Download Unit 7 Geometry: Shapes

Unit 7 Geometry: Shapes
Learning Geometric Terms
Most students find elementary geometry easy; what they find hard is all the
new terminology. Students won’t be able to describe or classify shapes if
they can’t spell the relevant terms. Therefore, JUMP recommends that you
teach the spelling of geometric terms during spelling lessons. The most
important terms are:
• side
• edge
• vertex, vertices
• line of symmetry
• right angle
• triangle
• square
• rectangle
• rhombus
• parallelogram
• quadrilateral
• pentagon
• hexagon
• trapezoid
Attributes and Properties
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Students will be introduced to attributes and properties through examples.
Color, gender, food, age, and length are attributes; red, green, boy, girl,
fruit, vegetable, age 9, and 4 cm long are properties. Properties are specific
instances of attributes.
Parallelograms and Trapezoids
There are two possible definitions of a trapezoid:
- a quadrilateral with exactly one pair of parallel sides
- a quadrilateral with at least one pair of parallel sides
When using the first definition, parallelograms are different from trapezoids,
whereas when using the second definition, all parallelograms are trapezoids.
Both definitions are legitimate. JUMP materials use the first definition.
Geometry
H-1
G4-1 Introduction to Classifying Data
Page 161
STANDARDS
preparation for 4.G.A.2
Vocabulary
attribute
classify
data
Goals
Students will group data into categories.
PRIOR KNOWLEDGE REQUIRED
Recognizes patterns and attributes
Sorting into two groups without common elements. Have eight
volunteers stand up. Ask students to suggest ways in which to sort or
classify the volunteers into two groups (for example, long or short hair,
boy or girl, nine years old or ten years old, wearing jeans or not wearing
jeans, wearing yellow or not wearing yellow). Then have one student
classify the eight volunteers without telling the class how he or she chose
to classify them. The student tells each of the eight volunteers which side
of the room to stand on. Each remaining student in the class then guesses
which group he or she belongs to. The student who classified the volunteers
then puts the student in the right group. Stop when students have guessed
correctly five consecutive times. The last student to guess correctly appoints
each remaining student to either of the two groups and is told if they’re
right or not. Repeat this entire exercise several times. Note that the student
classifying the students never reveals the classification. To make guessing
the classification harder, students may sort the volunteers using two or
more attributes. For example, they may group “boys not wearing yellow”
and “boys wearing yellow and girls.” Or they may group “boys or anyone
wearing yellow” and “girls or anyone not wearing yellow.”
Have students identify attributes shared by all members of
the following groups:
a)gray, green, grow, group (Sample answer: starts with gr,
one syllable, word)
c)39, 279, 9, 69, 889, 909 (Sample answer: odd, ones digit 9,
less than 1,000)
d)5,412, 9,807, 7,631, 9,000, 9,081 (Sample answer: number,
four digits, greater than 5,000)
e)hat, cat, mat, fat, sat, rat (Sample answer: three-letter word,
rhymes with at)
Have students write two attributes for each group:
a) 42, 52, 32, 62, 72
b) lion, leopard, lynx
Write the numbers below and ask how they can be categorized.
Group A: 321, 725, 129, 421
H-2
Group B: 38, 54, 16, 70, 82
Teacher’s Guide for AP Book 4.1
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b) pie, pizza, peas, pancakes (Sample answer: food, starts with p)
Have a volunteer add one more number to each group to help the class
identify categories. Then other students can guess the categories. The
student who guesses correctly chooses another way to categorize the
groups (but doesn’t reveal the categories!), gives a new number that fits
into each group, and asks the rest of the class to guess the new categories.
Play the game long enough to allow a variety of categorizations.
Possible categories include:
• Two-digit numbers, three-digit numbers
• Tens digit 2, tens digit other than 2
• Even numbers, odd numbers
• More than 100, less than 100
Play the same game with these words: trick, train, sick, stain, drain,
drink, sink, think, thick. Start by asking a volunteer to sort the words
into two or three groups.
Possible categories include:
• First letter is d, s, or t
• Rhymes with rain, rink, or brick
• One vowel, two vowels
• Four letters, five letters
• Last letter is n, last letter is k
Extension
a)Give pairs of students a copy of BLM Shapes (p. H-33), which is
composed of 16 shapes that are either striped or plain, big or small,
triangles or squares. The BLM has two of each shape, so students
can work individually. (Pairs can also use a Set™ card game.)
Ask students to separate the striped triangles from the rest of the shapes,
then challenge them to describe the remaining group of shapes (plain
or square). Allow them to use “or” or “and” in their answers, but do not
encourage use of the word “not” at this point since, in this case, “not
striped” simply means plain. If students need help, offer them choices:
plain or triangle, striped and square, plain or square.
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b)Challenge students to describe the remaining group of shapes when
they separate out the following:
Geometry 4-1
i) small squares
ii) plain squares
iii) big triangles
iv) shapes that are small or triangular
v) shapes that are striped or triangular
vi) shapes that are striped or big
vii) shapes that are both striped and big
viii)shapes that are both plain and big
ix) shapes that are striped or small
H-3
G4-2 Venn Diagrams
Pages 162–163
STANDARDS
preparation for 4.G.A.2
Vocabulary
and
not
or
property
Venn diagram
Goals
Students will sort data using Venn diagrams.
PRIOR KNOWLEDGE REQUIRED
Identifying attributes
Classifying according to attributes
Words like “and,” “or,” and “not”
MATERIALS
cardboard box
a variety of small objects, toys and not toys
pens, pencils, and other objects, some of them blue
two Hula-hoops
Sorting using one circle. Show students a variety of small objects, some
toys and some not toys. Label a cardboard box “toy box,” then ask students
if various items belong inside or outside the box. Then tell students that you
want to classify items as toys without having to put them in a box. Draw a
circle, write “toys” in the circle, and tell students that you want all of the toy
names written inside the circle, and all of the other items’ names written
outside the circle. Ask students to tell you what to write inside the circle.
To save space, have students problem-solve a way to avoid writing the entire
word inside the circle. If they suggest you write just the first letter, ask them
what will happen if two toys start with the same letter. Explain to them that
you will instead assign a different letter to each word. Example:
A. Lego piece
B. bowl
C. toy car
D. pen
Which of these letters go inside the circle, and which of the letters go
outside the circle? (Answer: A, C inside, B, D outside)
A.
