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Bridging the Gap

L3. L4. to. Problem-Solving Pupils’ Version. Bridging the Gap. Problem-Solving with Area and Perimeter. Note to Pupils. Do you know the difference between Area and Perimeter ? Do you have problems knowing how to get started on tricky maths problems ?.

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Bridging the Gap

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  1. L3 L4 to Problem-SolvingPupils’ Version Bridging the Gap Problem-Solving with Area and Perimeter .

  2. Note to Pupils Do you know the difference between Area and Perimeter? Do you have problems knowing how to get started on tricky maths problems? This resource will help you to… • Learn about the area and perimeter of rectangles • and shapes made from them • 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) • 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. Now you’re ready to try out some problems! How to become aPROBLEM-CRACKERin 4 Easy Steps! But first … Check out the basics about areas and perimeters of rectangles … 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. 10 m 6 m The Area of a Rectangle …means … the amount of surface inside and measured by … the number of squares inside(eg: square centimetres, square metres, square feet, square yards) How do you find area? Here are some ways you might have met … • COUNT THE SQUARES • 1, 2, 3, … 59, 60 • The area is 60 square metres - Or ROWS X COLUMNS 6 rows of 10 squares = 60 The area is 60 square metres But which way is best? - Or LENGTH X WIDTH = 10 X 6 = 60 The area is 60 square metres

  8. Area Example 1 What is the area of this rectangle? … HOW MANY SQUARES? • METHOD 1: COUNT THE SQUARES • USEFUL METHOD WHEN … • - You can see the squares • AND • there’s not too many to count! Easy! Just count the 12 squares Area = 12 squares centimetres

  9. Area Example 2 What is the area of this rectangle? … HOW MANY SQUARES? • METHOD 2: AREA = ROWS X COLUMNS • USEFUL METHOD WHEN … • - You can see the squares • BUT • there’s too many to count! Too many squares to count! Is there an easier way? You can see there are 6 rows with 10 in each row = 60 squares

  10. 7 cm 5 cm Area Example 3 What is the area of this rectangle? … HOW MANY SQUARES? No squares to count BUT 7cm means 7 squares fit in each row 5 cm means 5 squares fit in each column 2 Number of squares = length x width = 7 x 5 = 35 square centimetres METHOD 3: AREA = LENGTH X WIDTH USEFUL METHOD WHEN … - You can’t see the squares AND It’s very fast

  11. 9 cm 3 cm Area: Test Yourself 1 AREA = COUNT THE SQUARES Area ? Which method best suits each problem? AREA = ROWS X COLUMNS Area ? Area ? AREA = LENGTH X WIDTH

  12. 9 cm 3 cm Area: Test Yourself 1 AREA = LENGTH X WIDTH = 9 x 3 = 27 cm² = 4 x 2 = 8 cm² AND which way works for ALL 3? = 11 x 5 = 55 cm²

  13. Area: Test Yourself 2 A C B 8 cm 5 cm Too many to count! But it’s easy to see there are 6 rows of 7 COUNT THE SQUARES Match the method to the problem ROWS X COLUMNS No squares. Use length x width Easy to count - only a few squares LENGTH X WIDTH

  14. A C B 8 cm 5 cm Area Test Yourself 2 = 7 x 5 = 35 cm² AREA = LENGTH X WIDTH AND which way works for ALL 3? = 8 x 5 = 40 cm² = 3 x 4 = 12 cm²

  15. Area– General Rule for all Rectangles General Rule: The area of a rectangle = Length x Width Or if you like shorthand … A = L x W

  16. The school grounds has 6 fields, each 1 kilometre square. Its area is: 6 kilometre squares 6 kilometre squared 6 square kilometres 6 km ² A classroom floor can fit in 20 carpet tiles, each 1 metre square. The floor area is: 20 metre squares 20 metre squared 20 square metres 20 m ² A small chess board contains 64 centimetre squares. Its area is: 40 centimetre squares 40 centimetre squared 40 square centimetres 40 cm ² Area Units of area: ALWAYS IN SQUARES! 3 Egs

