Length, Perimeter and Area

Transcription

1 G Teacher Student Book SERIES Length, Perimeter and Area Name

2 Series G Length, Perimeter and Area Contents Topic Units of length (pp. 8) choose units of units length of measurement convert perimeter measurements 9 area 7 size me up! 7 how long? / / / / / / / / / / Topic Perimeter (pp. 9 6) units of length measure perimeters perimeter 7 perimeters of composite shapes area 9 circumference circle work perimeter puzzles Topic Area (pp. 7 6) square units animal rescue Date completed / / / / / / / / / / / / / / / / / / / / / / maps Series Authors: Rachel Flenley Nicola Herringer where will it take you? Please note: / / / / / / / / / / Copyright

3 Units of length choose units of measurement metre 000 m = km kilometre eg. 00 cm = m 0 m = 0.00 km etc. a The length of your nose mm km c swimming pool m d mm e The height of a basketballer m mm g The length of the Trans-Siberian km h cm Nose: mm or cm Height: cm or m Name things you would measure in mm, cm, km: mm cm km Teacher check. Length, Perimeter and Area G SERIES TOPIC

4 Units of length choose units of measurement 5 mm cm Answers will vary. m hand span a french fry London to Paris your tongue length G SERIES TOPIC Length, Perimeter and Area

5 Units of length convert measurements cm mm cm = ( 0) mm = 0 mm cm m cm = ( 00) m = 0. m Express the lengths shown on the ruler in ways: 0 cm a c d a mm. cm 8 mm.8 cm c mm. cm d 69 mm 6.9 cm a 00 mm = 0 cm 0.5 cm c 8 8 mm = 8.8 cm d m = 00 cm e 9 m = 900 cm cm Convert these lengths to metres: a 00 cm = m 8 cm = 0.8 m 0 mm = cm 00 cm = m c.5 m d 8 cm =.8 m 000 m = km e cm =. m mm = m g mm =. m h 87 cm =.87 m i 98 mm = 0.98 m Length, Perimeter and Area G SERIES TOPIC

6 Units of length convert measurements to cm: cm 8 mm. m convert cm.8 cm 0 cm a cm 0 mm m 0 mm cm m 5 m 50 cm mm c 00 cm 5 mm 00 cm.5 m 5 Use these Guinness World Record Source: Guinness World Book Records 008 metres millimetres 9.5 cm Tallest living person 570 mm 5.67 m mm 75. cm Smallest tooth 0.00 m 0. cm mm 0.7 m.7 cm 7 mm Teacher check. 7 Teacher check. G SERIES TOPIC Length, Perimeter and Area

7 Units of length estimate and measure a c d 0 a 6 cm 7 cm c 7 cm d 8 cm a A basketballer is about metres high. c centimetres d metres e 8.6 metres 8.6 Length, Perimeter and Area G SERIES TOPIC 5

8 Units of length estimate and measure Comparing lengths or heights with a known measurement is a useful strategy. The known a 8 m 90 cm c 5 m d m Answers will be approximates. 5 Actual measurement Teacher check. G SERIES TOPIC Length, Perimeter and Area

9 Size me up! investigate ready you will work with a partner to compare the length lengths of string. A ruler may also help. What to do elbow. Do you think this is true for you? Test it out. circumference of your wrist. Test that one out. Answers will vary. What to do next Answers will vary. Length, Perimeter and Area G SERIES TOPIC 7

10 How long? apply ready What to do A B C 5 cm 0 cm + 8 cm cm Group average. m 0. m 5 Teacher check. What to do next 8 G SERIES TOPIC Length, Perimeter and Area

11 Perimeter measure perimeters is the perimeter. Perimeter Teacher check. 5 a c cm P = cm cm cm P = cm cm cm cm d e P = 8 cm cm P = 9 cm cm P = 5 cm cm Do you need to P = cm Length, Perimeter and Area G SERIES TOPIC 9

12 Perimeter measure perimeters measuring cm. cm m m m m m m a P = 0 m P = 0 m c P = 9 m d P = 9 m Width Perimeter 6 cm. cm 6. cm mm. m mm 8. m 5.6 m 5 a cm 0 cm 0 cm c. cm cm. cm d e 6.6 cm mm 60 mm 0 G SERIES TOPIC Length, Perimeter and Area

