Geometry Part 2 In this unit, students will identify, describe, compare, and manipulate 3-D geometric shapes: cubes, prisms, pyramids, cones, cylinders, and spheres. They will also learn to describe location (e.g., below, above, between) and analyze simple maps. Manipulatives: 3-D Shapes For many lessons, you will need at least one set of the five basic 3-D shapes (we recommend having a set for each student) as well as additional 3-D shapes. We have provided nets of basic solids on online BLM Nets of 3-D Shapes to help you create manipulatives if you do not have a commercial set or need more pieces. You can also make shapes from modelling clay that dries in the air. You will also need a large assortment of everyday objects that are almost cylinders, prisms, pyramids and so on. Before starting the unit ask students to bring a variety of shapes (such as tins, cans, boxes, etc) from home. See Letters to Parents (p. xxx) for a sample letter. Vocabulary As students learn the names of different shapes and location words, add them to your word wall. Include pictures or samples. Activities These activities can be used and repeated throughout the unit, for practice and reinforcement. 1. Sorting. Make circles from yarn, big enough to use for sorting collections of 3-D shapes. Students will also need index cards to label the sorting groups. As an introduction to the unit, you might ask students to sort the shapes using a rule of their choice. Ask them to explain what rule they used. As students learn about different shapes, ask them to apply new knowledge to the task (e.g., sorting by shape, by number of faces, sorting into shapes that have only flat faces and shapes that have curved faces). Connection Probability and Data Management 2. Collages and posters. Invite students to make collages or posters for the different shapes they learn about. They can look for examples of each shape in old catalogues, magazines, and newspapers. They can also look for particular shapes in everyday objects and add drawings to their collages or posters. For example, after learning about cubes (G2-13), students could create a poster with the title What Looks Like a Cube? or I See Cubes. 3. Clay shapes. Students can create 3-D shapes they learn about from modelling clay. Let them use plastic knives to cut the flat faces. 4. Mystery shape. Place some shapes inside an opaque bag. Have students reach into the bag, grab a shape, and identify it by feel. As students learn attributes of 3-D shapes, such as the difference between curved faces and flat faces, they could describe the attributes of the shape they selected to a partner and ask the partner to identify the shape. 5. 20 Questions. Choose an object in the room and have students guess what it is. Students can ask only about its geometric attributes. (EXAMPLES: Does it have flat faces? Does it have a point?) Students can also play in pairs, with partners switching roles. 6. “I Spy” Play “I Spy” with 3-D shapes and geometric attributes.

7. Picking pairs. The deck of cards (e.g., 3-D shape cards) that students are using will depend on the lesson. Students can play in teams or individually. Place a 3 × 4 array of cards face up on the table. Students take turns picking pairs of matching cards and placing them into a common discard pile. When there are no more pairs in the array, more cards are added to it. The goal is to place all the cards into the discard pile. If no non-matching cards are left, the team wins. (This means that it is likely that all cards were paired correctly.) Connection—Literature Cubes, cones, cylinders, & spheres by Tana Hoban Photos of everyday objects illustrate 3-D figures in nature. Curriculum differences. Ontario curriculum in Grade 2 concentrates on shapes with flat faces only, i.e. cubes, prisms and pyramids. Cylinders, cones and spheres were covered in Grade 1 in Ontario, so Lessons G2-16 and G2-22 are optional for the Ontario students. WNCP curriculum in Grade 2 limits the polygons used as bases of pyramids to squares, triangles and rectangles. It also excludes prisms. The material in lessons G2-18 to G2-19 and in lessons G2-23 to G2-26 is optional for the students following WNCP curriculum framework.

G2-15 Cubes Workbook pages 174 Goals Students will identify and sort cubes. Prior Knowledge Required Recognize and can name squares and rectangles Can measure sides with a ruler (centimetre or non-standard units) Vocabulary cube two-dimensional (2-D) three-dimensional (3-D) Materials a large cardboard rectangle and square a large cube a cube for every student (different sizes, if possible) rulers, scissors, paper, stickers Curriculum expectations Ontario: 1m48, 1m49, 1m50, 2m1, 2m5, 2m7, 2m49 WNCP: 1SS3, 2SS6, 2SS7, 2SS9 [C, CN] Introduce cubes. Hold up a large cardboard rectangle and square. Ask students to identify the shapes. ASK: How are these shapes different? (A rectangle has two longer sides and two shorter sides and a square has four equal sides.) How can you check that? Invite a volunteer to measure the length of the sides of the rectangle and the square, to confirm that they are indeed different. Now show your students a large cube. Explain that the shape is called a cube. Activity 1 Give students cubes (of different sizes, if possible) and rulers and have them measure the cubes from side to side, front to back, and top to bottom (demonstrate what you mean on your large cube). Record the results of several measurements on the board. ASK: What do you notice? (the measurements are all the same) Is a cube more like a square or a rectangle? (square) How is a cube different from a square? (the square is flat) (PSS – Connecting) Explain that squares, rectangles, circles, triangles, and other flat shapes are called two-dimensional, or 2-D, shapes. Shapes like cubes, that are not flat, are called three-dimensional, or 3-D, shapes. Journal A cube is like a square because_______. Cubes and rectangular prisms in the environment. Ask students to think where they have seen cubes or shapes that are almost cubes. How are the “almost cubes” different from a cube? (EXAMPLES: Dice [some have rounded

vertices], blocks, some Kleenex boxes. Connecting cubes have little holes in their sides and the linking part “sticks out.” Some beads are cubic but have a hole in the centre. Ones blocks are nearly cubes—they have one side missing and a linking part protruding on the opposite side.) Students can draw and label or paste pictures or simply name cubes and almost cubes in their journals. Activity 2 Collages and posters (see Introduction). Sorting 3-D shapes using two attributes. Activity 3 Sorting (see Introduction). Give students a set of everyday objects such as boxes, tins, balls, paper cups, etc. and have them sort the shapes using two attributes – shape and colour or shape and size. (For example, sort the shapes into small cubes and large cubes; shapes that are not cubes stay outside both circles.) Introduce faces. Explain that sides of a cube are called faces. Show the faces of the cube, and ask students to count them. Discuss strategies the students use.(e.g., put stickers on each face, then remove stickers and count them; put stickers and tally them as you go) If the following strategy does not arise, show it to the students – count the top and the bottom first, then look on the shape from the top. From the top the cube looks like a square. Each side face looks like side of that square. Count the sides of the square (or use the fact that you know – it has 4 sides) and add it to the top and bottom. PSS – Reflecting on other ways to solve a problem, Splitting into simpler problems. Tracing flat faces. Invite a volunteer to trace a face of a cube on the board and have other students do the same with their cubes. What is the shape of the tracing? Ask students to compare other faces of the cube with the tracing. Are all faces of the cube the same? Have students check by placing all faces of their cubes in turn against the tracing. Emphasize the need of keeping track of the faces that were checked (e.g., by using stickers). Have students cut out the tracing they produced – they will use these cut-outs later. Identifying faces in pictures. Draw a picture of a cube on the board. Ask students to identify the shape and the shape of its faces. Shade the front face. ASK: Is this a square? (yes) Now shade the top face. ASK: Is this a face of a cube? Ask students to find this face on their cubes. ASK: What is the shape of the face on your cube? (square) Does it look like a square in the picture? (No; it has four sides, but it does not look like a square. Cover the rest of the picture to emphasize that.) Ask students to hold the square faces that they cut out in front of them, so that they look like squares. Then ask them to tilt the squares so that they lie horizontally at eye level (If they hold the squares too low, it is hard to see the change.). Are there sides that look shorter? (yes) Which sides? (the ones that were vertical) Present several pictures of cubes and not cubes (examples below), point at the shaded faces (and ask students to say whether these faces are squares. Students do not need to identify the shape of each shaded face at this point. For each shape ask whether it is a cube. If the shapes are not cubes, ask students to explain why these shapes are not cubes.

