9
Chapter
School-Home
Letter
plane shape A shape on a flat
surface that is formed by curves, line
segments, or both.
Dear Family,
During the next few weeks, our math class will be
learning about plane shapes. We will learn to identify
and describe polygons by the number and type of
sides, vertices, and angles.
polygon A closed plane shape made
up of straight line segments. Each
line segment on a polygon is a side.
You can expect to see homework that provides
practice with polygons such as triangles and
quadrilaterals.
Here is a sample of how your child will be taught to
identify polygons.
Identify a Polygon
This is how we will be identifying whether or not a plane shape is a polygon.
Which shape is a polygon?
A
B
C
Tips
STEP 1
STEP 2
STEP 3
Look for a closed
shape.
Look for a shape
with no curves.
Look at shape C.
Look at shape A.
Look at shape B.
Shape A is not a
closed shape.
Shape B has straight
line segments. But it
also has curves.
Shape A is not a
polygon.
Shape C is a closed
shape. All the sides
are straight line
segments.
Shape C is a polygon.
Describing Polygons by
the Number of Sides
A quadrilateral is a
polygon with 4 sides. Some
examples of quadrilaterals
are square, rectangle,
trapezoid, rhombus, and
parallelogram.
© Houghton Mifflin Harcourt
Shape B is not a
polygon.
Activity
Draw shapes and ask your child to explain whether or not a shape is a
polygon. Draw open shapes (square with a missing side, the letter W) as
well as closed shapes (circle, triangle, pentagon, heart).
Chapter 9
P207
9
Carta
Capítulo
figura plana Una figura en una superficie
plana que está formada por curvas,
segmentos o ambos.
para la casa
polígono Una figura plana cerrada
formada por segmentos rectos. Cada
segmento en un polígono es un lado.
Querida familia:
Durante las próximas semanas, en la clase de
matemáticas estudiaremos las figuras planas.
Aprenderemos a identificar y describir polígonos según
la cantidad y el tipo de lados, vértices y ángulos que
tengan.
Llevaré a la casa tareas con actividades polígonos con,
como triángulos y cuadriláteros.
Este es un ejemplo de la manera como aprenderemos a
identificar polígonos.
Identificar un polígono
Así es como podremos saber si una figura plana es un polígono.
A
B
C
¿Qué figura es un polígono?
PASO 1
PASO 2
PASO 3
Busca un figura
cerrada.
Busca la figura que
no tenga curvas.
Observa la figura C.
Observa la figura A.
Observa la figura B.
La figura A no es
una figura cerrada.
La figura B tiene
segmentos rectos.
Pero también tiene
curvas.
La figura A no es un
polígono.
La figura C es una
figura cerrada.
Todos los lados son
segmentos rectos.
La figura C es un
polígono.
Pistas
Describir polígonos según la
cantidad de lados
Un cuadrilátero es un
polígono con 4 lados. Algunos
ejemplos de cuadriláteros son
el cuadrado, el rectángulo,
el trapecio, el rombo y el
paralelogramo.
Actividad
Dibuje varias figuras y pida a su hijo que explique si cada figura es o no un
polígono. Dibuje figuras abiertas (un cuadrado sin un lado, la letra W) y figuras
cerradas (un círculo, un triángulo, un pentágono, un corazón).
P208
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La figura B no es un
polígono.
Lesson 1
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Describe Plane Shapes
Write whether each is a point, line,
line segment, or ray.
1.
2.
point
___
3.
___
4.
___
___
5.
6.
___
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7. Carl wants to show a rectangle in his
___
8. The shape of the pool in Ella’s
drawing. What does he have to do
to the drawing below to make the
rectangle a closed shape?
backyard is shown below. Is the
shape open or closed?
______
______
Chapter 9
P209
Lesson Check (MA.3.G.3.1)
1. How many line segments does this
shape have?
2. Which of the following is part
of a line, has one endpoint, and
continues in one direction?
