Bridging the Gap Problem-Solving Pupils Version. Note to Pupils D Do you know how to work out money totals? - - or change from £10? or the cost of 6 cakes

Bridging the Gap Bridging the Gap

Problem-SolvingProblem-SolvingPupils’ VersionPupils’ Version

Note to PupilsNote to Pupils Do you know how to work out Do you know how to work out money money totals?totals? - or - or changechange from £10? from £10? - or the - or the cost cost of 6 cakes when you know the price of 1? of 6 cakes when you know the price of 1? - the - the costcost of 1 cake when you know the total for 6? of 1 cake when you know the total for 6?

Do you have problems knowing how to get started on Do you have problems knowing how to get started on tricky tricky

maths maths problemsproblems??

This resource will help you to…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

How to use this resourceHow to use this resourceYou can control how fast or slow you go using:

FORWARD: OR OR Enter OR Left-hand mouse

BACK: OR OR Back Space

TO START POWERPOINT: F5 OR Slide Show > View Show

TO RETURN TO MENU: Escape

ContentsContents

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)

Which One Are You ???Which One Are You ???

R UR U a a PProblemroblem-C-Coward oward ??… … or …or …

R UR U a a PProblemroblem-C-Crackerracker??

PROBLEM!

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Read it ! Underline It !

Picture It! !

Calculate It !

R U PC?R U PC?

R U P CR U P C ? ?RRead it! ead it! … … what’s it about?what’s it about?

UUnderline it! nderline it! … … find the cluesfind the clues

PPicture it! icture it! … … add? subtract? multiply? divide?add? subtract? multiply? divide?

… … use a number line to helpuse a number line to help

CCalculate it!alculate it! … … work it out !work it out !

HOW?

Let’s try it and

see …

How to become How to become aa PROBLEM-CRACKERPROBLEM-CRACKER

inin 4 Easy Steps! 4 Easy Steps!

Step 1Step 1 - What do I know?STEP 1

Read it !

- What do I want to find out?

… I’ll read this again so I’m sure I

get it …

Crunch Bar 50p Jaz Juice 20p

How much altogether?

How much change from

£1?

STEP 1

Read it !

WORD CLUE! add

WORD CLUE! subtract

KEY NUMBER!

STEP 2 Underline

it !

KEY NUMBER!

KEY NUMBER!

LOOK FOR WORD CLUES!

… and …LOOK FOR

KEY NUMBERS

!

sumfewer plus

less total dividedeach altogether

lots of differencetimes share all left

groups ofincrease

sets of leavemore

Step 2Step 2

+ CLUES

sum

total

altogether

all

more

plus

increase

- CLUES

difference

leave

left

fewer

less

x CLUES

lots of

Sets of

Groups of

times

÷ CLUES

divided

share

each

Some word clues to watch out

for…

Step 3Step 3STEP 1 Read it !

STEP 2 Underline It !

STEP 3 Picture It! !

0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1



How much change

from £1?

This means ADD:50 + 20 = cost

… and this means SUBTRACT:

100 – cost = change

2 Steps so far …

CLICK for Step 3!

Step 4Step 4STEP 1 Read it !





How much change

from £1?

STEP 4 Calculate It !

Start at 50p and count on 20p …

60, 70,

So 50+ 20 = 70

Total cost is 70p

Count back from 100p to 70p…

90, 80, 70 = 30

So there is 30p change !

0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1

3 steps done

1 to go …

CLICK for

Step 4!

The 4 StepsThe 4 Steps

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4


Picture It! ! Calculate It !

The School Canteen Example 1The School Canteen Example 1STEP 1 Read

it !


Monday Monday Paul buys a 70p Paul buys a 70p salad and a 20p salad and a 20p

peach. peach.

How much did he How much did he pay altogether?pay altogether?

WORD CLUE! add

KEY NUMBER!

KEY NUMBER!


it !STEP 3 Picture

It! !

MondayMondayPaul buys a 70p Paul buys a 70p salad and a 20p salad and a 20p

peach. peach.


This means ADD:

70 + 20


0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1


it !STEP 3 Picture

It! !

MondayMondayPaul buys a 70p Paul buys a 70p salad and a 20p salad and a 20p

peach. peach.



Start at 70p and count on 20p … 80, 90,

So 70+ 20 = 90

Total cost is 90p


(Remember! Put your answer into a sentence!)

0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1

Easy Problem-Solving in 4 Steps!Easy Problem-Solving in 4 Steps!

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4




it !


TuesdayTuesday

Paul buys a 40p Paul buys a 40p

potato and leek potato and leek soup,soup,

the 90p mushroom the 90p mushroom curry and a curry and a

10p pear. 10p pear.

