STEP
3 x28 Underline It !
90
+ 24
114
Thursday
Paul spends £1.14
Paul spends £1.14
Paul buys 6 mini
19
cheese6‘nx tomato
YOU
CAN
pizzas
atPARTITION
19p each. 19
= 6 x 10 + 6 x 9
= How
60 much
+ 54 did
= 114
he
spend altogether?
Paul spends £1.14
STEP 4 Calculate It !
You can
work out
6 x 19 in lots o
Some
were
different ways:
6
6
3
6
x
x
x
x
easier than others!
19 - but only if you know your 19 times tables!
10 + 6Which
x9
- way
if you like to use partition
38
-do
if you like to double and halve
20 – 6you
x 1 prefer?
- if you like using nearest tens
Take a look …
Easy Problem-Solving in 4 Steps!
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
The School Canteen Example 6
STEP 1 Read it !
STEP 2 Underline It !
Friday Special
KEY NUMBER!
Paul pays 64p for 4
identical cakes
KEY NUMBER!
How much was each
cake?
WORD CLUE!
division
The School Canteen Example 6
STEP 1 Read it !
STEP 3 Picture It! !
STEP 2 Underline It !
Friday Special
Paul pays 64p for 4
identical cakes
How much was each
cake?
This means :
64 divided into 4
equal groups …
DIVIDE:
64 ÷ 4
64 ÷ 4
PARTITION
STEP 1 Read
it ! 60 and 4 …
Partition
64 into
60 ÷ 4 = 15
64 with:
÷ 4 CHUNKING
start
64
Altogether
you have
10many
x 4 4’s in
- 40
away
10 lots
4 keep
How
64? Take
To find
out,
you of
can
subtracted
subtracting
Leaving 4’s until
24 you reach 0.
The School Canteen Example 6
STEP 2 Underline It !
4÷4= 1+
16Special
Friday
Each egg roll costs 16p
STEP 3 Picture It! !
10away
+ 5 another
+ 1 lots5 of
x 4subtract- 20
Take
lots4 of 4
You5can
in chunks
to make
it easy:
Leaving
4
= 16 lots of 4
For example,
x 4 10 x -4 =4 40.Take away 1 lot of 4
You 1know
Each egg roll costs 16p
0
So subtract 4 lots of 10 (40). Keep subtracting …
STEP 4 Calculate It !
Paul pays 64p for 4
Which
way You
did can
youwork
prefer?
64
÷
4
out 64 ÷ 4 in lots of
identical cakes
HALVE & HALVE AGAIN
64 ÷ 2 = 32
How
32
÷ 2much
= 16 was each
cake?
Each egg roll costs 16p
different
64 ÷ways:
4
FORMAL WRITTEN METHOD
64 ÷ 2 ÷ 2
- halve
it4’s
and
halve
How
many
4’sinin
24?again
How
many
6?
32 ÷ 2
- if you halve
numbers 0
to start
with
6
remainder
STOP
1 both
2
64 - 40 1
- 206
-4
- chunking method
44 64 6
4
Each egg roll costs 16p
Take a look …
- written method
Now Your Turn!
The Lasagne Problem
Problem 1
Sara buys a 72p lasagne and a
two 39p peaches.
How much did she pay
altogether?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
She
Clickpays
£1.50
for
altogether
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Bolognese Problem
Problem 2
Sara buys a 86p bolognese
and a four 37p strawberry
whips .
What was her total cost?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
She
Clickpays
£2.34
for
altogether
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Beef Hotpot Problem
Problem 3
Ben buys a 39p tomato soup,
the 85p beef hotpot and three
8p pears.
How much did he pay
altogether?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
He paid
Click
£1.48
for
altogether
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Lamb Yuk Sung Problem
Problem 4
Ben buys a 62p pea soup, the
99p lamb yuk sung and seven
12p plums.
How much did he pay
altogether?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
He paid
Click
£2.45
for
altogether
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Salami Problem
Problem 5
Richie buys a two £1.19 salami
and cheese baguettes.