F ray
G line
A
2
C
4
H line segment
B
3
D
5
I point
Review Grade 3 (MA.3.A.1.1, MA.3.A.1.2)
3. Which multiplication expression
does the array show?
4. Find the missing factor and
quotient.
93
5 27
27 4 9 5
A
338
C
835
B
438
D
439
3
G
4
H
5
I
6
(MA.2.G.5.2)
5. What time does the clock show?
6. What time does the clock
show?
12:30
A
3:00
C
5:00
F
one thirty
H
eleven thirty
B
4:00
D
6:00
G
two thirty
I
twelve thirty
P210
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Look Back
F
Lesson 2
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Identify Polygons
A polygon is a closed shape
made up of line segments.
Each line segment of a polygon is a side.
Is the shape a polygon? Write yes or no.
1.
2.
no
__
3.
__
4.
__
__
Write the number of sides.
5.
6.
__
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7. Ava is drawing a shape. It has eight
__
8. Tim wants to make a polygon. He
straight sides and one curve. Is
Ava’s shape a polygon? Explain.
draws six straight line segments.
Each line segment connects to two
other line segments. Is Tim’s shape
a polygon? Explain.
______
______
______
______
Chapter 9
P211
Lesson Check (MA.3.G.3.1)
1. Which shape is a polygon?
A
C
B
D
2. The polygon below has how
many sides?
F
4
H
6
G
5
I
7
Review Grade 3 (MA.3.A.6.1, MA.3.A.2.3)
3. Subtract.
11,498
2 3,389
4. Compare.
7
__
8
1
__
4
A
7,099
F .
B
7,776
G ,
C
8,109
H 5
D
9,415
I 1
(MA.2.G.5.4)
5. Fernando is drinking a sports
drink. How much liquid is he
likely drinking?
6. Kyle has a pet kitten. How much is
it likely to weigh?
A
1 milliliter
F
2 ounces
B
10 milliliters
G
20 ounces
C
1 liter
H
10 pounds
D
10 liters
I
200 pounds
P212
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Lesson 3
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Classify Polygons
side
Polygons are named by the number of
sides and the number of vertices.
vertex
Name the polygon. Write the number of sides and the
number of vertices.
1.
2.
pentagon
________________________
________________________
5 sides
5 vertices
_
_
3.
sides
_
vertices
4.
________________________
________________________
_
sides
_
sides
_
vertices
_
vertices
5. Mr. Murphy has an old coin that has
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_
6. Lin says that a hexagon has six
ten sides. If its shape is a regular
polygon, how many vertices does
the old coin have?
sides. Chris says that it has eight
sides. Whose statement is correct?
________________________
________________________
Chapter 9
P213
Lesson Check (MA.3.G.3.1)
1. What is the name for this polygon?
2. How many sides does the polygon
below have?
A hexagon
F
4
B octagon
G
5
C quadrilateral
H
6
D pentagon
I
7
Review Grade 3 (MA.3.A.1.2, MA.3.A.6.1)
3. Find the quotient.
81 4 9
4. Add.
11,359
1 4,670
A
7
F
21,290
B
8
G
16,029
C
9
H
15,009
D
10
I
9,890
(MA.2.G.5.3)
5. Chelsea has 3 quarters and 1 dime.
James has 8 dimes. Peter has 2
quarters and 6 nickels. Denika has 10
nickels. Who has the most money?
6. How many nickels are in one
dollar?
A Chelsea
F
100
B James
G
80
C Peter
H
50
D Denika
I
20
P214
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Look Back
Lesson 4
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Types of Angles
A right angle forms An acute angle is
a square corner.
less than a right
angle.
An obtuse angle is
greater than a right
angle but less than
a straight angle.
In a straight angle,
two rays point in
opposite directions
and form a line.
Write how many of each type of angle the polygon has.
1.
2.
3.