What was his What was his total cost?total cost?

WORD CLUE! add

KEY NUMBER!

KEY NUMBER!

KEY NUMBER!


it !



TuesdayTuesday




10p pear. 10p pear.


This means ADD:

90 + 40 + 10

70p 80p 90p £1 £1.10 £1.20 £1.30 £1.40


it !STEP 3 Picture

It! !


TuesdayTuesday




10p pear. 10p pear.


70p 80p 90p £1 £1.10 £1.20 £1.30 £1.40

Start at 90p and count on 40p … £1, £1.10, £1.20, £1.30

Then count on 10p … £1.40

So 90 + 40 + 10 = £1.40

Total cost is £1.40

Which is easier –

Start at 90p and count on 40p orStart at 40p and count on 90p ?



STEP 1

?

STEP 2

?

STEP 3

?

STEP 4




it !


WednesdayWednesday

Paul buys a 68pPaul buys a 68p

chicken salad chicken salad bagel. bagel.

How much change How much change diddid

he get back from he get back from £1?£1?

KEY NUMBER!

KEY NUMBER!

WORD CLUE! subtract


it !STEP 3 Picture

It! !


WednesdayWednesday





This means SUBTRACT:

£1 – 68pOR 100 - 68

30p 40p 50p 60p 70p 80p 90p £1


it !STEP 3 Picture

It! !



You can subtract 68p from £1 in lots of different ways:

- Count on from 72p up to 80p then to £1 or £1 – 60p – 8p or £1 – 8p – 60p or £1 – 70p + 2p (Easier. Why?)

Let’s try one out …

WednesdayWednesday





30p 40p 50p 60p 70p 80p 90p £1

Count back from £1 by 70p instead of 68p: …

90p…80p…70p…60p…50p…40p…30p

2p too much!So count back by 2p …

…31p…32p

Paul gets 32p change

OR try one of the other ways

See way which you prefer!


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4




it !


ThursdayThursday


tomato soup and tomato soup and an apple pie. an apple pie.

Altogether he Altogether he spends £1.32. spends £1.32.

How much was the How much was the pie?pie? WORD CLUE!

Missing number

KEY NUMBER!

KEY NUMBER!

WORD CLUE! total


it !STEP 3 Picture

It! !


70p 80p 90p £1 £1.10 £1.20 £1.30 £1.40

ThursdayThursday




How much was the How much was the pie?pie?

This means SUBTRACT:

£1.32 – 54POR 132 - 54


it !STEP 3 Picture

It! !


Count back from £1.32 by 2p to the 1st friendly number: £1.30

Then count back by 50p … £1.20 … £1.10 … £1 … 90p … 80p

Then count back by 2p more … 78p

The pie cost is 78p


70p 80p 90p £1 £1.10 £1.20 £1.30 £1.40

You can subtract 54p from £1.32 in lots of different ways:

£1.32 – 50p – 4p£1.32 – 4p – 50p£1.32 – 52p – 2p (Easier. Why?)

£1.32 – 2p – 50p – 2p (Even easier! Why?)

Take a look …

ThursdayThursday




How much was the How much was the pie?pie?


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4




it !


ThursdayThursday

Paul buys 6 mini Paul buys 6 mini cheese ‘n tomato cheese ‘n tomato

pizzas at 15p each. pizzas at 15p each.

How much did he How much did he spend altogether?spend altogether?

WORD CLUE! total

KEY NUMBER!

KEY NUMBER!

WORD CLUE! multiply

MULTIPLY !

6 X 15p


it !STEP 3 Picture

It! !


ThursdayThursday




This means ADD:

6 groups of 15

15 + 15 + 15 + 15 + 15

BUT EASIER TO …

You can work out 6 x 19 in lots of different ways:

6 x 19 - but only if you know your 19 times tables!

6 x 10 + 6 x 9 - if you like to use partition

3 x 38 - if you like to double and halve

6 x 20 – 6 x 1 - if you like using nearest tens

Take a look …

Some were easier than others!

Which way do

you prefer?


it !STEP 3 Picture

It! !



ThursdayThursday




6 x 19 YOU CAN PARTITION

19

= 6 x 10 + 6 x 9 = 60 + 54 = 114

Paul spends £1.14

6 x 19 OR DOUBLE and

HALVE

= 3 x 38 = 3 x 30 + 3 x 8 = 90 + 24 = 114

Paul spends £1.14

6 x 19 OR USE NEAREST TENS

= 6 x 20 - 6 x 1 = 120 - 6 = 114

Paul spends £1.14


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4



Friday SpecialFriday Special

Paul pays 64p for 4 Paul pays 64p for 4 identical cakesidentical cakes

How much was How much was each cake?each cake?


it !