G2-16 Spheres, Cylinders, and Cones Workbook pages 175-178 Goals Students will identify spheres, cylinders, and cones. Prior Knowledge Required Recognize and can name circles, squares and rectangles Can measure sides with a ruler (centimetre or non-standard units) Vocabulary sphere cone cylinder three-dimensional (3-D) Materials a quarter and a paper “quarter” (see lesson for details) several play-money quarters real-life objects that are shaped like a cylinder, sphere, or cone paper rectangles of different proportions 1 wedge per student (see BLM Cones, p 1-3) paper for tracing bases scissors BLM Which Shape? (p 4) BLM Changed or Turned (p 5) Curriculum expectations Ontario: 1m48, 1m49, 1m50, 2m5, 2m7, optional WNCP: 1SS3, 2SS6, 2SS7, 2SS9 [C, CN, V] Introduce spheres. Draw a circle on the board. Have students identify the shape. Ask students if they can think of a 3-D shape that reminds them of a circle in the same way a cube reminds them of a square—a shape that looks like a circle but is not flat. (Students might identify or point to a cylinder or a sphere, both are good answers.) Show students a sphere and tell them what it’s called. Ask them to think of objects that are spheres or almost spheres. Have some spherical objects on display and ask students to say how they are different from a sphere. EXAMPLES: Balls, globes, and marbles are perfect spheres. Oranges, grapefruits, and grapes are spheres or almost spheres. Some Christmas ornaments are almost spheres: they have a protruding part for the loop used to hang them. Drops of water are almost spheres: they have a “point” on top (show a picture). Beads have a hole in the middle. Introduce cylinders. Show your students a paper circle with a picture of a quarter on it (you can place paper over a quarter, rub it with a pencil, cut out the shaded circle, turn both the paper and the coin and do it again to get a paper coin). Ask students to identify the shape. Then show them a real quarter and ask them to identify the shape again. ASK: How are they different? (The coin is thicker; have students look at both from the side.) Explain that the coin has thickness; it is a 3-D shape. To make thickness more visible, place several quarters in a stack. Introduce

the term cylinder for the resulting shape. Explain that both spheres and cylinders are in some way like circles, but they are not flat like circles. How are they different from circles and how are they the same? (a sphere gets thicker in the middle, a cylinder has the same thickness everywhere; a sphere looks a like a circle when you look at it from any side, a cylinder looks like a circle when you look right at the ends) Activities 1-4 1. Give students paper rectangles of various proportions and show them how to make cylinders: roll the rectangle into a cylindrical shape (carefully, so there is no paper sticking out at either end); tape the roll together; make bases by tracing around the holes at the top and bottom; attach the bases to the ends. Emphasize that a cylinder has bases—it is closed at the ends. 2. Ask students to work in small groups to compare spheres and cylinders using several 3-D shapes. Students can record the questions and answers in a chart:

cylinder sphere Is the shape round? yes yes Can the shape roll? yes yes Can the shape stand? yes No Can you place 3 of this shape side by side? yes No Can you build a tower from 3 of this shape? yes no

You can complete the first row together as a class. 3. Ask students to build towers using both cylinders and spheres. ASK: Can you make a tower that contains more than one sphere? Where can you place a sphere in a tower? Can it be on the top? On the bottom? In the middle? 4. Sorting (see Introduction) E.g., sort into spheres and cylinders, other shapes stay outside the circles. Ask students to think of cylindrical objects and to describe how some objects are like cylinders. Have on display objects such as cans of non-perishable food, new round pencils, hockey pucks, cans of pop (almost cylinders—there is a depression in the bottom), paper towel rolls or straws (almost cylinders—open on both sides), and so on. Connection Real world Snowmen are made from spheres stacked one on top of the other. How is that possible? (The snow ball changes its shape when stacked; it gets flattened at the top and at the bottom. You might demonstrate with modelling clay if snow is not available.) Introduce cones. Activity 5 Give each student a wedge of thick Bristol board (such as on BLM Cones, see also picture; you can also paste the BLM Cones onto Bristol board). Show students how to roll the wedges into cones, and secure them with tape (the edges can overlap), but do not introduce the term “cones” yet. Ask students to place their cones on sheets of paper, bases down, and trace the bases. What shapes did you get? (a circle) Students should cut out the bases and tape them to the cones. Ask students if they had seen anything in real life that looks like this shape (ice cream cone, party hat). Write the answers on the board and underline the word “cone” in “ice cream cone.” Explain that the shapes that look like this are called cones. Discuss with the students how cones are the same as cylinders and spheres and how they are different. Students can add a column for cones to the chart created in Activity 2 above, and add a new question to the chart: Does this shape have a sharp point?

Cones in the environment. Ask students to think of shapes that are cones or almost cones. Have some objects on display again, such as wooden blocks, paper cups, party hats, and ice cream cones (these are all almost cones because they are open at the end, so lack the base or circular face). Students can draw and label cones, cylinders, and spheres (or objects that are “almost” these shapes) on the worksheets and in their journals Activities 6-8 6. Collages and Posters (see Introduction). 7. Playdough shapes (see Introduction) 8. Mystery shape (see Introduction) Connection - Literature Hoban, Tana, Round and Round and Round. Greenwillow, 1983.

What is round? How is it round – like a sphere? Like a cylinder? Like a circle? Identifying shapes in different positions. Students will need individual sets of 3-D shapes. Present pictures of 3-D shapes in different positions (such as on BLM Which Shape? – you can photocopy the BLM onto a transparency) and have students identify them by holding up the shape of the same type. Then show two pictures of shapes at a time and say whether the shapes are the same type or not. When the shapes are of the same type ask whether it could be exactly the same shape shown from different sides or do BLM Which Shape? as a class. Use BLM Changed or Turned for extra practice (this BLM is a WNCP version of page 181 in the workbook). Extensions: 1. Alternative introduction to cones. Show your students a cube. Place it on the overhead or use a flashlight to create its shadow and ask students to identify the shape of the shadow (square). Repeat with a rectangular prism and a sphere. ASK: What flat shape have we not seen yet? (a triangle) Will a cylinder produce a triangle? Check, turning the cylinder so that it produces first a rectangle then a circle. Show your students a cone and introduce the term. What shape does the cone’s shadow have? Let students guess, then check with the overhead, first holding it so that the shadow it produces is a circle. ASK: How can I produce a triangle? If the right idea is suggested, let a volunteer do it. Otherwise, show the solution yourself. 2. Geometric shapes in nature.

Entwistle, T. R., Animal Homes, What geometric shapes can you see when you look at animal homes? (Point out the home of potter wasps – sphere, and of ant lion larvae – cone.)

