Reasoning and Problem Solving Step 9: Reasoning about 3D Shapes

National Curriculum Objectives:

Mathematics Year 5: (5G3b) Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

Differentiation:

Questions 1, 4 and 7 (Problem Solving) Developing Using one 2D shape from a net, identify which 3D shape could be made. Names (not images) of simple 3D shapes given (cubes, cuboids and triangular or rectangular based pyramids). Expected Using one 2D shape from a net, name two familiar 3D shapes (including prisms) which could be made. Greater Depth Using one 2D shape from a net, name at least three 3D shapes which could be made.

Questions 2, 5 and 8 (Reasoning) Developing Identify a simple 3D shape (cube, cuboid and triangular or rectangular based pyramids) from the shadow cast. Choice of two, with one correct answer. Expected Identify a familiar 3D shape (including prisms) from the shadow cast. Choice of three, with two correct answers. Greater Depth Identify a 3D shape (including unknown or complex shapes) from the shadow cast. Choice of three, with two correct answers.

Questions 3, 6 and 9 (Reasoning) Developing Use knowledge of vertices, edges and faces to identify an obvious odd one out from three simple 3D shapes (cubes, cuboids and triangular or rectangular based pyramids). Hint given. Expected Use knowledge of vertices, edges and faces to identify an obvious odd one out from three familiar 3D shapes, including prisms. Greater Depth Use knowledge of vertices, edges and faces to identify a subtle odd one out from three 3D shapes (including unknown or complex shapes).

More Year 5 Properties of Shapes resources.

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1a. This is one shape from the net of a 1b. This is one shape from the net of a 3D shape. 3D shape. Cube Square Based Triangular Pyramid Based Pyramid Cuboid

Which 3D shape could you create? Which 3D shape could you create? Name the other 2D shapes you would Name the other 2D shapes you would need to complete the shape. need to complete the shape.

D D PS PS 2a. Name which of these 3D shapes 2b. Name which of these 3D shapes could cast the shadow. could cast the shadow.

Explain your answer. Explain your answer.

D D R R 3a. Which 3D shape is the odd one out? 3b. Which 3D shape is the odd one out? Hint: Think of vertices. Hint: Think of the faces.

Explain your answer. Explain your answer.

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4a. This is one shape from the net of a 4b. This is one shape from the net of a 3D shape. 3D shape.

Which two 3D shapes could you create? Which two 3D shapes could you create? Name the other 2D shapes you would Name the other 2D shapes you would need to complete the shape. need to complete the shape.

E E PS PS 5a. Name which of these 3D shapes 5b. Which of these 3D shapes could could cast this shadow. cast this shadow?

Explain your answer. Explain your answer.

E E R R 6a. Which 3D shape is the odd one out? 6b. Which 3D shape is the odd one out? Hint: Think of the edges.

Explain your answer. Explain your answer.

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7a. This is one shape from the net of a 7b. This is one shape from the net of a 3D shape. 3D shape.

How many 3D shapes could you create? How many 3D shapes could you create? Name the shapes the other 2D shapes Name the shapes the other 2D shapes you would need to complete the shape. you would need to complete the shape.

GD GD PS PS 8a. Which of these 3D shapes could 8b. Which of these 3D shapes could cast this shadow? cast this shadow?

Explain your answer. Explain your answer.

GD GD R R 9a. Which 3D shape is the odd one out? 9b. Which 3D shape is the odd one out?

Explain your answer. Explain your answer.

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Developing 1a. Possible answer: Triangular based pyramid. The net needs 3 more triangles (attached to the sides of the given one). 1b. Possible answer: Cuboid. The net needs 3 more rectangles and 2 squares with sides the same length as the short side of the rectangle. 2a. The sphere. From any angle the sphere will cast a circular shadow. 2b. The pyramid. If the light is cast full onto one face of the pyramid it will cast a triangular shadow, as this is a triangular based pyramid from any face the shadow will be triangular. 3a. Answers may vary, but must make accurate reference to properties of 3D shapes to identify the odd one out. For example: The cone is the odd one out. The cylinder and the sphere have no vertices and the cone has 1. 3b. Answers may vary, but must make accurate reference to properties of 3D shapes to identify the odd one out. For example: The pyramid if the odd one out. The cube and cuboid have 6 faces but the pyramid only has 4.

Expected 4a. Possible answers: A cone. The net would need a triangle with a base which equals the circumference of the circle. A cylinder. The net would need a rectangle with two sides which equal the circumference of the circle and another circle of the same size. 4b. Possible answers: A pentagonal prism. The net would need one more pentagon plus 5 rectangles. A pentagonal based pyramid. The net would need 5 triangles attached at the base to the sides of the pentagon with a base equal to the length of the side. 5a. The cuboid. If the light is cast on to the smaller ends (and they are square) then the shadow cast will be square. 5b. The cone. If the light is cast on to the vertex then the shadow cast will be a circle. The sphere. From any angle the sphere will cast a circular shadow. 6a. Answers may vary, but must make accurate reference to properties of 3D shapes to identify the odd one out. For example: The pentagonal prism is the odd one out. The others (cube and octahedron) have 12 edges, the prism has 15 edges. 6b. Answers may vary, but must make accurate reference to properties of 3D shapes to identify the odd one out. For example: The cube is the odd one out as it is the only one without a circular face.

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Greater Depth 7a. Possible answers: Cuboid. The full net would need three more identical rectangles and two square faces with sides equal to two ends of the rectangles. Various prisms. The full nets would need more identical rectangles and two of the other shapes needed i.e. triangles for triangular prism, pentagons for pentagonal prism. Cylinder. The full net would need two circles with circumferences of two sides of the rectangle. 7b. Possible answers: Hexagonal based pyramid. The net would need 6 triangles attached to the sides of the hexagon. Each triangle would be identical and have a base the same length as the hexagon’s sides. Hexagonal prism. The full net would need another identical hexagon and 6 rectangles with two sides the same length as the side of the hexagon. There are also a number of other 3D shapes e.g. Truncated Octahedron: 8 regular hexagonal faces, 6 squares, Truncated Icosahedron: 20 regular hexagonal faces, 12 regular pentagons (football shape). 8a. The square based pyramid. If the light is cast directly onto one of the 4 triangular faces the shadow cast will be a triangle. The octahedron. If the light is cast directly onto one triangular face the shadow cast will be triangular. The triangular based pyramid. If the light is cast directly onto any face (including the base) then the shadow cast will be a triangle. The cone. If the light is cast onto the curved face of the cone the shadow cast will be triangular. 8b. The cube. If the light is cast onto one of the faces the shape will cast a square shadow. If it is cast directly onto one of the vertices it will also cast a square shadow. The octahedron. If the light is cast onto the top or bottom vertices where the four triangles meet this shape will cast a square shadow. The cuboid (if the top surface is square). If the light is cast on to the top surface the shadow will be square. 9a. Answers may vary, but must make accurate reference to properties of 3D shapes to identify the odd one out. For example: The pyramid as the others have quadrilateral faces and it does not. 9b. Answers may vary, but must make accurate reference to properties of 3D shapes to identify the odd one out. For example: The cylinder as it is the only one which could not cast a square shadow/has no square cross section.

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