WORD CLUE! division

KEY NUMBER!

KEY NUMBER!

DIVIDE:

64 ÷ 4





it !STEP 3 Picture

It! !


This means :

64 divided into 4 equal groups

…





it !STEP 3 Picture

It! !STEP 2 Underline

It !

You can work out 64 ÷ 4 in lots of different ways:

64 ÷ 2 ÷ 2 - halve it and halve again

32 ÷ 2 - if you halve both numbers to start with

64 - 40 - 20 - 4 - chunking method

4 64 - written method

Take a look …

64 ÷ 4HALVE & HALVE AGAIN

64 ÷ 2 = 32 32 ÷ 2 = 16

Each egg roll costs 16p

64 ÷ 4 PARTITION

Partition 64 into 60 and 4 … 60 ÷ 4 = 15

4 ÷ 4 = 1 + 16


64 ÷ 4 CHUNKING

How many 4’s in 64? To find out, you can keep subtracting 4’s until you reach 0. You can subtract in chunks to make it easy: For example,You know 10 x 4 = 40. So subtract 4 lots of 10 (40). Keep subtracting …

start with: 64 10 x 4 - 40 Take away 10 lots of 4

Leaving 24

5 x 4 - 20 Take away another 5 lots of 4

Leaving 4

1 x 4 - 4 Take away 1 lot of 4 0

Altogether you have subtracted

10 + 5 + 1 lots of 4

= 16 lots of 4


64 ÷ 4 FORMAL WRITTEN METHOD

4 6 4

How many 4’s in 6?

1 remainder 2

How many 4’s in 24?

6 remainder 0 STOP


1 6

Which way did you prefer?STEP 4 Calculate

It !

Now Your Turn! Now Your Turn! The Lasagne ProblemThe Lasagne Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 1 Problem 1 Sara buys a 72p lasagne Sara buys a 72p lasagne and a two 39p peaches. and a two 39p peaches.

How much did she pay How much did she pay altogether?altogether?

She pays £1.50

altogether

Click for

solution to

problem

Now Your Turn! Now Your Turn! The Bolognese ProblemThe Bolognese Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 2 Problem 2 Sara buys a 86p bolognese Sara buys a 86p bolognese and a four 37p strawberry and a four 37p strawberry

whips . whips .

What was her total cost?What was her total cost?

She pays £2.34

altogether

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Beef Hotpot ProblemThe Beef Hotpot Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

He paid £1.48

altogether

Problem 3Problem 3Ben buys a 39p tomato Ben buys a 39p tomato

soup, the 85p beef hotpot soup, the 85p beef hotpot and three 8p pears. and three 8p pears.

How much did he pay How much did he pay altogether?altogether?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Lamb Yuk Sung ProblemThe Lamb Yuk Sung Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

He paid £2.45

altogether

Problem 4Problem 4Ben buys a 62p pea soup, Ben buys a 62p pea soup,

the 99p lamb yuk sung and the 99p lamb yuk sung and seven 12p plums. seven 12p plums.


Click for

solution to

problem

Now Your Turn!Now Your Turn!The Salami ProblemThe Salami Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

She received £2.62 in change.

Problem 5Problem 5Richie buys a two £1.19 Richie buys a two £1.19

salami and cheese salami and cheese baguettes.baguettes.

How much change did she How much change did she receive from £5?receive from £5?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Kebabs ProblemThe Kebabs Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

She received £5.38 in change.

Problem 6Problem 6Richie buys a three £1.54 Richie buys a three £1.54

kebabs.kebabs.

How much change did she How much change did she receive from £10?receive from £10?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Trifle ProblemThe Trifle Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

The trifle costs £1.35

Problem 7 Problem 7 Zaynah buys a 39p Zaynah buys a 39p

mushroom soup, the £1.25 mushroom soup, the £1.25 shepherd’s pie and a trifle. shepherd’s pie and a trifle.

Altogether, she spends Altogether, she spends £2.99.£2.99.

How much is the trifle?How much is the trifle?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Noodle Soup ProblemThe Noodle Soup Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

The soup costs 86p

Problem 8 Problem 8 Zaynah buys a noodle Zaynah buys a noodle

soup, the £1.75 fish pie and soup, the £1.75 fish pie and two 72p apple turnovers. two 72p apple turnovers.

Altogether, she spends Altogether, she spends £4.05.£4.05.

How much is the noodle How much is the noodle soup?soup?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Pasty ProblemThe Pasty Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 9Problem 9Jamie buys 4 vegetable Jamie buys 4 vegetable

pasties costing 56p each.pasties costing 56p each.