Connection – Science

G2-17 Pyramids Workbook pages 179 Goals Students will identify pyramids. Prior Knowledge Required Recognize and name triangles, squares, rectangles and cubes Ontario – recognize and name other polygons Vocabulary pyramid triangular, rectangular, (Ontario only: pentagonal, hexagonal, heptagonal, octagonal) pyramids triangle, square, rectangle side faces Ontario only: pentagon, hexagon, heptagon, octagon Materials set of 3-D shapes for each student pictures of real-life structures that are pyramids Curriculum expectations Ontario: 2m1, 2m49, 2m55 WNCP: 2SS7, 2SS9 [R, V] Note: If you are teaching to the Ontario curriculum, your students have to be able to identify a variety of polygons in addition to the polygons mentioned in the vocabulary, and we suggest that you include examples of pyramids with different polygons as bases. Start the lesson with reviewing the names of different polygons. Faces of cubes and pyramids. Review faces of a cube – all faces are square. Then show several pyramids and check what shapes their faces have. If commercial 3-D shapes are available, students can press cubes and pyramids onto a piece of flattened modelling clay to see the shape of the faces. Do not use the term “pyramid” yet. Make face maps. Explain to the students that a convenient way to see all the faces of a 3-D shape is to make a face map – a tracing of all the faces of the shape. Discuss how to keep track of the faces already traced, (e.g. by marking each face already traced with a sticker). PSS – Making an organized list Make a face map of a cube as a class, then proceed to Activity: Activity 1: Give each student a pyramid and have them create a face map of their shape. Make sure there are several different types of pyramids used by the class so that students can compare findings later. Do not include a triangular pyramid that has four identical faces, use a tall triangular pyramid such as on BLM Nets of 3-D Shapes (p xxx)

Differences between pyramids and cubes. Compare the face map of a cube to the face maps of their shapes. ASK: How are these shapes different from cubes? How are they the same as each other? (All these shapes have many triangular faces, some have other faces – a rectangle, a square, or another polygon. All faces of a cube are exactly the same, they all are squares. Most of these shapes will not have the same number of faces as a cube. These shapes are really thin on top and thick at the bottom, but cubes are the same thickness everywhere.) Introduce the term pyramid. Explain that these shapes have a common name – pyramids. Write the word as part of the label for each face map, leaving the space for another word (such as triangular) to add later. Have you heard it before? Show pictures of pyramids used in real life, such as Egyptian pyramids, the entrance structure at the Louvre in Paris, France, some tents, etc. Compare face maps of different pyramids. ASK: How are all face maps of pyramids the same? How are they all different? (all pyramids have triangular faces, but all have one face that is different from the others) What is the shape of the face that is different in your pyramid? (this will depend on which shape you gave each student) Introduce bases and side faces. Explain that the face that is different is called a base, and the other faces are called side faces. Ask students to identify the bases of their pyramids. Then have students trade pyramids and ask them to identify the bases of the new pyramids without creating a face map. Have students trade their pyramids for a pyramid of a third type and identify the bases again. Ask students to trace the bases of the new pyramids. Naming pyramids. Explain that pyramids are often named using the shapes of bases – if the base is a rectangle, we’ll call the pyramid rectangular pyramid or rectangle-based pyramid. (Have students circle the same parts in the words rectangle and rectangular.) Practice naming using real shapes; add the adjectives to the labels of the face maps. Leave the names of the shapes on the word wall with the shapes and pictures of the bases for reference. All pyramids have a point on top. Ask students to place all pyramids base downwards. ASK: How are all pyramids the same? (They all have a point on top). PSS – Looking for a pattern Pyramids in structures. Activities 2-4 2. Give each student or each pair of students blocks including several pyramids and have them create structures. Ask students to identify different 3-D shapes learned to date in their structures. Then ask students to identify pyramids in structures built by a different pair. 3. Collages and posters. (see Introduction) 4. Playdough shapes (see Introduction) Extensions: 1. Show a triangular pyramid with 4 congruent faces. How is it different from other pyramids? All its faces are

triangles, all faces are the same (equal). Explain that in this pyramid you can call any face a base, but this pyramid is special, and it is not true in other pyramids. How is this pyramid similar to a cube? (They both have all faces that have the same shape and size.)

2. Ask students to count how many faces meet at the point on top of each pyramid. Then ask students to look at the tracing of the base. How many sides does it have? Have students make a chart with headings:

Pyramid Shape of base Number of sides in the base Number of faces meeting at the top

Students can glue cards from BLM 3-D Shapes (pp 8-9) in the first column. ASK: What do you notice about the

numbers in the last two columns? (The number of faces meeting at the point on top is the same as the number of sides at the base) PSS – Making a table

3. How is a pyramid different from a cone? Have students look at different pyramids, such as a hexagonal or an octagonal pyramid and describe how they are the same and how they are different. Students can also sort pictures of pyramids and cones using the BLM Pyramids or Cones? (p 6)

G2-18 Prisms Workbook pages 180 Goals Students will identify prisms. Prior Knowledge Required Recognize and can name polygons Can measure sides with a ruler (centimetre or non-standard units) Vocabulary prism pyramid triangular, rectangular, pentagonal, hexagonal, heptagonal, octagonal triangle, square, rectangle, pentagon, hexagon, heptagon, octagon side face base Materials pattern blocks 3-D shapes (prisms, pyramids, cubes) for every student face maps of pyramids rectangular box with height, width and length different for every student Curriculum expectations Ontario: 2m1, 2m7, 2m49, 2m55 WNCP: optional, [C, R], 3SS6 Introduce prisms. Show your students a paper triangle that is an enlarged copy of a pattern block triangle. Ask them to identify the shape. Then show a pattern block and ask them how the pattern block is different from the triangle you’ve shown. (The paper triangle is larger, it is flat, the pattern block is thick, the pattern block is a 3-D shape.) Give students pattern blocks, have them stack several triangles one on top of the other (different number of blocks for different students) and discuss what the result looks like. (It has a triangle on top and the same triangle on the bottom, the sides are rectangles) Explain that this shape is called triangular prism. Then have students stack some square pattern blocks, hexagonal pattern blocks, and introduce the terms square prism and hexagonal prism. Review pyramids. Pyramids have one base, all other faces are triangles. The base gives the pyramid its name. Have face maps of pyramids from the previous lesson on display, have students identify the bases and the side faces in the face maps. Prisms have two bases and side faces that are rectangles. Activity 1:

Distribute different prisms to the students, so that each student has one prism. Do not include rectangular prisms or cubes to avoid complications in identifying bases, you will teach them later; square prisms are OK. Have students create face maps of prisms. ASK: What shapes do you see in your face maps? Do all prisms have rectangles as faces? (yes) Ask students to look at the faces that are not rectangles. How many faces like that does their prism have? (2). Explain that the faces that are different (non-rectangular) are called bases, and the other faces are called side faces. In prisms the side faces are rectangles. Explain that similar to pyramids, prisms are named by the shape of bases – if a base is a hexagon, the prism is called a hexagonal or hexagon-based prism. Ask students to identify the bases of their pyramids. Then have students trade prisms and ask them to identify the bases of the new prisms without creating a face map. Have students trade their prisms for a prism of a third type and identify the bases again. Ask students to trace the bases of the new prisms. Rectangular prisms. Give each student a rectangular box (with length, width and height all different), and have them make a face map of their boxes. ASK: How many faces that are the same do you have on your face map? Ask students to pick a pair of faces that are the same (have them check that the faces are the same by placing the same face against both rectangles) and colour them. ASK: Are all the other faces rectangles? (yes) Does your box look like a very thick rectangle? (yes) Explain that this means that this 3-D shape is also a prism, with rectangular base. What should this prism be called? (rectangular prism or rectangle-based prism) Ask students to choose another pair of identical faces as bases (and colour them with a different colour). Are all the rest of the faces rectangles? (yes) Point out that rectangular prism is special – any pair of opposite faces can be called bases, and the rest will be called side faces. Compare pyramids and prisms. Present a hexagonal pyramid and a hexagonal prism, together with their face maps and have students say what is the same and what is different in the shapes and face maps. (Shape of base is the same, and both have the word “hexagonal” as part of the name, both have six side faces. All the rest is different – a pyramid has a point on top, a prism does not; a pyramid has one base, prism has two; side faces are triangles in a pyramid and rectangles in a prism; the total number of faces is different.) Activity 2: Give students a number of pyramids and prisms, and ask them to create towers with prisms and pyramids. Do prisms stack well? Do pyramids stack well? Ask students to identify various prisms and pyramids in their towers. After that students can identify prisms and pyramids in the towers of their partners. Ask if anybody has a tower where there is a pyramid in the middle or at the bottom of the tower. Can you put a pyramid in the bottom or in the middle of the tower? Why not? (They do not stack well, you cannot place a pyramid so that it has a level surface on the top) Prisms in the environment. Have some objects (prisms and almost prisms) on display, such as boxes of various shapes (note that a typical milk carton is almost a pentagonal prism – with a thin strip of paper sticking out on top and some dips on the bases; in the picture the front face is the base), some chocolate boxes (e.g., Toblerone) are triangular or hexagonal prisms). Have students identify the bases of their prisms. Activity 3:

dip

Sorting (see Introduction). Sort the objects into prisms and not prisms; triangular or rectangular prisms and prisms with five or more sides at the base, non-prisms stay outside the circles. (Connection – Probability and Data Management) Have students identify prisms in pictures – modern urban photos and old castles will be particularly useful. Journal: Students can draw, paste pictures or simply make a list of objects that are prisms or almost prisms in their journals. Extension: As a class, make a chart with the headings below, using the face maps students created. Name of prism Base (picture and name) Number of sides in each base Number of side faces in the prism

Ask students what relationship they see in the chart. (The number of rectangles is the same as the number of sides in the base.) Invite volunteers to circle the parts of the words that are the same in the names of a base and the names of the prisms themselves. PSS – Looking for a pattern

G2-19 Turning 3-D Shapes Workbook pages 181 Goals Students will identify 3-D shapes in different positions. Prior Knowledge Required Recognize and can name 3-D shapes Can measure height indirectly Vocabulary cube prism pyramid base side face Materials blocks of different shapes real-life objects made up of different shapes a set of 3-D shapes BLM 3-D Shapes (p 8-9) BLM Sorting 3-D Shapes (p 7) sorting circles made of yarn Curriculum expectations Ontario: 1m48, 1m49, 1m53, 2m5, 2m55 WNCP: 1SS3, optional [CN, V] Note: In this lesson use only the shapes with flat faces, also, use only the cards without hidden lines from the BLM 3-D Shapes. Review 3-D shapes learned to date and their names. Present several 3-D shapes in different positions and have students identify them by holding up the shape. Ask students to name the shapes as well. Identify shapes in pictures. Put a set of the basic 3-D shapes where students can easily see them (or ask students to refer to their own set). Draw a cube on the board and ask students to identify the shape (students can hold up a cube, but ask a volunteer to name the shape as well). Repeat with the other shapes students have learned, drawing them from different angles (as on BLM 3-D Shapes). Extra Practice: BLM Sorting 3-D Shapes. Activities 1-5 Students will need the cards from BLM 3-D Shapes that do not show the hidden lines for Activities 1 and 2. 1. Students will need three yarn sorting circles. Have students sort the cards into the circles. Students can use the actual shapes—pick them up and view them from different angles—to identify the shapes on the cards. Connection Probability and Data Management—Sorting

2. Picking pairs. (see Introduction) Matching cards: a) Any pyramid matches to any pyramid, any prism matches to any prism and any cube matches to any cube. If your students know that cubes are also prisms (See Extension 2), you can match cubes to prisms as well. b) Remove cards 5 and 11. Two cards match if the shapes have the same name (e.g. rectangular prism). c) Use only cards 1, 2, 8, 9, 24, 25, 27, 28. Two cards match if they show the same shape (not just the same type of shape). For example, a long thin rectangular prism would not match a short thick rectangular prism. 3. Students can use a chart (with the 3-D shapes as column headings) to tally all the objects in the classroom which resemble 3-D shapes. Connection - Probability and Data Management 4. Place several 3-D shapes on a table. Have students view the shapes for a limited time, then cover them up. Can students recall the shapes? VARIATION: Remove one shape while students are not looking. Can students identify the missing shape? This game can also be played in pairs. 5. Mystery shape. (see Introduction) Extension: 1. Geometry and bees

Read the book Honeybees by J. Lecht to the students. What geometric 2-D shapes and 3-D shapes do you see in this book? Point out the shapes of the honeycomb cells in the pictures – hexagons, if you see the entrance only; pentagons, if you cut through the cell; (hexagonal) prism with a (hexagonal) pyramid on top if you look at the 3-D shape of each cell. What is the shape of bee’s egg? (almost a sphere) Of a larvae? (Cylinder, though rolled into a doughnut) Connection Science

2. Rectangles are shapes that have 4 sides and 4 right angles. Squares also have 4 sides and 4 right angles, so squares are a special case of rectangles. Similarly, square prisms are also rectangular prisms, and even more – cubes are square or rectangular prisms – pick any pair of opposite faces as bases, the side faces are squares. Since squares are also rectangles, cubes are also prisms. PSS - Connecting

G2-20 Shapes in Structures Workbook pages 182-184 Goals Students will identify 3-D shapes in drawings, models, and real-life objects. They will sort 3-D shapes and identify the sorting rules. Prior Knowledge Required Recognize and can name 3-D shapes Can measure height indirectly Vocabulary cube prism cone cylinder sphere pyramid Materials blocks of different 3-D shapes that vary in colour and size binders or any other divider real-life objects made up of different shapes sorting circles made of yarn BLM Colour 3-D Shapes (p10) BLM Sort the Shapes (p 11) Curriculum expectations Ontario: 1m48, 1m49, 1m53, 2m2, 2m55 WNCP: 1SS3, 2SS7, 2SS9 [C, R] Note: Page 182 is optional for Ontario students. Page 183 is optional for students following the WNCP. Review 3-D shapes learned to date and their names. Identify shapes in structures built from separate shapes. Activity 1 Give each of your students 5 or 6 blocks of different types of shapes and ask them to create free-standing towers. Ask them to predict how tall their towers will be compared to other objects in the classroom (e.g., my structure is taller than the workbook (if the workbook is standing), but shorter than a desk). Let them build their towers and check their predictions using indirect measurement. Then let them work in pairs to identify the 3-D shapes in the towers of their partners. Connection Measurement

Describe structures. Present two towers, such as the ones at left. Ask students to explain how the structures are the same and how they are different. If necessary, draw the attention to the way the pyramid on top is positioned. Activity 2 Each pair of students needs two identical sets of blocks and a divider (such as a standing binder) between them. Player 1 creates a tower, describes it to player 2, Player 2 has to recreate the structure. Then they compare the results and say how the structures are different. This is a good opportunity to assess communication skills by seeing how much geometric terminology (cylinder, cube, pyramid, prism) is used and how well students describe the location (at the bottom, the top, or in the middle) of each shape and where the pyramid points (to the side or to the top). Identify shapes when some are partly obscured. Choose a structure created by the students and point at some of the shapes on the bottom of the structure (such as the cylinder in the example above). Ask students to identify the shapes. ASK: Do you see the entire cylinder? (no) How do you know it is a cylinder? (we can see part of the curved face) Could it be a cone? Why not? (a cone cannot be at the bottom of the structure, cones do not stack) Could it be a sphere? PSS – Justifying the solution Repeat with a picture of a structure. BLM Colour 3-D Shapes provides extra practice identifying partially obscured shapes (cylinders, cubes, cones, pyramids, spheres) in pictures. Sort 3-D shapes and identify the sorting. Review with the students possible attributes of 3-D shapes – both geometric and non-geometric attributes that can be used for sorting. Write a list of possible attributes that students suggest on the board (e.g., size, colour, number of faces, have a point on top, have a square face). BLM Sort the Shapes can be used for extra practice. Activity 3 Ask students to work in pairs with sets of 3-D shapes. One of the partners sorts the 3-D shapes using one or two attributes, (such as size and whether the shape has a triangular face) and tells the other partner whether they used one or two attributes. The other partner has to guess the attributes used to sort the shapes. Partners exchange roles. Identify shapes in real-life objects. Provide several real-life objects that appear to consist of different 3-D shapes. (EXAMPLES: bottles, candles, connecting cubes, round and hexagonal pencils, toys) Students can draw lines on the objects (using a washable marker) where the geometric shapes change. Activity 4 Take bottles (or jars) of different shapes, remove any labels, and fill each bottle with coloured water for easy identification. Which shapes are the bottles made of? (EXAMPLE: The red bottle consists of two balls and a small cylinder.) Connection - Social Studies Yue, D. and C., The Tipi: A Centre of Native American Life. Ask questions about the geometric shapes of various objects, such as the tipi itself (almost a cone), the cover of tipi (almost half a circle), the base of tipi (egg-shaped, oval), the bath-house (half a sphere), and so on.