Shapes
Triangles
H-4
B.
C.
D.
E.
F.
Draw the diagram in the margin. Ask students if all the letters belong inside
the box (yes) and invite them to explain why. Which letters belong inside
the circle? Which letters belong outside the circle but still inside the box?
Then ask students why the circle is inside the box. Are all of the triangles
shapes? Explain that everything inside the box is a shape, but in order to be
inside the circle, the shape has to be a triangle. Change the word inside the
circle and repeat the exercise. (Suggested words to use include dark, light,
quadrilaterals, polygons, circles, dark triangles, dark circles.) ASK: Why is
the circle empty when it’s labeled “dark circles”?
Teacher’s Guide for AP Book 4.1
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Draw several shapes and label them with letters:
What other property could you use to label the circle so that it remains
empty? Remind students that the word inside the circle should reflect the
fact that the entire box consists of shapes, so “rockets” isn’t a good choice,
even though the circle would still be empty.
ACTIVITY 1
Create a large circle on the floor (using masking tape, for example)
and have students who are nine years old stand inside the circle.
Label the circle “9 years old.” Repeat with several examples: wearing
yellow, girl, wearing blue, takes the school bus. Have students stand
inside the circle when the property applies to them and outside the
circle when it does not.
Play a game: Invite students to suggest properties and challenge them
to sort themselves correctly before you finish writing the label. Students
should learn to strategically pick properties that take a long time to write.
Introduce Venn diagrams. Clearly label one Hula-hoop “pens” and another
“blue,” then ask students to assign several colored pens (black and red)
and pencils (blue, red, and yellow) to the proper position—inside one
of the hoops or outside both of them. Do not overlap the hoops at this point.
Then present students with a blue pen and explain that it belongs in both
hoops. Allow students to problem-solve a way to move the hoops so that
the blue pen is circled by both hoops at the same time. Have a volunteer
show the others how it’s done. If students move the hoops closer together
without overlapping them, so that part of the blue pen is circled by the “blue”
hoop and part of the blue pen is circled by the “pens” hoop, be sure to ask
them if it makes sense for part of the pen to be outside of the “pens” hoop.
Shouldn’t the entire pen be in the “pens” hoop?
Draw and label the same shapes used previously:
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A.
Shapes
Dark
Geometry 4-2
Triangles
B.
C.
D.
E.
F.
Then draw the diagram in the margin. Explain to students that this picture
is called a Venn diagram. ASK: Why do the two circles overlap? Have a
volunteer shade the overlapping area of the circles and ask the class which
letters go in that area. Have a second volunteer shade the area outside the
circles and ask the class which letters go in that area. Finally, ask students
which shape belongs in the “dark” circle and which shape belongs in the
“triangle” circle. Change the labels for both circles and repeat the exercise.
(Suggested words to use include light and quadrilateral, light and dark,
polygon and light, circles and light.)
H-5
Connection
Social Studies, Health,
Language Arts
This is a good opportunity to tie in ideas learned in other subjects. For
example, have students categorize words by their first or last letters,
by their sound, by the number of syllables, etc. (“rhymes with tin” and
“2 syllables”: A. begin, B. chin, C. mat, D. silly). Start with four words, then
add four more words to be sorted into the same categories. Encourage
students to suggest words and their place in the diagram. (Cities, states,
or food groups are also good categories.)
ACTIVITY 2
Repeat Activity 1 using two overlapping circles. Example: circle 1:
wearing blue; circle 2: has dark hair.
Extensions
1.Have students sort the eight shapes from BLM Shapes (p. H-33) into
Venn diagrams. (The BLM has two of each shape, so you’ll need one
copy for every two students.) Possible categories include:
a)
Shapes
Striped or
Triangle
plain or triangle; plain squares
plain triangles; big or plain
small or triangle; striped and big
small or striped; big or square
big squares; small squares
In addition, you can distribute copies of BLM Circles (p. H-34)—one
copy for every four students—and have students sort the shapes from
both BLMs into Venn diagrams. Possible new categories include:
g) plain or triangle; not a circle
h) striped, but not a square; circle or big
(MP.6)
2.Combine the shapes BLM Circles and BLM Shapes and have students
repeat Extension b) from G4-1. Allow them to use the word “not” when
describing the separated shapes. For example, when you separate the
plain triangles, the remaining shapes can be described as “striped or
not a triangle” or “striped or square or circle.” Although “not a plain
triangle” is also correct, students should be encouraged to use a
more precise description.
Students can complete BLM Venn Diagram (Advanced) (p. H-35).
H-6
Teacher’s Guide for AP Book 4.1
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b)
c)
d)
e)
f)
Big squares
G4-3 Sides and Vertices of 2-D Shapes
Pages 164–165
STANDARDS
preparation for 4.G.A.2
Vocabulary
hexagon
pentagon
polygon
quadrilateral
side
three-dimensional, 3-D
triangle
two-dimensional, 2-D
vertex, vertices
(MP.8)
Goals
Students will identify polygons, sides, and vertices and will distinguish
polygons according to the number of sides.
PRIOR KNOWLEDGE REQUIRED
Can count to ten
Can distinguish a straight line
MATERIALS
large paper shapes (see vocabulary and lesson)
various polygons from BLM Polygons (pp. H-36–H-37)
geoboards
pattern blocks or tangrams or BLM Pattern Blocks (p. I-1)
or BLM Tangrams (p. H-38)
Sides and vertices. Draw and label a polygon with the words “sides” and
“vertex/vertices.” Remind students of what a side and vertex are. 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 students 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 shape with its name
and display the shapes on the board. Explain that “gon” means corner
(vertex) and “lateral” means side. You might want to leave these shapes
posted on a wall throughout the geometry unit. Later (G4-8), you can
add special quadrilaterals.
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not polygons
Polygons. Explain that flat shapes such as squares, triangles, and circles
are called two-dimensional, or 2-D for short. That is because they have two
dimensions: length and width. Shapes such as cubes (show a cube) have
length, width, and height, and so are called three-dimensional or 3-D.