_
right
_
right
_
right
_
acute
_
acute
_
acute
_
obtuse
_
obtuse
_
obtuse
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4. Jeff has a square piece of art paper.
5. Kaylee tells Aimee that a stop sign
He cuts it from one corner to the
opposite corner to make two pieces.
How many sides and angles are
there in all for the two new shapes?
has at least one right angle. Aimee
says that none of the angles are
right angles. Who is correct?
__________________________
________________________
Chapter 9
P215
Lesson Check (MA.3.G.3.1)
1. What is the name for this angle?
2. How many right angles does the
shape below have?
A right
F
1
B acute
G
2
C obtuse
H
3
D scalene
I
4
Review Grade 3 (MA.3.A.1.2, MA.3.A.6.1)
3. Find the product.
4. Which number is less than 207,043
(2 3 4) 3 3
but greater than 198,562?
F
189,674
A
12
G
207,403
B
17
H
207,019
C
20
I
198,395
D
24
(MA.2.A.4.3)
5. What is the 8th number in
6. What number is missing in
the table?
the pattern?
1
2
3
4
5
1
2
3
12
16
20
24
28
33
30
27
A
32
F
24
B
40
G
23
C
44
H
21
D
50
I
17
P216
4
5
6
21
18
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Look Back
Lesson 5
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Describe Sides of Polygons
Lines that cross or meet
are intersecting lines.
Intersecting lines form
angles.
Intersecting lines
that cross or meet to
form right angles are
perpendicular lines.
Lines that appear never
to cross or meet and are
always the same distance
apart are parallel lines.
They do not form any
angles.
Look at the dashed sides of the polygon. Tell if they
appear to be intersecting, perpendicular, or parallel.
2.
1.
parallel
____
____
4.
3.
6.
5.
____
____
7. Tamara is thinking of a shape. It has
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____
2 pairs of parallel lines and 4 right
angles. All the sides are the same
length. Which shape is Tamara
thinking about?
____
8. Niko is thinking of a shape with
three straight sides that intersect.
None of the sides are equal. Draw
Niko’s shape.
____
Chapter 9
P217
Lesson Check (MA.3.G.3.1)
1. How many pairs of parallel lines are
2. Which sides are parallel?
in the quadrilateral?
b
c
a
d
A
1
F a and c only
B
2
G b and d only
C
3
H a and b, c and d
D
4
I a and c, b and d
Review Grade 3 (MA.3.A.2.3, MA.3.A.1.1)
3. Compare.
1
3
__
__
4
4
4. George has three pairs of pants
and four shirts. How many
combinations can he make of
1 shirt and 1 pair of pants?
A .
F
7
B ,
G
12
C 5
H
18
D 3
I
20
(MA.2.A.6.1)
5. Joe earns $5 a day for 3 days. How
can you show how much money he
earned?
6. Denise works for 4 days at the local
hot dog stand. She earns $4 each
day. How can you show how much
money she earned?
A
5 1 5 1 5 5 15
F
4 1 4 1 4 1 4 5 16
B
5 1 5 1 4 5 14
G
6 1 6 1 6 5 18
C
3131359
H
41458
D
3 1 3 1 5 5 11
I
12 1 12 5 24
P218
© Houghton Mifflin Harcourt
Look Back
Lesson 6
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Classify Triangles
Triangles can be named by the number of
equal sides and by their angles.
equilateral triangle
3 equal sides
3 cm
right triangle
1 right angle
3 cm
3 cm
isosceles triangle
2 equal sides
obtuse triangle
1 obtuse angle
3 cm
2 cm
3 cm
scalene triangle
0 equal sides
3 cm
acute triangle
3 acute angle
4 cm
2 cm
Name the triangle. Write right, obtuse, or acute.
9 cm
1.
6 cm
2 cm
2.
5 cm
____
3 cm
3.
4 cm
3 cm
3 cm
____
Name the triangle by the lengths of its sides. Write
equilateral, isosceles, or scalene.