cylinder

cone

Connection - Nature Are there animals that look like some geometric shapes? (A body of a spider – sphere, or two; some caterpillars look like cylinders, pangolins, and armadillos roll into perfect spheres.) Talk of parts of animal bodies: some dogs have heads in the shape close to triangular pyramid, and ears of some dogs and most cats have the shape of a triangular pyramid too. Extension: Have students build a city with a small number of blocks. Then they should chart and count how many of each shape they used. Give each shape a monetary value (EXAMPLE: cones are worth 5¢). How much will the city cost to build? Connection Number Sense

G2-21 Faces Workbook pages 185–187 Goals Students will sort actual 3-D shapes and drawings by the shape and number of faces. Prior Knowledge Required Recognize and can name 3-D shapes Recognize and can name 2-D shapes Can identify vertices and edges of 2-D shapes Vocabulary cube prism pyramid cone cylinder sphere edge corner face Materials a set of 3-D shapes for each student small stickers paper (to trace shapes) cards from BLM 3-D Shapes (p 8-9) Curriculum expectations Ontario: 1m47, 1m48, 2m6, 2m49 WNCP: 1SS2, 1SS4, 2SS7, 2SS9 [V] Students will need individual 3-D shapes for most of the activities in this lesson. Count faces of 3-D shapes. Ask students to discuss how they could count the number of faces in a cube in pairs and to try their ideas. How can they make sure that all faces were counted, and no face was counted twice? (Examples: put small stickers with numbers on the faces; put small stickers on all faces, then remove stickers and count them.) (PSS – Making a diagram) Discuss strategies as a class. After that ask students to use a different strategy from the one they used to count the number of faces on a different 3-D shape. Students can check their answers using the face maps produced earlier in the course. Summarize the results obtained by the class in a chart showing the number of faces and the names and pictures of the shapes. Later you will add the pictures of the possible faces to the chart.

Number of faces Shape and number of faces Cube 6 Square pyramid 5 4 and 1

Activity 1: Sorting (see Introduction). Have students sort the actual 3-D shapes by the number of faces (Example: 4 or 5 faces, 6 or more faces; sphere, note that cone and cylinder will stay outside the circles). Review shape of faces of 3-D shapes. Review shapes of different faces using the face maps. Students should also trace a face of a cube, check that all faces of the cube fit that tracing. Add the information about the shapes of the faces to the chart made earlier. Sort 3-D shapes by the shape of faces. Activity 2 Sorting (see Introduction). Have students use the following categories to sort actual 3-D shapes: • Shapes with circular faces and shapes with triangular faces (note that no shape will be in both groups at the

same time); • shapes with one base or with two bases; • small cubes, large cubes, small pyramids, large pyramids. Bonus: sort a group of prisms (or pyramids) by the number of faces that are rectangles (or triangles). Super-bonus: Sort the same set of shapes by the shape of base. What do you notice? (The sorting will be the same in most groups. Exceptions: e.g., triangular and rectangular pyramids will fall into the same group when sorted by number of triangles.) Review identifying faces in pictures. Draw a picture of a cube on the board. Ask students to identify the shape and the shape of its faces. Shade different faces in turn and have students identify what shapes they are, starting with the front face. Encourage students to find the face on their own copy of a cube, so that they see that all faces are squares. If necessary, repeat the exercise with cutting out a tracing of one of the cube faces used in lesson G2-15 (Identifying faces in pictures). Draw more pictures of 3-D shapes and shade various sides. Students can use their concrete 3-D shapes to identify the shape of each shaded face. Students can make squares, rectangles, or triangles from their fingers to show the answer. Activity 3: Sorting (see Introduction). Use the cards from BLM 3-D Shapes to sort the shapes first using one attribute (e.g. shapes that have a square face), then using two attributes (e.g., shapes with rectangular faces and shapes with circular faces; note that no shape falls into both groups). Use only cards without hidden lines for this activity. Online guide: More Extensions. Extension Face of a sphere. Have students trace the flat faces of a cylinder and a cone. Pick one of the tracings and cut it out very carefully. Show the students how it can cover the face traced, and it will fit exactly – no folding, no gaps. ASK: Can you trace the face of a sphere? Why not? Can you make the sphere touch the paper completely without rolling? (no) If students are not convinced in the answer, they might try to wrap the sphere in paper, cut it out and see whether the cut-out matches the face of the sphere. Are there parts of the sphere that are covered more than once? Are there parts that are not covered? (yes to one or both of the questions)

Activity Have students sort the five basic 3-D shapes (cube, cylinder, sphere, cone and a square or triangular pyramid) into two groups: “Square and triangular faces” and “Circular faces.” Where does the sphere go? (outside both circles) Explain that the sphere has only one face and it is different from a circle.

G2-22 Roll, Slide, Stack Workbook pages 188-189 Goals Students will identify curved and flat faces of 3-D shapes on actual shapes and in pictures. Students will sort shapes according to geometrical attributes and identify shapes from descriptions. Prior Knowledge Required Recognize and can name 3-D shapes Recognize and can name 2-D shapes Can identify faces of 3-D shapes on actual shapes and in drawings Vocabulary cube cone cylinder sphere pyramid face slide roll stack Materials a set of 3-D shapes and a plank or piece of cardboard for each student large collections of 3-D shapes Curriculum expectations Ontario: 1m47, 1m48, 1m53, 2m1, 2m5, optional WNCP: 1SS2, 1SS3, 1SS4, 2SS7 [CN, R] Have ready a new chart with the basic shapes across the top and these attributes in the first column: How many curved faces?, Can roll, How many flat faces?, Can slide. You will complete the chart over the course of the lesson. Online Guide: See a completed attribute chart. Roll and slide. Write “rolls” and “slides” on the board. Ask students to explain (or to show with their bodies or shapes) what each word means. Then hold up 3-D shapes, one at a time, and ASK: Will this shape roll? Will it slide? Call a vote for each shape and record the results on the board. Let some students explain their predictions. Call another vote to allow students to change their mind. Give each student or small group of students a plank or a piece of cardboard to use as a ramp, and let them check the predictions using their 3-D shapes. Discuss and record the results in the correct rows on the chart and compare them to the predictions. PSS – Making and investigating conjectures. Curved and flat faces. Review the terms “curved line” and “straight line” with students. Explain that faces can be curved or straight, just like lines. Show various shapes and check the faces one by one—which faces are flat and

