# Unit 8 Angles, 2D and 3D shapes, perimeter and area

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1 Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest degree. Unit Objectives Year 6 Check that the sum of the angles in a triangle is 180 degrees. Calculate angles in a triangle or around a point. Describe and visualise properties of solid shapes such as parallel or Pages 103, 109 perpendicular faces or edges. Visualise 3D shapes from 2D drawings and identify different nets for Page 105 a closed cube. Calculate the perimeter and area of simple compound shapes Page 97 that can be split into rectangles. (Key objectives in bold) Year 5 Link Objectives Year 7 Use a protractor to measure and draw acute and obtuse angles to the nearest 5 degrees. Identify, estimate and order acute and obtuse angles. Calculate angles in a straight line. Make shapes with increasing accuracy. Visualise 3D shapes from 2D drawings and identify different nets for an open cube. Understand area measured in square centimetres(cm 2 ). Understand and use the formula in words length times breadth for the area of a rectangle. Know the sum of angles at a point, on a straight line and in a triangle and recognise vertically opposite angles. Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles. Use a ruler and protractor to measure and draw lines to the nearest millimetre and angles to the nearest degree. Use 2D representations to visualise 3D shapes. Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals; solve geometrical problems involving these properties, using step by step deduction and explaining reasoning with diagrams and text. Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles. This Unit Plan is designed to guide your teaching. You will need to adapt it to meet the needs of your class. Resources needed to teach this unit: Resource sheet 8.1 Resource sheet 8.2 Activity sheet 8.1 Activity sheet 8.2 Activity sheet 8.3 Activity sheet 8.4 OHT 8.1 OHT 8.2 OHT 8.3 OHT 8.4 OHT 8.5 CD from Using ICT to Support Numeracy pack Protractors OHP protractor Arrow cards Whiteboards Centimetre squared paper Interlocking cubes Cardboard box Models of prisms and pyramids Related Key Stage 2 national test questions

2 Unit 8 Year 6 (Spring Term) Resource sheet 8.1 b c a

3 Unit 8 Year 6 (Spring Term) Resource sheet 8.2

4 Unit 8 Year 6 (Spring Term) Activity sheet 8.1 A 1. Draw these angles: 35, 66, 47, 161, 120, Measure these angles to the nearest degree. B 1. Draw these angles: 24, 150, 55, 128, 133, Measure these angles to the nearest degree. a) a) b) b) c) c) d) d)

5 Unit 8 Year 6 (Spring Term) Activity sheet 8.2

6 Unit 8 Year 6 (Spring Term) Activity sheet 8.3

7 Unit 8 Year 6 (Spring Term) Activity sheet 8.4 Shape A Shape B Shape C Shape D Shape E Shape F Shape G

8 Unit 8 Year 6 (Spring Term) OHT 8.1

9 Unit 8 Year 6 (Spring Term) OHT 8.2

10 Unit 8 Year 6 (Spring Term) OHT 8.3

11 Unit 8 Year 6 (Spring Term) OHT 8.4

12 Unit 8 Year 6 (Spring Term) OHT 8.5

13 Unit 8 Year 6 (Spring Term) Related Key Stage 2 National test questions: 2001 Test A 17 Measure accurately the longest side of this shape. Give your answer in millimetres. mm 17a 1 mark Measure accurately the smallest angle in the shape. Use a protractor (angle measurer). 17b 1 mark Total

14 Unit 8 Year 6 (Spring Term) 2001 Test A 13 This shape is three-quarters of a circle. x 13 How many degrees is angle x? 1 mark 13 1 mark Total

15 Unit 8 Year 6 (Spring Term) 2001 Test B 26 Here is an equilateral triangle inside a rectangle. x Not to scale 12 Calculate the value of angle x. Do not use a protractor (angle measurer). Show your method. You may get a mark marks Total

16 Unit 8 Year 6 (Spring Term) 2001 Test B 18 These two shaded triangles are each inside a regular hexagon. Under each hexagon, put a ring around the correct name of the shaded triangle. equilateral isosceles equilateral isosceles scalene scalene 1 mark 18 Total

