Download G3-1 Sides and Vertices

G3-1 Sides and Vertices
Goals: Students will identify polygons, sides and vertices, and distinguish polygons according to the
number of sides.
Prior Knowledge Required: Count to 10
Distinguish straight line
Vocabulary: polygon, sides, vertex, vertices, triangle, quadrilateral, pentagon, hexagon
Draw and label a polygon with the words “polygon,” “sides” and “vertex/vertices”. Remind your students of
what a side and vertex are and explain that a side has to be straight. Show students how to count sides—
marking the sides as you count—then have them count the sides and the vertices of several polygons. Ask
them if they can see a pattern between the number of vertices and the number of sides. Be sure that all
students are marking sides properly and circling the vertices, so they don’t miss any sides or vertices.
Construct a large triangle, quadrilateral, pentagon and hexagon using construction paper or bristol board.
Label each figure with its name and stick them to the chalkboard. Explain that “gon” means angle or corner
(vertex), “lateral” means sides. You might want to leave these figures on a wall throughout the geometry unit.
Explain that “poly” means many, and then ask your students what the word polygon means (many angles or
vertices). Explain that a polygon is a shape that only has straight sides. Draw a shape with a curved side and
ask if it is a polygon. Label it as “not polygon”.
Draw several shapes on the board and ask students to count the sides and sort the shapes according to the
number of sides. Also ask them to draw a triangle, a pentagon, a figure with six sides, a figure with four
angles, and a figure that is not a polygon but has vertices.
Bonus:
Draw a figure that has:
a) Two curved sides and three straight sides
b) Two straight sides and three curved sides
Assessment:
1. Draw a polygon with seven sides.
2. Draw a quadrilateral. How many vertices does it have?
3. Draw a figure that is not a polygon and explain why it is not a polygon.
Possible answers: it has a curved side, a circle is not a polygon, a rectangle with rounded edges does
not have proper vertices.
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Activity:
Give each student a set of pattern blocks or several tangram pieces with the following instructions:
a) Group your pieces according to how many sides they have.
How many of each type do you have?
b) Can you make a shape with four sides using two triangles?
Three triangles?
c) Can you make a large triangle using four triangles?
d) Can you make a triangle from two small tangram triangles and a square?
S
S
e) Can you make a pentagon with pattern blocks?
f)
Can you make a seven-, eight- or nine-sided figure with pattern blocks or tangram pieces?
Extension:
1. How many sides does each group of shapes have?
a) 2 pentagons
b) 3 pentagons
c) 4 pentagons
Students should see the connection with multiplication: 4 pentagons have 4 × 5 = 20 sides.
2. How many sides would 2 pentagons and 3 hexagons have?
3. Count the sides of a paper polygon. Count the vertices. Cut off one of the vertices. Count the sides and vertices
again. Cut off another vertex. Repeat the count. Do you notice a pattern? (The number of sides will increase by
one and the number of vertices will increase by one.)
4. “Word Search Puzzle (Shapes)” in the BLM section.
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G3-2 Introduction to Angles
Goals: Students will identify right angles in drawings and objects.
Vocabulary: right angle
Ask your students if they know what a right angle is—a right angle is the corner of a square, but there is no
need to define it in terms of degrees at this stage. Ask them where they can see right angles in real life
(EXAMPLE: of a sheet of paper corners, doors, windows, etc.). Draw a right angle and then show them how
to mark right angles with a small square. Explain to your students that not all angles are right angles; some
are sharper than a right angle, some are less sharp. Tell them to think of corners; the sharper the corner is,
the smaller the angle is. NOTE: You may want to perform Activity 1 here.
Draw two angles.
Ask your students which angle is smaller. Which corner is sharper? The diagram on the left is larger, but the
corner is sharper, and mathematicians say that this angle is smaller. The distance between the ends of the
arms is the same, but this does not matter. What matters is the “sharpness”. The sharper the angle is, the
narrower the space between the angle’s arms. Explain that the size of an angle is the amount of rotation
between the angle’s arms. The smallest angle is closed—with both arms together. Draw the following picture
to illustrate what you mean by smaller and larger angles.
larger
smaller
With a piece of chalk you can exhibit how much an angle’s arm rotates. Draw a line on the chalkboard then
rest the chalk along the line’s length. Fix the chalk to one of the line’s endpoints and rotate the free end
around the endpoint to any desired position.
