AUTUMN UNIT 3. first half. Perimeter. Centimetres and millimetres. Metres and centimetres. Area. 3D shapes PART 3 MEASURES AND PROPERTIES OF SHAPES


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1 PART AUTUMN first half MEASURES AND PROPERTIES OF SHAPES SECTION Perimeter SECTION Centimetres and millimetres SECTION Metres and centimetres SECTION Key Stage National Strategy CROWN COPYRIGHT 00 Area SECTION 5 D shapes
2 !! MEASURES AND PROPERTIES OF SHAPES SUGGESTED TIME 5 hours TEACHING OBJECTIVES Suggest suitable units to measure length. Measure and draw lines to the nearest millimetre. Understand, measure and calculate the perimeter of rectangles and regular polygons. Use, read, and write metric units of length, and convert between units. Record estimates and measurements from scales to a suitable degree of accuracy. Understand area measured in square centimetres. Use formula in words for the area of a rectangle. Use all four operations to solve measurement word problems. Visualise D shapes from D drawings and identify nets of an open cube. SECTION Perimeter SECTION Centimetres and millimetres SECTION Metres and centimetres SECTION Area SECTION 5 D shapes HOMEWORK Several of the Star Challenges are suitable homework activities. Learn and use metric units of length, including conversions between units. Consolidate multiplication and division by working on area calculations. Key Stage National Strategy CROWN COPYRIGHT 00 0
3 Key Stage National Strategy PART CHECKLIST Unit Checklist for pupils Perimeter You will: measure lines to the nearest centimetre understand perimeter find perimeters by measuring, counting and calculating solve word problems and puzzles involving perimeter Centimetres and millimetres You will: measure lines to the nearest millimetre work with measurements given in centimetres and millimetres (cm and mm) or centimetres (cm), to one decimal place add together measurements given in centimetres and millimetres solve word problems using centimetres and millimetres Metres and centimetres You will: work with measurements given in metres (m) and centimetres (cm) add together measurements given in metres and centimetres solve word problems using metres and centimetres Area You will: measure areas by counting squares work out areas measured in square centimetres learn and use the formula for the area of a rectangle Key Stage National Strategy CROWN COPYRIGHT 00 D shapes You will: work with drawings of D shapes work with nets of an open cube 05
4 SECTION : PERIMETER DIRECT TEACHING POINTS Teach pupils how to measure lengths correctly using a ruler. Model the process pointing out common errors. Oops and Ouch were asked to measure this line: Oops put the ruler like this: This line is 6 cm long. Explain why Oops is wrong:... Ouch put the ruler like this: What did Ouch do wrong?... Make sure pupils understand perimeter as the distance around the edge of a shape. Exercises and reinforce this idea. You need to explain the difference between measure and calculate. Star Challenges and provide opportunities for investigative work. KEY TO VOCABUL ARY LEAR USE AND length distance width breadth perimeter centimetre square rectangle equilateral triangle regular pentagon hexagon octagon Key Stage National Strategy CROWN COPYRIGHT 00 06
5 Key Stage National Strategy PART SECTION Perimeter Distance round the edge Measure the distance round the edge of each shape. Give each answer in centimetres Example 5 cm cm cm 6 cm 5 cm The distance round the edge of this rectangle is: 5 cm cm 5 cm cm 6 cm A B C D E Key Stage National Strategy CROWN COPYRIGHT
6 Key Stage National Strategy PART SECTION Perimeter Calculating perimeters Example cm cm cm cm A cm cm The perimeter of shape A is: cm cm cm cm cm cm 0 cm All the shapes below are made from a number of squares joined together. Each square has cm sides. Calculate the perimeter of each of these shapes: Imagine walking around the outside. B C D E F G Key Stage National Strategy CROWN COPYRIGHT