  17. Which way do you prefer? The Perimeter of a Rectangle …means - the distance around the outside and is measured by - the sum of the lengths of the 4 sides(eg: millimetres, centimetres, metres, kilometres, feet, yards) There’s lots of ways to find the perimeter… ADD 4 LENGTHS IN ORDER 10 + 6 + 10 + 6 = 32 m 10m ADD 1 LENGTH + 1 WIDTH THEN DOUBLE IT 10 + 6 = 16m 2 X 16 = 32m 6m 6m 2 LENGTHS + 2 WIDTHS = 2 X 10 + 2 X 6 = 20 + 12 = 32m 10m

  18. Perimeter Units of perimeter: Any units of length METRIC UNITS Millimetres mm Centimetres cm Kilometres km IMPERIAL UNITS Miles Yards Feet Inches

  19. The school grounds has 6 fields, each 1 kilometre square. The length of the perimeter fencing is: 10 kilometre 10 km A classroom floor can fit in 20 carpet tiles, each 1 metre square. The classroom perimeter is: 20 metres 20m A small chess board contains 64 centimetre squares. The perimeter has a brown edging: 64 centimetres long 64 cm long Perimeter 3 Egs

  20. Example 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 …

  21. … and … LOOK FOR KEY NUMBERS! Example 1 STEP 1 Read it ! STEP 2 Underline it ! … and WORD CLUES – area or perimeter? The history classroom is 10m long and 4m wide. How much carpet is needed for the floor? KEY NUMBER! PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length KEY NUMBER! AREA CLUES surface cover coverage amount of carpet how much carpet WORD CLUE! area

  22. Some word clues to watch out for… PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length AREA CLUES surface cover coverage amount of carpet how much carpet

  23. 10m 4m Example 1 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! The history classroom is 10m long and 4m wide. How much carpet is needed for the floor? 2 Steps so far … CLICK for Step 3! KEY NUMBER! This means AREA KEY NUMBER! WORD CLUE! area

  24. 10m 4m Example 1 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! The history classroom is 10m long and 4m wide. How much carpet is needed for the floor? 3 steps done 1 to go … CLICK for Step 4! STEP 4 Calculate It ! Area of a rectangle = length x width = 10 x 40 = 40 An area of 40m ² carpet is needed.

  25. 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 !

  26. Example 2 - 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 …

  27. Example 2 … and … LOOK FOR KEY NUMBERS! STEP 1 Read it ! STEP 2 Underline it ! … and WORD CLUES – area or perimeter? The history classroom is 10m long and 4m wide. How much edging strip is needed for the classroom floor? KEY NUMBER! PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length KEY NUMBER! AREA CLUES surface cover coverage amount of carpet how much carpet WORD CLUE! perimeter

  28. 10m 4m 4m 10m Example 2 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! The history classroom is 10m long and 4m wide. How much edging strip is needed to go around the classroom floor? 2 Steps so far … CLICK for Step 3! This means PERIMETER

  29. 10m 4m 4m 10m Example 2 STEP 1 Read it ! Remember – there’s lots of ways to do this! For example: 10 + 4 + 10 + 4 = 28 OR 10 + 4 = 14 2 X 14 = 28 OR 10 X 2 = 20 and 4 X 2 = 8 20 + 8 = 28 STEP 3 Picture It! ! STEP 2 Underline It ! The history classroom is 10m long and 4m wide. How much edging strip is needed to go around the classroom floor? 3 steps done 1 to go … CLICK for Step 4! STEP 4 Calculate It ! Perimeter of a rectangle = sum of the lengths of the 4 sides = 10 + 4 + 10 + 4 = 28 A 28 m length of edging strip is needed.

  30. 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 !

  31. Example 3 - 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 …

  32. … and … LOOK FOR KEY NUMBERS! Example 3 STEP 1 Read it ! STEP 2 Underline it ! LOOK FOR WORD CLUES – area or perimeter? The history room floor is 12m by 6m. The project corner is a 1m by 3m rectangle. The rest is tiled. How much of the floor surface is tiled? KEY NUMBERS! PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length AREA CLUES surface cover coverage amount of carpet how much carpet KEY NUMBER! WORD CLUE! area

  33. 6m 3m 1m 3m SURFACE MEANS AREA! But the shape you’re interested in is not a rectangle! One way is to PICTURE IT AS 2 RECTANGLES JOINED TOGETHER. Work out each area and ADD. Example 3 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! The history room floor is 12m by 6m. The project corner is a 1m by 3m rectangle. The rest is tiled. How much of the floor surface is tiled? 2 Steps so far … CLICK for Step 3!