You might also illustrate what the size of an angle means by opening a book to different angles.
Draw some angles and ask your students to order them from smallest to largest. EXAMPLE:
a)
A
B
C
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b)
A
B
C
Students that have trouble comparing the angles could use a book and open its pages so that the cover
halves coincide with arms of the angles.
Discuss whether flipping the third angle changed its size.
Bonus: Provide longer lists of angles.
Draw a polygon and explain that the polygon’s angles are inside the figure, not outside the figure. Draw
several polygons and ask volunteers to mark the smallest angle in each figure.
A
B
Note that the smallest angle in the rightmost figure is A and not B—B is actually the largest angle, since the
angles are inside the polygon. (You might hold up a pattern block or a cut-out of a polygon so students can
see clearly which angles are inside the figure.)
Do some of the activities before proceeding to the worksheets.
Draw several angles and ask volunteers to identify and mark the right angles. For a short assessment, you
can also draw several shapes and ask your students to point out how many right angles there are. Do not
mark the right angles in the diagram.
Activities:
1. Make a key from an old postcard. Have students run their fingers over the corners to identify the
sharpest corner. The sharper the corner is, the smaller the angle is.
2.
Ask students to use any object (a piece of paper, an index card) with a square corner to identify various
angles in the classroom that are “more than," “less than” or “equal to” a right angle.
• corner of a desk
• angle made by an open door and the wall
• window corners
• corners of base ten materials
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3. Use a geoboard with elastics to make …
a) a right angle
b) an angle less than a
right angle
c) an angle greater than
a right angle
4. Use a geoboard with elastics to make a figure with…
a) no right angles
b) 1 right angle
c) 2 right angles
5. Have your students compare the size of angles on pattern blocks by superimposing various pattern
blocks and arranging the angles in order according to size.
Students may notice that there are two angles on the trapezoid that are greater than the angles in the
square, and that there are two angles that are less than the angles in the square.
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G3-3 Equilateral Shapes
Goals: Students will classify polygons according to the number and the lengths of sides and the number of
right angles. Students will also identify equilateral shapes.
Prior Knowledge Required: Sides, vertices
Right angles
Vocabulary: polygon, sides, vertex, vertices, triangle, quadrilateral, pentagon, hexagon
Write the word “equilateral” on the board. Ask the students what little words they see in it. What might the
parts mean? Where did they meet these parts? (“Equi” like in “equal” and “lateral” like in “quadrilateral”). Give
your students the set of shapes below. Students can either cut out the shapes and fold them to check if the
sides are equal or measure the sides with a ruler. Ask your students to extend the following chart to classify
the shapes.
Number of
Right Angles
Number of
Sides
Equilateral
4
4
Yes
Include the word “equilateral” on your next spelling test.
Extensions:
1. Pick a property (i.e. same number of sides, vertices, right angles, etc.) and find three shapes in
QUESTION 3 that all have that property in common.
2. Find a group of four shapes where three share a common property and one doesn’t belong.
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G3-4 Quadrilaterals and Other Polygons
Goals: Students will distinguish the quadrilaterals from other polygons.
Prior Knowledge Required: Count sides of polygons
What is a polygon
Measure straight lines with a ruler
Vocabulary: polygon, sides, vertex, vertices, triangle, quadrilateral, pentagon, hexagon
Draw a quadrilateral on the board. Ask how many sides it has. Write the word “quadrilateral” on the board
and explain what it means. Explain that “quad” means “four”, “lateral” means “sides” in Latin. Ask if students
have ever encountered any other word having either of these parts in it. (EXAMPLES: quadrangle,
quadruple). You might also mention that “tri” means “three” and ask if they know what the French words are
for 3 and 4.
