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Bridging the Gap

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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Bridging the Gap

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  1. to L3 L4 Problem-SolvingPupils’ Version Bridging the Gap Problem-Solving with Money .

  2. 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? 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

  3. 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 TO RETURN TO MENU: Escape

  4. Which One Are You ??? R U a Problem-Coward ? … or … R U a Problem-Cracker? PROBLEM!

  5. R U PC? Problem Cracker ? R U a Picture it Read it Underline it Calculate it STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Underline It ! Calculate It ! Picture It! ! Read it !

  6. How to become aPROBLEM-CRACKERin 4 Easy Steps! HOW? Let’s try it and see … R U P C ? Read it! … what’s it about? Underline it! … find the clues Picture it! … add? subtract? multiply? divide? … use a number line to help Calculate it!… work it out !

  7. Step 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 …

  8. … and … LOOK FOR KEY NUMBERS! Step 2 STEP 1 Read it ! 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! add WORD CLUE! subtract KEY NUMBER!

  9. 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

  10. Step 3 STEP 1 Read it ! 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 This means ADD: 50 + 20 = cost … and this means SUBTRACT: 100 – cost = change

  11. Step 4 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? 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 !

  12. 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! ! Read it !

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

  14. 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. How much did he pay altogether? 0p 10p 20p 30p 40p 50p 60p 70p 80p 90p £1 This means ADD: 70 + 20

  15. 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. 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 (Remember! Put your answer into a sentence!)

  16. 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! ! Read it !

  17. 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

  18. 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? STEP 3 Picture It! ! 70p 80p 90p £1 £1.10 £1.20 £1.30 £1.40 This means ADD: 90 + 40 + 10

  19. 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 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

  20. 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! ! Read it !

  21. 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 KEY NUMBER!

  22. 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 £1 This means SUBTRACT: £1 – 68p OR 100 - 68

  23. The School Canteen Example 3 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! OR try one of the other ways See way which you prefer! 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 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 instead of 68p: … 90p…80p…70p…60p…50p…40p…30p 2p too much! So count back by 2p … …31p…32p Paul gets 32p change

  24. 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! ! Read it !

  25. 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? KEY NUMBER! WORD CLUE! total KEY NUMBER! WORD CLUE! Missing number

  26. 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. 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

  27. 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. 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

  28. 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! ! Read it !

  29. 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

  30. The School Canteen Example 5 STEP 1 Read it ! STEP 3 Picture It! ! This means ADD: 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

  31. 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 1 Read it ! 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 …

  32. 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! ! Read it !

  33. The School Canteen Example 6 STEP 1 Read it ! 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

  34. 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? DIVIDE: 64 ÷ 4

  35. 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 ÷ 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 start with: 64 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 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? 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

  36. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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 ?

  37. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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 ?

  38. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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 ?

  39. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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 ?

  40. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture 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? She received £2.62 in change. Click for solution to problem R U P C ?

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

  42. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture 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? The trifle costs £1.35 Click for solution to problem R U P C ?

  43. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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 ?

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

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

  46. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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? She receives £5.80 change Click for solution to problem R U P C ?

  47. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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? She receives £17.04 change Click for solution to problem R U P C ?

  48. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture 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? Each portion costs 34p Click for solution to problem R U P C ?

  49. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture 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? Each bap costs 29p Click for solution to problem R U P C ?

  50. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! 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? Each one received £4.65 change. Click for solution to problem R U P C ?

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