  34. 6m 3m 1m 3m Example 3 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! = 3 x 3 = 9m² Area? = 3 x 2 = 6m² Area? The history room floor is 12m by 6m The project corner is a 1m by 3m rectangle. The rest is tiled. How much of the floor surface is tiled? 2m ?m 3 steps done 1 to go … CLICK for Step 4! ?m 3m STEP 4 Calculate It ! Total Area = 6 + 9 = 15m² The tiled area is 15m² Work out area of each rectangle and add! Can you think of any other ways you could work this out?

  35. 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 !

  36. Example 4 - 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 …

  37. … and … LOOK FOR KEY NUMBERS! Example 4 STEP 1 Read it ! STEP 2 Underline it ! … and WORD CLUES – area or perimeter? The history room floor is 12m by 6m. The project corner is a 1m by 3m rectangle. The rest is tiled and surrounded by wooden edging. What length of edging is needed? KEY NUMBERS! PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length KEY NUMBER! AREA CLUES surface cover coverage amount of carpet how much carpet WORD CLUE! perimeter

  38. 6m 3m 1m 3m EDGING MEANS PERIMETER But the shape you’re interested in is not a rectangle! One way is to start at the top left-hand corner and write down each length around the perimeter. Then ADD. Example 4 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! The history room floor is 12m by 6m. The carpeted area in the corner is a 1m by 3m rectangle. The rest is tiled and surrounded by wooden edging. What length of edging is needed? 2 Steps so far … CLICK for Step 3!

  39. 6m 3m 1m 3m Example 4 STEP 1 Read it ! STEP 3 Picture It! ! STEP 2 Underline It ! The history room floor is 12m by 6m. The carpeted area in the corner is a 1m by 3m rectangle. The rest is tiled and surrounded by wooden edging. What length of edging is needed? 2m ?m 3 steps done 1 to go … CLICK for Step 4! ?m 3m STEP 4 Calculate It ! Work out the length of each side and add! = 18 6 + 3 + 3 + 1 + 3 + 2 18m of edging is needed.

  40. 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 !

  41. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture It! ! Now Your Turn! 1 Problem 1 The history classroom is 9m long and 5m wide. How carpet is needed to cover the floor? An area of 45m² carpet is needed Click for solution to problem 6m 1.5m 2m 4m R U P C ?

  42. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture It! ! Now Your Turn! 2 Problem 2 The history classroom is 9m long and 5m wide. How edging tape is needed for the carpet perimeter? A length of 28medging strip is needed 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! 3 Problem 3 The history classroom is 15m long and 6m wide. How carpet is needed to cover the floor? An area of 90m² carpet is needed Click for solution to problem 6m 1.5m 2m 4m R U P C ?

  44. STEP 1 ? STEP 3 ? STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture It! ! Now Your Turn! 4 Problem 4 The history classroom is 15m long and 6m wide. How edging tape is needed for the carpet perimeter? A length of 42medging strip is needed 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! 5 Problem 5 The history classroom floor is a 12m and 6m rectangle. The resource corner is 2m x 2m square. How much floor space is still free? An area of 68m² carpet is needed 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! 6 Problem 6 The history classroom floor is a 12m by 6m rectangle. The resource corner is 2m x 2m square. A tiled border marks the perimeter of the remaining floor. How long is the border? The perimeter border is 36m long 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! 7 Problem 7 The history classroom floor is a 15m and 7m rectangle. The computer corner is 3m x 3m square. How much floor space is left? An area of 96m² carpet is needed 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! 8 Problem 8 The history classroom floor is a 15m by 7m rectangle. The computer corner is 3m x 3m square. A tiled border marks the perimeter of the remaining floor. How long is the border? The perimeter border is 44m long Click for solution to problem R U P C ?

  49. 15m 7m STEP 1 ? STEP 3 ? 6m STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture It! ! 11m Now Your Turn! 9 Problem 9 How much floor space is there in this classroom? The floor area is 81m² Click for solution to problem KEY Door (0.5m wide) R U P C ?

  50. 15m 7m STEP 1 ? STEP 3 ? 6m STEP 2 ? STEP 4 ? Read it ! Underline It ! Calculate It ! Picture It! ! 11m Now Your Turn! 10 Problem 10 What length of skirting board is needed this classroom? (Remember to allow for the door!) An area of 43.5m² carpet is needed Click for solution to problem KEY Door (0.5m wide) R U P C ?

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