13 Perimeter perimeters of composite shapes 7 m 6. m. m 8 m m m 6. m. m. m.8 m 7. m m m. m. m. m m. m a P = 0 m P = 0 m c P = 6.8 m * m km km km m m m m m km a P = m P = m c P = km * Teacher check. Length, Perimeter and Area G SERIES TOPIC

14 Perimeter perimeters of composite shapes 0 m 6 m m? m m +? m = 6 m 6 m m = m? m The perimeter of this shape is therefore m. 8 mm 60 mm. m mm 8 mm 0 mm mm. m. m mm a P = 00 mm P =.6 m c P = 60 mm * 5 0 mm 0 mm 6. m. m cm 0 mm 6 m.6 cm P = 0 mm P = 6.6 m P = cm * a in length. Another is cm. What is my perimeter? What is my perimeter? c in length. What is my perimeter?.7 mm 6.8 cm cm G SERIES TOPIC Length, Perimeter and Area

15 Perimeter perimeters of composite shapes 7 Teacher check. 8 Teacher check. Length, Perimeter and Area G SERIES TOPIC

16 Perimeter circumference are no straight lines to help us. Diameter Teacher check. 5 the circumference? The circumference is about three times as long as the diameter. Your answer is always about. G SERIES TOPIC Length, Perimeter and Area

17 Circle work investigate ready What to do (walker) stretches the string out. Answers will vary. What to do next be? Answers will vary. Length, Perimeter and Area G SERIES TOPIC 5

18 Perimeter puzzles solve What to do Solve these perimeter puzzles: a The perimeter of the triangle is m. m 5. mm long. c 8 m W = m d what was the perimeter of the original square? P = 8 m G SERIES TOPIC Length, Perimeter and Area

19 Area square units cm cm a c Area = cm Area = cm Area = cm d e Area = 5 cm Area = 7 cm Area = 6 cm Teacher check. Do you need to use whole Length, Perimeter and Area G SERIES TOPIC 7

20 Area square units For larger areas such as a tennis court we use square metres (m²) A square kilometre is m². m m km km a Teacher check. Answers will vary. We also use hectares (ha) to measure area. These are larger than square metres but smaller than square kilometres. We use them for measuring spaces such as farms or parks. 00 m 00 m 00 m 00 m = = ha a m² ha m² 8 ha c m² ha d m² ha e m² 5 ha m² ha g ha m h 9 ha m i ha m m² 0.5 ha k m².5 ha l m² 0.75 ha 5 a This page cm ² km ² c A farm ha d A mobile phone screen cm ² e A city park ha km ² g cm ² h m ² 8 G SERIES TOPIC Length, Perimeter and Area

21 Area find area using formulae Area = cm cm = 8 cm² cm cm a c m m cm m cm m A = 6 m ² A = cm ² A = 9 m ² * a 0 cm ² 0 cm ² c 50 m ² d 5 cm ² e 0 cm ² 500 m ² g 0 m ² h A rug measuring 0. m. m.68 m ² a $600 0 cm² c 5 m d 6 cm W = 8 cm cm W = cm Answers will vary. Two possible answers. Length, Perimeter and Area G SERIES TOPIC 9

22 Area find area using formulae Triangle = cm² = The formula for this is: cm cm m cm 0 cm m a Area = cm Area = 0 cm c Area = 0.5 m 6 cm cm cm d Area = cm e Area = 7.5 cm * 5 6 cm m 6 m cm 9 m 8 m a Area = 9 cm Area = 8 m c Area = m d cm ² e 9 m ² 5.9 m ² * 0 G SERIES TOPIC Length, Perimeter and Area

23 Area find area of irregular and composite shapes Not all shapes are regular triangles or rectangles. We have to shapes as well. m 70 m cm m 0 m 0 m 6 cm 6 cm cm 8 m 0 m a m ² 000 m ² c 8 cm ² 6 cm m 0 cm 8 cm m 0 cm 8 cm d 0 m ² e 0 cm ² 0 cm ² * Teacher check. Length, Perimeter and Area G SERIES TOPIC