Emphasize the similarities: “tri” and “trois”, “quad” and “quatre”. Draw several polygons on the board and
ask whether they are quadrilaterals. Write the number of sides for each and mark the answer on the board.
Make two columns (quadrilaterals and non-quadrilaterals) on the board.
Use the polygons from the shape game (see the BLM section) with tape on the back side. Invite volunteers
to come and affix the shapes at the right column on the board. You may ask them to explain their choice.
You may also ask the students to sort the pattern block pieces into quadrilaterals and non-quadrilaterals.
You may also ask your students to sort shapes according to different properties—those that have right
angles and those that do not, number of sides or angles or right angles, equilaterality, etc. Include the word
“quadrilateral” on your next spelling test.
Activities:
1. Give each of your students a set of 4 toothpicks and some model clay to hold them together at vertices.
Ask to create a shape that is not a quadrilateral. (This might be either a 3-dimensional shape or a selfintersecting one). Ask also to make several different quadrilaterals.
2. Provide each of your students a set of 10 toothpicks. Ask them to check how many different triangles
they can make with these toothpicks. Each figure should use all the picks. How many different
quadrilaterals you can make using 10 toothpicks? The answer for the second problem is infinity—a slight
change in the angles will make a different shape.
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Extension: Explain that a kite is a quadrilateral with two pairs of equal adjacent sides. Draw a kite and
ask a volunteer to mark the equal pairs of sides. Point out that a kite has no indentation – illustrate the
meaning with a picture.
Indentation, so this is not a kite.
Draw several polygons on the board, some kites, some not, some resembling kites, and ask your students to
measure the sides of the shapes and to determine which of these shapes are kites.
Hold up a cut-out paper kite and ask your students how they could check whether this shape is a kite
without measuring the sides. Would folding help? Invite a volunteer to fold the shape and to check whether
the sides are equal. Ask: Are all the angles in a kite different? How do you know? (Folding the kite along the
diagonal that is also a line of symmetry will show that the opposite angles between the non-equal sides are
also equal.)
Fold
These angles are equal
What about the other pair of opposite angles? Ask a volunteer to check whether these two angles are equal
by folding the kite along the other diagonal. (The Atlantic curriculum)
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G3-5 Tangrams
Goals: Students will become familiar with polygons and develop the use of the vocabulary.
Prior Knowledge Required: Quadrilateral, square, rectangle, pentagon, hexagon
Vocabulary: polygon, sides, vertex, vertices, triangle, quadrilateral, pentagon, hexagon
Give your students copies of the Tangram sheet in the BLM section of this manual. Have them cut out the
pieces and follow the instructions on the worksheet.
Activity:
Communication Game. Two players are separated by a barrier that prevents each player from seeing the
table directly in front of the other player. Player 1 makes a simple shape using a limited number of tangram
pieces. (For instance
). Player 1 then tells player 2 how to build the shape. For instance: “I used the
small triangle and the square. I put the triangle on the left side of the square.”
NOTE: There are several ways to carry out this instruction:
or
or
or
so Player 1
would have to give more precise instructions such as “Put one of the short sides of the triangle against the
side of the square so the right angle of the triangle is at the bottom”.
As students play this game (and as they see how difficult it is to describe their shapes) teach them the
terms they will need (“right”, “left”, “short side”, “long side”, “horizontally”, “vertically”, etc.) and show them
some situations in which more precise language would be needed. For instance, in the example above you
might say that the short side of the triangle is adjacent to the square and the long side goes from top left
corner right and down.
NOTE: Each player is allowed to ask questions but students should only use only geometric terms in the
game, rather than describing what a shape looks like (EXAMPLE: NOT “It looks like a house.”) Here are
some simple shapes students could start with.
S = small triangle
S
S
M = medium triangle
S
S
S
S
L = large triangle
S
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S
S
M
M
L
M
S S
S
L
S
S
L
9
Extensions:
1. How many rectangles can you make using the tangram pieces? (REMEMBER: squares are
rectangles.)
