Bridging the Gap

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# Bridging the Gap - PowerPoint PPT Presentation

to. L3. L4. Problem-Solving Pupils’ Version. Bridging the Gap . Problem-Solving with Money . 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?

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## PowerPoint Slideshow about 'Bridging the Gap' - Mercy

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Presentation Transcript

to

L3

L4

Problem-SolvingPupils’ Version

Bridging the Gap

Problem-Solving with Money .

Note to Pupils
• Do you know how to work out money totals?
• - or changefrom £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?

• 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

You 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

Which One Are You ???

R U a Problem-Coward ?

… or …

R U a Problem-Cracker?

PROBLEM!

R U PC?

Problem

Cracker ?

R

U

a

Picture it

Underline it

Calculate it

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

How to become aPROBLEM-CRACKERin 4 Easy Steps!

HOW?

Let’s try it and see …

R U P C ?

Underline it! … find the clues

Picture it! … add? subtract? multiply? divide?

… use a number line to help

Calculate it!… work it out !

Step 1

- What do I know?

STEP 1

- What do I want to find out?

… I’ll read this again so I’m sure I get it …

… and …

LOOK FOR KEY NUMBERS!

Step 2

STEP 1

STEP 2 Underline it !

LOOK FOR WORD CLUES!

Crunch Bar 50p

Jaz Juice 20p

How much altogether?

How much

change from £1?

KEY NUMBER!

sum

fewerplus

less total divided

each altogether

lots of difference

timesshareall left

groups of

increase

sets ofleave

more

KEY NUMBER!

WORD CLUE! subtract

KEY NUMBER!

Some word clues to watch out for…

+ 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

Step 3

STEP 3 Picture It! !

STEP 2 Underline It !

2 Steps so far …

CLICK for Step 3!

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

50 + 20 = cost

… and this means SUBTRACT:

100 – cost = change

Step 4

STEP 3 Picture It! !

STEP 2 Underline It !

Crunch Bar 50p

Jaz Juice 20p

How much altogether?

How much change

from £1?

3 steps done

1 to go …

CLICK for

Step 4!

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

The 4 Steps

Uuuuuuu

Rrrrrrr

Problem

Cracker?

a

R U P C?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

The School Canteen Example 1

KEY NUMBER!

STEP 2 Underline It !

Monday

How much did he pay altogether?

KEY NUMBER!

The School Canteen Example 1

STEP 3 Picture It! !

STEP 2 Underline It !

Monday

How much did he pay altogether?

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

70 + 20

The School Canteen Example 1

STEP 3 Picture It! !

STEP 2 Underline It !

Monday

How much did he pay altogether?

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

STEP 4 Calculate It !

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

So 70+ 20 = 90

Total cost is 90p

Easy Problem-Solving in 4 Steps!

Uuuuuuu

Rrrrrrr

Problem

Cracker?

a

R U P C?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

The School Canteen Example 2

STEP 2 Underline It !

Tuesday

potato and leek soup,

the 90p mushroom curry and a

10p pear.

What was his

total cost?

KEY NUMBER!

KEY NUMBER!

KEY NUMBER!

The School Canteen Example 2

STEP 2 Underline It !

Tuesday

potato and leek soup,

the 90p mushroom curry and a

10p pear.

What was his

total cost?

STEP 3 Picture It! !

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

90 + 40 + 10

The School Canteen Example 2

STEP 3 Picture It! !

STEP 2 Underline It !

Tuesday

potato and leek soup,

the 90p mushroom curry and a

10p pear.

What was his

total cost?

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

STEP 4 Calculate It !

Which is easier –

Start at 90p and count on 40p or

Start at 40p and count on 90p ?

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

Easy Problem-Solving in 4 Steps!

Uuuuuuu

Rrrrrrr

Problem

Cracker?

a

R U P C?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

The School Canteen Example 3

STEP 2 Underline It !

Wednesday

How much change did

he get back from £1?

KEY NUMBER!

WORD CLUE! subtract

KEY NUMBER!

The School Canteen Example 3

STEP 3 Picture It! !

STEP 2 Underline It !

Wednesday

How much change did

he get back from £1?

30p 40p 50p 60p 70p 80p 90p £1

This means SUBTRACT:

£1 – 68p

OR 100 - 68

The School Canteen Example 3

STEP 3 Picture It! !

STEP 2 Underline It !

OR

try one of the other ways

See way which you prefer!

Wednesday

How much change did

he get back from £1?

30p 40p 50p 60p 70p 80p 90p £1

STEP 4 Calculate 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 …

Count back from £1 by 70p

90p…80p…70p…60p…50p…40p…30p

2p too much!

So count back by 2p …

…31p…32p

Paul gets 32p change

Easy Problem-Solving in 4 Steps!

Uuuuuuu

Rrrrrrr

Problem

Cracker?

a

R U P C?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

The School Canteen Example 4

STEP 2 Underline It !

Thursday

tomato soup and an apple pie.

Altogether he spends £1.32.

How much was the pie?

KEY NUMBER!

WORD CLUE! total

KEY NUMBER!

WORD CLUE! Missing number

The School Canteen Example 4

STEP 3 Picture It! !

STEP 2 Underline It !

Thursday

tomato soup and an apple pie.

Altogether he spends £1.32.

How much was the pie?