24 Area find area of irregular and composite shapes cm cm a A = cm² A = 6 cm² c A = 6 cm² one colour, then d A = cm² e A = cm² the right, draw an irregular area amount: a 800 m 00 m c 0 m 0 m Answers will vary. G SERIES TOPIC Length, Perimeter and Area

25 Area area and perimeter Do shapes with the same area have the same perimeter? cm cm Width Area cm Teacher check. cm cm Teacher check. cm Length, Perimeter and Area G SERIES TOPIC

26 Area area and perimeter a The perimeter of a square is 8 cm. What is its area? cm ² what is the area of the rectangle? 6 cm ² c The area of a square is 6 m². What is its perimeter? m Teacher check. G SERIES TOPIC Length, Perimeter and Area

27 Area and perimeter puzzles solve What to do family room using the sofa cushions. There are 8 she can make for herself that is brother-free? wall m ² Cushions 50 cm = m wall Cushions 50 cm = m a 9 m ² be the area? c 8 m ² 0 m are involved in work out the area Total area to be painted: ( m.5 m ) + ( m.5 m ) m² = m² m ² 9 m ² =.78 (Paige needs at least pots of paint.) pots = $55 = $0 Therefore she can do it for under $50. Length, Perimeter and Area G SERIES TOPIC 5

28 Animal rescue investigate ready Four African animals have been stolen by smugglers. animals to their natural habitat. You have four enclosures in which to transport the animals select the right one for each animal. What to do the animals. Guess, check and improve 7 m m m m² m² 6 m² m² W m m².5 m m² m Elephant m 6 m² 6 m² m² m W m m m 5 m 0 m² W m m m W m G SERIES TOPIC Length, Perimeter and Area

29 Scale and distance scale drawings cm = 5 km right represents km, a c 9 6 km km km d 5 km e km a 60 cm 0 cm c 0 cm d 00 cm e 80 cm 50 cm 5 mm 5 a From the roller coaster to the show bags. 50 m From the clowns to the big top. 00 m c From the Ferris wheel to the big top. 50 m d to the roller coaster. You are now feeling e 50 m Length, Perimeter and Area G SERIES TOPIC 7

30 Scale and distance scale drawings Now design your own map: a Teacher check. c Write problems on another piece d e cm represents 7 Bath Bedroom Wall A a What is the scale? cm = m What is the perimeter of the apartment? 7 m 8 m c 6 m d m m e You want to buy a plasma TV that takes up the length of m.5 m 0 6 cm metres g No. h It only has one bedroom and it has a tiny bathroom. 8 G SERIES TOPIC Length, Perimeter and Area

31 Scale and distance maps Parliament Captain Cook East What does each Arena Sidney Bowl Park cm = 000 m a.5 km km c Walk, because it is only km. d Approx 7 km e Teacher check. Length, Perimeter and Area G SERIES TOPIC 9

32 Scale and distance maps Berri a 0 km 50 km c Teacher check. d Teacher check. cm = 0 km a 8 km km Walford 7 km c 8 km Summer Bay d The car costs are as follows: $9 0 G SERIES TOPIC Length, Perimeter and Area

33 Scale and distance speed, time and distance a 0 km in hours 60 km/h 0 km in 8 hours 0 km/h c 0 km in hour 0 km/h d 0 km in hours 65 km/h e 80 km in 6 hours 80 km/h 5 km/h a c d km/h 05 km/h 65 km/h 00 km/h a c 0 6 d Distance Distance Distance Distance 0 km 60 km 00 km 0 km Time Time Time Time.5 hours hours.5 hours 0.5 hour Length, Perimeter and Area G SERIES TOPIC

34 Scale and distance speed, time and distance a c hours. What is its average 75 km 50 km/h 00 km/h into three 0 minute does the plane travel in d hours. What is his 6 km/h e A miniature train travels 00 km in hours. What is 0 km 5 B E cm A cm cm D C cm = m a.5 m/h 8 m/h G SERIES TOPIC Length, Perimeter and Area

35 All roads lead to Rome apply ready Copenhagen Amsterdam Prague Paris 87 Vienna 587 Naples What to do a Copenhagen to Vienna? c hours 7 hours 6 hours d 0 hours 0 km/h Length, Perimeter and Area G SERIES TOPIC