Divide the board in two. On one side, draw a variety of polygons, including
regular polygons (shapes with equal sides and equal angles) and irregular
polygons. Label the shapes “Polygons,” reading the label aloud. Label the
other side of the board “Not Polygons.” Draw a pentagon with a little part of
one side missing on the “Not Polygons” side and ASK: How is this different
from the polygons? (It is a line with endpoints, not a shape.) Repeat with a
shape that has one curved side, a shape that has a “tail” (or loose endpoint),
and a shape with self-intersecting sides (it looks like a combination of two
shapes; it has a vertex where more than two edges meet). Add a variety of
other non-polygons and ASK: What is the same about all the polygons? Do
they all have straight sides? (yes) Do they have endpoints? (no) Are they all
Geometry 4-3
H-7
flat? (yes) Conclude by telling students that all 2-D shapes that have
straight sides and no loose endpoints are called polygons. Explain that
“poly” means many, then ask students what the word “polygon” might
mean. (many corners, many vertices)
shapes with indentations
Draw several more shapes and ask students to decide whether each is a
polygon or not. Include shapes that have indentations. Students can point to
the correct side of the board to indicate whether a shape is a polygon or not.
Sorting polygons by the number of sides. Give students an assortment
of polygons (use BLM Polygons) and have them count the sides of the
polygons. Ask students to sort the shapes by the number of sides. (Help
struggling students by providing group names, such as 3 sides, 4 sides,
5 sides, 6 sides, more than 6 sides.) After giving students time to work,
make a chart on the board with columns labeled according to the number
of sides and display larger copies of the same shapes. Have students show
in which column each shape belongs (they can raise the number of fingers
equal to the number of sides).
(MP.6)
Draw a pentagon on the board. ASK: How many sides does this polygon
have? What is the name for this polygon? How do you know that this is a
pentagon? If students do not say that it has 5 sides and 5 vertices and all
sides are straight, draw another pentagon (different size, color, or pattern)
and ask what the two pentagons have in common. Repeat with a triangle
and a quadrilateral that is neither a rectangle nor a square (e.g., a parallel­
ogram, rhombus, or trapezoid). Finally, draw a square and a rectangle.
For each, ASK: How many sides does this polygon have? What is a polygon
with 4 sides called? (quadrilateral) What is another name for this shape?
(square/rectangle)
ACTIVITY 1
Use a geoboard to create a shape (do each shape introduced
in the lesson). Ask students to re-create the exact same shape
on their geoboards.
Draw a group of 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.
H-8
Teacher’s Guide for AP Book 4.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Introduce the names of polygons. Explain that mathematicians give
special names to polygons according to the number of sides and vertices
they have. Present the names (see vocabulary) on cards, explain each one
(e.g., hexagons have 6 straight sides and 6 vertices), and invite volunteers
to assign each card as the label for a column. Students may notice that the
column for shapes with 4 sides, labeled “quadrilateral,” includes shapes
that they would call “squares” and “rectangles.” Explain that, just as there
is more than one word that describes a student (e.g., boy/girl, child, person),
many shapes have more than one name. Tell students that squares and
rectangles are special types of quadrilaterals.
Bonus
Draw a figure that has:
a) two curved sides and three straight sides
b) two straight sides and three curved sides
Students who need additional practice can do these Exercises:
1. Draw a polygon with seven sides.
2. Draw a quadrilateral. How many vertices does it have?
3.Altogether, how many vertices are there in two pentagons
and a triangle?
4. Draw a shape that is not a polygon and explain why it is not a polygon
(for instance, the rectangle with rounded edges at left does not have
proper vertices).
ACTIVITY 2
(MP.1)
Give each student a set of pattern blocks or several tangram pieces
with the following instructions (answers are shown):
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?
e) Can you make a pentagon with pattern blocks?
Extensions
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(MP.8)
1.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.)
2.
BLM Word Search (Shapes), p. H-39. This can also be assigned
as homework.
(MP.3)
Geometry 4-3
3.After students have sorted polygons by the number of sides, ask if
anybody has a polygon with two sides only. Then suggest that students
try to draw a polygon with two sides. Let them discuss in pairs why
this is impossible. Debrief as a class.
H-9
G4-4 Right Angles
Pages 166–167
Goals
STANDARDS
4.G.A.2
Students will identify right angles in drawings and objects.
Vocabulary
perpendicular lines
perpendicular sides
right angle
PRIOR KNOWLEDGE REQUIRED
Can identify polygons
MATERIALS
rectangular sheets of paper
paper polygons (see lesson)
cards from BLM Polygons (pp. H-36–H-37)
geoboards
Introduce right angles. Explain that a right angle is the corner of a square
(there is no need to define it properly at this stage). Ask students where
they can see right angles in real life (corners of a sheet of paper, doors,
windows, etc.). Draw a right angle and show students how to mark right
angles with a small square. Explain to 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.
B
Explain to students that when they want to check whether the angles of a
polygon are right angles, they need to look at the parts that are inside the
shape. Draw the shape at left and explain that angle B of this polygon is not
a right angle. Show the same shape made from bristol board, and compare
the angle with a corner of a piece of paper. The angle inside the shape is
visibly larger than a right angle. The angle outside the shape might be a
right angle, but that’s not the angle we’re interested in!
Give students cards from BLM Polygons and have them compare the
angles of the polygons on the cards with a corner of a sheet of paper.
Show students how to mark right angles with a small square and have
them mark the right angles on the cards. Students who have trouble
identifying the correct angles in shapes with indentations will benefit
from cutting out the shapes.
Draw several angles and ask volunteers to identify and mark the right
angles. For a short assessment, you can also draw several shapes
(see below) and ask students to signal how many right angles there are.
H-10
Teacher’s Guide for AP Book 4.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Demonstrate how to compare angles to a corner of a piece of paper by
superimposing. Emphasize that you need to match one side of the angle
to a side of the piece of paper and that the corner of the piece of paper
should match the vertex of the shape (or the angle). If the paper or the
angle are “sticking out,” the angle is not a right angle. Have students
compare various corners with a corner of a piece of paper to decide
whether the corners are right angles.
Do not mark the right angles in the diagram.
Introduce perpendicular lines. Explain to students that when two lines
meet and make a right angle, they are called perpendicular lines. Write the
term on the board and draw several pairs of lines intersecting at a right
angle as in Question 6 on AP Book 4.1 p. 167. Show how to compare the
angles with a square corner again. Draw several pairs of intersecting lines
on the board (perpendicular and not) and have students predict whether
the lines are perpendicular. Students can show thumbs up for perpendicular
lines and thumbs down for lines that are not perpendicular. Include pairs
of lines that are not horizontal and line segments that intersect in different
places and at different angles (see examples below). Invite volunteers to
check whether the lines are perpendicular using the corner of a page.