7 Key Stage National Strategy PART SECTION Perimeter Rectangle perimeters Calculate the perimeter of each of these rectangles: 6 cm cm cm 6 cm Perimeter... 5 cm cm cm 5 cm Perimeter... 7 cm Perimeter... cm! "! " length width cm 8 cm Perimeter... Key Stage National Strategy CROWN COPYRIGHT A rectangle has length 0 cm and width 0 cm. What is its perimeter?... A square has side 0 cm. What is its perimeter?... The short side of a rectangle is cm. The perimeter is 0 cm. What is the length of its long side?... 09
8 Key Stage National Strategy PART SECTION Perimeter # Different perimeters marks stars 0 5 marks star This shape has a perimeter of 6 cm. P = 6 cm Use centimetre squared paper. Make two different shapes with squares. Write down the perimeter of each shape. ( marks) Make five different shapes with squares. Write down the perimeter of each shape. (5 marks) Make ten different shapes with 5 squares. Write down the perimeter of each shape. (0 marks) Key Stage National Strategy CROWN COPYRIGHT 00 0
9 Key Stage National Strategy PART SECTION Perimeter # Regular polygons The shapes below are all regular polygons. All the sides are the same length. All correct star Calculate the perimeter of each regular polygon. Example square 5 cm A square has sides. Each side of this square is 5 cm long. The perimeter of this square is 5 cm 0 cm 0 cm A hexagon has... sides. regular hexagon Each side of this hexagon is... cm long. The perimeter of this hexagon is... cm. cm A pentagon has... sides. regular pentagon Each side of this pentagon is... cm long. The perimeter of this pentagon is... cm. cm A triangle has... sides. Each side of this triangle is... cm long. The perimeter of this triangle is... cm. 6 cm Key Stage National Strategy CROWN COPYRIGHT 00 regular octagon An octagon has... sides. Each side of this octagon is... cm long. The perimeter of this octagon is... cm. 0 cm
10 Key Stage National Strategy PART SECTION Perimeter # Perimeter puzzle The shape drawn has a perimeter of cm. There are 5 more shapes with a perimeter of cm that can be made on a grid like this shapes stars shapes stars shapes star How many can you find? Rotations and reflections of the same shape only count as. Key Stage National Strategy CROWN COPYRIGHT 00
11 SECTIONS AND : CENTIMETRES AND MILLIMETRES METRES AND CENTIMETRES DIRECT TEACHING POINTS Teach the three forms of giving a measurement: mm, cm and mm, and cm using decimals. Star Challenge links to work on perimeter. Consolidate use of ruler to measure accurately to mm. Mental work can concentrate on recall of conversion of units, for example: km = 000 m, m = 00 cm, cm = 0 mm, 0.5 m = 50 cm, mm =. cm, cm =. m. Teach three forms: cm, m and cm, m using decimals to give measurements. Exercise in Section can form the basis of oral mental work. It reinforces complements of 00. Use example below as the basis of oral mental problems. Work out the following:! " m 5 cm! " 50 cm! " m 80 cm! "? Key Stage National Strategy CROWN COPYRIGHT 00 Paula is standing on tiptoe. She can just reach the light switch. She stands on a stool. How high can she reach?... She wants to reach the biscuit tin. What is the height of the smallest stool she could use?... KEY TO VOCABUL ARY LEAR USE AND kilometre km metre m centimetre cm millimetre mm
12 Key Stage National Strategy PART SECTION Centimetres and millimetres Measuring lines mm Measure each of these lines to the nearest mm: cm Length of line...mm Length of line... cm...mm Length of line... cm...mm Length of line...mm... cm... mm... cm... mm... mm... cm... mm... cm... mm... mm... mm Longer and shorter lines Line A is cm 6 mm long. A (a) Line B is 8 mm longer than A How long is line B? cm... mm Line P is cm 8 mm long. P (a) Line Q is 5 mm longer than P. How long is line Q?... cm... mm Key Stage National Strategy CROWN COPYRIGHT 00 (b) Line R is cm mm longer than P. How long is line R?... cm... mm (c) Line S is cm mm shorter than P. How long is line S?... cm... mm
