G4-34: Prism and Pyramid Bases page 339 Melissa is exploring differences between pyramids and prisms. She discovers that ... A pyramid has one base. Example: (There is one exception — in a triangular pyramid, any face is a base.) . A prism has two bases. Example: ZN] (There is one exception — in a rectangular prism any pair of opposite faces are bases.) IMPORTANT NOTE: The base(s) are not always on the “bottom” or “top” of the shape. TEACHER: The activity that goes with this worksheet will help your students identify the base of a 3-D figure. pyramids. The first one is done for you. 1 . Shade a base jj4 circle the point of the following NOTE: The base will not necessarily be on the “bottom” of the shape (but it is always at the end opposite the point). c) /d) a)/\ % SI I I I S II ‘I f) h)/7 2. Shade a pair of bases for each prism. REMEMBER: Unless all its faces are rectangles, a prism has two bases. b)::II e) f) g) h) .o jump moth G4-35: Properties of Pyramids and Prisms (continued) page 342 4. a) Complete the chart. Use actual 3-D shapes to help you. Colour the number of sides in each base to help you name the shape Number of Shape Picture of Base •• Name edges vertices faces I b) Circle the prisms c) Compare the number of vertices in each prism to the number of sides in the base. What do you notice? c: Write a paragraph outlining how the shapes are the same and how they are different. jumpmoth I I G4-31: Building Prisms page 335 To make a skeleton for a prism, start by making a base (as you did for a pyramid). However, your prism will also need a top, so you should make a copy of the base. c$bd base top base top Now joineach vertex in the base to a vertex in the top. you made. I . Fill the first three rows of the chart, using the skeletons Draw Shape Number of Sides Number of Edges Number of Vertices of Base of Base of Prism : ofPrism Triangular Prism Rectangular . Prism . Pentagonal Prism Hexagonal : . Prism Li 2. Describe the pattern in each column of your chart. 3. Use the pattern to fill in the row for the hexagonal prism. 4. What relationship do you see between the number of sides in the base of a prism and the number of edges in the prism? O jump moth i) MULFfl’LY;N( oTNTL: ?WM( I 4 Jj :r G4-30: Building Pyramids page334 balls of To make a skeleton for a pyramid, start by making a base. modellng clay • Your base might be a triangle or a square. toothpicks —------ Now add an edge to each vertex on your base and join the edges at a point. Triangular Pyramid Square Pyramid Make a triangular pyramid, a square pyramid, and a pentagonal pyramid. 1 . Fill in the first three rows of the chart. Using the skeletons you made. Number of Sides Number of Edges Number of Vertices Draw Shapeof Base of Base of Pyramid of Pyramid Triangular Pyramid Square Pyramid Pentagonal Pyramid Hexagonal Pyramid -,“,, . 2. Describe the pattern in each column of your chart. 3. Use the pattern to fill in the row for the hexagonal pyramid. 4. What relationship do you see between the number of sides in the base of a pyramid and the number of edges in the pyramid? 4P; ____ ____ ____ ‘ 04-32: Edges, Vertices, and Faces page 336 The faces are the flat surfaces. Faces meet at edges. Candice builds a skeleton of a She covers the skeleton The dotted ilnes show the rectangular prism using wire. with paper. hidden edges. 1 . Draw dotted lines to show the hidden edges. 2. Shade all of the edges (the first one is started for you). Count the edges as you shade them. a) b) c) d) edges edges edges edges f) e)© h): edges edges edges edges 3. Vertices are the points where the edges of a shape meet. Put a dot on each vertex (the first one is startedfor you). Count the vertices. a) b) c) d) tiL vertices vertices vertices vertices __ G4-32: Edges, Vertices, and Faces (continued) page 337 4. Shade the front face: b)fl back face: f) L:jJ side faces: I) j) [T’] k) top and bottom faces: m)_ O) p) back face: t)3 bottom face: W)/ x)Z%Z:S 5. Shade the edges that would be hidden if the skeleton was covered in paper and placed on a table. a) b) c) d) BONUS 6. Shade the edges that would be hidden if the skeleton was covered with paper and was hung above you in the