Quadrangles - Everyday Math

Quadrangles
Objective To provide opportunities to explore various types
of quadrangles.
o
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Identify right angles and parallel and
intersecting sides of quadrangles. [Geometry Goal 1]
• Draw and name quadrangles. [Geometry Goal 2]
• Use straws and twist-ties to model and
compare quadrangles. [Geometry Goal 2]
• Identify the sides, vertices, and adjacent
sides of quadrangles. [Geometry Goal 2]
• Measure the sides of a quadrangle. [Measurement and Reference Frames Goal 2]
Key Activities
Children construct quadrangles and observe
their properties. They measure the sides of
a quadrangle to the nearest _12 inch and
estimate the perimeter.
Ongoing Assessment:
Recognizing Student Achievement
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Name That Number
Student Reference Book, pp. 299
and 300
per partnership: 4 each of number
cards 0–10 and 1 each of number
cards 11–20 (from the Everything Math
Deck, if available)
Children practice finding equivalent
names for numbers.
Math Boxes 6 5
Math Journal 1, p. 137
Children practice and maintain skills
through Math Box problems.
Home Link 6 5
Math Masters, p. 177
Children practice and maintain skills
through Home Link activities.
Use journal page 136. [Geometry Goal 1]
Ongoing Assessment:
Informing Instruction
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Playing Touch-and-Match Quadrangles
Math Masters, p. 467 (copied onto cardstock
or cardboard)
paper bag or box
Children identify similarities and differences
among quadrangles.
ENRICHMENT
Playing Shading Shapes
Math Masters, pp. 457 and 458
Children explore the properties of
quadrangles.
ELL SUPPORT
Adding to the Vocabulary Chart
Differentiation Handbook, p. 133 (optional);
2 copies per child
Vocabulary Chart (from Part 3, Lesson 6 1)
Children add the terms rectangle,
rhombus, square, trapezoid, and kite to
the Vocabulary Chart.
See pages 428 and 429.
Key Vocabulary
quadrangle square rhombus parallelogram
sides kite
rectangle trapezoid adjacent
Materials
Math Journal 1, p. 136
Student Reference Book, pp. 108 and 109
Home Link 64
Differentiation Handbook, p. 139 (optional)
straws and twist-ties straightedge ruler
Advance Preparation
Each child will need 16 twist-ties and 16 straws—4 straws each of the following four lengths: 2", 4", 6", and 8". Place these materials in
4 separate containers near the Math Message. For the optional Readiness activity in Part 3, make 2 copies of Math Masters, page 467
on cardstock paper. Cut out the shapes and place one set in a paper bag.
Teacher’s Reference Manual, Grades 1–3 pp. 136–138
426
Unit 6
Geometry
426_EMCS_T_TLG1_G3_U06_L05_576809.indd 426
2/23/11 11:45 AM
Getting Started
Mental Math and Reflexes
Math Message
Have children stand facing you to perform turn
calisthenics.
Take 4 straws of each size and 16 twist-ties.
Complete Part 1 on page 136 of your journal.
Make a half-turn clockwise. Make a half-turn
counterclockwise. Ask: What do you notice? Children
are back in the starting position.
Make a three-quarter turn counterclockwise. Make a half-turn
counterclockwise. Make a quarter-turn clockwise. Ask: What
do you notice? Children are back in the starting position.
Have girls make a three-quarter turn clockwise and boys
make a quarter-turn counterclockwise. Ask: What do you
notice? Girls and boys are facing in the same direction.
Home Link 6 4 Follow-Up
Ask partners to explain how they found the right
angle in Problem 4.
1 Teaching the Lesson
Math Message Follow-Up
E
WHOLE-CLASS
DISCUSSION
(Math Journal 1, p. 136)
Discuss Part 1 on journal page 136.
Draw and label a quadrangle on the board. Label it EFGH.
Point out that another name for quadrangle is quadrilateral.
Referring to the diagram on the board, review the characteristics
of quadrangles.
H
G
Quadrangle EFGH
All quadrangles are 2-dimensional.
All quadrangles have 4 vertices.
Student Page
All quadrangles have 4 sides.
Date
All quadrangles have 4 angles.
Time
LESSON
Exploring Quadrangles
6 5
䉬
夹
Part 1
Adjusting the Activity
ELL
B
Use a straightedge. Connect points to form
a quadrangle.
A
Part 2
Remind children that the meaning of the prefix quad- is four. Ask for
other words that use the prefix. Quadruplets, quadruple, quadrupled, quadrant,
and quadrilateral (as another name for quadrangle) Draw or show pictures of a
few of the objects children might suggest that have the prefix quad.
Write all 4-letter names that are possible
for your quadrangle. The first letter of each
name is given below.