which faces are curved? Record the number of flat and curved faces in the chart. ASK: Which faces roll—the curved faces or the flat faces? Which faces slide? Activities 1 and 2 Give students a spinner divided into 3 parts, labelled “only curved faces,” “only flat faces,” and “both curved and flat faces.” 1. Students spin the spinner and create shapes from modelling clay that have the faces indicated. 2. Give each pair of students a large number of 3-D shapes (more than one of each kind). Player 1 spins four times and chooses shapes with faces as indicated by the spinner, creating the core of a pattern. Player 2 has to extend the pattern. Connection Patterns and Algebra Guessing shapes from clues. Display some 3-D shapes and ask students to guess which shape you are thinking of. Give clues one at a time and remove shapes from the collection accordingly. For example, if you are thinking of a cylinder, SAY: My shape can slide. Which shape cannot slide? (a sphere) Why can we remove the sphere from the collection? (A sphere does not slide and your shape does; your shape cannot be a sphere.) (PSS – Using logical reasoning) Continue until students find the shape and repeat with other shapes. Activities 3 and 4 3. 20 Questions (see Introduction) 4. I Spy (see Introduction) Sort the shapes using geometric and non- geometric properties learned in the unit. Activity 5 Sorting (see Introduction). Have students use actual 3-D shapes. Use charts instead of sorting circles. Start with a chart for one attribute, such as “shapes that roll”, “shapes that do not roll” and continue with a chart for two attributes, such as sorting by size and shape of faces (triangular faces, circular faces) at the same time. Include a case such as “shapes that have only square faces”, “shapes that have triangular faces” , “shapes that have both square and triangular faces” and “other shapes”. Connection – Probability and Data Management Review finding common attributes for a pair of objects. Use a pair of 3-D shapes of different size, colour, shape, such as a small black cube and a large white cone. Ask: How are these shapes the same? How are they different? To highlight the similarities, you might present different other shapes and ask what the cube and the cone can do that this shape cannot (Examples: a square (flat, both shapes are 3-D), a sphere (cannot slide, both shapes can slide)) Activity 6 How was it sorted? Have students work in pairs with a set of 3-D shapes of different colours and sizes. One partner sorts the shapes according to a rule of their choice, the other partner has to determine how the objects were sorted, starting with 1 group, then 2 groups or more. Variation: Player 1 decides on a sorting rule that the second player will have to guess. Player 1 places a shape that fits the sorting rule into the circle and another shape that does not outside the sorting circle. Player 2 tries to guess the rule. Player 1 adds shapes one by one inside or outside the circle, allowing Player 2 to guess after each shape

was placed. The goal is to find the answer in as few steps as possible (as a pair), so Player 1 has to think what shape will be the best to show what the sorting rule is. Extension: A curved face that does not roll. Show your students half of a ball with some of the inside scooped out (e.g., a melon with the seeds cleaned out). Ask students to identify the curved and the flat faces. Which faces roll? (only the outside curved face, not the inside curved face) Explain that curved faces usually roll, but not always.

G2-23 Vertices Workbook pages 190 Goals Students will identify vertices of 3-D shapes in actual shapes and drawings. Prior Knowledge Required Recognize and can name 3-D shapes Recognize and can name 2-D shapes Can identify vertices and edges in 2-D shapes Vocabulary cube prism pyramid edges vertices Materials a paper square a set of 3-D shapes for each student Curriculum expectations Ontario: 1m47, 1m48, 2m1, 2m3, 2m49 WNCP: optional, [R, V], 3SS6 NOTE: Over the course of the next two lessons, you and your students will create this chart:

Triangular pyramid

Square/ rectangular

pyramid

cube Triangular prism

Rectangular prism

How many vertices? 4 5 8 6 8 How many faces? 4 5 6 5 6 How many edges? 6 8 12 9 12 Feel the vertices of 3-D shapes. Show your students a paper square. Invite a volunteer to identify the vertices. ASK: How do you know these are vertices? Do they feel different? (they are sharp turns, so they feel the sharpest) Ask students to hold up a cube. Ask them to feel their cubes and to show which places on the cubes feel the sharpest. Explain that these are also called vertices in mathematics. Ask a volunteer to show the vertices of a cube. Then have students show the vertices of the other 3-D shapes. Count the vertices of a pyramid. Ask students to count the vertices of a triangular or a square pyramid (e.g., half the class can have one shape, and the other half can use the other). Students can problem-solve in pairs how to

track the number of vertices. Let students share their strategies with the class. (EXAMPLE: Tape a piece of masking tape to each corner. When all vertices are marked, remove the pieces and count them.) Count the vertices of a cube. Explain that the next task will be harder, and ask students to count the vertices of a cube. Guide students through the following strategy, if no one suggests it: Set the cube on a sheet of paper on a table. Point at two vertices, one on the bottom face and the other on the top face, and ASK: How are these two vertices different? (one is on the top and the other is on the bottom, or one touches the table and the other does not) Can we first count the vertices on the bottom, then the vertices on the top? How many vertices are on the top? How many vertices are on the bottom? Explain that by counting the bottom vertices separately from the top vertices, we solved two simpler problems and used them to solve the harder problem. (PSS – Splitting into simpler problems) ASK: Why was it so easy to find the number of vertices on the bottom? Invite a volunteer to trace the cube. ASK: What shape is the tracing? (square) Where do the vertices of the cube touch the paper? (in the vertices of the square) How many vertices does a square have? How many vertices touched the paper? (4) (PSS – Changing into a known problem) Repeat with the top face of the cube. Ask students to count the vertices of a triangular and a rectangular prism (they can use whatever strategy they want) and complete the first row of the attribute chart. After that add the information on the number of faces to the chart, using the face maps created during the previous lessons. Bonus: How many vertices does a pentagonal prism have? Vertices on pictures of 3-D shapes. Draw a picture of a cube without the hidden edges. Ask students to identify the shape. Invite a volunteer to place a dot on each corner they can see in the picture. Count the vertices together (write the numbers beside the dots as you do so). ASK: How many vertices are in the picture? (7) How many vertices does the cube have? (8) Why did we get 7 instead of 8? (there is a corner on the back that we do not see) (PSS - Reflecting on the reasonableness of the answer.) Explain that in mathematics people often draw the parts of shapes that we cannot see (because they are hidden behind other parts) with dashed lines. The dashed lines are behind the solid lines and do not meet them. (Show the relative positions of the lines in space with your hands or with two pencils.) We call them hidden lines, because we do not see them on an actual object unless we look at it from the other side. Add the dashed lines to the cube and invite a volunteer to mark the hidden vertex. Draw a picture of a prism and mark false vertices where the dashed lines intersect the solid lines (sample shown). Ask students to identify the shape, then to count the dots, and to explain why the answer is not the same as the number in the table. (PSS - Reflecting on the reasonableness of the answer. Invite volunteers to show which dots are not vertices. Students can practice counting vertices in pictures using the worksheet. Extensions 1. How many vertices do two cubes have? Three cubes? Four? Repeat with rectangular prisms. Online guide: Extensions: Vertices of other 3-D shapes; Hidden faces

