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Bridging the Gap Problem-Solving Teachers’ Version

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Teacher Notes This resource is … A simple guide to problem-solving - using an easy 4-step approach to solving tricky problems about area and perimeter: 1. Read it! 2. Underline it! 3. Picture it! 4. Calculate it! The 4 steps are reinforced throughout, both in this activity and the other problem- solving activities. The aim is that pupils will feel confident in applying the four steps when trying out problems independently, regardless of mathematical topic. Flexible - suitable both for whole-class teaching and individual pupil revision. The mouse- activated steps allow time for whole-class interactions or individual thinking time. User-friendly The activity introduces the concepts of area and perimeter alongside the 4-step strategy, R U PC? using stepwise examples for interactive teaching. A Test Yourself Section follows with 8 problems to test your pupils’ learning. More problems are available in the pupils version (see Main Menu).

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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 Content Slide 4 Learn to solve problems about area and perimeter Slides 4-19 Intro: Solving Problems, area and perimeter Slides 4-19 Slides 20 – S40 4 Examples Slides 20 – S40 Slide 41 Test Yourself Slides 41 – 49 Now Your Turn: 8 Problems Slides 41 – 49 Slide 50Where To Next? Slide 50 (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! … 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 ! But first … Check out the basics about areas and perimeters of rectangles … How to become a PROBLEM-CRACKER in 4 Easy Steps! Now you’re ready to try out some problems!

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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) - Or LENGTH X WIDTH - Or LENGTH X WIDTH = 10 X 6 = 60 The area is 60 square metres - Or ROWS X COLUMNS - Or ROWS X COLUMNS 6 rows of 10 squares = 60 The area is 60 square metres COUNT THE SQUARES 1, 2, 3, … 59, 60 The area is 60 square metres 10 m 6 m But which way is best? But which way is best? How do you find area? Here are some ways you might have met … How do you find area? Here are some ways you might have met …

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

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

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Area Example 3 Area Example 3 What is the area of this rectangle? … HOW MANY SQUARES? 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 METHOD 3: AREA = LENGTH X WIDTH USEFUL METHOD WHEN … - You can’t see the squares AND It’s very fast 7 cm 5 cm

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

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

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

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

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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

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3 Egs Area Area Units of area: ALWAYS IN SQUARES! A small chess board contains 64 centimetre squares. Its area is: 40 centimetre squares 40 centimetre squared 40 square centimetres 40 cm ² 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

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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) 2 LENGTHS + 2 WIDTHS = 2 X 10 + 2 X 6 = 2 X 10 + 2 X 6 = 20 + 12 = 32m ADD 1 LENGTH + 1 WIDTH THEN DOUBLE IT 10 + 6 = 16m 2 X 16 = 32m ADD 4 LENGTHS IN ORDER 10 + 6 + 10 + 6 = 32 m 10m 6m Which way do you prefer? There’s lots of ways to find the perimeter… 10m 6m

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Perimeter Perimeter Units of perimeter: Any units of length METRIC UNITS Millimetres mm Centimetres cm Kilometres km IMPERIAL UNITS MilesYardsFeetInches

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

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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 …

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

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

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

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

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

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Example 2 STEP 1 Read it ! - What do I want to find out? … I’ll read this again so I’m sure I get it … - What do I know?

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

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

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

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

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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 …

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STEP 1 Read it ! STEP 2 Underline it ! … and … LOOK FOR KEY NUMBERS! Example 3 AREA CLUES surface cover coverage amount of carpet how much carpet PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length 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? WORD CLUE! area KEY NUMBER! KEY NUMBERS!

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1m 6m 3m Example 3 STEP 1 Read it ! STEP 2 Underline It ! STEP 3 Picture It! ! 2 Steps so far … CLICK for Step 3! 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. 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?

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1m 6m 3m 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? Example 3 STEP 1 Read it ! STEP 2 Underline It ! STEP 3 Picture It! ! ?m 2m ?m3m Area? = 3 x 2 = 6m ² = 3 x 3 = 9m ² STEP 4 Calculate It ! 3 steps done 1 to go … CLICK for Step 4! Work out area of each rectangle and add! Total Area = 6 + 9 = 15m ² The tiled area is 15m ² Can you think of any other ways you could work this out?

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

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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 …

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STEP 1 Read it ! STEP 2 Underline it ! … and … LOOK FOR KEY NUMBERS! Example 4 AREA CLUES surface cover coverage amount of carpet how much carpet PERIMETER CLUES edge edging outside distance outside length perimeter fencing total outside length external length … 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? WORD CLUE! perimeter KEY NUMBER! KEY NUMBERS!

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1m 6m 3m Example 4 STEP 1 Read it ! STEP 2 Underline It ! STEP 3 Picture It! ! 2 Steps so far … CLICK for Step 3! 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? 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.

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1m 6m 3m Example 4 STEP 1 Read it ! STEP 2 Underline It ! STEP 3 Picture It! ! ?m 2m ?m3m STEP 4 Calculate It ! 3 steps done 1 to go … CLICK for Step 4! Work out the length of each side and add! 6+ 3+ 3+ 1+ 3+ 2 = 18 18m of edging is needed. 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?

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

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

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Now Your Turn! 2 STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Problem 2 The history classroom is 9m long and 5m wide. How edging tape is needed for the carpet perimeter? A length of 28m edging strip is needed Click for solution to problem

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Now Your Turn! 3 STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Problem 3 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? The resource corner is 2m x 2m square. How much floor space is still free? An area of 68m ² carpet is needed Click for solution to problem

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

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Now Your Turn! 5 STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Problem 5 How much floor space is there in this classroom? The floor area is 81m ² Click for solution to problem KEY Door (0.5m wide) 15m 7m 6m 11m

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

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Now Your Turn! 7 STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Problem 7 How much floor space is there in this classroom? The floor area is 59m ² Click for solution to problem KEY Door (1/2 m wide) 10m 7m 5.5m 8m

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Now Your Turn! 8 STEP 1 ? STEP 2 ? STEP 3 ? STEP 4 ? Underline It ! Picture It! ! Calculate It ! Read it ! Problem 8 What length of skirting board is needed this classroom? (Remember to allow for the door!) 33.5m of skirting board is needed. Click for solution to problem 4m KEY Door (1/2 m wide) 10m 7m 5.5m 8m

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Now U R PC with Area and Perimeter … Why not have a go on your own with THE PUPIL VERSION IN THE HISTORY CLASSROOM? Or are you ready to try … THE FIENDISH SPANISH CLASSROOM PROBLEMS ? - about Money with Area and Perimeter PRESS ESCAPE TO RETURN TO MENU

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