Perpendicular sides. Explain that sides of polygons that make a
right angle are called perpendicular sides. So when you are looking
for perpendicular sides in a polygon, you are looking for right angles.
Draw several polygons (without indentations) and number the sides.
Have students identify pairs of sides that are perpendicular (e.g., side
1 and 2 are perpendicular).
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Return to the shape from the beginning of the lesson, where the sides that
make a reflex angle (greater than 90°) inside the shape are perpendicular.
Trace the two sides that make a reflex angle on the board, remove the shape
and ASK: Are these lines perpendicular? (yes) Explain that although the
angle of the polygon is not a right angle, the sides are still perpendicular,
because the angle on the outside of the shape is a right angle. So when we
are looking for perpendicular sides, it is a good strategy to look for right
angles, but we also might have some other perpendicular sides.
ACTIVITY
Have students use geoboards to make shapes with a given number
of right angles:
a) 4 right angles
b) 2 right angles
c) 1 right angle
Geometry 4-4
H-11
Bonus
d) 3 right angles
e) 6 pairs of perpendicular sides and 5 right angles
Sample answers: a) rectangle or square, b) right trapezoid
c)
d)
e)
Extension
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Sometimes you need to extend the sides of a shape to check whether they
are perpendicular. Have students individually extend the sides of an octagon
to check which sides are perpendicular. Do one pair of sides with them:
H-12
Teacher’s Guide for AP Book 4.1
G4-5 Parallel Lines
Pages 168–169
STANDARDS
4.G.A.1
Vocabulary
parallel lines
Goals
Students will identify and mark parallel lines.
PRIOR KNOWLEDGE REQUIRED
Can identify straight lines
MATERIALS
grid paper
rulers
cards from BLM Polygons (pp. H-36–H-37)
pictures from magazines or newspapers that show
examples of parallel lines
Lines that are the same distance away at all points. Tell students that
an engineer wants to build a bridge over a river. Draw a picture of the river,
as shown, on the board. The engineer wants the bridge to be as short as
possible. Where should he build the bridge? Have students come over and
show where they would build a bridge. Have students measure the width
of the river at different points. Where should the engineer build a bridge?
Repeat with another picture of a river whose width varies. Finally, present
a “river” with straight, parallel banks. Have students measure its width
in different places. ASK: What do you notice about the distance between
the banks? (it is always the same) Is there one place that is best to build
a bridge? (no)
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Parallel lines. Explain that lines that look like the banks of the last river
are called parallel lines. Parallel lines are straight lines that are always the
same distance apart. Like railway tracks, they never meet. Ask students
where they can see parallel lines in the classroom (shelves, table sides or
legs, the lines where the walls meet, etc.). Draw several parallel lines on
the board. Show how to mark parallel lines with arrows.
Draw a pair of lines that are not parallel but will intersect if extended on the
board. ASK: Could a train go along a pair of tracks like this? Why not?
(they are getting closer together, and the wheels of a train do not get closer
together) Explain that lines can be extended in either direction, and parallel
lines will never meet, even if extended. Invite volunteers to extend the lines
so that they clearly intersect. ASK: Are these lines parallel? (no)
Geometry 4-5
H-13
(MP.7)
Discuss with students how they can draw parallel lines. One strategy could
be to draw a line using a ruler, then slide the ruler without turning it and draw
another line. Point out that just as railway tracks go in the same direction,
parallel lines also go in the same direction. So if one parallel line on grid
paper goes 3 squares up and 4 squares left, the other parallel line will also
go 3 squares up and 4 squares left.
Ask students to draw a line (first horizontal, then vertical, then diagonal)
on grid paper and to draw another one parallel to it. Mark the parallel lines
with arrows. On a grid on the board draw a right-angled but not isosceles
triangle (sides of 4 and 3 squares). Ask students to copy the triangle and
to draw lines parallel to each of the sides. The purpose of this exercise is
to draw a line parallel to a diagonal line that does not pass through every
point of intersection on the grid.
Draw several shapes that contain parallel sides on the board (it is important
to have parallel lines with different slopes and of different lengths—use
various trapezoids, parallelograms, and hexagons, and not only rectangles
and parallelograms) and ask volunteers to mark pairs of parallel sides. You
may also do the opposite task—draw a pair of parallel line segments and
ask students to join the ends to make a quadrilateral.
Students who need additional practice can identify parallel sides on
polygons from BLM Polygons.
ACTIVITY
In a picture from a magazine or a newspaper, find as many parallel
lines as you can, marking each set with a different color.
Extension
(MP.1)
Draw a polygon that has:
Sample answers
a)
b)
H-14
c)
Teacher’s Guide for AP Book 4.1
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a) more than one pair of parallel sides.
b) more than two pairs of parallel sides.
c) three parallel sides.
G4-6 Quadrilaterals
Page 170
STANDARDS
preparation for 4.G.A.2
Goals
Students will distinguish quadrilaterals from other polygons.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
quadrilateral
Can identify polygons
Can measure sides with a ruler
Can count the sides of a polygon
MATERIALS
cards from BLM 2-D Shape Sorting Game (pp. H-40–H-41)
cards from BLM Polygons (pp. H-36–H-37)
larger cards from the same BLMs for demonstration (see below)
pattern blocks or BLM Pattern Blocks (p. I-1)
toothpicks
modeling clay
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
(MP.6)
(MP.6)
Introduce quadrilaterals. 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” and “lateral” means “side”
in Latin. Ask if students have ever encountered any other word having either
of these parts in it. (square, quadruple) You might also mention that “tri”
means “three” and ask if students 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.
Give students shape cards from BLM 2-D Shape Sorting Game (you can
add cards from BLM Polygons as well). Have students sort the shapes
individually into quadrilaterals and non-quadrilaterals using a chart with
two columns, then check the answers on the board using a larger version
of the same cards with tape on the back side. (To make larger cards,
photocopy the BLM onto A3 paper (11 1/2 by 17) using enlargement factor
150%.) For each card, ask students to explain their choice. Repeat with
polygons and non-polygons. Finally, have students sort the shapes by
the number of sides.