G2-24 Edges Workbook pages 191–192 Goals Students will identify edges of 3-D shapes in actual shapes and drawings. Prior Knowledge Required Recognize and can name 3-D shapes Recognize and can name 2-D shapes Can identify vertices and edges of 2-D shapes Can identify vertices and faces of 3-D shapes Vocabulary cube prism pyramid edge vertices face skeleton Materials a set of 3-D shapes for each student small stickers BLM Too Few Edges (p 12) Clay and straws or toothpicks Old newspapers and tape BLM I am… (p 13) BLM I am Not… (p 14) BLM 3-D Shapes (pp 8-9) Curriculum expectations Ontario: 1m47, 1m48, 2m1, 2m2, 2m6, 2m7, 2m49, 2m50 WNCP: optional, [C, R, V], 3SS6 Feel the edges of 3-D shapes. Hold up a cube. Run your finger along one of the edges and explain that the place where two faces meet is called an edge. Edges go from one vertex to another. Ask students to show the edge on their cubes. Count the edges of a cube. Ask students to count the edges of a cube. Ask students to remember how they counted vertices and faces. (PSS – Looking for a similar problem for ideas, Making a diagram, Splitting into simpler problems) After they count the edges, let them explain their solutions. For example, students can mark the edges with small stickers (as they did the faces). ASK: Does anyone remember how we counted the vertices of the cube by splitting the vertices into two groups? What two groups did we use? (vertices on the top and vertices on the bottom) Challenge students to find three groups of edges that they can count separately. SOLUTION: Look at the

cube sitting on the desk. There are edges that lie on the desk, edges that touch the desk only at one end, and edges that do not touch the desk at all because they are on the top face. Count the number of edges in each group separately and add the numbers. Assign different shapes (triangular prism or pentagonal pyramid) to different students and have them count the edges of the shapes using any method. Record the numbers in the attribute chart. After that ask students to point out two shapes that have exactly the same number of vertices, edges and faces. (cube and rectangular prism) Ask students to explain why does that happen. (A cube is a special rectangular prism; if you squish a cube on the sides, you will get a rectangular prism, so they are very similar.) PSS – Justifying the solution Skeletons of shapes. Place a cube in front of students. ASK: How many edges do you see from where you sit? (9) Why? (Some edges are on the back.) What hides these edges? (faces) If the cube was made of glass, would you see them? If you have a transparent model of a cube or an aquarium that is a rectangular prism, look at it together. Explain to students that sometimes people make models of geometric shapes that do not have faces, only edges and vertices. This allows them to see all the edges clearly. These models are called “skeletons” and the edges are the “bones.” Activities 1. Create skeletons of prisms and pyramids. For pyramids, start by making a base, then stick an additional straw

to each ball of clay and join the edges together to a ball at the point of the pyramid. For prisms, start with two bases, then stick an additional straw into each vertex of one base and place the second base on top of the straws joining the first base. For large skeletons use old newspapers rolled tightly into thick sticks, starting from a corner, and secured with tape. Use the sticks as edges and bind them together near the ends to create vertices. (The sticks are thinner at the ends, which makes binding them together easier.) For small skeletons use clay and toothpicks of different lengths or straws.

2. Students with skeletons of different 3-D shapes can pair up and describe their skeletons to each other. How many edges and vertices do their skeletons have? If you were attaching faces to your skeleton, what should they be? Variation: Place a divider (standing binder) between the students. Player 1 describes the skeleton, Player 2 guesses the shape. Attribute chart should be visible to all students at all times – for reference.

Edges in pictures of 3-D shapes. Draw a picture of a triangular prism with hidden edge shown and ask a volunteer to identify the hidden edge. Point out that it is drawn with a dashed line. Compare the picture with a skeleton, and ask the volunteer to show these edges on the skeleton. Draw a cube, mark too many edges, and ask students to identify the mistake. EXAMPLE: Count one of the edges where a hidden line intersects a solid line as two separate edges (the part to one side of the intersection and the part to the other side). Students can practise identifying edges in pictures on BLM Too Few Edges. Remind them to compare their answers against the attribute chart. Activities 3-5 Students will need the cards from BLM 3-D Shapes.

3. Ask students to identify all pictures that show the same type of shape, then show pairs of shapes of the same type and have students decide whether it is the same shape viewed from different sides. After that students can sort the shapes and identify how the shapes were sorted as in Activities 3 and 4 of Lesson G-22.

4. Memory (see Introduction). 5. Picking pairs (see Introduction). Two cards match if they show shapes with the same name (e.g., both are

hexagonal prisms. Bonus: BLM I am… and BLM I am not… Extension How many edges meet at the vertices of a cube? (3) Of a prism? (3) Can you find a 3-D shape that has a vertex where more than 3 edges meet? (Yes. For example, 4 edges meet at the point of a square pyramid.)

G2-25 Left, Right, Above, Below Workbook pages 193–195 Goals Students will learn words to describe location and will create structures according to descriptions that feature these words. Prior Knowledge Required Recognize and can name 3-D shapes Recognize and can name 2-D shapes Vocabulary above below left right between Materials connecting cubes a set of 3-D shapes BLM 2-cm Grid Paper BLM Between (p 15) Curriculum expectations Ontario: 1m53, 1m55, 2m56 WNCP: 1SS3, optional Write the new vocabulary on cards and use these word cards throughout the lesson, as needed. Above and Below. Place the words “above” and “below” where students can see them, and read them together. On the board, draw a 3 × 3 grid. Shade the middle horizontal row and ask volunteers to identify the row above the shaded row and the row below the shaded row. Add a row at the top of the grid (making it 4 × 3) and ask students if the row directly above the shaded row has changed (no). Do the same at the bottom of the grid (now 5 × 3) and ask if the row directly below the shaded row is still the same (yes). How many rows are now above the shaded row? (2) Below the shaded row? (2) Activity 1 Give students three connecting cubes of different colours (say, red, blue and green). Tell them to put the cubes on their desks so that the red cube is above the blue cube. Then tell them to put the green cube below the blue cube. Finally, ask them to rearrange their cubes so that the blue cube is below the green cube and the red cube is above both cubes. Write on the board for reference: “Blue is below green. Red is above both.” Observe students as they work. Are they placing the cubes correctly? Prompt or assist individuals as necessary. Continue asking the class to

position cubes in different ways until all students show understanding. Then ask students to identify the location of various objects in the classroom. EXAMPLE: Are the desks below or above the ceiling? Draw three pictures as shown and ASK: Which picture am I describing if I say, The square is below the circle and the triangle is above the square. (All of them!) Can you draw another picture that fits that description? Ask students to draw as many pictures as they can for more such descriptions. (EXAMPLE: A circle is above a triangle, and a square is below a heart.) Have students share their answers. Bonus: Include size and colour and use two attributes at the same time. EXAMPLE: Draw a small blue circle above a large red triangle. Right and Left. Have students raise their right hand, then their left. Have students put two thumbs together to make a U. Then ask them to move their hands apart. Which hand makes an L? (left) Write the words Right and Left on the board and underline the L in the Left. Draw two figures on the board and have students identify the one that is on the right and the one which is on the left. Repeat. Draw a 3 × 3 grid and tell students you want to shade the middle column—can they show you where it is? Shade it in. Invite volunteers to put Xs in the column to the left and Os in the column to the right. Repeat Activity 1 using the terms left and right instead of above and below. Between. Invite three volunteers to stand in a line. ASK the person in the middle: Who are you between? Invite more volunteers to stand in front of the class and tell you who they are standing between. Then ask other students to describe the positions of some of the volunteers. Finally, draw the picture in the margin and ask students to describe the position of each shape. Point out, if necessary, that the light square is between the dark square and the dark circle, but the position of the triangle could also be described using the word between—it is between the light square and the striped circle. Extra practice: BLM Between. Use all five terms. Repeat Activity 1 using all the terms together. Observe students as they work and assess understanding. Activities: 2. Play “Simon Says” using left, right, above, and below. 3. Students will need a 3 × 3 square drawn on 2 cm grid paper, pencil crayons and a spinner divided into 6 parts

marked left, right, above, below, between, you choose. The game starts with shading the square in the middle. Player 1 spins the spinner and asks Player 2 to draw a symbol (e.g., green heart, red triangle) in a square defined by the word on the spinner and an earlier symbol. Example: Spinner shows “above”. Draw a blue circle

in the square above the yellow star. The object of the game is to fill in all of the cells. Players exchange roles after each move.