EXAMPLES:
S
S
S
L
M
M
SS
S
M
S
2. How many ways can you find to construct a square as in QUESTION 5 on the worksheet? Which way
uses the smallest number of shapes? The greatest number of shapes? (The Ontario curriculum)
3. Try to make various polygons using all the tangram pieces. Sample shapes may be found at
www.tangrams.ca. SEE ALSO:
http://tangrams.ca/puzzles/asso-02.htm and
http://tangrams.ca/puzzles/asso-02s.htm
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G3-6 Congruency
Goals: Students will become familiar with polygons and develop the use of the vocabulary.
Prior Knowledge Required: Count to 10
Vocabulary: congruent shapes
Explain that two shapes are congruent if they are the same size and shape. A pair of congruent twodimensional figures will coincide exactly when one is placed one on top of the other. Have students actually
do this with tangrams or pattern blocks. As it isn’t always possible to check for congruency by superimposing
figures, mathematicians have found other tests and criteria for congruency.
A pair of two-dimensional figures may be congruent even if they are oriented differently in space (see, for
instance, the figures below):
As a first test of congruency, your students should try to imagine whether a given pair of figures would
coincide exactly if one were placed on top of one another. Have them copy the shapes onto grid paper.
Trace over one of them using tracing paper and try to superpose it. Are the shapes congruent? Have your
students rotate their tracing paper and draw other congruent shapes. Let your students also flip the paper!
You might also mention the origin of the word: “congruere”—“agree” in Latin.
Assessment:
Circle the pair of shapes that are congruent:
a)
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b)
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G3-7 Congruency (Advanced)
Goals: Students will identify congruent shapes regardless of their position and colour.
Prior Knowledge Required: Count to 10
Vocabulary: congruent shapes
Review the previous lesson. Draw two congruent shapes of different colours and ASK: Are the shapes
congruent? Are they of the same size? Are they of the same shape? Remind your students that congruent
shapes are of the same size and shape, and they can have different colors. Give your students several
shapes of different colours and with different patterns (stripes, dots, etc.) and ask them to find congruent
pairs. Increase the number of congruent pairs in the same group of shapes gradually.
Make several shapes of blocks, such as the shapes below and ask your students to explain why these
shapes are not congruent. Repeat with pairs of polygons.
Ask your students to build shapes that are congruent to the shapes above.
Activities:
1. Give each student a set of pattern block shapes and ask them to group the congruent pieces. Make sure
students understand that they can always check congruency by superimposing two pieces to see if they
are the same size and shape.
2. Give students a set of square tiles and ask them to build all the non-congruent shapes they can find
using exactly 4 blocks. They might notice that this is like Tetris game. Guide them in being organized.
They should start with two blocks, and then proceed to three blocks. For each shape of 3 blocks, they
should add a block in all possible positions and to check whether the new shape is congruent to one of
the previous ones.
SOLUTION:
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G3-8 Recognizing and Drawing Congruent
Shapes
Goals: Students will identify and draw congruent shapes.
Prior Knowledge Required: Count to10
Identify congruent shapes
Vocabulary: congruent shapes
Review the previous lesson. Draw a group of shapes as shown below and ask your students to find a pair of
congruent shapes among the shapes below. Ask your students also to explain why the other shapes are not
congruent to the two congruent shapes.
Activity: Review the names of the following polygons: triangle, rectangle, square, rhombus, pentagon,
hexagon. Each pair of students will need a spinner as shown. Player 1 spins the spinner and draws a
polygon according to the result of the spinner. Player 2 has to draw two polygons of the same type, so that
one is congruent to the polygon drawn by Player 1, and the other polygon is not.
Rectangle
Triangle
Pentagon
Rhombus
Square
Hexagon
Advanced: Review the concepts of attributes before starting the activity. Player 1 spins the spinner and
draws a polygon according to the result on the spinner. Player 1 decides on an attribute (such as striped
pattern) and then names the attribute. Player 2 draws a shape congruent to the shape drawn by her partner,
so that it differs in the given attribute (in this case, a different pattern). Then Player 2 draws a shape that is
not congruent to the given shape so that it shares the given attribute (it will still be striped). For example, the
spinner reads “Triangle”:
Player 1 says:
Pattern
Different pattern
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Same pattern
13
G3-9 Exploring Congruency with Geoboards
Goals: Students will create congruent and non-congruent shapes on a geoboard.