4. 6 inches, 8 inches,
5. 11 inches, 10 inches,
10 inches
11 inches
____
____
7. Chris is making a painting with only
© Houghton Mifflin Harcourt
5 cm
triangles. He wants each side of
the triangles to be the same length.
What kind of triangle will he paint?
____
6. 7 inches, 7 inches,
7 inches
____
8. Jaime says that a right triangle can
be an equilateral triangle. Is she
correct?
Chapter 9
P219
Lesson Check (MA.3.G.3.1)
1. Name the triangle by the number of
2. Name the triangle by its angles.
equal sides.
5 inches
4 inches
2 inches
A scalene
F scalene
B isosceles
G obtuse
C equilateral
H right
D acute
I acute
Review Grade 3 (MA.3.A.2.1)
1
3. Four blocks are __ of a group. How
5
many are in the whole group?
18
B
20
C
24
D
36
Look Back
has been shaded?
__
F 1
3
2
G __
3
2
3
__
I
3
(MA.2.G.5.4)
5. Which unit would you use to
measure the weight of a hairbrush?
6. Jeremiah made a pitcher of iced
tea. Which is most likely the
capacity of the pitcher?
A gallon
F
1 cup
B ounce
G
2 cups
C cup
H
1 quart
D quart
I
4 gallons
P220
__
H 1
© Houghton Mifflin Harcourt
A
4. Which fraction of the rectangles
Lesson 7
Name
MA.3.G.3.1 Describe, analyze, compare and
classify two-dimensional shapes using sides
and angles—including acute, obtuse, and
right angles—and connect these ideas to the
definition of shapes.
Classify Quadrilaterals
Quadrilaterals are named by their sides
and by their angles.
Circle every name that describes the quadrilateral.
1.
3.
2.
parallelogram
parallelogram
square
rectangle
rectangle
rectangle
rhombus
rhombus
rhombus
trapezoid
trapezoid
trapezoid
Use the quadrilaterals below for 4–5.
B
A
D
4. Which quadrilaterals
C
have only 1 pair of
parallel sides?
E
___
© Houghton Mifflin Harcourt
6. A board on the wall in Jeremy’s
class has 4 right angles, 4 equal
sides, and 2 pairs of parallel sides.
Which quadrilateral is it?
____
5. Which quadrilaterals
have 4 right angles?
___
7. Sofia has a plate that has 4 equal
sides, 2 pairs of parallel sides, and
no right angles. Which quadrilateral
is it?
____
Chapter 9
P221
Lesson Check (MA.3.G.3.1)
1. Which name describes the
quadrilateral?
2. Which quadrilaterals have 2 pairs of
parallel sides?
A
B
C
A square
F A and B
B trapezoid
G A, B, and C
C rhombus
H A
D rectangle
I B
Review Grade 3 (MA.3.A.2.1, MA.3.A.1.2)
3. What mixed number is modeled
below?
6
48
__
21
C
__
12
4
2
D 1 __
6
2
6
B 1 __
4
Look Back
F
8
G
9
H
10
I
11
(MA.2.A.4.1)
5. There are 3 books on 1 shelf. How
many books are on 6 shelves?
6. There are 4 fish in 1 tank. How
many fish are in 7 tanks?
1
2
3
4
1
2
3
4
3
6
9
12
4
8
12
16
A
11
F
15
B
15
G
18
C
18
H
22
D
30
I
28
P222
© Houghton Mifflin Harcourt
A
4. Divide.
PROBLEM SOLVING
Name
Search for Patterns • Plane Shapes
Lesson 8
MA.3.A.6.2 Solve non-routine problems by
making a table, chart, or list and searching
for patterns.
Solve.
1. Josh is making the following pattern. How many
blocks will he need to make the eighth tower?
1
2
3
4
____
2. Emma is making a pattern. What is the fourteenth
shape in the pattern?