For additional practice, you may ask students to sort pattern block pieces
into quadrilaterals and non-quadrilaterals.
Include the word “quadrilateral” on your next spelling test.
Geometry 4-6
H-15
ACTIVITIES 1–2
1.Give each student 4 toothpicks and some modeling clay to hold
them together at vertices. Ask students to create a shape that is
not a quadrilateral. (It might be either a three-dimensional shape or
a self-intersecting one.) Also ask students to make several different
quadrilaterals.
(MP.1, MP.3)
2.Give each student 10 toothpicks and ask them to check how many
different triangles they can make with these toothpicks. Each
triangle should use all the picks. Then ASK: How many different
quadrilaterals can you make using 10 toothpicks? The answer
to the first problem is two: 2, 4, 4, and 3, 3, 4. The answer to the
second problem is infinity—a slight change in the angles will make
a different shape.
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
(MP.3)
H-16
Teacher’s Guide for AP Book 4.1
G4-7 Properties of Shapes
Pages 171–172
STANDARDS
4.G.A.2
Vocabulary
equilateral
hexagon
parallel lines
pentagon
quadrilateral
triangle
Goals
Students will sort shapes according to the number of sides,
parallel sides, or right angles.
PRIOR KNOWLEDGE REQUIRED
Polygons
Quadrilaterals
Parallel lines
Right angles
MATERIALS
cards from BLM Polygons (pp. H-36–H-36)
cards from BLM 2-D Shape Sorting Game (p. H-40–H-41)
toothpicks
geoboards
Sort shapes by properties. Review with students how to check that sides
of a polygon are parallel (e.g., by sliding a ruler from one side to the other—
if you can slide the ruler without turning, and both sides line up with the
ruler, the sides are parallel). Review how to check that angles in a polygon
are right angles (by using a corner of a page). Give each student several
shapes from BLM Polygons and have students identify parallel sides and
right angles on each shape. Then ask them to sort the shapes:
a) by name (triangle, quadrilateral, pentagon, hexagon, other)
b)by the number of right angles (0 right angles, 1 right angle,
2 right angles, more than 2 right angles)
c)by the number of pairs of parallel sides (0 pairs, 1 pair,
more than 1 pair)
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Draw the table below on the board. Leave enough space in each cell
to draw a shape and to write a few names. Do not fill in the table with
the numbers shown—they are included for your convenience.
Geometry 4-7
Property
No parallel
lines
1 pair of
parallel lines
2 or more pairs
of parallel lines
No right angles
1, 7, 10, 12, 13
3, 23
8, 11, 14, 15
1 right angle
4, 9
17, 18
16, 21
2 or more right
angles
19, 24
6, 22
2, 5, 20
H-17
Go through the table cell by cell and ask volunteers to draw an example of a
shape that has these properties. Remind students to mark parallel lines and
right angles on their pictures. Then assign each student a single card from
BLM Polygons, and have them decide how many pairs of parallel sides
and how many angles the polygon has. Ask students to decide which cell
their shape belongs to and write their name in the cell. This will separate
students into groups according to the numbers on the cards as written in
the table. If you want to obtain 9 pairs, include only two cards from each
group in the activity.
(MP.8)
Find sorting rules for a pre-sorted group of shapes. After the sorting
activity above, let students play a game. Students will need a set of shapes
from BLM 2-D Shape Sorting Game in addition to those they were given
for the sorting activity. Player 1 (or Team 1) lays down 3 shapes that have
a common feature (for instance, they might all have the same number of
sides). Player 2 or Team 2 adds a fourth shape with the same feature.
Player 1 tells Player 2 if the addition is correct. If it is, Player 2 guesses what
the shapes have in common. If the addition is incorrect, Player 1 adds another
shape with the same feature, to give Player 2 more information, and Player 2
guesses again. Players continue adding shapes and guessing until Player 2
correctly identifies what the shapes have in common.
(MP.3)
Shapes with all equal sides. Draw a rectangle and a square on the board.
ASK: How are these shapes different? (one has two pairs of longer sides
and two pairs of shorter sides, and the other has all sides equal) Draw an
equilateral triangle and ask students if it is more like a rectangle or a square.
(square) Why? (it has all sides equal) Point out that a square and a rectangle
look the same from many directions. For example, if you turn a square on
its side, it will look exactly the same. ASK: Do all shapes with all sides equal
have this property? To help students realize that shapes with all sides equal
do not have to look the same from many directions, provide students with
at least 5 toothpicks of the same length. Ask them to check that the tooth­
picks are all the same length. Ask students to create several polygons using
all of their toothpicks. Can they make polygons that do not look the same
from all sides? Can they make “ugly” polygons? Have students trace the
polygons they created and then share their results with the class.
Ask students to sort the shapes from BLM Polygons or BLM 2-D Shape
Sorting Game into shapes that have all sides of the same length (cards
1, 2, 11, 13, 15) and shapes that have some sides that are not the same
lengths as others. Point out that the shapes in the second group still might
have some equal sides, but not all sides are the same length.
H-18
Teacher’s Guide for AP Book 4.1
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Advanced variation: Player 1 puts down 3 shapes that have a common
feature and 1 extra shape that doesn’t have that feature, and Player 2 tries
to find the shape that doesn’t belong and explains the choice.
ACTIVITY
Ask students to make each shape shown below with an elastic on a
geoboard. Then ask them to connect two pins with another elastic
to change the given shape into:
a) two triangles
b) a quadrilateral and a triangle
Extension
Find the names of polygons for all polygons with up to 20 sides. If you are
looking for “names of polygons” on the Web, check at least three sources
to see that they give the same name for the same polygon.
Are there coins that have polygons on them or that are in the shape of
a polygon? Which (not-so-common) US coin has a polygon on it? What
coins from other countries are polygons, and what polygons are they?
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Answers: The US $1 coin with the portrait of Susan B. Anthony has a
hendecagon (11 sides) drawn on it. Many other countries have polygonal
coins. For example, a Canadian $1 coin is a hendecagon. A UK 20-pence
coin is a heptagon (7 sides).