Prior Knowledge Required: Count to10
Identify congruent shapes
Vocabulary: congruent shapes
Draw a shape on a grid on the board and ask your students to make a copy of it on their geoboards. (This
exercise could also be done on dot paper). Then ask your students to create a new shape, congruent to the
first one, but differently oriented. Repeat with several other shapes. Ask your students also to make shapes
that are not congruent to the given shape, and to explain why these shapes are not congruent.
Activities:
1. Make 2 shapes on a geoboard. Use the pins to help you say why they are not congruent.
EXAMPLE:
The two shapes are not congruent: one has a larger base
(you need 4 pins to make the base).
2.
Repeat the activity from the previous lesson with geoboards.
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G3-10 Exploring Congruency with Grids
Goals: Students will create congruent and non-congruent shapes on a grid.
Prior Knowledge Required: Congruent shapes
Vocabulary: congruent shapes
Ask your students to check how many different squares they can draw on a 4 × 4 grid. Ask your students:
How can you check if the squares are congruent? What do you have to check to make sure your shape is a
square? Suggest that your students measure the sides with rulers and angles with benchmarks to make sure
that the shapes they created are squares, and then to check congruency.
Include the word “congruent” into your next spelling test.
Bonus: Repeat with the 5 × 5 grid. Can you find eight non-congruent squares? (HINT: some of the squares
may be oriented so that their sides are diagonal to the grid).
Extension: The picture shows one way to cut a 3 × 4 grid into 2 congruent shapes. Show how many
ways you can cut a 3 by 4 grid into 2 congruent shapes.
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G3-11 Symmetry
Goals: Students will find lines of symmetry using paper folding.
Prior Knowledge Required: Congruent shapes
Vocabulary: line of symmetry
Explain that a line of symmetry is a line that divides a figure into parts that have the same size and shape
(i.e. into congruent parts), and that are mirror images of each other in the line of symmetry. You can check
whether a line drawn through a figure is a line of symmetry by folding the figure along the line and verifying
that the two halves of the figure coincide.
Hold up a large paper parallelogram. Mark a line on it as shown below.
Ask your students: Is this line a line of symmetry? Are the halves of the figure on both sides of the line
congruent? Fold the shape along the line and ask: Do the halves of the figure coincide? Students should see
that the two halves do not coincide so they are not mirror images of each other in the line. Hence the line is
not a line of symmetry. Invite volunteers to check if other lines on the shape are lines of symmetry. (They can
try a line that connects the other pair of the diagonals or pairs of sides.) They will find that the shape has no
lines of symmetry.
Let your students cut out various polygons and check how many lines of symmetry the shapes have. You
might suggest that your students predict the number of lines of symmetry first and then check their prediction.
Extension: These shapes are called regular shapes. All their sides and angles are equal. Fill in the
T-table:
Figure
Number of Sides
Number of Symmetry
Lines
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G3-12 Lines of Symmetry
Goals: Students will find lines of symmetry in pictures and draw mirror images.
Prior Knowledge Required: Congruent shapes
Horizontal
Vertical
Vocabulary: lines of symmetry horizontal, vertical
Review the definition of a line of symmetry. Give an example using the human body. You may wish to draw
a symbolic human figure on the board and mark the line of symmetry. Review the meaning of the words
“horizontal” and “vertical”. To help the students remember the word “horizontal”, remind them of how they
might draw the horizon line in art class.
Draw several pictures and ask students to find the horizontal and the vertical lines of symmetry.
Ask them to circle the pictures that have a vertical line of symmetry and to draw a square around the
pictures that have a horizontal line of symmetry. Does every picture have a line of symmetry? Are there
pictures with more than one line of symmetry?