A
C
BCD
BAD
A
C
DCB
DAB
B
D
CDA
ABC
B
D
D
C
ADC
CBA
Part 3
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
Ongoing Assessment:
Recognizing Student Achievement
V I S U A L
Journal
page 136
Part 1
Work in a group.
Make quadrangles with straws and twist-ties. Make at least one of
each of the following kinds of quadrangles.
䉬 all 4 sides equal in length
䉬 2 pairs of equal-length sides, but opposite sides not equal in length
䉬 2 pairs of equal-length opposite sides
䉬 only 2 parallel opposite sides
䉬 only 1 pair of equal-length opposite sides
Part 4
Measure each side of the quadrangle you drew in Part 1 to the nearest
1
ᎏᎏ centimeter.
2
Use journal page 136, part 1 to assess children’s progress toward identifying
points and drawing line segments to form a quadrangle. Children are making
adequate progress if they are able to successfully complete Part 1. Some
children may be able to identify the vertices of the quadrangle.
side AB
5ᎏ12ᎏ
cm side BC
4
cm side CD
6ᎏ12ᎏ
cm side DA
2
cm
Try This
The perimeter of my quadrangle is about
18
centimeters.
[Geometry Goal 1]
Math Journal 1, p. 136
Lesson 6 5
EM3cuG3TLG1_427-431_U06L05.indd 427
427
1/22/11 1:32 PM
Student Page
Geometry
Naming Quadrangles
Quadrangles
A quadrangle is a polygon that has
4 sides. Another name for quadrangle
is quadrilateral. The prefix “quad-”
means four. All quadrangles have 4 sides,
4 vertices, and 4 angles.
WHOLE-CLASS
DISCUSSION
(Math Journal 1, p. 136)
A quadricycle is a vehicle
similar to the bicycle and
tricycle but having 4 wheels.
Name the parts of the quadrangle.
The sides are RS, ST, TU, and UR.
The vertices are R, S, T, and U.
The angles are  R,  S, T, and U.
Some quadrangles have 2 pairs of parallel sides.
These quadrangles are called parallelograms.
Explain that the name of a quadrangle can begin with the letter at
any vertex and can be read either clockwise or counterclockwise.
Vertices must be named consecutively. For example, the
quadrangle on the board can be named HEFG, EFGH, FGHE, and
so on—but not HFGE.
Have children complete Part 2 on journal page 136.
Two sides are parallel if they are parts
of lines that are parallel (never cross).
Figures That Are Parallelograms
Ongoing Assessment: Informing Instruction
Opposite sides are parallel in each figure.
Figures That Are NOT Parallelograms
no parallel sides
only 1 pair of parallel sides
3 pairs of parallel sides,
but a parallelogram
must have 4 sides
Watch for children who have difficulty naming the quadrangle. Emphasize the
importance of naming the vertices in order. Suggest that children trace the
quadrangle with their fingers in order to determine the correct sequences.
Student Reference Book, p. 108
Constructing Quadrangles
(Math Journal 1, p. 136; Student Reference Book,
pp. 108 and 109)
NOTE Unlike triangles, quadrangles are not
rigid. Their shapes and areas may easily be
changed. But for any given quadrangle, the
perimeter does not change and, for any given
parallelogram, opposite sides remain parallel
in spite of the changes to their inner angles.
Student Page
Geometry
Some quadrangles have special names.
Some of them are parallelograms.
Others are not parallelograms.
Quadrangles That Are Parallelograms
Rectangles are parallelograms.
They have 4 right angles (square corners).
The sides of a rectangle do not all have to be
the same length.
Rhombuses are parallelograms.
Their 4 sides are all the same length.
Squares are parallelograms.
They have 4 right angles (square corners).
Their 4 sides are all the same length.
All squares are rectangles.
All squares are rhombuses.
Quadrangles That Are NOT Parallelograms
Trapezoids have exactly 1 pair of parallel sides.
Their 4 sides can all be different lengths.
Kites are 4-sided polygons with 2 pairs of equal sides.
The equal sides are next to each other.
Their 4 sides cannot all be the same length.
A rhombus is not a kite because all 4 sides of the
rhombus are the same length.
others Any polygon with 4 sides that is not a
parallelogram, a trapezoid, or a kite
SMALL-GROUP
ACTIVITY
ELL
PROBLEM
PRO
P
R
RO
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
IIN
NG
Children construct the quadrangles listed in Part 3 on journal
page 136. Have children make their constructions on flat surfaces
and keep them (approximately) in a plane as they pick them up to
show them.
When most of the groups have completed their constructions,
bring them together to share observations about quadrangles.
Children hold up quadrangles in each category as you and the
class discuss their properties. To support English language
learners as the geometric terms are introduced, write the terms
on the board next to a picture or a straw model. Suggestions for
discussion:
Ask one person in each group to hold up any quadrangle with
four sides of equal length and four right angles. Ask: How are
all these quadrangles alike? They are all squares; their angles
are all right angles. How are they different? They are not all the
same size.
