Lines G2-1 Students will: JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 2.1 Unit 5 Geometry pp. F-4–7 New Canadian Edition G2-1 Lines Students will: • identify straight and curved lines and sides, and open and closed lines. AB: required BC: required MB: required ON: required AP Book 2.1 pp. 70–71

Straight lines Curved lines Describe each type of line. Have volunteers draw more examples.

What shape is this? Are its sides curved or straight?

What shape is this? Are its sides curved or straight?

What shape is this? Are its sides curved or straight?

What shape is this? Are its sides curved or straight?

Is each side straight or curved?

Exercises: Does the shape have at least one straight side? Does it have at least one curved side? a) b)

c) d) e) Bonus:

Have volunteers draw shapes on the board Have volunteers draw shapes on the board. Are the sides straight or curved?

• Shapes with all straight sides This activity is essential. Activity 1: Sorting shapes.   • Shapes with all straight sides   • Shapes with at least one curved side Give students attribute blocks from BLM Attribute Blocks (1), p. M-8.

Here are two paths. closed open In each case, where will the person end up? See p. F-5 for details.

Is this line open or closed? Draw several examples using curved lines. Is this line open or closed? Hint: Can you get back where you started without turning around?

Exercises: Is the line closed or open? a) b)

c) d) e) f)

Is this an open line or a closed line? Add the fourth side and repeat the question. Be sure students understand that sharp turns (such as corners) are not the end of the line.

If you draw a closed line on paper, it makes a shape ​ that you can cut out. Is this a closed line? Discuss how the shape is different from a square.

Are these closed lines?

Exercises: Does the line make a shape? a) b) c)

lines How are the two types of lines different? Draw closed lines in one box and open lines in the other. Ask students to label the groups. lines How are the two types of lines different? See p. F-6 for details.

Journal Draw examples of closed and open lines, ​using both straight and curved lines.

Exercises: a) Draw a closed line. b) Draw an open line.

Complete "Find Closed Lines." This activity is optional. Activity 2: Tic-tac-toe. Complete "Find Closed Lines." When you are done, play this version of tic-tac-toe with a partner. Distribute BLM Find Closed Lines (p. F-34). See p. F-6 for details.

Make a poster showing different types of lines. This activity is optional. Activity 3: Make a poster showing different types of lines. See p. F-6 for details.

1. Look at the shape I made on the floor. Extensions: 1. Look at the shape I made on the floor. How would you describe each line? Which line will take longer to walk? See p. F-7 for details.

2. Copy the shape onto grid paper. Draw the shape without lifting your pencil from ​the paper. Draw each line only once. a) b) c)

3. These are images of traditional Irish designs. Pretend the designs are knots made of lines.   • Are the lines open or closed?   • How many separate lines are in each design? See p. F-7 for details.

AP Book 2.1 pp. 70–71 New Canadian Edition

Sides and Vertices G2-2 Students will: JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 2.1 Unit 5 Geometry pp. F-8–11 New Canadian Edition G2-2 Sides and Vertices Students will: • identify and count sides and vertices of shapes; and • sort shapes by the number of vertices. AB: required BC: required MB: required ON: required AP Book 2.1 pp. 72–73

Hand out triangles from BLM Attribute Blocks (1) and (2), pp. M-8–9. What shape is this? side Have students run their fingers along the sides of their triangles. How do they feel? Are there places that feel different?

This triangle has ____ vertices. A corner of a shape is a called a vertex. vertex This triangle has ____ vertices.

Counting vertices game. This activity is essential. Activity 1: Counting vertices game. See p. F-8 for details.

This line has one vertex. A vertex is created when two sides meet. This line has one vertex. Is this line open or closed?

These lines are all open. vertex vertices vertices vertices

Are these lines open or closed? ASK: How many sides and vertices does each shape have?

Guess the number of vertices in this shape. Use tape to create different shapes on the floor. Guess the number of vertices in this shape. Have a volunteer stand at each vertex. Count the people to check your guess. We can also use numbered cards. See p. F-9 for details.

This triangle has ____ vertices. Number each vertex. Then repeat, starting at a different vertex. This triangle has ____ vertices. Hint: Does it matter where you start counting? See p. F-9 for details.

This square has ____ vertices. Repeat with a square. This square has ____ vertices.

Count the vertices by numbering them.

Exercises: Copy the shapes onto grid paper. Count the vertices. a) b) c)

Bonus:

This shape has ____ vertices. Number the vertices and sides to help. This shape has ____ vertices. This shape has ____ sides. Hint: Are they straight or curved? See p. F-10 for details.

Exercises: Look back at the shapes you drew on grid paper. Count the sides in each shape.

Draw a shape on grid paper. Students will work in pairs. Draw a shape on grid paper. Switch notebooks and count the sides and vertices ​in your partner's shape.