EXAMPLES:
Challenge your students to find all the possible lines of symmetry for the following shapes:
Assessment:
Draw all the possible lines of symmetry:
a)
b)
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c)
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Activities:
1. Find a picture in a magazine that has a line of symmetry and mark the line with a pencil. Is it a horizontal
or a vertical line? Try to find a picture with a slanted line of symmetry.
2. Cut out half an animal or human face from a magazine and glue it on a piece of paper, draw the missing
half to make a complete face.
Extension:
Cross-curriculum Connection: Check the flags of Canadian provinces for lines of symmetry.
Possible Source: http://www.flags.com/index.php?cPath=8759_3429.
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G3-13 Completing Symmetric Shapes
Goals: Students will draw mirror images and find lines of symmetry in figures.
Prior Knowledge Required: Congruent shapes
Symmetry lines
Vocabulary: symmetry line, mirror line, mirror image
Draw several simple images such as the ones below and ask your students to draw the missing halves so
that the resulting pictures have a line of symmetry. Ask students to mark the line of symmetry. Is it a
vertical or a horizontal line?
Explain to your students that the halves of pictures that they have drawn are called mirror images of the
original pictures. Can your students explain why the pictures are called so? Let your students put a mirror or
a MIRA along the symmetry line and compare the images in the mirror with their pictures. Explain that the
symmetry line is also often called mirror line.
Activities:
1. Using each pattern block shape at least once, create a figure that has a line of symmetry. Choose one
line of symmetry and explain why it is a line of symmetry. Draw your shape in your notebook.
2.
Using exactly 4 pattern blocks, build as many shapes as you can that have at least one line of symmetry.
Record your shapes in your notebook.
Extension: Take a photo of a family member’s face (such as an old passport photo) and put a mirror
along the line of symmetry. Look at the face that is half the photo and half the mirror image. Does it look the
same as the photo?
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G3-14 Completing Symmetric Shapes
Goals: Students will compare shapes according to a given pattern.
Prior Knowledge Required: Congruent shapes
Lines of Symmetry
Sides and vertices
Polygons
Right angles
Equilateral
Vocabulary: line of symmetry, equilateral shapes, polygon, square, rectangle, triangle, pentagon,
hexagon, right angle, vertices, vertex, sides
Draw a regular hexagon on the blackboard. ASK: How many sides and how many vertices does it have?
What is it called? Does it have any right angles? Is it an equilateral shape? How many lines of symmetry
does it have? Have volunteers mark the lines of symmetry. Then draw a hexagon with two right angles and
make the comparison chart shown below. Ask volunteers to help you fill in the chart.
Property
Number of vertices
Same?
6
6
Different?
Number of edges
Number of right angles
Any lines of symmetry?
Number of lines of symmetry
Is the figure equilateral?
Ask students to summarize the information from the table in a short paragraph that describes any
similarities and differences of the shapes.
Use the worksheet for more practice.
Assessment:
Write a comparison of the two shapes. Be sure to mention the following properties:
The number of vertices
The number of sides
The number of right angles
Number of lines of symmetry
Whether the figure is equilateral
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G3-15 Sorting Shapes by Property
Goals: Students will compare shapes according to a given pattern.
Prior Knowledge Required: Congruent shapes
Symmetry lines
Sides and vertices
Polygons
Right angles
Equilateral
Vocabulary: symmetry line, equilateral shapes, polygon, square, rectangle, triangle, pentagon, hexagon,
right angle, vertices, vertex, sides
Give each student (or team of students) a deck of shape cards and a deck of property cards from “2-D
Shape Sorting Game” of the BLM section. Let them play the first game in Activity 1 below. The game is an
important preparation for Venn diagrams.
Draw a Venn diagram on the board. Show an example—you may do the first exercise of the worksheets
using volunteers. In process remind your students that any letters that cannot be placed in either circle
should be written outside the circles (but inside the box). FOR EXAMPLE, the answer to QUESTION 1 a)
of the worksheet should look like this:
C
D
A
E
I
Has at least
2 right angles
Quadrilateral
A B F GH
Also remind students that figures that share both properties, in this case D and A, should be placed in the
overlap. Ask your students where they would put a figure that looks like the one shown below:
Let your students play the game in the second activity. Then draw the following set of figures on the board.