He paid £2.24

altogether

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Fajitas ProblemThe Fajitas Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 10Problem 10Jamie buys 3 fajitas costing Jamie buys 3 fajitas costing

£0.79 each.£0.79 each.


He paid £2.37

altogether

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Spring Roll ProblemThe Spring Roll Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

She receives

£5.80 change

Problem 11Problem 11Jan buys 5 vegetable Jan buys 5 vegetable

spring rolls costing 84p spring rolls costing 84p each.each.

How much change does How much change does she get back from £10?she get back from £10?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Mini Samosas ProblemThe Mini Samosas Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

She receives £17.04 change

Problem 12Problem 12Jan buys 8 mini samosas Jan buys 8 mini samosas

costing 37p each.costing 37p each.

How much change does How much change does she get back from £20?she get back from £20?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Salad Bar ProblemThe Salad Bar Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Each portion

costs 34p

Problem 13Problem 13There’s a big choice at the salad There’s a big choice at the salad

bar!bar!

Philip spends £2.38 on: tomato, Philip spends £2.38 on: tomato, lettuce, egg, onion, beans, potato, lettuce, egg, onion, beans, potato,

celery. celery.

Each salad portion is the same Each salad portion is the same price! How much is each portion?price! How much is each portion?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Salad Bar ProblemThe Salad Bar Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Each bap costs 29p

Problem 14Problem 14Ben buys 9 mini cheese ‘n Ben buys 9 mini cheese ‘n

pickle baps for £2.61pickle baps for £2.61

How much is each bap?How much is each bap?

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Banana Smoothie ProblemThe Banana Smoothie Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 15Problem 15Lee and his three mates Lee and his three mates

each bought a small banana each bought a small banana smoothie. They paid £1.40 in smoothie. They paid £1.40 in

total.total.

How much change did each How much change did each pupil get back from £5?pupil get back from £5?

Each one received

£4.65 change.

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Banana Smoothie ProblemThe Banana Smoothie Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 16Problem 16Paula and her 5 friends each Paula and her 5 friends each bought a strawberry yoghurt bought a strawberry yoghurt ice-cream. They paid £6.84 ice-cream. They paid £6.84

in total.in total.

How much change did each How much change did each pupil get back from £10?pupil get back from £10?

Each one received

£8.86 change.

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Tropical Juice Problem The Tropical Juice Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 17Problem 17Alisha buys three tropical Alisha buys three tropical

juices and an 85p tuna juices and an 85p tuna mayo cob.mayo cob.

She receives £2.05 change She receives £2.05 change from a £5 note. How much from a £5 note. How much

is each juice?is each juice?

Each juice

costs 70p

Click for

solution to

problem

Now Your Turn!Now Your Turn!The Veggie-Burger Problem The Veggie-Burger Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Each burger costs £1.54

Click for

solution to

problem

Problem 18Problem 18Anya buys four veggie-Anya buys four veggie-

burgers and an 64p fruit burgers and an 64p fruit salad.salad.

If she receives £13.20 change If she receives £13.20 change from a £20 note, how much is from a £20 note, how much is

each burger?each burger?

4 for £1 is best

value for money (25p each)

Now Your Turn!Now Your Turn!The Hot Cross Buns ProblemThe Hot Cross Buns Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Click for

solution to

problem

Problem 19 Problem 19 Special Offer: Hot Cross Special Offer: Hot Cross

Buns!Buns!

4 for £1 10 for £2.70 8 for 4 for £1 10 for £2.70 8 for £2.08£2.08

Which offers the best value Which offers the best value for money?for money?

8 for £2.24 is

best value for money (32p each)

Now Your Turn!Now Your Turn!The Rock Cakes ProblemThe Rock Cakes Problem

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Click for

solution to

problem

Problem 20 Problem 20 Special Offer: Rock Cakes!Special Offer: Rock Cakes!

3 for £1 10 for £3.40 8 for 3 for £1 10 for £3.40 8 for £2.56£2.56

Which offers the best value Which offers the best value for money?for money?

Now U R PC with Money,Now U R PC with Money,

Why not try …Why not try …

THE THE FIENDISH SPANISH CLASSROOM FIENDISH SPANISH CLASSROOM PROBLEMS ?PROBLEMS ? - about Money with Area and Perimeter - about Money with Area and Perimeter

THE FIENDISH SCIENCE LAB PROBLEMS ? THE FIENDISH SCIENCE LAB PROBLEMS ? - about Money with Measurements - about Money with Measurements

Documents

Bridging the Gap Problem-Solving Pupils Version. Note to Pupils D Do you know how to work out money totals? - - or change from £10? or the cost of 6 cakes