position shown. z: f//i / /)/// I’ ()i 1,4 /F ‘‘ ,, / 7 L ,- / K / I I ___________ __________________ 04-36: Nets page 344 TEACHER: Give your students copies of the nets for the 3-D shapes below (from the Teacher’s Guide). nets. I . Make the following figures from their Then fill out the chart like the one below in your notebook. Il triangular square pentagonal triangular cube pentagonal pyramid pyramid pyramid prism prism Name of Figure Number of Faces Number of Edges Number of Vertices 2. Draw the missing face for each net. (i) 7 (ii) (iii) a) What is the shape of each missing face? b) Are the nets pyramids or prisms? How do you know? 3. Draw the missing face for each net. (i) (ii) (iii) . c:::: :i a) What is the shape of each missing face? b) Are the nets pyramids or prisms? How do you know? 4. Copy the following nets onto centimetre grid paper (use 4 grid squares for each face) Predict which nets will make cubes. Cut out each net and fold it to check your predictions. a) b) fl I I d) e) f) fl I I fl I ‘c ___________ __ G4-35: Properties of Pyramids and Prisms (continued) page 343 6. Sketch all the faces that make up the following 3-D shapes. The first one has been done for you. 3-D Shape 2-D Faces a) AA__H__H__ b) Show your work for parts c), d), and e) in your notebook. 7. Match the description of the figure with its name. cone A. I have 6 congruent faces. triangular prism B. I have 5 faces: 2 triangles and 3 rectangles. cube C. I have 4 faces. Each face is a triangle. cylinder D. I have 2 circular bases and a curved face. triangular pyramid E. I have 1 circular base and a curved face. 8. “I have a square base.” Name two 3-D solids that this sentence could describe. 9. Name the object you could make if you assembled the shapes. a) [ II I b)A I I c)DA Eli II I VI I 1 0. Sketch two faces that you can’t see. 11. a) Which face of the net has the most vertices? b) Which face shares a side with every other face? 12. Sketch a netfor a) a triangular pyramid. b) a rectangular pyramid. c) a triangular prism. jump mQth O’o&i ‘ , A ‘1A / . G4-37: Sorting 3-0 Shapes page 345 Eve sorts the following figures using a Venn diagram. She first decides on two properties might have. She then makes a chart. that a figure A B C D E Property Figures with this property 1. One or more rectangular faces 2. Fewer than 7 vertices 1 a) Which figure(s) share both properties? b) Using the information in the chart above, complete the following Venn diagram. One or more Fewer rectangular faces than 7 vertices 2. Complete both the chart and the Venn diagram below using the shapes A to E. a) Property Figures with this property 1. Triangularbase 2. Prism b) Which figures share both properties? c) Using the information in the chart above, complete the following Venn diagram. Triangular base Prism // # , , £‘Z ‘/‘ ;‘: G4-35: Properties of Pyramids and Prisms (continued) page342 4. a) Complete the chart. Use actual 3-D shapes to help you. Colour the number of sides in each base to help you name the shape. Numberof... Shape Picture of Base Name . edges vertices faces l * A b) Circle the prisms. ;L . c) Compare the number of vertices in each prism to the number of sides in the base. What do you notice? c: . Write a paragraph outlining how the shapes are the same and how they are different. a) / cAr Q)o jump moth tc PG jg’ wi%ç1w ‘ . 04-2: Introduction to Angles page 150 An angle is formed when two lines intersect. /_-c The ilnes that form an angle . ,,_/,ANGZ are called the arms. vertex The size of an angle measures the amount A of rotation between the lines. larger smaller _ RIGHT ANGLES Right angles are found in many places, including the corners of squares, rectangles and some triangles. I ‘rightangIe You can always check for right angles using the corner of a piece of paper. NOTE: To identify right angles, pieceofpaper . special _%c’ mathematicians use a symbol — a small square! right angle or (ii) greater than a right angle. I . Mark each angle as: (i) less than a right angle, Check your answers with the corner of a piece of paper. a) / b)\ c) d) / L less than [ r I e)4 f) g) / L [ *1 L 2. Mark the angles that are right angles with a small square.