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Bridging the Gap Problem-Solving Pupils Version

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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

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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)

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

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

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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!

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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 …

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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

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+ 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…

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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!

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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!

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The 4 Steps STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Read it ! Underline It ! Picture It! ! Calculate It !

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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!

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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

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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

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

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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!

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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

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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 !

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

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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

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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

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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!

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

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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

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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

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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?

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

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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

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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 …

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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

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

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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!

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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 …

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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 !

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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?

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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?

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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?

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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

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