13 Key Stage National Strategy PART SECTION Centimetres and millimetres Adding cm and mm Work out the following The diagrams are not drawn to scale. cm 5 mm mm A B C The length of AC... cm... mm 5 cm mm 6 mm D E F The length of DF... cm... mm 7 cm mm cm 5 mm The length of GJ... cm... mm G H J The length of LN is 5 cm mm. cm 7 mm cm 5 mm L M N The length of LN is cm mm. RINGO RINGO Ringo is right. Bingo is wrong. Explain why Bingo is wrong. BINGO... 5 cm 6 mm cm 5 mm cm 8 mm W X Y Z The length of WY... cm... mm The length of XZ... cm... mm Key Stage National Strategy CROWN COPYRIGHT 00 6 My pencil is cm 8 mm long. Bob s pencil is mm longer. How long is Bob s pencil?... 7 I have a zip 0 cm 7 mm long. The zip on my pencil case is twice as long. How long is the pencil case zip?... 5
14 Key Stage National Strategy PART SECTION Centimetres and millimetres Three ways to measure lines There are three ways to measure the same line mm cm GUESS WHAT? This line is 6 mm long. This line is cm 6 mm long. This line is.6 cm long. Measure each of these lines to the nearest mm Length of line... mm Length of line... cm... mm Length of line... cm Length of line... cm... mm Length of line... mm Length of line... cm Length of line... mm 5 Length of line... cm... mm Length of line... cm Key Stage National Strategy CROWN COPYRIGHT 00 6 Length of line... mm 7 Length of line... cm 6
15 Key Stage National Strategy PART SECTION Centimetres and millimetres # Rectangle perimeters Calculate the perimeter of each shape. Give the answer in cm or in cm and mm. 5 cm 6 correct stars 5 correct star 6 cm 6 mm cm A cm mm B P =.... P =.... cm 8 mm cm 5 mm cm C cm 5 mm D P =.... cm 5 mm E 0 cm mm cm mm P =.... Key Stage National Strategy CROWN COPYRIGHT 00 cm mm F P =.... P =.... 7
16 Key Stage National Strategy PART SECTION Centimetres and millimetres # 5 Rectangle measurements ABCD is a rectangle. E is the midpoint of AB. F is the midpoint of BC correct stars 5 correct star! " 5 cm mm! " 9 cm 8 mm D C A E B 98 mm! " 7 mm cm 7 mm! "! " F The length of BC is... mm. The length of BC can also be written as... cm... mm. AB is 98 mm long. AB is also 9 cm 8 mm long or 9.8 cm long. Write the length of BF in the same three ways.... Measure DE. Give its length in the same three ways Give the length of DF in the same three ways.... CE is not drawn, but it can be measured. Is CE the same length as DE?... Key Stage National Strategy CROWN COPYRIGHT 00 7 AC and EF are not drawn. Is AC twice the length of EF?... 8
17 Key Stage National Strategy PART SECTION Metres and centimetres Equivalent measurements Example m 70 cm m 00 cm m 0 cm 0 cm.7 m Complete the following: m 50 cm m 0 cm... cm... cm... m... cm... m... cm.8 m 560 cm... cm... m... cm 05 cm.5 m Key Stage National Strategy CROWN COPYRIGHT cm... cm m 0 cm... m 9
18 Key Stage National Strategy PART SECTION Metres and centimetres Measurement problems m 00 cm 5 What length do I add to 70 cm to make m?... What length do I add to 5 cm to make m?... What length do I add to m 50 cm to make m?... What length is 0 cm less than m?... What length is 5 cm less than m?... 6 How high is the tower?... Bob! " m 80 cm Fred! " m 60 cm! "! "! " 60 cm 80 cm m 60 cm 7 8 Bob is taller than Fred. How much taller is he?... Ellie is 5 cm taller than Mary. Mary is m 50 cm. How tall is Ellie?...! " 5 cm! " m 50 cm Ellie Mary 9 0 Carl s desk is 90 cm long. His bookshelf is twice as long as his desk. How long is his bookshelf?... I need two pieces of wood for my project. The long piece is m 0 cm long. The short piece is half the length of the long piece. Key Stage National Strategy CROWN COPYRIGHT 00 How long is the short piece?... 0
19 Key Stage National Strategy PART SECTION Metres and centimetres # 6 Petros tower correct stars correct star! " m 5 cm! " A 5 cm! " B 5 cm! " C 0 cm! " 5 cm 0 cm D E! "! " 50 cm! " 60 cm F G Petros wishes to build a tower of cubes exactly as tall as himself. Which three different cubes could he use?... Key Stage National Strategy CROWN COPYRIGHT 00 Which four different cubes could he use?... Find another combination of four cubes he could use.... What is the height of the tallest tower of cubes he could build using five different cubes only?...