36 Where will it take you? investigate ready Styler Stomper What to do Use a separate piece of paper. Teacher check. Car: Distance to travel: Day Start End Distance Did you travel more distance or less than G SERIES TOPIC Length, Perimeter and Area

37 Units of length Name a mm 0 cm 8 00 mm c 0 cm a mm m c cm mm m 8 00 cm mm m d. cm mm m 5 a Skills Not yet Got it Series G Topic Assessment 5

38 Units of length Name Answers will vary. Answers will vary. a mm 0 cm 8 00 mm c 0 cm mm 0 cm 0.56 m 5 m 50 cm 8 00 mm 50 mm 0 cm 500 m a 500 mm 0.5 m c cm 0 mm. m 8 00 cm mm 8 m d. cm mm 0.0 m 5 a No. 0 cm off. No. They would still be cm off. Skills Not yet Got it Series G Topic Assessment

39 Perimeter Name a c cm cm 0 cm cm cm cm cm cm cm cm cm cm cm cm cm a measuring. m. c An equilateral triangle with by 7 cm. 6 m 6 m a mm 60 mm 60 mm 0 mm 8 m 6 m P = P = * cm cm Skills Not yet Got it Calculates the perimeters of polygons Series G Topic Assessment 7

40 Perimeter Name a c cm cm 0 cm cm cm cm cm cm cm cm cm cm cm cm cm cm 80 cm 8 cm a measuring. m. 6.8 m by 7 cm. 9 cm c An equilateral triangle with. cm 6 m 6 m a mm 60 mm 60 mm 0 mm 7 mm 6 m 8 m 6 m 00 mm 70 m P = 9 mm P = 68 m * Answers will vary. cm cm Sample answers. Skills Not yet Got it Calculates the perimeters of polygons 8 Series G Topic Assessment

41 Area Name a Area = cm Area = cm c Area = cm a A book measuring cm cm c A rectangle measuring cm 9 cm d Name two things: a c ²: ²: d ²: a The perimeter of a square is 6 cm. What is its area? total area: 8 m² m m² 8 m² Series G Topic Assessment 9

42 Area Name 5 cm 9 cm 9 m m 8 m c 0 m a Area = cm Area = m c Area = m * 7 Create shapes with cm cm 8 Skills Not yet Got it 0 Series G Topic Assessment

43 Area Name a Area = cm Area = 6 cm c Area = Approx 0 cm a cm ² A book measuring cm cm 8 cm ² c A rectangle measuring cm 9 cm 6 cm ² d.7 m ² Name two things: a Sample answers: ²: paddock park c ²: bedroom backyard book computer screen d ²: national park France a The perimeter of a square is 6 cm. What is its area? 8 cm ² total area: 8 m² m m² 8 m² Series G Topic Assessment

44 Area Name 5 (Base Height) or (Base Height) cm 9 cm 9 m m 8 m 0 m a Area = 8 cm Area = 8 m c Area = 0 m * 7 Create shapes with cm cm 8 Its perimeter might be 0 cm (6 cm + cm + 6 cm + cm) Answers will vary. Skills Not yet Got it Series G Topic Assessment

45 Scale and distance Name how long is line: a c km km d km km a c d e km e a c Denver d cm = 0 km Washington a km Nashville km km Atlanta 80 km c km/h San Diego 690 km d hours Skills Not yet Got it Series G Topic Assessment

46 Scale and distance Name how long is line: a c 8 km km d 0 km km a c d e 6 km e a km 7 km c Denver Stone d km cm = 0 km Washington a 75 km Nashville km 70 km Atlanta 80 km c 80 km/h San Diego 690 km d 8.5 hours Skills Not yet Got it Series G Topic Assessment

47 Series G Length, Perimeter and Area Perimeter Area NSW to compare lengths appropriate unit measures of length for a unit longer than a metre km problems using of a large area compare perimeters triangles between the the perimeter for isosceles triangles perimeters of lengths for a unit larger than a m² a more convenient unit than a km² hectares appropriate unit to calculate area units of measure Series G Outcomes 5

48 Series G Length, Perimeter and Area Perimeter Area SA metric units or variety of purposes of comparison in planning measurement units to measure the precision of measurements metric units or terms of metric units use formulae in the perimeter of polygons between measurable communicate language calculate the area of shapes changing units or instruments) Series G Outcomes