How much change did she
receive from £5?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
She
Click
received
for
£2.62 in
solution
change.
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Kebabs Problem
Problem 6
Richie buys a three £1.54
kebabs.
How much change did she
receive from £10?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
She
Click
received
for
£5.38 in
solution
change.
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Trifle Problem
Problem 7
Zaynah buys a 39p mushroom
soup, the £1.25 shepherd’s pie
and a trifle.
Altogether, she spends £2.99.
How much is the trifle?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
The
Clicktrifle
costs
for £1.35
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Noodle Soup Problem
Problem 8
Zaynah buys a noodle soup,
the £1.75 fish pie and two 72p
apple turnovers.
Altogether, she spends £4.05.
How much is the noodle soup?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
The
Clicksoup
costs
for 86p
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Pasty Problem
Problem 9
Jamie buys 4 vegetable pasties
costing 56p each.
How much did he pay
altogether?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
He paid
Click
£2.24
for
altogether
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Fajitas Problem
Problem 10
Jamie buys 3 fajitas costing
£0.79 each.
How much did he pay
altogether?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
He paid
Click
£2.37
for
altogether
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Spring Roll Problem
Problem 11
Jan buys 5 vegetable spring
rolls costing 84p each.
How much change does she
get back from £10?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
She
Click
receives
for
£5.80
solution
change
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Mini Samosas Problem
Problem 12
Jan buys 8 mini samosas
costing 37p each.
How much change does she
get back from £20?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
She
Click
receives
for
£17.04
solution
change
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Salad Bar Problem
Problem 13
There’s a big choice at the salad bar!
Philip spends £2.38 on: tomato, lettuce,
egg, onion, beans, potato, celery.
Each salad portion is the same price!
How much is each portion?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
Each
Click
portion
for
costs 34p
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Salad Bar Problem
Problem 14
Ben buys 9 mini cheese ‘n
pickle baps for £2.61
How much is each bap?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
Each
Click bap
costs
for 29p
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Banana Smoothie Problem
Problem 15
Lee and his three mates each
Each
Click one
bought a small banana smoothie. received
for
They paid £1.40 in total.
£4.65
solution
How much change did each
change.
to
pupil get back from £5?
problem
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Now Your Turn!
The Banana Smoothie Problem
Problem 16
Paula and her 5 friends each
Each
Click one
bought a strawberry yoghurt ice- received
for
cream. They paid £6.84 in total. solution
£8.86
How much change did each
change.
to
pupil get back from £10?
problem
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Now Your Turn!
The Tropical Juice Problem
Problem 17
Alisha buys three tropical juices
Click
Each
juice
and an 85p tuna mayo cob.
for 70p
costs
She receives £2.05 change from solution
a £5 note. How much is each
to
juice?
problem
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Now Your Turn!
The Veggie-Burger Problem
Problem 18
Anya buys four veggie-burgers
and an 64p fruit salad.
If she receives £13.20 change
from a £20 note, how much is
each burger?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
Clickburger
Each
for
costs
solution
£1.54
to
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Hot Cross Buns Problem
Problem 19
Special Offer: Hot Cross Buns!
4 for £1 10 for £2.70 8 for £2.08
Which offers the best value for
money?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
4Click
for £1 is
best
for value
for money
solution
(25p
to each)
problem
STEP 4
Calculate It !
?
Now Your Turn!
The Rock Cakes Problem
Problem 20
Special Offer: Rock Cakes!
3 for £1 10 for £3.40 8 for £2.56
Which offers the best value for
money?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
8Click
for £2.24
is best
for
value for
solution
money
to
(32p each)
problem
STEP 4
Calculate It !
?
Now U R PC with Money,
Why not try …
THE FIENDISH SPANISH CLASSROOM PROBLEMS ?
- about Money with Area and Perimeter
THE FIENDISH SCIENCE LAB PROBLEMS ?
- about Money with Measurements