20 Key Stage National Strategy PART SECTION Metres and centimetres # 7 Trains and lorries All correct star (a) What is the total length of the toy lorry and trailer in cm?... (b) What is its total length in m and cm?...! "! " 5 cm 60 cm (c) What is its total length in m?... A toy train has an engine and six identical carriages. (a) What is the total length of the train in cm?! "! " 5 cm 0 cm (b) What is its total length in m and cm?... (c) What is its total length in m? Low Bridge Height.0 m A lorry is m 70 cm tall. It goes under this low bridge. What is the size of the gap between the top of the lorry and the bridge? Key Stage National Strategy CROWN COPYRIGHT 00...
21 SECTION : AREA DIRECT TEACHING POINTS Clarify the meaning of area. Exercises and are consolidation exercises. Consolidate multiplication and division using area calculations, for example, 6 x = 0. Applications include finding the area of compound figures and rightangled triangles, for example, exercise 5 and Star Challenge 0. Star Challenge 9 can be extended to include other perimeters. KEY TO VOCABUL ARY LEAR USE AND area square centimetre cm square metre m Key Stage National Strategy CROWN COPYRIGHT 00
22 Key Stage National Strategy PART SECTION Area What is area? The area of a shape is how much space it covers. The area of this shape is squares. Write down the area of each shape. Area squares Area... squares Area... squares Area... squares Key Stage National Strategy CROWN COPYRIGHT 00 Area... squares
23 Key Stage National Strategy PART SECTION Area Square centimetres cm cm The most common unit of area is the square centimetre. The area of this shape is.5 cm. Area cm Write down the area of each shape. Each answer must have the correct units. Area... cm Area... cm Area... cm 5 6 Area... cm Area... Area Key Stage National Strategy CROWN COPYRIGHT 00 Area... Area... 5
24 Key Stage National Strategy PART SECTION Area Areas of rectangles A B C D E F G rectangle with length 0 cm width cm H rectangle with length 6 cm width 5 cm Complete this table for rectangles A, B, C, D, E, F, G, H. Rectangle Length Width Area in cm in cm in cm A 5... B C D ! "! " length width E F G 0... Key Stage National Strategy CROWN COPYRIGHT 00 H
25 Key Stage National Strategy PART SECTION Area The rule for the area of a rectangle Area of rectangle length width Use the rule to work out the area of each rectangle. Each answer must have the correct units. 0 cm 5 cm Area... cm 8 cm 8 cm 5 cm Area... cm Area... 5 Area problems Work out these problems. Use the correct units in each answer. 5 What is the area of a rectangle of length 0 cm and width cm?... A rectangle has width 5 cm. The length is twice the width. What is the area of the rectangle?... What is the area of a square with 5 cm sides?... Area 0 cm 0 cm What is the length of the side of this square?... What is the width of this rectangle?... Area 6 cm Key Stage National Strategy CROWN COPYRIGHT 00 6 The area of triangle A is half the area of rectangle B. What is the area of triangle A?... A cm 0 cm B cm 0 cm 7 What is the area of triangle C?... C 8 cm 5 cm 7