Two (or more) squares above, below, right or left. Draw a 4 × 4 grid on the board and draw the triangle, star and the circle as shown at left. (Do not draw the square and the heart yet). ASK: Is the star below or above the circle? Is the triangle below or above the circle? Are the triangle and the star both below the circle? Are they at the same place? How could we describe the location of the star and the triangle without saying that one of them is above the other? Could we use the grid to help ourselves? Record students’ ideas. If the idea below does not arise, say that you too have a way to describe the location. ASK: How many squares down will I need to go from the circle to get to the star? (2) To the triangle? (3). Explain that we say that the star is two squares below the circle. How many squares below the circle is the triangle? (3) Ask students to fill in the blanks in the following sentences: The triangle is ___ square ___ the star. The circle is ___ squares ___ the star. The circle is ___ squares ___ the triangle. Erase the three sentences and have students fill in the blank in “The ________ is 3 squares below the circle.” Add the heart and the square to the grid and ask students to describe the positions of the shapes in different ways. Always use the shapes that are in the same row or column. EXAMPLE: How many squares to the left of the star is the square? Bonus: Have students answer similar questions about shapes on a 5 × 5 grid. Activity 4 Use the game from Activity 3, but make the instructions more complicated, to include the number of squares above/below or to the left/right. EXAMPLE: Draw a blue circle two squares above the yellow star. When students are comfortable finding one or two squares in one direction from a given square, make the task more complicated, such as: Find the square to the left of a yellow star, place a dot in it. Then shade two squares below the dot. Bonus: Omit the mentioning of the dot, “shade two squares below the square to the left of the yellow star”. Extension: Teach the students the difference between “my left/right” and “your left/right” by asking them to get a partner. Face them and ask them to place an object in their partner’s right hand. Then check by standing behind their partners. Online guide: More ways too look at the meaning of “between”.

G2-26 Maps Workbook pages 196–197 Goals Students will create maps of the classroom and use vocabulary words to describe the position of various objects on these maps. Prior Knowledge Required Can use location words to describe position Vocabulary above below between right left map Materials grid paper shapes representing furniture and other objects in the classroom BLM Treasure Map (see p 16) Curriculum expectations Ontario: 1m56, 2m56, 2m57 WNCP: 1SS4, optional Discuss with your students when and why people use maps. Create maps by tracing. Give students sheets of grid paper and ask them to place on the paper two small objects from their desks, such as an eraser and a stapler, so that there is some space between and around them. Ask students to trace the objects without changing their location. Have them place a third object between the eraser and the stapler and trace it as well. Repeat with an object above the stapler and another beside the eraser. Ask students to remove the objects and to write on each tracing what the object was. Explain that they have created a map. ASK: Can you tell which object was between the eraser and the stapler by looking only at your map? What was on the left of the eraser? On the right of the eraser? Ask students to exchange maps with a partner, and have partners ask each other questions about the position of the objects on their maps. Player 1 gives Player 2 his map, which only Player 2 looks at. Player 2 asks Player 1 questions about Player 1’s objects using left, right, above and below. Player 1 guesses from memory and Player 2 uses the map to check. Students could put their maps away for a day (so that they forget where each object was) and answer questions about the positions of the objects later. Create a classroom map. Explain to your students that they will each create a map of their classroom. They should pretend they are looking at their classroom from above, as if they were spiders on the ceiling. In small

groups or in pairs, students should list all the objects that they think should appear on the map. Compare the lists and discuss how the objects should be represented on the maps. ASK: If we look at our desks from above, what geometric shape will we see? What kind of rectangle—a long thin rectangle or a short and squat rectangle? If we look at the teacher’s desk, what will we see? Is this rectangle larger or smaller than the rectangles representing the students’ desks? Repeat with other items, such as a sink or shelves. (Empty a shelf for students to examine, since they will not be able to look at the whole bookshelf from above. Compare it to a box—it is long and rather thin if we look at it from the side, but it looks different from above.) ASK: How would you represent the blackboard? (It could be a very thin rectangle, or even a line.) Prepare ahead of time a BLM with the outlines of shapes that could represent the furniture and other objects in your classroom. Have students cut out the shapes and label them. Give students sheets of paper. Explain that the sheets represent the classroom, and the sides of the sheets represent the walls. Have students identify which sides of the paper represent walls with windows and then mark the windows. Ask a volunteer to tell how the furniture is positioned along one of the walls, using the appropriate vocabulary. (EXAMPLE: The sink is in the corner, the bookshelf is to the left of the sink, and so on.) Have students place the paper shapes that represent these objects along that wall on their sheets. Allow another volunteer to describe the wall using different terms so that students can check their work (EXAMPLE: The bookshelf is between the sink and the carpet.) Repeat for the remaining walls. Then have more volunteers describe the position of objects in other parts of the room and have students add those pieces to their maps. At the end students should trace the shapes and label the traces on their maps. Activity 1 Students think about an object shown on their maps and describe its position to a partner, who has to guess what the object is. Partners swap roles and repeat. Distances on a map. Display a map on a grid, such as the one on the BLM Treasure Map and explain that each square on the grid is one step. ASK: How many squares right from the old tree is the small hill? How many steps that is? What is two steps left from___? What is two steps in front of___? Repeat Activity 1, this time asking students to use more precise clues, including the number of squares needed to get from one object to the other. Movement along the map. Move a token along the map and have students describe the movement. Then invite volunteers to move the token and have others describe the movement (Example: two right and one down). Reverse the task – describe movement of a token, and have volunteers move the token according to the given directions. Students can practice in pairs using their maps of classroom.

G2-27 Problems and Puzzles This is a review worksheet.

Online Materials G2-21 Extensions: 1. How many faces do two cubes have? What about three cubes and four cubes? Repeat with rectangular

prisms. Do two rectangular prisms have the same number of faces as two cubes? Repeat for three and four of each shape. Why? (A rectangular prism is very similar to a cube, it is just longer in one direction and shorter in the other.)

2. You might say that a face is any part of the shape where you can draw a face. To draw a face you need room to draw eyes, a nose, and a mouth, so any part of the shape that provides even a small amount of room for you to do so is a face. ASK: Where can we draw a face on a cone? (Have a volunteer demonstrate.) How many faces does a cone have? Repeat for a cylinder and a sphere.

G2-22

Attribute Chart: Shape How many curved faces? Can roll How many flat faces? Can slide Cube

0 no 6 yes

Triangular pyramid 0 no 4 yes

Square pyramid 0 no 5 yes

Cylinder

1 yes 2 yes

Cone

1 yes 1 yes

Sphere 1 yes 0 no

G2-23 Extensions: 1. Hidden faces in pictures. Draw a prism on the board, as shown. ASK: How many faces do you

see in this picture? (3) Present a real prism and have a volunteer count the faces. How many faces does this prism have? Where are the other two faces? (they are hidden) Add the dotted line that represents the hidden edge and invite a volunteer to shade one of the hidden faces. ASK: What is the shape of the hidden face? (triangle or rectangle) Find and mark the hidden faces in drawings of the other shapes (pyramids, prisms, cubes).

2. Vertices of sphere, cylinder and cone. ASK: Does a sphere have any vertices? (no) How many vertices does a cylinder have? (0) Point out that a cylinder has a part that is sharper than the other (run your finger along one of the edges), but it is more like the edge of a cube than a corner (run your finger along the edge of a cube to illustrate the location of the edge; students can feel the edges on their own shapes). Tell students you will talk about those parts (edges) later.

How many corners does a cone have? (one, the point) Explain that this corner is not called a vertex, but has a special name, the point or the apex. It is different from the other corners because there are no edges joining it.

G2-25 Extension: Match the pictures and the descriptions: (PSS – Making a model) Give students a grey triangle, a white circle and a black square as in the pictures and have them recreate the pictures to help themselves answer the question.

The square is between the circle and the triangle.

The triangle is between the circle and the square.

The circle is between the square and the triangle.