Length, Perimeter and Area

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1 E Student Book 4 Nae

2 Series E Contents Topic Units of length (pp. 7) etres and centietres length and decial notation illietres convert it apply Date copleted Topic Perieter (pp. 8 4) easuring shapes calculating perieter perieter word probles perieter challenges solve harder perieter challenges solve Topic Area (pp. 5 ) square centietres square etres investigating area and perieter area challenges apply area challenges apply Series Author: Nicola Herringer Please note: These pages have been designed to print to shrink to printable area as this is a coon default setting on any coputers. There ay be inor discrepancies with easureents as individual printers and photocopiers print to slightly different proportions. Copyright

3 Units of length etres and centietres We use etres, centietres and illietres regularly in everyday life. There are 00 centietres in etre. Another way to think about this relationship is that centietre is one hundredth of a etre. 00 = = 00 or 0.0 So = 50 = Convert each etre easureent into centietres: a = d 9 = b 4 = e = c 4 = f 4 = Convert each centietre easureent to etres: a 0 = d 50 = b 0 = e 75 = c 90 = f 80 = Estiate and easure three things that fit in each category: a About etre b About 4 etre Estiate in Measure in c About etre 4 Match these objects to their correct easureent by connecting the with a line: E

4 Units of length etres and centietres 5 Measure the length of the lines below using a ruler. Write each length in centietres, to the nearest centietre. a b c 6 Answer these questions about the lines above: a How uch longer is line b than line c? b What would the length of line b be if it was shorter? c What would the length of line c be if it was 9 longer? 7 Draw lines for the following easureents. Make sure you start each line on the dot. a 4 b c 8 8 Work with a partner to easure the following parts of your body with a tape easure. Label your easureents to the nearest centietre in the boxes. a Across your b Around your head. shoulders. c Around one ankle. d Around one wrist. e Fro your foot to the top of your thigh. f Around one knee. g Fro the top of your forehead to your chin. E

5 Units of length length and decial notation When we easure things that are in etres and centietres it is useful to record such lengths in decial notation. Reeber that = 00. This can be written as 0.0. So if we easure soething that is etre and 6 centietres long, we would write it like this:.6 Hundredths of a etre Tenths of a etre Metres in whole nubers Write the easureents in decial for: a etre 69 centietres = b etres 9 centietres = c etres centietres = e 9 etres 4 centietres = d 4 centietres = f 5 etres 9 centietres = Write these centietres as etres using decial notation: a 46 = b 9 = c 567 = d 607 = e 50 = f 4 = Write these easureents as centietres: a 9.4 = b.45 = c 6.07 = d 5.47 = e 0.94 = f 9.5 = 4 Draw lines for the following easureents. Make sure you start each line on the dot and keep each line parallel to the top of the page. a 0.07 b 0.4 c 0.0 E

6 Units of length length and decial notation 5 Charlotte thinks that how far you can jup depends on your height. Do you think she is right? Work in a group of four to coplete this table. You will need a tape easure and a space to do long jup. First easure each person s height and record it under their nae in decial notation. Then each person jups as far as they can. Measure this distance and record it under their height in decial notation. Nae Height Long jup a Order the naes in your group fro tallest to shortest: b Order the long jups fro longest to shortest by writing the naes: c Do you agree with Charlotte? Why or why not? 6 Find the lines that connect to ake these lengths:, and. Show you have found the by tracing over lines that connect in different colours. To start you off, the first length has been done for you. a = b = c = You can use a calculator E

7 Units of length illietres We use etres, centietres and illietres regularly in everyday life. You should learn these illietre facts: centietre = 0 illietres = 0 45 = = Estiate and easure these objects in illietres: Object Estiate Millietres a b c Width of your thub Length of your hand Length of a grape Convert these centietre easureents into illietres: a 4 = b = c 0 = d 6 = e 7 = f = Write these as centietres and illietres: a 7 = c 4 = b 9 = d 6 = 4 Write these easureents as centietres: a = b 46 = c 6 = d 48 = E 5

8 Units of length illietres 5 Follow these steps to easure these lines accurately in centietres and illietres = Line up the zero on your ruler with the start of the line. Read the last that is at the end of the line. Write down the nuber. Count the after the and write it next to the. a = b = c = d = 6 Coplete the table for these deadly spiders: Length in Length in and Length in a Redback 0.7 b Funnel web and 5 c Black widow d Brown recluse.5 e List these deadly spiders in order fro sallest to largest: 6 E

9 Convert it apply Getting ready This is a gae for two players. Players need a counter each, a copy of this page and a die. copy What to do The object of this gae is to get to the finish line first. Decide who will go first. That player rolls the die and oves that any spaces on the board. If you land on a easureent that is white, you ust convert to OR to. If you land on a easureent that is grey, you ust either convert to OR to. The other players decide if you are correct. If you are, then you ove forward space. If you are incorrect, you ove backwards spaces Finish Start E 7

10 Perieter easuring shapes Perieter is the total length around the outside of an enclosed space. To find the perieter of this shape, we add the lengths of all the sides. 6 P = = 6 6 Find the perieters of these shapes: a 6 b P = = P = = 4 4 c 5 d P = + + = P = = Find the perieter of this shape. Set your working out clearly E

