Cubes and Rectangular Prisms JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 1.2 Unit 16 Geometry pp. S-15–18 New Canadian Edition G1-15 Cubes and Rectangular Prisms Students will: • identify cubes and rectangular prisms; and • identify similarities and differences between real-world objects and the 3-D shape (cube or rectangular prism) they look like. AB: required BC: required MB: required ON: required AP Book 1.2 pp. 141–142

Which has sides that are the same length? Hold up a paper rectangle and square. Identify the shapes. Identify the shapes.
 Which has sides that are the same length? Which has sides that are different lengths? Hint: How can you check? See p. S-15 for details.

This shape is called a cube. Distribute small cubes. Hold up a large cube. This shape is called a cube. This shape is called a cube. 
 It isn't flat like a square or a rectangle. It is a 3-D shape. The sides of 3-D shapes are called faces. Trace a face of the cube on the board. Have students do the same. See p. S-15 for details.

What is the shape of your tracing? Compare other faces of your cube with the tracing. Are they all the same? See p. S-16 for details.

Does the object look like a cube? Justify your answer. Have students signal their answers. Exercises: Does the object look like a cube? Justify your answer. a) a die b) a book c) a domino d) a block e) a connecting cube f) a cereal box Adapt to reflect objects in your classroom.

Here is another 3-D shape. Show students a rectangular prism. Here is another 3-D shape. Like before, I will trace one of its faces on the board. What is the shape of the tracing? What is the shape of the tracing?
 Compare other faces of the shape with this tracing. What do you notice? Repeat with a book. See p. S-16 for details.

These shapes are called rectangular prisms. How is a rectangular prism more like a rectangle than a square? See p. S-16 for details. In a prism, the faces go straight up and down.

Is this a prism? How do you know? Show students a sphere. Repeat for a cone. See p. S-16 for details.

What shape does the bottom face look like? Let's trace it to check. Show students a cylinder. In this shape, the faces go straight up and down but the bottom is not a rectangle. What shape does the bottom face look like? Let's trace it to check. See p. S-16 for details. This shape is not a rectangular prism.

Does the object look like a rectangular prism? Have students signal their answers. Exercises: Does the object look like a rectangular prism? If not, explain why not. a) a ball b) a book c) a domino d) a can e) a party hat f) a cereal box Adapt to reflect objects in your classroom.

How is it similar to a block? How is it different? Hold up each object as you go. Here is a cube. How is it similar to a block? How is it different? See p. S-16 for details. Let's also compare a cube to: • a die • a connecting cube

Show the class a rectangular prism. Exercises: Take turns with a partner saying things that are the same or different about each object and a rectangular prism. a) a softcover book b) a box c) a desk drawer d) a bookshelf e) a stack of paper f) dominoes Adapt to reflect objects in your classroom.

Sorting rectangular prisms. This activity is essential. Activity 1: Sorting rectangular prisms. Which are cubes? Note: These four activities can also be done as stations. See p. S-17 for details.

Making cubes and other rectangular prisms from clay. This activity is essential. Activity 2: Making cubes and other rectangular prisms from clay. See p. S-17 for details.

Using strips of paper to measure cubes. This activity is optional. Activity 3: Using strips of paper to measure cubes. What do you notice? See p. S-17 for details.

"I Spy" (cubes and rectangular prisms) This activity is optional. Activity 4: "I Spy" (cubes and rectangular prisms) See p. S-18 for details.

Journal A cube is like a square because _________. A rectangular prism is like a rectangle because_________.

Extensions: 1. a) Stack two pattern block squares one on top of the other. Is your shape a cube or a rectangular prism? b) Stack three pattern block squares one on top of the other. Is your shape a cube or a rectangular prism? c) If you keep stacking pattern blocks one on top of the other, can you make a cube? How do you know?

2. Make a tile floor using four pattern block squares, like this: Keep stacking until you make a cube. How many levels do you need?

• How many squares are there? • What shape are the other sides? Show a square prism that is not a cube. 3. Trace around the prism. • How many squares are there? • What shape are the other sides? • How many of the non-square sides are the same? See p. S-18 for details.

4. a) What is the same about the two shapes? Hand out triangular and rectangular prisms. 4. a) What is the same about the two shapes? b) What is different about them?