Have children tug gently on two corners opposite each other.
Ask: What happens when you do this? The shape and area
change; the angles are not right angles, but the opposite sides
are still parallel. Does the perimeter change? No What is the
name of this shape? rhombus
Have children make one angle a right angle. Ask: What
happens when you do this? All angles become right angles.
What is the name of this kind of shape? square
Note that squares and rhombuses are examples of
parallelograms.
Student Reference Book, p. 109
428
Unit 6 Geometry
EM3cuG3TLG1_427-431_U06L05.indd 428
1/20/11 8:43 AM
Ongoing Assessment: Informing Instruction
Watch for children who believe that squares are only squares and not rectangles
or rhombuses. You may wish to make an analogy to address this misconception.
For example, the girls in the classroom are students, daughters, citizens, and
neighbors; they may also be sisters, granddaughters, or nieces. Likewise, the
square also belongs to several groups.
K
Have children hold up quadrangles having two pairs of equal
sides. Kites and rectangles From those quadrangles, find the ones
that have right angles. Rectangles The quadrangles with two pairs
of equal sides and 4 right angles are called rectangles.
N
Have children hold up quadrangles having only two parallel
opposite sides. Trapezoids, which include those with one pair of
equal-length sides Those quadrangles are called trapezoids.
●
Can you make a trapezoid that has a right angle? Yes
●
Can you make a trapezoid with exactly one right angle? Try it.
No. If a trapezoid has one right angle, it must have a second
right angle as well because opposite sides must be parallel.
●
Can you make a trapezoid with four right angles? No. If a
trapezoid had four right angles, it would be a rectangle. There
would be two pairs of parallel sides instead of one.
Sides that meet at a vertex are called adjacent sides. Have
children hold up one of their quadrangles and trace its adjacent
sides with their fingers. To support English language learners,
write adjacent sides and draw some pictures illustrating adjacent
sides on the board. Ask children in each group to hold up all
quadrangles in which some or all adjacent sides are the same
length. Have them set aside all the quadrangles in which all sides
are the same length. Next, have them hold up any quadrangles in
which there are just two pairs of equal adjacent sides. Such
quadrangles are called kites. A kite is a quadrangle that has two
pairs of equal adjacent sides and opposite sides that are not equal.
To support English language learners, discuss the everyday
meaning of the word kite as well as its meaning in this context.
L
M
Kite
Adjusting
the Activity
ELL
Use a Venn diagram, Differentiation Handbook,
page 139, to organize information about
similarities and differences between
2 quadrangles.
AUDITORY
KINESTHETIC
of
ties e
l
per
Pro ctang
e
aR
4 square
corners
TACTILE
Properties of
a Square
4 equal sides
and
4 square
corners
VISUAL
Pro
p
a R erties
hom
of
bus
4 equal
sides
Finally, have children hold up straw constructions that do not have
four right angles or two pairs of parallel sides. Trapezoids and kites
Add one straw construction of each kind of quadrangle and its
description to the Polygon Museum. Children can read more about
quadrangles on pages 108 and 109 of the Student Reference Book.
Finding the Perimeter of
a Quadrangle
INDEPENDENT
ACTIVITY
PROBLEM
PRO
P
RO
R
OBL
BLE
B
L
LE
LEM
EM
SO
S
SOLVING
OL
O
LV
VIIIN
VIN
NG
(Math Journal 1, p. 136)
Children complete Part 4 on journal page 136.
Lesson 6 5
EM3cuG3TLG1_427-431_U06L05.indd 429
429
1/22/11 1:32 PM
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Math Boxes
65
1. The grid is ONE. Shade 0.41 of
2. Circle the pair of lines that are
the grid.
parallel.
Playing Name That Number
Write the fraction
that shows how
much is shaded.
41
_
100
0.41 =
SMALL-GROUP
ACTIVITY
(Student Reference Book, pp. 299 and 300)
34
99
Children play Name That Number. See pages 299 and 300 in the
Student Reference Book or Lesson 1-6 for directions. Encourage
children to use as many cards and operations as they can to name
the target number.
4. Draw a ray,
. Draw a line
_DO
3. Fill in the oval for the best answer.
.
segment, RE. Draw a line, MI
The turn of the angle is
1
less than a _
2 turn.
1
less than a _
4 turn.
1
greater than a _
turn.
2
a full turn.
D
O
R
M
E
I
6. Complete.
all equal in length.
⫻4
⫼2
6
24
12
48
192
48
96
24
any square or rhombus
square
This shape is a
or rhombus
Math Boxes 6 5
100
167 168
5. Draw a shape with 4 sides that are
(Math Journal 1, p. 137)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-7. The skill in Problem 6
previews Unit 7 content.
.