17 Unit 8 Year 6 (Spring Term) Test B Here is a shape on a square grid. A D C B For each sentence, put a tick ( ) if it is true. Put a cross ( ) if it is not true. Angle C is an obtuse angle. Angle D is an acute angle. Line AD is parallel to line BC. Line AB is perpendicular to line AD marks Total

18 Unit 8 Year 6 (Spring Term) Test B Look at each of these diagrams. Put a tick ( ) if it is the net of a square based pyramid. Put a cross ( ) if it is not marks 13 Total

19 Unit 8 Year 6 (Spring Term) Test B Tom makes this shape from four cubes stuck together. Two circles are drawn on the shape. Tom moves the shape. Draw the circles on the shape in its new position. 8 1 mark Total

20 Unit 8 Year 6 (Spring Term) Test B Lauren has three small equilateral triangles and one large equilateral triangle. The small triangles have sides of 7 centimetres. Lauren makes this shape. 7cm Not actual size Calculate the perimeter of the shape. Do not use a ruler. cm 20 1 mark Total

21 Unit 8 Year 6 (Spring Term) 2001 Test A 25 This is a centimetre grid. Draw 3 more lines to make a parallelogram with an area of 10cm 2. Use a ruler mark Total

22 Unit 8 Year 6 (Spring Term) 2000 Test B 11 On the grid, draw a rectangle which has the same area as this shaded pentagon. Use a ruler mark Total

23 Unit 8 Year 6 (Spring Term) 2000 Test A 19 Liam has two rectangular tiles like this. 11cm 5cm He makes this L shape. What is the perimeter of Liam s L shape? cm 19 1 mark Total

24 Unit 8 Year 6 (Spring Term) 2000 Test A 23 Look at this diagram, Not to scale x 35 y Calculate the size of angle x and angle y. Do not use a protractor (angle measurer). x = 23a 1 mark y = 23b 1 mark Total

25 Unit 8 Year 6 (Spring Term) 2002 Test B 12 Here are four triangles drawn on a square grid. A B D C Write the letter for each triangle in the correct region of the sorting diagram. One has been done for you. has a right angle has an obtuse angle has a 3 acute angles is isosceles A is not isosceles 12 2 marks Total

26 Unit 8 Year 6 (Spring Term) 2002 Test B 19 A cube has shaded triangles on three of its faces. Here is the net of the cube. Draw in the two missing shaded triangles mark Total

27 Unit 8 Year 6 (Spring Term) 2002 Test B 22 What is the area of this shape? 4cm Not to scale 10cm 7cm 10cm 1 mark Mental Arithmetic 12 An equilateral triangle has a perimeter of twenty-four centimetres. How long is one of its sides? cm Total

30 Planning Day Three Unit 8 Angles, 2D and 3D shapes, Term: Spring Year Group: 6 sheet perimeter and area Oral and Mental Main Teaching Objectives and Vocabulary Teaching Activities Objectives and Vocabulary Teaching Activities Recall multiplication and division facts up to Use these facts to derive associated facts. Give the children quick-fire questions involving multiplication and division. Q What is 4 7? Q What is 72 9? Say: If 4 7 = 28 how can we use this to work out 4 17? Demonstrate using arrow cards if necessary and write out (4 10) + (4 7) Establish that the answer is = 68. Repeat using facts such as 2 9 = 18 to work out 2 19 and Say: If 72 9 = 8 how can we use this to work out 7.2 9? Establish the answer will be less than 1 and 10 times smaller at 0.8. Describe and visualise properties of solid shapes. Visualise 3D shapes from 3D drawings and identify different nets for a closed cube. Show the children a closed cardboard box, an empty container such as a cereal box. Q If this box was opened out into a single piece of cardboard, what would it look like? Give the children centimetre squared paper and ask them to sketch the single piece of cardboard to give the shape but not to scale, only a small diagram is needed. Remind them this single piece of cardboard is called the net of the shape it can be folded into the shape exactly. Agree the net is something like the shape below: Sketch the shape below on the board. Q Could this be the net of a cube? Agree that it cannot be and if necessary demonstrate using a strip of six squares. Ask children to continue to find nets for the 3cm cube on the cm squared paper. Collect answers, discuss which are correct and why. Establish there is more than one answer and compare different nets for the cube. Remind children of the names and features of prisms and pyramids. Explain that the cube and cuboids are both prisms, and the name given to any pyramid refers to the shape of the base, e.g. square-based pyramid. Plenary Teaching Activities / Focus Questions Hold up a square-based pyramid. Q How many faces has it? Q What shapes are they? Give out Activity sheet 8.2. Ask children which of the diagrams shown represents the net of a square-based pyramid. Repeat, asking children to identify the other pyramids represented. On the board draw: Agree that this is the net of an open cube. HOMEWORK Give children a sheet of squared paper. Q How many nets of an open cube made of 5 squares can you find? RESOURCES Arrow cards Repeat using facts such as 24 6 = 4 to work out and VOCABULARY net cube cuboid pyramid prism RESOURCES Centimetre squared paper Cardboard box Models of prisms and pyramids Activity sheet 8.2 Open the box to confirm this. Explain that the box is called a cuboid and you want the children to work on cubes now. Discuss the differences between cubes and cuboids, reminding them that all the faces of a cube are identical squares. Q What is the net of a closed cube with dimensions 3cm by 3cm by 3cm? Give children time to sketch a net on the squared paper. Collect one correct net from the children and discuss why this works. Remind them that you have already given them one net and the others are to be different. By the end of the lesson children should be able to: Construct models, shapes and patterns with increasing accuracy. (Refer to supplement of examples, section 6, page 105.)