Ask your students to make a list of figures satisfying each of the properties in a given question below they
draw a Venn diagram to sort the figures.
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B
F
D
H
J
A
C
G
E
K
I
Here are some properties students could use to sort the figures in a Venn diagram.
a) 1. At least two right angles
2. Equilateral
b) 1. Equilateral
2. Has exactly one line of symmetry
(In this case the centre part contains only one irregular pentagon—figure J)
c) 1. Quadrilateral
2. Has at most one right angle
d) 1. Pentagon
2. Equilateral
Assessment:
Use the same list of figures to create a Venn diagram with properties:
1. Has at least one line of symmetry
2. Has at least two right angles
Activities:
Students will need a deck of shape cards and a deck of property cards from the “2-D Shape Sorting Game”
of the BLM section.
1. 2-D Shape Sorting Game
Each student flips over a property card and then sorts their shape cards onto two piles according to
whether a shape on a card has the property or not. Students get a point for each card that is on the
correct pile. (If you prefer, you could choose a property for the whole class and have everyone sort
their shapes using that property.) Once students have mastered this sorting game they can play the
next game.
2. 2-D Venn Diagram Game
Give each student a copy of the Venn diagram sheet in the BLM section (or have students create their
own Venn diagram on a sheet of construction paper or bristol board) in addition to the shape cards and
property cards. Ask students to choose two property cards and place one beside each circle of the
Venn diagram. Students should then sort their shape cards using the Venn diagrams. Give 1 point for
each shape that is placed in the correct region of the Venn diagram.
Extension:
A Game for Two: Player 1 draws a shape without showing it to the partner, then describes it in terms
of number of sides, vertices, right angles, lines of symmetry, etc. Player 2 has to draw the shape from
description.
Geometry Teacher’s Guide Workbook 3:1
Copyright © 2007, JUMP Math For sample use only – not for sale.
22
G3-16 Finding Polygons
Goals: Students will identify polygons in drawings.
Prior Knowledge Required: Congruent shapes
Symmetry lines
Sides and vertices
Polygons
Right angles
Equilateral
Vocabulary: symmetry line, equilateral shapes, polygon, square, rectangle, triangle, pentagon, hexagon,
right angle, vertices, vertex, sides
As a preparation for QUESTION 2 of the worksheet, draw two shapes on the board:
Invite volunteers to make a comparison chart and to write a comparison paragraph for these two shapes.
Properties you might mention:
• The number of vertices
• The number of sides
• The number of right angles
• Number of lines of symmetry
• Whether there are pairs of equal sides
• Whether the equal sides adjacent or opposite
• Whether the figure is equilateral
QUESTION 5 on the worksheet can be done with pattern blocks.
Activity: On a picture from a magazine or a newspaper, ask the students to mark as many polygons as
possible.
Geometry Teacher’s Guide Workbook 3:1
Copyright © 2007, JUMP Math For sample use only – not for sale.
23
G3-17 Problems and Puzzles
This worksheet is the final review and may be used for practice.
Activities:
1. Give students a set of circular tiles of two colours. Ask them to make as many 3-tile triangles as they can
inside a 6-tile triangle.
Solution:
Repeat this exercise with a larger triangle:
2. Take any 2 congruent pattern blocks. Predict the shapes you can make by putting the blocks edge to
edge. (Can you make a quadrilateral? a pentagon? a hexagon? or a shape with more sides?) Trace
around the pattern blocks to show how they combine to make your figure. Repeat this exercise with 3
different pairs of pattern blocks.
3. Using pattern block triangles, try to make the following shapes:
a) A quadrilateral.
b) A hexagon.
c) A bigger triangle.
d) A pentagon.
Extension: In QUESTION 6 students can make a square as shown:
Geometry Teacher’s Guide Workbook 3:1
Copyright © 2007, JUMP Math For sample use only – not for sale.
24