AP Book 1.2 pp. 141–142 New Canadian Edition

Spheres, Cylinders, and Cones JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 1.2 Unit 16 Geometry pp. S-19–23 New Canadian Edition G1-16 Spheres, Cylinders, and Cones Students will: • identify spheres, cylinders, and cones; and • identify similarities and differences between real-world objects and the 3-D shape (sphere, cylinder, or cone) they look like. AB: required BC: required MB: required ON: required AP Book 1.2 pp. 143–145

This shape is called a sphere. Show students a sphere. This shape is called a sphere. It is perfectly round and curves the same everywhere. Demonstrate with your hand. Show an egg-shaped object. This is not a sphere. How is it different? See p. S-19 for details.

Is this a sphere? Hold up a cylinder. Point out the curved parts and the flat parts. See p. S-19 for details. Repeat with a cone, a rectangular prism, and a cube.

• perfectly round all over, and • curved the same everywhere. Hold up two different spheres. Which sphere is bigger? See p. S-19 for details. Spheres can different sizes and colours, but they are spheres if they are: • perfectly round all over, and • curved the same everywhere.

Does the object look like a sphere? Have students signal their answers. Exercises: Does the object look like a sphere? a) a tennis ball b) a box c) a soup can d) a ping pong ball e) a waffle cone f) an orange g) a snowball h) a party hat

This shape is called a cylinder. Show students a cylinder. This shape is called a cylinder. What shape is this flat end? Hint: Let's trace it on the board to check. Show students the other end. What shape is the other flat end? Demonstrate that it fits into the tracing exactly. See p. S-20 for details.

This shape is called a cone. A cylinder has a circle at both ends. The two circles are the same size. Show students a cone. Is this a cylinder? This shape is called a cone. How do a cone and a cylinder compare? See p. S-20 for details.

Let's identify these shapes. How do you know? Display a cylinder, a cone, and a sphere. Let's identify these shapes. How do you know? See p. S-20 for details. Is this a circle? Is this a triangle? Point to the sphere and cone in turn. Discuss how they are different.

Which shape does this party hat look like? Show a party hat with the point up. Which shape does this party hat look like? Discuss how it compares to a solid cone. Include the idea of open and closed cones. See p. S-20 for details.

Have students signal their answers. Exercises: 1. Does the object look like a sphere, a cylinder, or a cone? Is it open or closed? a) a hockey puck b) a party hat c) a soup can d) a ping pong ball e) a paper towel roll f) a snowball g) a new pencil h) a waffle cone i) a globe j) a straw

2. In partners, take turns saying differences between the object and the solid 3-D shape it looks like. a) a soup can b) a water bottle c) a pylon d) a ping pong ball e) a straw f) a globe g) a waffle cone

Making spheres, cylinders, and cones from clay. This activity is essential. Activity 1: Making spheres, cylinders, and cones from clay. See p. S-22 for details.

Using clay and tracing to name flat sides. This activity is essential. Activity 2: Using clay and tracing to name flat sides. See p. S-22 for details.

Building towers with clay shapes. This activity is optional. Activity 3: Building towers with clay shapes. See p. S-22 for details.

"I Spy" (all the shape names) This activity is optional. Activity 4: "I Spy" (all the shape names) See p. S-22 for details.

1. Snowmen are made from spheres stacked on top of the other. Extensions: 1. Snowmen are made from spheres stacked on top of the other. How is that possible? Demonstrate with modelling clay. See p. S-22 for details.

2. a) How would you have to change this bowl to make it a cylinder? Show students a bowl. 2. a) How would you have to change this bowl to make it a cylinder? b) How would you have to change this bowl to make it a sphere?

3. Think of fruits and vegetables. Can you describe them as being like one of these shapes? cubes prisms spheres cylinders cones

4. Does the shape have symmetry? What parts match: left and right, front and back, or top and bottom? a) a cube b) a rectangular prism c) a sphere d) a cylinder e) a cone

5. Find objects that have each type of symmetry. Count how many of each type you find. a) The left and right side look the same. b) The top and bottom look the same. c) The front and back look the same What is the most common type of symmetry? See p. S-23 for details.

AP Book 1.2 pp. 143–145 New Canadian Edition

Flat and Curved Faces G1-17 Students will: JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 1.2 Unit 16 Geometry pp. S-24–27 New Canadian Edition G1-17 Flat and Curved Faces Students will: • identify and count faces of 3-D shapes; and • distinguish between flat and curved faces, and between faces that roll and slide. AB: required BC: required MB: required ON: required AP Book 1.2 pp. 146–147

The sides of 3-D shapes are called faces. Remember: The sides of 3-D shapes are called faces. They are any part of the shape where you can draw a human face: J Let's look at these 3-D shapes. Where could we draw a face J ? Hold up a cube, a cone, a cylinder and a sphere.