Sorting shapes by their vertices. This activity is optional. Activity 2: Sorting shapes by their vertices. See p. F-10 for details.

Closed lines shapes Open lines Review open and closed lines. __________________ have loose ends. __________________ do not. Closed lines make _____________. Closed lines shapes Open lines Draw arrows from the words to fill in the blanks.

vertices Straight sides Review sides and vertices. _________________ do not bend or turn. _________________ bend or wiggle. Sides meet at . vertices Curved sides Straight sides Remind students that loose ends are not vertices.

Exercises: Are there 4 sides? Are there 4 vertices? Is the line closed? Are all the sides straight? a) b)

c) d) e) Bonus:

Extensions: 1. Here is fancy way of writing the numbers 1 to 6. a) Count the vertices on the numbers 1, 2, 3, and 5. ​What do you notice? b) Draw numbers from 1 to 6 with the same number ​of sides as the value of the number.

2. Is it possible to draw a closed shape with straight ​ sides and two vertices? If it is, draw an example. If it is not, explain why.

3. Is it possible to draw a closed shape with ​two vertices? If it is, draw an example. If it is not, explain why.

AP Book 2.1 pp. 72–73 New Canadian Edition

Squares G2-3 Students will: JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 2.1 Unit 5 Geometry pp. F-12–14 New Canadian Edition G2-3 Squares Students will: • identify squares by their attributes and draw squares. AB: required BC: required MB: required ON: required AP Book 2.1 p. 74

What shape is this? Are these squares? How do you know?

Is this a square? The shape didn't change. It was just turned.

Complete "Find the Squares." Exercises: Complete "Find the Squares." Each student needs BLM Find the Squares (p. F-36) and a pattern block square.

This square has ____ sides and ____ vertices. Number and count to find the answer. This square has ____ sides and ____ vertices. Repeat for more squares. Discuss the results.

Do all squares have all straight sides? Is this a square? Why or why not? Have a volunteer fix the drawing. Do all squares have all straight sides?

Is a square a closed or an open line? Is this a square? Why or why not? Have a volunteer fix the drawing. Is a square a closed or an open line?

We call these square corners. Circle the corner that matches the corners on all the squares. We call these square corners.

squares not squares Sort the shapes as a class. See p. F-13 for details.

Continue with examples from the class. Include one or two open lines. squares not squares See p. F-13 for details.

Distribute BLM Square or Not? (p. F-37). Which shapes will be squares? Mark your guesses. Which is easier to identify as a square: my paper shape or the drawing on the board? Why? Show students a paper square, held up like a diamond. See p. F-13 for details.

Add the missing side. Was your guess correct? Exercise: Complete "Square or Not?" Add the missing side. Was your guess correct? As a class, discuss what prevents shapes from being squares. See p. F-13 for details.

a) Draw 2 different squares. Exercises: a) Draw 2 different squares. b) Draw 2 different shapes with 4 sides that are not squares. Distribute BLM 2 cm Dot Paper (p. F-38).

Bonus: Draw a square that has sides that do not run along ​the rows or columns of dots.

Do these shapes look like squares? Point to various objects around the room. Do these shapes look like squares? Have volunteers find objects that include squares. See p. F-14 for details.

Journal Trace a square and use it to create a picture.

Extensions: 1. We will use an overhead projector to explore the differences between a patterned square and its shadow. See p. F-14 for details.

2. Use grid paper to create a pattern made ​up of squares. a) Use at least 3 colours. b) Use 2 different sizes of squares.

3. Squares are often used in designs. Look around the classroom. Do you see any? These are called tartans, which are very important ​ to the people in Scotland. Use grid paper to create your own tartan. See p. F-14 for details.

AP Book 2.1 p. 74 New Canadian Edition

Rectangles G2-4 Students will: • identify and model rectangles; and JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 2.1 Unit 5 Geometry pp. F-15–18 New Canadian Edition G2-4 Rectangles Students will: • identify and model rectangles; and • compare squares and rectangles. AB: required BC: required MB: required ON: required AP Book 2.1 pp. 75–76

Are these rectangles? How do you know? This is a rectangle. Are these rectangles? How do you know? See NOTE on p. F-15, re: squares and rectangles.

Exercises: Is this a rectangle? a) b)

c) d) e) f) Discuss what prevents a shape from being a rectangle. See pp. F-15–16 for details.

Making different rectangles. This activity is essential. Activity 1: Making different rectangles. Journal Trace your rectangles and tell how they are different. Students will need up to 6 pattern block squares. See p. F-16 for details.

Activity 2: Drawing rectangles. This activity is essential. Distribute BLM 2 cm Dot Paper (p. F-38). See p. F-16 for details.

Which sides of the rectangle are longer than this side? Hold up a paper rectangle. Point to one of the shorter sides. Which sides of the rectangle are longer than this side? How could we check? Fold the shorter side down to compare.