Geometry 4-7
H-19
G4-8 Special Quadrilaterals
Pages 173–174
Goals
STANDARDS
4.G.A.2
Students will distinguish between special quadrilaterals.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
parallelogram
rectangle
rhombus
square
trapezoid
Quadrilaterals
Parallel sides
Right angles
Can measure sides with a ruler
MATERIALS
large paper quadrilaterals (see vocabulary and lesson)
cards from BLM Polygons (pp. H-36–H-37)
cards from BLM 2-D Shape Sorting Game (pp. H-40–H-41)
geoboards
pictures from magazines or newspapers with shapes
containing quadrilaterals
Give students cards with quadrilaterals from BLM Polygons and BLM
2-D Shape Sorting Game and have them sort the shapes into a chart
with headings Parallelogram, Trapezoid, Other. Check answers on the
board with large copies of the cards. Then SAY: I want to sort the shapes
into rectangles, rhombuses, and squares. Will I find these shapes in all
columns? (no) Which column are they all in? (parallelograms) Why?
(because they are all parallelograms—they all have two pairs of parallel
sides) Have students sort the parallelograms into squares, rectangles,
rhombuses, and other parallelograms.
Have students fill in the following table with their parallelograms:
(MP.8, MP.5)
H-20
4 equal sides
4 right angles
ASK: What name can we attach to the shapes in the first row? (rhombuses)
In the second row? (rectangles) What problem did students encounter?
Which shape should be placed in both rows at the same time? (square)
Which sorting tool would be more convenient than this table? (a table with
Teacher’s Guide for AP Book 4.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Introduce special quadrilaterals (parallelograms, rectangle, rhombus,
square, trapezoid). Use large special quadrilaterals made from construction
paper or bristol board to introduce these shapes to students. Label each
shape with its name. Ask students where they have seen these shapes in
real life. (e.g., a rhombus may be found in the diamond shape on playing
cards) Add the special quadrilaterals to any other shapes already posted
on the wall, and leave them up for as long as you are studying geometry.
Include the names of the special quadrilaterals in your next spelling text.
three rows or a Venn diagram) Point out that just as a person can be given
several names (boy, David, McDonald) because he has the properties for
each of these names (he is male, his name is David, and he belongs to
the McDonald family), the same quadrilateral can be given different names
because it has the properties that define each name.
AP Book 4.1 Questions 6 and 7 on p. 174 may be done with a geoboard.
Students who need additional practice can answer these questions:
What shape am I?
a)I am a quadrilateral and all my sides are equal. None of my angles
are right angles.
b)I have four sides and all my angles are the same. One of them is a
right angle.
c) I have four sides and two of them are parallel. The other two are not.
d) I am a quadrilateral and my opposite sides are parallel.
e) I am a rhombus that has equal angles.
f) I am a quadrilateral with two parallel sides. One of my parallel sides
is twice as long as the other one. Draw me first!
Answers: a) rhombus, b) rectangle or square, c) trapezoid,
d) parallelogram, e) square, f) trapezoid
ACTIVITIES 1–2
1.Ask students to mark as many special quadrilaterals as possible
on a picture from a magazine or a newspaper. Make sure that there
are examples of regular parallelograms as well (some train or car
windows, for instance).
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2. h
ttp://www.mathsisfun.com/geometry/quadrilaterals-interactive.html
Ask students to play with quadrilaterals on this Web site and to
sketch various shapes they obtain for each special quadrilateral.
Extensions
1.There are three vertices of a square on the grid paper.
Can you finish the square?
2.Can you draw a square without vertical sides on blank
(non-grid) paper? Use a ruler.
Geometry 4-8
H-21
3.Miss Maple is a Fourth Grade teacher. She wants to teach her students
about Venn diagrams. To help her students sort shapes, she decides
to label all the regions of the diagram, and not only the circles. The first
diagram she makes looks like this:
Names
Boys’
names
Girls’
names
Names that both boys and girls can have
Miss Maple starts another Venn diagram but doesn’t finish it. Place the words parallelograms, rectangles, rhombuses, and squares in the right place in an empty Venn diagram.
Answer:
Parallelograms
Rectangles
Squares
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Rhombuses
H-22
Teacher’s Guide for AP Book 4.1
G4-9 Symmetry
Pages 175–176
STANDARDS
preparation for 4.G.A.3
Goals
Students will identify shapes with a line of symmetry.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
Can identify figures of the same shape and size
horizontal
line of symmetry
symmetrical
vertical
MATERIALS
large paper right triangle
paper squares
shapes from BLM Shapes to Fold (pp. H-42–H-43)
Miras
cards from BLM Polygons (pp. H-36–H-37)
Folding shapes so that parts match exactly. Show students a right
triangle created from a rectangular sheet of paper by cutting the rectangle
along the diagonal. Fold the triangle once as shown below. Show students
how the two parts do not match—one part “sticks out.” From one side,
the wider part of the triangle covers the narrower part, but when you flip
the folded shape over, the narrower part doesn’t cover the wider part.
Fold
Nothing “sticks out”
Flip
This part
“sticks
out”
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Give each student a paper square. Ask students to fold their square so that
one of the vertices matches up with any other vertex. (All students don’t have
to—and likely won’t—fold the square the same way.) ASK: Does the top part
of your folded square cover the bottom part? Flip the folded square over—
does the top part cover the bottom part now, too? Unfold your square—
what parts do you see? Are the shapes of the same kind? Are the shapes of
the same size? How do you know? (nothing “sticks out”) What can you say
about the parts of the square? (They are the same, or equal.) Explain that in
this case we say that the parts of the square match exactly. Ask students to
check whether they folded the square so that the parts match exactly. If not,
ask them to fold the square again so that the parts match exactly.
ACTIVITY 1
(MP.3)
Geometry 4-9
Give students several shapes from BLM Shapes to Fold and ask
them to fold the shapes along the dotted lines. Do the parts match
exactly? For the shapes in which the parts do not match, discuss
how students can trace and cut to make the shapes match, then
have them test their predictions.
H-23
Bonus
Find another way to fold the square so that the parts match exactly.
How many different ways can you find to fold a square so that the parts
match exactly?
E
Miras. Ask students what object they know that can show an exact match
of anything. (a mirror) Give students Miras. If students have not used
Miras before, ASK: What does this kind of mirror do? Let students experiment
with personal objects. When students understand that this mirror is
transparent, show them the way to check whether parts of objects match
exactly. For example, you could write a large E (as shown) on the board and
ask whether the top part is exactly the same as the bottom part. ASK: if you
could fold the board, would the top of this E fall precisely on the bottom?