Determine how many faces your shape has. Hand out cubes and other rectangular prisms. Exercises: Determine how many faces your shape has. How did you count the faces? See pp. S-24–25 for possible strategies.

There are curved faces and flat faces. Show various shapes and check each face. There are curved faces and flat faces. What type of face is this?

Sort the shapes into the group "has curved faces." Distribute 3-D shapes to student groups. Exercises: Sort the shapes into the group "has curved faces." See p. S-25 for details.

Who has a shape that rolls? Explain each word. rolls slides Show students a ramp. Who has a shape that rolls? Which shapes slide? Can any shapes do both? Discuss which faces that roll versus slide. See p. S-25 for details.

Sort the shapes into the group. Distribute 3-D shapes to student groups. Exercises: Sort the shapes into the group. a) can slide b) can roll c) can slide and roll See p. S-25 for details.

Sorting and pretending with 3-D shapes. This activity is essential. Activity: Sorting and pretending with 3-D shapes. This activity involves two stations. See p. S-26 for details.

Extensions: 1. Edges of 3-D shapes. This is a teacher-led extension. See p. S-26 for details.

2. How many edges does a cube have? Hint: Count separately three types of edges: (1) the edges on the table, (2) the edges that go up and down, and (3) the edges on top. Bonus: Count the edges of a pentagonal prism or a hexagonal prism.

3. Sort the objects into the group "closed." Distribute BLM 3-D Objects (p. S-63).

Pick a shape and use it to make a mould in the clay. 4. Match the shape. Partner A: Close your eyes. Partner B: Pick a shape and use it to make a mould in the clay. Find the shape your partner used. Switch roles. See p. S-27 for details.

AP Book 1.2 pp. 146–147 New Canadian Edition

Identifying 3-D Shapes G1-18 Students will: JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 1.2 Unit 16 Geometry pp. S-28–34 New Canadian Edition G1-18 Identifying 3-D Shapes Students will: • recognize 3-D shapes from pictures, descriptions, and from feel; and • sort 3-D shapes, or pictures of 3-D shapes, by various attributes. AB: required BC: required MB: required ON: required AP Book 1.2 pp. 148–150

Identifying shapes from pictures. This activity is essential. Activity 1: Identifying shapes from pictures. This activity involves two stations. See pp. S-28–29 for details.

Who has a shape with a flat face? Distribute 3-D shapes to students. Who has a shape with a flat face? What flat shape is it? Allow many volunteers to answer. Who has a shape without any flat faces? What 3-D shape do you have?

Did I colour the flat face or the curved face? What shape is this? Did I colour the flat face or the curved face? What shape is the face I coloured? Hold up an actual cylinder in the same position as the picture. What do you notice about the shape of the flat face in the picture and in real life? See p. S-29 for details.

What shape is the shaded face? Give students solid shapes to compare. Exercises: What shape is the shaded face? a) b) c) d) e) f) If students have trouble, have them trace the faces. See pp. S-29–30 for details.

Sort the 3-D shapes into the group. Divide students into small groups. Exercises: Sort the 3-D shapes into the group. a) has a face that is a square b) has a face that is a non-square rectangle c) has a face that is a circle Distribute BLM Sorting Circle (p. S-55) and BLM 3-D Shapes (p. S-64).

Will the tower stay up if we put one cylinder on top of the other? Show students two cylinders. Let’s build towers. Let's build towers. 
 Will the tower stay up if we put one cylinder on top of the other? Repeat for cones, cubes, rectangular prisms, and spheres. See p. S-30 for details.

Making towers from 3-D shapes. This activity is essential. Activity 2: Making towers from 3-D shapes. See p. S-29 for details.

In mathematics, corners are sharp points. Give each student a cube. In mathematics, corners are sharp points. Find the corners on your cubes. Hint: In math, rounded corners aren't really corners. Hold up a cylinder. Does this shape have any corners? Repeat for a cone, a rectangular prism, and a sphere. See p. S-30 for details.

Reach into your bag and feel the shape. Prepare bags and display a cube, a sphere, a cylinder, and a cone. Reach into your bag and feel the shape. Answer my questions based on what you feel. Can you guess your shape? See pp. S-30-31 for a list of questions. Have students justify their predictions. Then switch bags and play again.

Exercises: Partner A: Describe your shape by feel to your partner. Partner B: Guess your partner's shape. Partner A: Reveal your shape. Switch roles and play again.