109
INDEPENDENT
ACTIVITY
200 201
Math Journal 1, p. 137
EM3MJ1_G3_U06_128-155.indd
137
2/10/10
1:18 PM
Home Link 6 5
INDEPENDENT
ACTIVITY
(Math Masters, p. 177)
Home Connection Children identify characteristics of
familiar quadrangles using the terms equal, parallel,
and right angles in their answers.
3 Differentiation Options
Home Link Master
Name
Date
HOME LINK
READINESS
Time
Playing Touch-and-Match
Quadrangles
65
Family
Note
108 109
Please return this Home Link to school tomorrow.
(Math Masters, p. 467)
equal
parallel right angles
1. Rectangle (Squares are special rectangles.)
All angles are
right angles
parallel
To provide experience with identifying similarities and differences
among quadrangles, make two copies of Math Masters, page 467 on
cardboard or cardstock paper. Cut out all of the quadrangles
and place one set in full view on a table. Without children seeing,
place one of the quadrangles from the other set in a bag or box. A
child reaches inside the container, feels the shape without looking,
and tries to find the matching shape from those on the table.
.
equal
Pairs of opposite sides are
length and
in
to each other.
2. Rhombus (Squares are also rhombuses.)
All sides are
equal
in length.
parallel
Opposite sides are
to each other.
3. Parallelogram (Squares and rhombuses are
also parallelograms.)
Opposite sides are
equal
Opposite sides are
parallel
in length.
Ask children to explain how they made their matches. Expect
responses like the following: “The shape I was holding had four
square corners, but I knew it was the square and not the rectangle
because all of the sides were the same length.”
to each other.
4. Kite
Opposite sides are not
equal
5–15 Min
Quadrangles
Help your child complete the statements. A right angle is a square corner. Parallel sides are
the same distance apart and will never meet. Opposite sides are directly across from each
other. Adjacent sides meet at a vertex (corner).
Fill in the blanks using the following terms:
SMALL-GROUP
ACTIVITY
in length.
Practice
Solve.
5. 6 × 3 =
18
6.
12
=3×4
7.
6×6=
36
Math Masters, p. 177
EM3MM_G3_U06_167-205.indd
430
177
2/10/10
1:18 PM
Unit 6 Geometry
EM3cuG3TLG1_427-431_U06L05.indd 430
1/20/11 8:43 AM
Game Master
ENRICHMENT
Playing Shading Shapes
PARTNER
ACTIVITY
Name
Time
Shading Shapes
Materials
□ gameboard and Shading Shapes Reference Page
(Math Masters, p. 458)
Object
To claim the most quadrangles
15–30 Min
(Math Masters, pp. 457 and 458)
Date
Directions
Players take turns.
To further explore properties of quadrangles, have children play
Shading Shapes. Directions are on Math Masters, page 457.
When children have finished, have them share their strategies.
SMALL-GROUP
ACTIVITY
ELL SUPPORT
Adding to the
1. Shade one small triangle on the gameboard.
2. Players shade triangles to make quadrangles they see on the reference page.
3. When a player shades the final triangle of a quadrangle from the reference
page, that player claims the quadrangle by tracing the shape with a finger
and saying the name of the quadrangle. When a player claims a quadrangle,
he or she scores a point and that quadrangle is no longer available to claim.
4. Finished quadrangles may overlap each other (the same small triangle may
be colored twice), but no one can shade exactly the same quadrangle once
it has been claimed.
5. The game ends when time runs out or when the gameboard is completely
shaded. The winner is the player with the most points.
5–15 Min
Vocabulary Chart
(Differentiation Handbook, p. 133)
To provide language support for geometry terms, have children
add the terms rectangle, rhombus, square, trapezoid, and kite to the
Vocabulary Chart. Children may also add the terms to their Math
Word Banks using the template on Differentiation Handbook,
page 133. See the Differentiation Handbook for more information.
457
Math Masters, p. 457
EM3MM_G3_U06_167-205.indd
457
2/10/10
2:25 PM
Quadrangles (Quadrilaterals)
parallelogram
2 pairs of
parallel sides
rectangle
2 pairs of equal
sides;
4 right angles
rhombus
4 equal sides;
opposite sides
parallel
square
4 equal sides;
4 right angles
trapezoid
only 2 sides
parallel;
parallel sides
not equal
kite
Game Master
Name
Date
Time
Shading Shapes Reference Page
Shade triangles on the gameboard to make the following quadrangles:
2 pairs of
adjacent equal
sides;
opposite sides
not equal
Rectangle
Square
Parallelogram
Trapezoid
py g
g
p
Trapezoid
Math Masters, p. 458
EM3MM_G3_U06_167-205.indd
458
2/10/10
Lesson 6 5
EM3cuG3TLG1_427-431_U06L05.indd 431
2:25 PM
431
1/22/11 1:32 PM