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

This means SUBTRACT:

£1.32 – 54P

OR 132 - 54

The School Canteen Example 4

STEP 3 Picture It! !

STEP 2 Underline It !

Thursday

tomato soup and an apple pie.

Altogether he spends £1.32.

How much was the 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 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 …

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

Easy Problem-Solving in 4 Steps!

Uuuuuuu

Rrrrrrr

Problem

Cracker?

a

R U P C?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

The School Canteen Example 5

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 3 Picture It! !

6 groups of 15

15 + 15 + 15 + 15 + 15

BUT EASIER TO …

STEP 2 Underline It !

Thursday

Paul buys 6 mini cheese ‘n tomato pizzas at 15p each.

How much did he spend altogether?

MULTIPLY !

6 X 15p

6 x 19

OR USE NEAREST TENS

= 6 x 20 - 6 x 1

= 120 - 6

= 114

Paul spends £1.14

The School Canteen Example 5

6 x 19

OR DOUBLE and HALVE

= 3 x 38

= 3 x 30 + 3 x 8

= 90 + 24

= 114

Paul spends £1.14

STEP 3 Picture It! !

STEP 2 Underline It !

Thursday

Paul buys 6 mini cheese ‘n tomato pizzas at 19p each.

How much did he spend altogether?

STEP 4 Calculate It !

6 x 19

YOU CAN PARTITION 19

= 6 x 10 + 6 x 9

= 60 + 54

= 114

Paul spends £1.14

Some were

easier than others!

Which way

do

you prefer?

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 …

Easy Problem-Solving in 4 Steps!

Uuuuuuu

Rrrrrrr

Problem

Cracker?

a

R U P C?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

The School Canteen Example 6

STEP 2 Underline It !

Friday Special

Paul pays 64p for 4 identical cakes

How much was each cake?

KEY NUMBER!

KEY NUMBER!

WORD CLUE! division

The School Canteen Example 6

STEP 3 Picture It! !

STEP 2 Underline It !

This means :

64 divided into 4 equal groups …

Friday Special

Paul pays 64p for 4 identical cakes

How much was each cake?

DIVIDE:

64 ÷ 4

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

64 ÷ 2 ÷ 2 - halve it and halve again

64 - 40 - 20 - 4 - chunking method

4 64 - written method

Take a look …

64 ÷ 4

FORMAL WRITTEN METHOD

4 6 4

64 ÷ 4

PARTITION

Partition 64 into 60 and 4 …

60 ÷ 4 = 15

4 ÷ 4 = 1 +

16

Each egg roll costs 16p

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 …

The School Canteen Example 6

10 x 4 - 40Take away 10 lots of 4

Leaving 24

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

Leaving 4

1 x 4 - 4Take away 1 lot of 4

0

Altogether you have

subtracted

10 + 5 + 1 lots of 4

= 16 lots of 4

Each egg roll costs 16p

STEP 3 Picture It! !

STEP 2 Underline It !

Friday Special

Paul pays 64p for 4 identical cakes

How much was each cake?

STEP 4 Calculate It !

Which way did you prefer?

64 ÷ 4

HALVE & HALVE AGAIN

64 ÷ 2 = 32

32 ÷ 2 = 16

Each egg roll costs 16p

How many 4’s in 24?

6 remainder 0 STOP

Each egg roll costs 16p

How many 4’s in 6?

1 remainder 2

1

6

2

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Now Your Turn! The Lasagne Problem

Problem 1

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

How much did she pay altogether?

She pays £1.50 altogether

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

She pays £2.34 altogether

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

He paid £1.48 altogether

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

He paid £2.45 altogether

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Problem 5

Richie buys a two £1.19 salami and cheese baguettes.

How much change did she receive from £5?

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Problem 6

Richie buys a three £1.54 kebabs.

How much change did she receive from £10?

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

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?

The trifle costs £1.35

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

The soup costs 86p

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Problem 9

Jamie buys 4 vegetable pasties costing 56p each.

How much did he pay altogether?

He paid £2.24 altogether

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Problem 10

Jamie buys 3 fajitas costing £0.79 each.

How much did he pay altogether?

He paid £2.37 altogether

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

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?

Each portion costs 34p

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Problem 14

Ben buys 9 mini cheese ‘n pickle baps for £2.61

How much is each bap?

Each bap costs 29p

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Now Your Turn!The Banana Smoothie Problem

Problem 15

Lee and his three mates each bought a small banana smoothie. They paid £1.40 in total.

How much change did each

pupil get back from £5?

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Now Your Turn!The Banana Smoothie Problem

Problem 16

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

How much change did each

pupil get back from £10?

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Now Your Turn!The Tropical Juice Problem

Problem 17

Alisha buys three tropical juices and an 85p tuna mayo cob.

She receives £2.05 change from a £5 note. How much is each juice?

Click

for

solution

to

problem

Each juice costs 70p

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture It! !

Problem 18

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

Click

for

solution

to

problem

Each burger costs

£1.54

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

4 for £1 is best value for money (25p each)

Click

for

solution

to

problem

R U P C ?

STEP 1

?

STEP 3

?

STEP 2

?

STEP 4

?

Underline It !

Calculate It !

Picture 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?

8 for £2.24 is best value for money (32p each)

Click

for

solution

to

problem

R U P C ?

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