32 Planning sheet Day Five Unit 8 Angles, 2D and 3D shapes, perimeter and area Oral and Mental Main Teaching Objectives and Teaching Activities Objectives and Vocabulary Vocabulary Calculate the perimeter and area of simple compound shapes. Give the children Activity sheet 8.4. Q What is the perimeter and area of the rectangle A? Calculate the perimeter and area of simple compound shapes that can be split into rectangles. Term: Spring Year Group: 6 Teaching Activities On the board, draw: Plenary Teaching Activities / Focus Questions On the board draw the shape below. Emphasise it is not drawn to scale or accurately. Ask the children to write down the perimeter and area of shape A on their whiteboard. Collect responses and ensure that the correct units are used: cm and cm 2. Remind children the area of a rectangle is length times breadth. Repeat for shapes B and C. Establish that all three shapes have the same area, but different perimeters. Ask children to name shapes D and E and to find their areas. Draw attention to the fact that shape D is half of shape B and drawing the rectangle around the triangle is a useful strategy. Collect responses and discuss children s strategy for finding the area of shape E. Q What are the names of shapes F and G? Q What information do we need to find the area and perimeter of this shape? Once this has been established add some dimensions, in cm, to the L-shape: Q What is its perimeter? Q What is its area? Agree the perimeter and show that the area can be found by dividing into rectangles and adding or by drawing a large outer rectangle and subtracting. Q What L-shapes can you draw that have an area of 36cm 2? Discuss how to do this and demonstrate on the board. Find its perimeter and record this. Say it is an equilateral triangle made up of smaller equilateral triangles. Each small equilateral triangle has sides 5cm. Q What is the perimeter of the big triangle? Establish each side is 15cm and the perimeter is 3 15 = 45cm. Remove smaller triangles, one at a time, e.g. Q What is the perimeter of this shape? Collect responses and check spelling of these words. Q What strategy can we use to find their areas? Children work in pairs to find different L-shapes with area 36cm 2 and record perimeters. Q What is the L-shape with the longest perimeter? Q What L-shape has the shortest perimeter? Repeat until only one small triangle is left. Remind children how to find the area of a rectangle and how using rectangles can help to find other areas. VOCABULARY parallelogram hexagon factor area perimeter RESOURCES Activity sheet 8.4 Whiteboards Discuss the children s responses and ask them to find the areas. Collect answers and correct errors. Q What rectangle could we draw that would have same area as shape F? Q What rectangle would have the same area as shape G? Collect answers and identify that finding the factors of the two areas of the shapes will give the rectangles. VOCABULARY square centimetre (cm 2 ) equilateral triangle perimeter RESOURCES Centimetre squared paper Discuss their answers and correct any errors or misunderstandings. By the end of the lesson children should be able to: Know the formula for finding the area of a rectangle; Begin to find the areas of compound shapes that can be split into rectangles. (Refer to supplement of examples, section 6, page 97.)

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