Finding 3-D shapes in real life. This activity is optional. Activity 3: Finding 3-D shapes in real life. See p. S-31 for details.

Guessing shapes from clues. This activity is optional. Activity 4: Guessing shapes from clues. See p. S-31 for details.

Extensions: 1. How many corners does the shape have? Explain to a partner how you found your answer. a) a cone b) a sphere c) a cylinder d) a cube

2. Complete "Describing Shapes." slide roll square circle rectangle Distribute BLM Describing Shapes (p. S-65).

3. What shape am I? a) I am a cone, a cube, or a cylinder. I have a curved face. I have no corners. b) I am a cylinder, a cube, or other rectangular prism. I have straight edges. I have 6 matching faces. c) I am a cylinder, a rectangular prism, or a sphere. I have 1 curved face. I have no edges. d) I am a cylinder, sphere, cone, cube, or other rectangular prism. I have no corners. I have no edges.

a) edges touch each corner of the cube? Give students a cube, a rectangular prism, and a cone. 4. How many... a) edges touch each corner of the cube? b) faces touch each corner of the cube? c) edges touch each corner of the rectangular prism? d) faces touch each corner of the rectangular prism? e) edges touch the corner of the cone? f) faces touch the corner of the cone?

a) How are cylinders like circles? 5. Discuss with a partner. a) How are cylinders like circles? b) How are cylinders different from circles? c) How are cylinders like rectangles? d) How are cylinders different from rectangles? Bonus: Is a cylinder more like a circle or a rectangle?

6. What is the same about these shapes? What is different? Each pair will need a cone and a square pyramid. 6. What is the same about these shapes? What is different? Discuss with a partner.

a) How are cones like circles? 7. Discuss with a partner. a) How are cones like circles? b) How are cones different from circles? c) How are cones like triangles? d) How are cones different from triangles? Bonus: Are cones more like triangles or circles?

8. Stacking cones. See p. S-34 for details. Students will need open and closed cones. 8. Stacking cones. See p. S-34 for details.

9. Look at your die. Is it a cube? Distribute a suitable die to each student. 9. Look at your die. Is it a cube? See p. S-34 for details.

AP Book 1.2 pp. 148–150 New Canadian Edition

Composing 3-D Shapes G1-19 Students will: JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 1.2 Unit 16 Geometry pp. S-35–38 New Canadian Edition G1-19 Composing 3-D Shapes Students will: • compose and decompose 3-D Shapes. AB: required BC: required MB: required ON: required AP Book 1.2 pp. 151–153

What 3-D shapes would you use to show: • a person's head Lots of things in the real world look like they're made out of 3-D shapes. What 3-D shapes would you use to show: • a person's head • a person's arms • a desk Where do the shapes change in these objects? Show me with your finger. Provide several real-life objects as examples. See p. S-35 for details.

Let's play I Spy.
 Let’s play I Spy. See p. S-35 for details.

How can I use theses shapes to make a table? Show four small cylinders and a large rectangular prism. How can I use theses shapes to make a table? How can I use these shapes to make a table?
 See p. S-35 for details.

What two shapes make this crayon? Show students a suitable crayon. What two shapes make this crayon? What two shapes make this crayon?
 Bring out a cylinder and three different-sized cones. Let's build a crayon ourselves. Which cone fits best? See p. S-36 for details.

What shapes are used to make... Build and display the structures on p. S-36. Exercises: What shapes are used to make... a) the train? b) the tower? c) the lamp? d) What part of the lamp is a cone? e) Which structure has different-sized squares? f) Describe the circles in the cylinders and cone in the lamp. How do they compare?

What shape would you use to make... Display shapes for students to choose from. What shape would you use to make... g) a longer train? h) a taller lamp? Invite students to demonstrate. See p. S-36 for details.

Activity: Building structures This activity is essential. Activity: Building structures This activity requires three separate stations. See p. S-37 for details.

1. Build a city out of blocks. Extensions: 1. Build a city out of blocks. How many of each shape did you use? How much will your city cost to build? Give each shape a monetary value. See p. S-38 for details.

2. Stack different shapes to build a tower. Hint: If you use a cone, be careful where you place it! How tall do you think your tower will be? See p. S-38 for details.

3. In a group of four, work together to make a large block design. See p. S-38 for details.

4. Challenge: Make a structure with spheres on the bottom.

AP Book 1.2 pp. 151–153 New Canadian Edition