Which sides of this square are equal? Hold up a paper square. Which sides of this square are equal? How could we check? Hint: Two sides are equal if they have the same length. Which sides of our rectangle are equal? See p. F-16 for details.

___ equal short sides and ___ equal long sides Have students think about their observations. square ___ equal sides rectangle ___ equal short sides and ___ equal long sides Is this true for any square and any rectangle?

Activity 3: Rectangle or square? This activity is essential. Activity 3: Rectangle or square? Distribute BLM Rectangles or Squares? (p. F-39). See p. F-16 for details.

What shape is your sheet of paper? How do you know? Hand out scissors and sheets of paper. What shape is your sheet of paper? How do you know? Let's fold and cut the paper to make a square. Have students explain why the final shape is a square.

Do these look like squares or rectangles? Point to various objects around the room. Do these look like squares or rectangles? Have volunteers identify other examples. See p. F-17 for details.

Journal Trace a square and rectangle. Use them in a picture.

1. Shapes like these are common in northwest-coast First Nations art. This extension is required for the BC curriculum. Extensions: 1. Shapes like these are common in northwest-coast First Nations art. They are called ovoids. How are they similar to rectangles? How are they different? See p. F-17 for details. During the discussion, show vertices with dots. Have students look for ovoids in examples ​of northwest-coast First Nations art.

2. Trace a square into your notebook. Create a picture that uses the square. See p. F-17 for details.

3. Draw a shape with 4 sides that has opposite sides ​equal and is not a rectangle. Students will need 2 cm dot paper.

4. Is it possible to draw a shape with 4 equal sides, 4 square corners, and no other vertices that is not a square? If yes, draw an example. Students will need 2 cm dot paper.

5. Is it possible to draw a shape with straight sides, 4 square corners, and no other vertices that is ​not a rectangle or a square? If yes, draw an example. Students will need 2 cm dot paper.

6. Is it possible to draw a shape with straight sides and 4 square corners that is not a rectangle or a square? If yes, draw an example. Students will need 2 cm dot paper.

AP Book 2.1 pp. 75–76 New Canadian Edition

Triangles G2-5 Students will: • identify and model triangles. JUMP Math™ Copyright © 2017 JUMP Math Teacher's Guide 2.1 Unit 5 Geometry pp. F-19–22 New Canadian Edition G2-5 Triangles Students will: • identify and model triangles. AB: required BC: required MB: required ON: required AP Book 2.1 p. 77

This is a triangle. Are these triangles? How do you know?

Exercises: Is this a triangle? a) b) c) Discuss why or why not. See p. F-19 for details.

What is the same about all the triangles? Explain that these are all triangles. What is the same about all the triangles? How do they change in each row?

Triangle or not triangle? This activity is essential. Activity 1: Triangle or not triangle? Students will need attribute blocks. See p. F-20 for details.

Why aren't these shapes triangles? See p. F-20 for details.

Sort attribute blocks and ask volunteers to draw shapes. Bonus: Can you draw a shape that is not a triangle but has 3 sides and 3 vertices?

Exercises: Is this a triangle? c) a) b) d) e) Bonus: Discuss the results as a class. See p. F-20 for details.

Making triangles on geoboards. This activity is optional. Activity 2: Making triangles on geoboards. See p. F-21 for details.

Making triangles with straws. This activity is optional. Activity 3: Making triangles with straws. See p. F-21 for details.

a) Draw 3 triangles of different shapes. Exercises: a) Draw 3 triangles of different shapes. b) Draw a shape that has 3 sides but is not ​a triangle. Students will need grid paper.

Triangles are everywhere. Can you think of ones you see everyday? Have students find triangles around the room and in photographs or magazines.

Journal Trace some triangles and use them in a picture.

Count the sides and vertices in these U-shapes. This extension is required for the BC curriculum. Extensions: 1. This traditional U-shape is used in northwest-coast​ First Nations art. Count the sides and vertices in these U-shapes. Discuss the geometric properties. See p. F-22 for details.

I made it by adding a triangle in a different colour. This is a split U-shape. I made it by adding a triangle in a different colour. How did the number of sides and vertices change? Have students look for U- and split U-shapes in northwest-coast First Nations art. Discuss how the shapes are used. Students can also draw pictures using ovoids, U-shapes, and split U-shapes.

2. Look for squares and triangles in examples of traditional designs from different cultures. On grid paper, try to produce a design in a chosen style. See p. F-22 for details.

3. Quilts are often made of square and triangular ​pieces of fabric. What shapes do you see in these quilts? Create a quilt design on grid paper that uses ​ at least 4 different colours and has both triangles ​ and squares. See p. F-22 for details.

Some quilts have a core pattern that is repeated again and again. Can you identify and draw the core pattern ​ in these quilts? Create your own core pattern and draw three ​repetitions of it. See p. F-22 for details.

AP Book 2.1 p. 77 New Canadian Edition