11 Perieter easuring shapes Find the perieters of these irregular shapes. Use the dot paper as your guide. a b P = P = c d P = P = e f P = P = 4 Use a ruler to draw soe shapes with the following perieters. You can experient first with a geoboard and soe rubber bands. a Draw a rectangle with a perieter of. b Draw a rectangle with a perieter of 0. E 9

12 Perieter calculating perieter Use what you know about squares and rectangles to work out the perieter of these shapes. Measuring will not help because they are not to scale. Look carefully at the diensions a b P = P = 4 c 5 d P = P = Show how to find the perieter of these shapes with an addition sentence and a ultiplication sentence for each. Shape A has been done for you. 5 4 Shape A Shape B Shape C Shape Perieter by addition Perieter by ultiplication A = 6 4 sides 4 = 6 B C 0 E

13 Perieter calculating perieter Predict the perieter of each of these shapes on the square centietre grid below. Show what the perieter is by drawing and labelling. a A square with 4 sides. b A rectangle with two sides and two sides. P = P = 4 Use the grid paper to construct the following shapes at each starting point with the stated perieter. a 0 b 4 c 8 5 Here are ore square centietre grids. a What is the perieter of this irregular shape? b Draw a square with the sae perieter. P = E

14 Perieter perieter word probles Solve these perieter probles: a Pablo drew a rectangle in his workbook. The perieter of the rectangle was 4. Two sides are long. How long are the other two sides? b The perieter of a square shaped pool is 00. What are the easureents of the pool? c West Thye Priary School is adding a new fence around the outside of the playground. The playground is rectangular shaped. One length is 6. The perieter is 5. What are all the easureents of the playground? d Lia ade a pentagon fro agnetic sticks. If the perieter of his shape is 55, what is the length of one side? Length of one side = E

15 Perieter challenges solve What to do Try these perieter challenges: a The perieter of this square is. When it is cut in half, we get two identical rectangles. What is the perieter of one rectangle? P = b This rectangle is 6 wide. How long is it if the perieter is? 6 Length The lines on soe of the sides are to show you they are all the sae length. c Find the perieter of this shape if the length is. P = E

16 Harder perieter challenges solve What to do Use the clues in each of these diagras to find the perieter. Diagra Perieter = Diagra Perieter = 4 E

17 Area square centietres Area is the aount of space a shape covers. It is a D easureent. We easure area in square units. For sall areas, we use square centietres. = square centietre = Each square covers an area of square centietre ( ²). Record the area of each shape: a b c d Area = Area = Area = Area = Find the area of these irregular shapes. Use the grid paper as your guide: a b c Area = Area = Area = E 5

18 Area square centietres Use the square centietre grid paper to shade soe irregular shapes with the following areas: a 4 square centietres b 6 square centietres 4 How any shapes can you ake with an area of 9 square centietres? Show the on the grid below. The first one has been done for you. 5 What is the area of each rectangle? Each square in the grid has an area of ². a b c Area = Area = Area = 6 E

19 Area square etres When we need to find the areas of large spaces, we use square etres. The sybol for square etres is ². In groups, stick pieces of newspaper together to ake a square that is etre long and etre wide. a How any people can fit standing inside one square etre? b Cut your square into five pieces and then stick it back together. It can be any shape. Draw it here: Is this still one square etre? Use your square etre to easure five areas in your school. Estiate first. Space to be easured Estiate Actual area a b c d e E 7

20 Area square etres Rewrite these easureents the short way. The first one has been done for you. a Twenty nine square etres = 9 ² b Thirty seven square etres = c Three hundred and two square etres = d Six hundred and ninety one square etres = e Eighty point seven square etres = f Seven point two square etres = 4 Miss Farbio has a rectangular garden with six fence posts. The distance between each post is etre and the area of her garden is ². Her neighbour Mr Gubbio has 4 fence posts, also etre apart. What is the area of his garden in square etres if one side of the fence has three posts, just like Miss Farbio s garden? Area of Mr Gubbio s garden = 8 E

21 Area investigating area and perieter What is the area and perieter of these shapes? a P = A = b P = A = c P = A = d P = A = Use the grid below to draw two shapes with a perieter of but with different areas: Colour a square with a side length of 4. Label its area and perieter. Now colour a square with a side length of 5 and label its area and perieter. What do you notice? E 9

22 Area investigating area and perieter 4 Look at this square grid. Soe of the grid is shaded. Work out the area of the part that is shaded. The area of the part that is shaded is ² A faster way to calculate area is to ultiply the length by the width. Look at this square. If we ultiply the length by the width, we get 6 ². This is the sae as counting all the squares Calculate the area of each of these shapes by ultiplying the length by the width: a A = 5 8 b A = 0 c A = 9 4 d A = E

23 Area challenges apply What to do Solve these area challenges based on the diensions: a A fraed photograph is 6 5. The frae itself is 5 wide. Use these clues to find the area of the photograph inside the frae The area of the photograph is. b Using a ruler, copy this shape so it reflects on the right of the irror line. Then work out the total area of this shape. Mirror The total area of this shape is. E

24 Area challenges apply What to do next Solve these area challenges based on the diensions: a Max folded a rectangular piece of paper in half three ties to ake a square. If one side of the final square was, what was the area of the piece of paper he started with? The area of the piece of paper he started with was. b Aber received a drawing fro her cousin Caeron. The drawing was on a square piece of paper folded in half four ties. If the area of the folded drawing was 4 ², what was the area of the original piece of paper that Caeron drew on? The area of the original piece of paper that Caeron drew on was. E

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