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 when you know the price of 1? the cost of 1 cake when you know the total for 6? D Do you have problems knowing how to get started on tricky maths problems? This resource will help you to… -L-Learn about money calculations -a-and become an expert at cracking problems! -U-Using a simple 4-step guide to problem-solving

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 TO RETURN TO MENU: Escape Contents A. Learning Area (Start here to revise your learning)Learning Area B. Test Yourself: Now Its Your Turn! (Start here if you just want to test yourself)Test Yourself: Now Its Your Turn! C. Where To Next? (Suggestions for main menu)Where To Next? (TO GO TO LINK, HOLD DOWN CONTROL AND CLICK ON YOUR CHOICE)

Which One Are You ??? R U a P roblem -C oward ? … or … R U a P roblem -C racker ? PROBLEM !

STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! Calculate It ! R U PC?

R U P C ? Read it! … … whats it about? Underline it! … find the clues Picture it! … add? subtract? multiply? divide? … use a number line to help Calculate it! … … … … work it out ! HOW? Lets try it and see … How to become a PROBLEM-CRACKER in 4 Easy Steps!

Step 1 - What do I know? STEP 1 Read it ! - What do I want to find out? … Ill read this again so Im 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! LOOK FOR WORD CLUES! … and … LOOK FOR KEY NUMBERS! sum fewer plus less total divided each altogether lots of difference times share all left groups of increase sets of leave more Step 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 3 STEP 1 Read it ! STEP 2 Underline It ! STEP 3 Picture It! ! 0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1 Crunch Bar 50p Jaz Juice 20p How much altogether? How much change from £1? This means ADD: = cost … and this means SUBTRACT: 100 – cost = change 2 Steps so far … CLICK for Step 3!

Step 4 STEP 1 Read it ! STEP 2 Underline It ! STEP 3 Picture It! ! Crunch Bar 50p Jaz Juice 20p How much altogether? How much change from £1? STEP 4 Calculate It ! Start at 50p and count on 20p … 60, 70, So = 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 Steps STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! Calculate It !

The School Canteen Example 1 STEP 1 Read it ! STEP 2 Underline It ! Monday Paul buys a 70p salad and a 20p peach. How much did he pay altogether? WORD CLUE! add KEY NUMBER!

The School Canteen Example 1 STEP 1 Read it ! STEP 3 Picture It! ! Monday Paul buys a 70p salad and a 20p peach. How much did he pay altogether? This means ADD: STEP 2 Underline It ! 0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1

The School Canteen Example 1 STEP 1 Read it ! STEP 3 Picture It! ! Monday Paul buys a 70p salad and a 20p peach. How much did he pay altogether? STEP 4 Calculate It ! Start at 70p and count on 20p … 80, 90, So = 90 Total cost is 90p STEP 2 Underline It ! (Remember! Put your answer into a sentence!) 0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1

Easy Problem-Solving in 4 Steps! STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! 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? WORD CLUE! add KEY NUMBER!

The School Canteen Example 2 STEP 1 Read it ! STEP 3 Picture 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? This means ADD: p 80p 90p £1 £1.10 £1.20 £1.30 £1.40

The School Canteen Example 2 STEP 1 Read it ! STEP 3 Picture 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? 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 = £1.40 Total cost is £1.40 Which is easier – Start at 90p and count on 40p or Start at 40p and count on 90p ? STEP 4 Calculate It !

Easy Problem-Solving in 4 Steps! STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! Calculate It !

The School Canteen Example 3 STEP 1 Read it ! STEP 2 Underline It ! Wednesday Paul buys a 68p chicken salad bagel. How much change did he get back from £1? KEY NUMBER! WORD CLUE! subtract

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? This means SUBTRACT: £1 – 68p OR p 40p 50p 60p 70p 80p 90p £1

The School Canteen Example 3 STEP 1 Read it ! STEP 3 Picture It! ! STEP 4 Calculate It ! STEP 2 Underline 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?) Lets try one out … Wednesday Paul buys a 68p chicken salad bagel. How much change did he get back from £1? 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!

Easy Problem-Solving in 4 Steps! STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! Calculate It !

The School Canteen Example 4 STEP 1 Read it ! STEP 2 Underline It ! Thursday Paul buys a 54p tomato soup and an apple pie. Altogether he spends £1.32. How much was the pie? WORD CLUE! Missing number KEY NUMBER! WORD CLUE! total

The School Canteen Example 4 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! 70p 80p 90p £1 £1.10 £1.20 £1.30 £1.40 Thursday 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

The School Canteen Example 4 STEP 1 Read it ! STEP 3 Picture It! ! STEP 4 Calculate It ! Count back from £1.32 by 2p to the 1 st 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 STEP 2 Underline It ! 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 … Thursday Paul buys a 54p tomato soup and an apple pie. Altogether he spends £1.32. How much was the pie?