____
3. Christina is making a pattern using arrays. She has
75 tiles. Does she have enough tiles to make the
next part of the pattern? How many tiles will be in
the next array?
____
4. In a flower box there are nine red flowers and
six white flowers. There are three times as many
yellow flowers as white ones. How many flowers
are there in all?
© Houghton Mifflin Harcourt
____
5. What is a rule for the pattern?
1
2
4
8
16
____
Chapter 9
P223
Lesson Check
(MA.3.A.6.2)
1. Valeria notices a pattern on her
kitchen floor. What is the next tile
in the pattern?
2. What is the next shape in
the pattern?
A
C
F
H
B
D
G
I
Review Grade 3 (MA.3.A.6.1)
3. Divide.
4. Find the product.
8
35
3
27
A
6
F
32
B
7
G
35
C
8
H
40
D
9
I
45
Look Back
(MA.2.G.5.4)
5. How much money is shown below?
6. Jan has 2 quarters and
4 pennies. Teddy has 3 dimes
and 2 pennies. Patrick has
1 quarter and 4 nickels. Maria has
5 dimes, 1 nickel, and 2 pennies.
A
$0.23
C
$0.32
F Jan
H Patrick
B
$0.29
D
$0.41
G Teddy
I Maria
P224
© Houghton Mifflin Harcourt
Who has the most money?
MA.3.G.3.1, MA.3.A.6.2
Name
Chapter 9 Extra Practice
Lesson 9.1 (pp. 377–380)
Write whether each is a point, line, line segment, or ray.
1.
2.
3.
4.
Write whether the shape is open or closed.
5.
7.
6.
8.
Lesson 9.2 (pp. 381–384)
Is the shape a polygon? Write yes or no.
1.
2.
3.
5.
6.
Write the number of sides.
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4.
Chapter 9
P225
Lesson 9.3 (pp. 385–388)
Name the polygon. Write the number of sides
and the number of vertices.
1.
2.
__________________________
__________________________
______________ sides
______________ sides
______________ vertices
______________ vertices
3.
4.
__________________________
__________________________
______________ sides
______________ sides
______________ vertices
______________ vertices
Lesson 9.4 (pp. 389–392)
Use the corner of a sheet of paper to tell if the angle
is right, acute, or obtuse.
2.
__________________
P226
3.
__________________
__________________
© Houghton Mifflin Harcourt
1.
Lesson 9.5 (pp. 393–396)
Look at the dashed sides in the polygon. Tell if they
appear to be intersecting, perpendicular, or parallel.
1.
2.
3.
Lesson 9.6 (pp. 399–402)
Name the triangle. Write equilateral, isosceles, or
scalene.
1.
4 in.
2.
6 in.
4 in.
3.
10 in.
16 in.
10 in.
18 in.
4 in.
10 in.
4.
5.
11 in.
6.
4 in.
11 in.
17 in.
4 in.
.
13in
2 in.
4 in.
1 in.
Name the triangle. Write right, obtuse, or acute.
7.
8.
© Houghton Mifflin Harcourt
8 in.
6 in.
7 in.
16 in.
10 in.
12 in.
9.
7 in.
8 in.
7 in.
Chapter 9
P227
Lesson 9.7 (pp. 403–406)
Circle every name that describes the quadrilateral.
1.
2.
3.
square
square
trapezoid
p
parallelogram
rhombus
rectangle
trapezoid
trapezoid
rhombus
rectangle
parallelogram
parallelogram
Lesson 9.8 (pp. 407–410)
Solve
1. Roy is making an apple design with
28 stencils. The bottom 3 rows are
shown at the right. How many more
rows will Roy need to put on top to
complete the pattern?
2. Marti is stringing pumpkin and leaf cutouts
in a pattern to make a fall garland. So far her
garland looks like this:
What is a rule for the pattern?
P228
© Houghton Mifflin Harcourt
To continue the pattern, how many pumpkins
and leaves should she string to make the next
group?