How could we check? Take guesses, then show students how to check this
using the Mira. Students should clearly see that the parts do not match.
ACTIVITY 2
Have students use Miras to check whether some objects, such as letters
on the cover of their JUMP Math AP Book 4.1, have matching parts.
Introduce lines of symmetry. Have students unfold their squares and
explain that the line along the fold is called a line of symmetry. This line
indicates that the parts of the shape match exactly when folded over.
Introduce symmetrical shapes. Explain that a shape that has a line of
symmetry is called symmetrical.
Check symmetry with a Mira. Draw a symmetrical heart or a stick person
on the board and ask students where and how they would place a Mira to
check that this picture has two matching parts. Invite a volunteer to show
how to place a Mira and to draw its location on the board. ASK: What do we
call the line you drew? (a line of symmetry) Explain that a line of symmetry
is also called a mirror line.
H-24
Teacher’s Guide for AP Book 4.1
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Explore lines of symmetry. Show students a rectangular sheet of paper.
Invite a volunteer to fold it in half so that the vertices match. Point out that
when the sheet is folded in this way, the sides match also. The parts of the
rectangle match exactly—one part is exactly the same as the other. The
line along the fold is a line of symmetry. Now fold the rectangle along the
diagonal. Do the parts match exactly? (no) Is this line a line of symmetry?
(no) Are both parts the same size and shape? (yes) Explain that even though
the shapes would match if cut and turned, cutting is not allowed in symmetry.
Only folding is allowed.
ACTIVITY 3
(MP.3)
Give students an assortment of shapes from BLM Polygons and
ask them to determine which shapes from their collection have
lines of symmetry. Let them check the shapes with Miras, trace the
shapes in their notebooks, and use a ruler or straight edge to draw
the lines of symmetry.
Before assigning pages in AP Book 4.1, review with students the meaning of
the terms “horizontal” and “vertical.”
Bonus
Add something to the figures in Questions 6 and 7 on AP Book 4.1
p. 176 that don’t already have both horizontal and vertical lines of
symmetry so that they do.
Extension
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Which states have symmetrical flags? Search the Web for “United States
sub national flags” and check.
Geometry 4-9
H-25
G4-10 More Symmetry
Page 177
Goals
STANDARDS
4.G.A.3
Students will find lines of symmetry and identify shapes that have
lines of symmetry.
Vocabulary
PRIOR KNOWLEDGE REQUIRED
hexagon
horizontal
line of symmetry
parallelogram
pentagon
rectangle
rhombus
square
vertical
Special quadrilaterals
Can identify and draw a line of symmetry
MATERIALS
large paper rectangle
paper and scissors
sheets of paper with a straight line down the middle (see Activity 1) and
pattern blocks (or BLM Pattern Blocks p. I-1)
BLM Lines of Symmetry (p. H-44)
BLM Paper Quadrilaterals (p. H-45)
Miras
pictures from magazines or newspaper (see Activities 4 and 5)
Creating symmetrical shapes and patterns. Hold up a large paper
rectangle. Fold it in four along the lines of symmetry. Ask students to
identify the folded shape. Unfold once and ask students to identify the
new shape. Unfold completely and ask students to identify the shape
again. Refold the paper and cut the folded vertex as shown (each end
of the cut-line should be the same distance from the vertex).
(MP.1)
ASK: What shape will the hole be when I unfold the paper? Unfold once
and let students adjust their predictions. Then unfold completely to check
their predictions. Ask students to predict how they could produce holes
of different shapes (e.g., rhombus, circle, rectangle, square). Let them
experiment with paper and scissors.
Bonus
How would you cut the folded paper to create a star-shaped hole?
Bonus
Making snowflakes. Fold a sheet of paper three times (into eight parts).
Cut out some small pieces from the sides. For each piece you cut out,
predict the shape of the hole it produces. Unfold in stages and check your
predictions. How does the way you fold the sheet of paper affect the number
of lines of symmetry of your snowflake?
H-26
Teacher’s Guide for AP Book 4.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
cut
ACTIVITY 1
Give pairs a sheet of paper with a straight line drawn down the middle
(either vertically or horizontally) and a set of pattern blocks. Player 1
places a pattern block so that it touches the line. Player 2 places a
block on the other side of the line to make the design symmetrical. Then
Player 2 places a second block on his or her side of the page such that
the two blocks have a common side. Now Player 1 must add a block
to his or her side of the page to maintain the symmetry and then add
another block.
Players continue placing pairs of pattern blocks in turn. At the end,
ask students how they could check whether the design is symmetrical
(sample answer: using a Mira). Example (three turns were taken):
3
2
1
2 1
3
Have pairs display their designs and describe them to classmates,
naming the shapes used and explaining how they know the design is
symmetrical. Ask students to consider whether any of the designs have
more than one line of symmetry.
Students who need extra help can complete BLM Lines of Symmetry.
Remind students that a line of symmetry can also be found by folding.
Take a large paper shape with several lines of symmetry (such as a regular
pentagon or hexagon) and fold it to find any lines of symmetry. Students
can use paper shapes from BLM Paper Quadrilaterals to complete
Question 1 on AP Book 4.1 p. 177).
ACTIVITIES 2–5
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
2.Using each pattern block shape at least once, create a figure
that has at least one line of symmetry. Choose one line of
symmetry and explain why it is a line of symmetry. Draw
your shape in your notebook.
3.Using exactly four pattern blocks, build as many shapes as you
can that have at least one line of symmetry. Draw your shapes
in your notebook.
4.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.
5.
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.
Geometry 4-10
H-27
Extensions
1.
The figure shown has four lines of symmetry.
a)Show how you could move one square so the resulting figure has
no lines of symmetry.
b)Show two different ways to move a square so the resulting
figure has one line of symmetry. You are allowed to move the
center square.
(MP.1, MP.3)
2.Make a shape on a geoboard (or on grid paper) with the given number of lines of symmetry:
a)
b)
c)
d)
a quadrilateral with 1 line of symmetry
a quadrilateral with 4 lines of symmetry
a triangle with 1 line of symmetry
a triangle with 3 lines of symmetry
Bonus: Is it possible to make…
e) a triangle with exactly 2 lines of symmetry?
f) a quadrilateral with exactly 3 lines of symmetry?