26 Key Stage National Strategy PART SECTION Area # 8 Measure and work out the area For each rectangle: measure the length and width work out the area. work out the perimeter correct star A B C Area... P... Area... P... Area... P... D Area... P... F Area... P... E Area... P... G Area... P... Key Stage National Strategy CROWN COPYRIGHT 00 8
27 Key Stage National Strategy PART SECTION Area # 9 Wire rectangles Imagine that you have a piece of wire 0 cm long. It could make this rectangle. 68 marks star mark for each correct rectangle and mark for each correct area 6 cm cm cm 6 cm Sketch four more different rectangles that you could make with this wire. Write the length and width on each rectangle. Inside each rectangle, write its area. Remember: a sketch is not an accurate drawing. P S SST! Key Stage National Strategy CROWN COPYRIGHT 00 9
28 Key Stage National Strategy PART SECTION Area # 0 Units of area correct star Work out the area of each of these shapes. They are not drawn to scale. Each answer must have the correct units. cm A cm B m C 5 cm 6 cm 5 m D 5 m mm E m F 0 m mm 5 m cm H m G m cm 8 cm mm I 6 mm Remember: these shapes are not drawn to scale. P S SST! Key Stage National Strategy CROWN COPYRIGHT 00 0
29 SECTION 5: D SHAPES DIRECT TEACHING POINTS Some pupils will need a practical approach to solving the problems. Star Challenges and can form the basis of a class discussion use an OHT of the shapes to help guide the discussion. EY VOCABUL ARY Knet view TO LEAR USE AND Key Stage National Strategy CROWN COPYRIGHT 00
30 Key Stage National Strategy PART SECTION 5 D shapes Drawings of D shapes A B D C E F H G Each of these shapes has been made with four cubes. Work out which drawings are different views of the same shapes. A... Make each shape. Use your shapes to check whether your answers are right Nets of open boxes Here are some nets. For each net, decide whether it will fold up to make an open box. Under each net, write Yes or No. A... D... B... E... C... For each Yes, shade the square that is at the bottom of the open box. Key Stage National Strategy CROWN COPYRIGHT 00
31 Key Stage National Strategy PART SECTION 5 D shapes # Pairs of shapes A All correct star B C D G E F I H Each of these shapes has been made with six cubes. There are four pairs of identical shapes. Try to find them all. Key Stage National Strategy CROWN COPYRIGHT 00
32 Key Stage National Strategy PART SECTION 5 D shapes # Mind the paint This cube has been standing in a pool of paint. All correct star Which of these nets could be this cube? A B C D E For this net, the painted face is shown. Copy the net and shade in the edges of the four faces that are also painted. Key Stage National Strategy CROWN COPYRIGHT 00
33 Key Stage National Strategy PART ANSWERS Unit Answers Section Perimeter Distance round the edge A 9 cm B cm C cm D cm E cm Calculating perimeters A F 0 cm B cm C cm D cm E cm cm G cm Rectangle perimeters 8 cm 8 cm cm 0 cm 5 60 cm 6 0 cm 7 7 cm Section Centimetres and millimetres Measuring lines 6 mm; cm 6 mm 5 cm 9 mm; 59 mm 5 cm mm cm 8 mm 8 mm 5 mm 6 cm mm cm 5 mm Key Stage National Strategy CROWN COPYRIGHT mm Longer and shorter lines (a) cm mm (a) 5 cm mm (b) 5 cm 9 mm (c) cm 7 mm 5