Easy Problem-Solving in 4 Steps! STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! 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? WORD CLUE! total KEY NUMBER! WORD CLUE! multiply

MULTIPLY ! 6 X 15p The School Canteen Example 5 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! Thursday Paul buys 6 mini cheese n tomato pizzas at 15p each. How much did he spend altogether? This means ADD: 6 groups of 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 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? The School Canteen Example 5 STEP 1 Read it ! STEP 3 Picture It! ! STEP 4 Calculate It ! STEP 2 Underline It ! Thursday Paul buys 6 mini cheese n tomato pizzas at 19p each. How much did he spend altogether? 6 x 19 YOU CAN PARTITION 19 = 6 x x 9 = = 114 Paul spends £ x 19 OR DOUBLE and HALVE = 3 x 38 = 3 x x 8 = = 114 Paul spends £ x 19 OR USE NEAREST TENS = 6 x x 1 = = 114 Paul spends £1.14

Easy Problem-Solving in 4 Steps! STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! Calculate It !

Friday Special Paul pays 64p for 4 identical cakes How much was each cake? The School Canteen Example 6 STEP 1 Read it ! STEP 2 Underline It ! WORD CLUE! division KEY NUMBER!

DIVIDE: 64 ÷ 4 Friday Special Paul pays 64p for 4 identical cakes How much was each cake? The School Canteen Example 6 STEP 1 Read it ! 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? The School Canteen Example 6 STEP 1 Read 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 chunking method written method Take a look … 64 ÷ 4 HALVE & AGAIN 64 ÷ 2 = 32 ÷ 2 = 16 Each egg roll costs 16p 64 ÷ 4 PARTITION Partition 64 into 60 and 4 … 60 ÷ 4 = 15 4 ÷ 4 = Each egg roll costs 16p 64 ÷ 4 CHUNKING How many 4s in 64? To find out, you can keep subtracting 4s 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: x Take away 10 lots of 4 Leaving 24 5 x Take away another 5 lots of 4 Leaving 4 1 x Take away 1 lot of 4 0 Altogether you have subtracted lots of 4 = 16 lots of 4 Each egg roll costs 16p 64 ÷ 4 FORMAL WRITTEN METHOD How many 4s in 6? 1 remainder 2 How many 4s in 24? 6 remainder 0 STOP Each egg roll costs 16p 1 6 Which way did you prefer? STEP 4 Calculate It !

Now Your Turn! The Lasagne Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! 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

Now Your Turn! The Bolognese Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! 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

Now Your Turn! The Beef Hotpot Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! He paid £1.48 altogether Problem 3 Ben buys a 39p tomato soup, the 85p beef hotpot and three 8p pears. How much did he pay altogether? Click for solution to problem

Now Your Turn! The Lamb Yuk Sung Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! He paid £2.45 altogether Problem 4 Ben buys a 62p pea soup, the 99p lamb yuk sung and seven 12p plums. How much did he pay altogether? Click for solution to problem

Now Your Turn! The Salami Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! She received £2.62 in change. 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

Now Your Turn! The Kebabs Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! She received £5.38 in change. Problem 6 Richie buys a three £1.54 kebabs. How much change did she receive from £10? Click for solution to problem

Now Your Turn! The Trifle Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! The trifle costs £1.35 Problem 7 Zaynah buys a 39p mushroom soup, the £1.25 shepherds pie and a trifle. Altogether, she spends £2.99. How much is the trifle? Click for solution to problem

Now Your Turn! The Noodle Soup Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! The soup costs 86p 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? Click for solution to problem

Now Your Turn! The Pasty Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read 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

Now Your Turn! The Fajitas Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read 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

Now Your Turn! The Spring Roll Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! She receives £5.80 change 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

Now Your Turn! The Mini Samosas Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! She receives £17.04 change Problem 12 Jan buys 8 mini samosas costing 37p each. How much change does she get back from £20? Click for solution to problem

Now Your Turn! The Salad Bar Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Each portion costs 34p Problem 13 Theres 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? Click for solution to problem

Now Your Turn! The Salad Bar Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Each bap costs 29p Problem 14 Ben buys 9 mini cheese n pickle baps for £2.61 How much is each bap? Click for solution to problem

Now Your Turn! The Banana Smoothie Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! 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? Each one received £4.65 change. Click for solution to problem

Now Your Turn! The Banana Smoothie Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! 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? Each one received £8.86 change. Click for solution to problem

Now Your Turn! The Tropical Juice Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! 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? Each juice costs 70p Click for solution to problem

Now Your Turn! The Veggie-Burger Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Each burger costs £1.54 Click for solution to 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?

4 for £1 is best value for money (25p each) Now Your Turn! The Hot Cross Buns Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Click for solution to problem Problem 19 Special Offer: Hot Cross Buns! 4 for £1 10 for £ for £2.08 Which offers the best value for money?

8 for £2.24 is best value for money (32p each) Now Your Turn! The Rock Cakes Problem STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Click for solution to problem Problem 20 Special Offer: Rock Cakes! 3 for £1 10 for £ for £2.56 Which offers the best value for money?

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