3.Draw a shape that has a horizontal and vertical line of symmetry,
but no diagonal line of symmetry.
4. How many lines of symmetry does an oval have?
reflection
5.Sudha drew a mirror line on a square. Then she drew and shaded the
reflection of the corner of the square in the mirror line.
a)Try Sudha’s method. Draw a large square on grid paper. Draw a
mirror line on the square and reflect part of the square in the line.
(MP.1)
b)Repeat part a) but move the mirror line. Can you place the mirror
line so that the two parts of the square on either side of the mirror
line make:
ii) a hexagon
iii ) an octagon
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
i) a rectangle
H-28
Teacher’s Guide for AP Book 4.1
G4-11 Comparing Shapes
Page 178
Goals
STANDARDS
4.G.A.2
Students will compare shapes according to a given pattern.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
names of polygons
Parallel sides
Right angles
Lines of symmetry
Distinguishing polygons
Shapes with all equal sides
Draw a regular hexagon on the board. Ask students if it has any right angles.
How many pairs of parallel sides does it have? Are all its sides equal? How
many lines of symmetry does it have? Have volunteers mark the parallel
sides and the lines of symmetry. Then draw a hexagon with two right angles
and display the comparison chart shown below. Ask volunteers to help you
fill in the chart.
Property
Number of vertices
Same? Different?
6
6
Number of edges
Number of pairs of
parallel sides
Number of right angles
Any lines of symmetry?
Number of lines of symmetry
Are all sides equal?
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Are some sides equal?
Point out that the hexagon with the right angles has two groups of equal
sides: the horizontal sides are equal and the other four sides are equal,
but the four equal sides are shorter than the horizontal sides.
Have students compare the two shapes shown at left. Ask them
to mention the following properties:
Geometry 4-11
The number of vertices
The number of sides
The number of pairs of parallel sides
The number of right angles
The number of lines of symmetry, if any
Whether all or some sides are equal
H-29
G4-12 Sorting and Classifying Shapes
G4-13 Problems and Puzzles
Pages 179–182
Goals
STANDARDS
4.G.A.2
Students will sort and compare shapes systematically.
PRIOR KNOWLEDGE REQUIRED
Vocabulary
names of polygons
Parallel sides
Right angles
Lines of symmetry
Equal sides
Distinguishing polygons
MATERIALS
cards from BLM 2-D Shape Sorting Game (p. H-44–H-45)
BLM Polygons to Sort (p. H-46)
BLM Always, Sometimes, Never (Shapes) (p. H-47)
Give each student (or team of students) a deck of shape cards and a deck
of property cards from BLM 2-D Shape Sorting Game. The game in Activity 1
below is important preparation for sorting shapes with Venn diagrams.
ACTIVITY 1
Answer:
ADFG
C
B
E
Draw a Venn diagram on the board. Complete Question 1 on AP Book
p.179 as a class, using volunteers. In the process, remind students that
any letters that cannot be placed in either circle should be written outside
the circles (but inside the box). Also remind students that figures that share
both properties, in this case B and H, should be placed in the overlap.
Note that shape A is not a polygon, so it cannot be placed in the circles.
(See Lesson G4-3: Sides and Vertices of 2-D Shapes).
H
ACTIVITY 2
Quadrilateral
H-30
At least
2 right angles
2-D Venn Diagram Game
Have students create a Venn diagram on a sheet of construction paper
or bristol board. 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 diagram.
Teacher’s Guide for AP Book 4.1
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
2-D Shape Sorting Game
Each student flips over a property card and then sorts their shape
cards onto two piles according to whether the shape on each card has
the property or not. (If you prefer, you could choose a property for the
whole class and have everyone sort their shapes using that property.)
Exercises: Display the following set of shapes and give students a copy of
the shapes to work with (see BLM Polygons to Sort). For questions a) to d)
below, ask students to determine which shapes satisfy each property and
then draw a Venn diagram to sort the shapes.
H
B
F
J
A
G
D
C
E
I
a)1. At least two right angles
2. All sides equal
b)1. All sides equal
2.Has exactly one line of symmetry
(In this case the overlapping part contains only one
irregular pentagon—shape J)
c)1. More than one pair of parallel sides
2. At least one pair of perpendicular sides
d)1. Pentagon
2. At least two right angles
Bonus
1. Exactly one line of symmetry
2. At least two right angles
COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION
Comparing shapes. Draw the two shapes at left on the board. You could
tell students that young wizards in a wizard school learn to transform
figures. However, they have to be able to give a complete description of
a figure before and after the transformation. Have volunteers describe
each figure completely. Do not ask “How many vertices does the shape
have?”, but rather let students recall the properties themselves. Students’
descriptions should mention:
• Number of sides
• Number of right angles
• Number of vertices
• Number of lines of symmetry
• Number of pairs of parallel sides • Are all sides of the shape equal?
After that ask students to write the comparison of the shapes.
Bonus
Write a “magic transformation formula”: all the changes that will turn one
shape into the other. (Change the number of vertices from 4 to 5, etc.)
Students who need extra help can solve this problem instead:
Name all properties the figures at left have in common.
Then describe any differences.
Geometry 4-12, 4-13
H-31
(MP.3)
Have students complete BLM Always, Sometimes, Never True
(Shapes). Doing so will help students sharpen their understanding
of 2-dimensional shapes.
Use pp. 181–182 of AP Book 4.1 to review the Geometry unit.
(MP.1)
More Review Questions
a)I have five sides and one line of symmetry. Two of my angles are
right angles. Draw me.
b)I have five sides and one line of symmetry. Three of my angles are
right angles. Draw me.
c)I have four sides and no lines of symmetry. I do not have right angles.
Draw me.
d)I have four sides and two lines of symmetry that go through the
vertices. I do not have right angles. Draw me. What is my name?
e)I am a quadrilateral with four lines of symmetry. What am I?
Sample answers
a)b)or
c)
d)
e)
or
square
rhombus
(MP.6)
H-32
Player 1 draws a shape without showing it to Player 2, then describes it in
terms of the number of sides, vertices, parallel sides, right angles, lines of
symmetry, etc. Player 2 has to draw the shape based on Player 1’s description.
Teacher’s Guide for AP Book 4.1
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Extension