34 Key Stage National Strategy PART ANSWERS Unit Answers Centimetres and millimetres continued Adding cm and mm cm 9 mm 5 cm 9 mm 9 cm 7 mm mm should be changed to cm mm 5 WY 7 cm mm XZ 6 cm mm 6 5 cm mm 7 cm mm Three ways to measure lines 8 mm; cm 8 mm;.8 cm 6 5 cm mm; 5 mm; 5. cm 7 mm 5 cm mm cm 7 mm 7.7 cm Section Metres and centimetres Equivalent measurements cm 0 cm 50 cm m 80 cm 5 m 60 cm 5 cm m 5 cm 0 cm Measurement problems 7.5 m 7 0 cm 75 cm 50 cm 90 cm 5 75 cm 6 m 0 cm 8 m 75 cm 9 m 80 cm Key Stage National Strategy CROWN COPYRIGHT 00 0 m 5 cm 6
35 Key Stage National Strategy PART ANSWERS Unit Answers Section Area What is area? squares 5 squares 6 squares squares Square centimetres cm cm 6 cm cm 5.5 cm 6 cm 7 5 cm 8 5 cm Areas of rectangles Rectangle Length Width Area in cm in cm in cm A 5 0 B C 9 D 6 8 E 8 F 6 G 0 0 H The rule for the area of a rectangle 50 cm 6 cm 0 cm Area problems 60 cm 50 cm 5 cm cm 5 6 cm 6 60 cm 7 0 cm Section 5 D shapes Key Stage National Strategy CROWN COPYRIGHT 00 Drawings of D shapes A E D G B F H Nets of open boxes A Yes B Yes C Yes D No E Yes 7
36 Key Stage National Strategy PART ANSWERS Unit Answers! Star Challenge answers Different perimeters P 8 cm P 8 cm P 8 cm P 0 cm P 0 cm P 0 cm 6 7 marks stars 0 5 marks star P 0 cm! Any ten of these shapes: Regular polygons P cm P cm P cm P 0 cm P cm P cm P cm P cm P cm P cm P cm P cm A hexagon has 6 sides. Each side of this hexagon is cm long. The perimeter of this hexagon is 6 cm= cm A pentagon has 5 sides. Each side of this pentagon is cm long. The perimeter of this pentagon is 5 cm= 5 cm A triangle has sides. Each side of this triangle is 6 cm long. The perimeter of this triangle is 6 cm= 8 cm An octagon has 8 sides. Each side of this octagon is 0 cm long. The perimeter of this octagon is 8 0 cm= 80 cm All correct star Key Stage National Strategy CROWN COPYRIGHT 00 8
37 Key Stage National Strategy PART ANSWERS Unit Answers Key Stage National Strategy CROWN COPYRIGHT 00!!!!! Square Star Challenge numbers answers Perimeter puzzle Rectangle perimeters A E Rectangle measurements 5 6 continued 5 mm 5 cm mm 7 mm; cm 7 mm;.7 cm 7 mm; 7 cm mm; 7. cm 0 mm; 0 cm mm; 0. cm Yes; both are 7 mm Yes; AC = mm and EF = 56 mm Petros tower correct correct stars star B, F, G and A, C, E, F and B, C, E, G m 0 cm or 0 cm Trains and lorries (a) 05 cm (b) m 5 cm (c).05 m (a) 0 cm (b) m 0 cm (c). m 50 cm B 7 5 shapes stars shapes stars shapes star 6 correct stars 5 correct star 6 cm 9 cm 6 mm 0 cm 6 cm cm F 9. cm or 9 cm mm C D 67 correct stars 5 correct star All correct star 9
38 Key Stage National Strategy PART ANSWERS Unit Answers! 8 Star Challenge answers Measure and work out the area continued 67 correct star A 8 cm B 6 cm C cm D 6 cm P = cm P = 0 cm P = cm P = 0 cm!! 9 0 E cm F 0 cm G 9 cm P = 0 cm P = 6 cm P = cm Wire rectangles The expected rectangles and their areas: Units of area Length Width 5 Area marks star 90 correct star A 5 cm B cm C 0 m D 50 m E 6 mm!! F 0 m G m H 8 cm I mm Pairs of shapes All correct star A and H B and C D and G E and F Mind the paint All correct star A, B, E Key Stage National Strategy CROWN COPYRIGHT 00 0
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