10


   

  acute triangle A triangle with three
acute angles

line segment A part of a line that

includes two points, called endpoints,
Dear Family, and all the points between them

obtuse triangle A triangle with one

Throughout the next few weeks, our math class will obtuse angle
be studying two-dimensional figures. The students will
ray A part of a line, with one
use definitions to identify and describe characteristics endpoint, that is straight and
of these figures. continues in one direction

You can expect to see homework that includes right triangle A triangle with one
right angle and two acute angles
identifying types of triangles and quadrilaterals.
Here is a sample of how your child will be taught to
classify a triangle by its angles.

Classify a triangle by the sizes of its angles.


Angle sizes
Classify triangle KLM.
Angles are classified by the
STEP 1 STEP 2
size of the opening between
Determine how many Determine the correct the rays. A right angle forms a
angles are acute. classification. D square corner. An acute angle
is less than a right angle. An
acute
/K is ___. A triangle with __3 C
obtuse angle is greater than
acute angles is a right angle and less than a
acute
/L is ___. straight angle.
____.acute B
acute
/M is ___.
To classify angles in a figure,
use the corner of an index
card as a right angle and
compare.

Activity
© Houghton Mifflin Harcourt Publishing Company

Help your child commit most of the classifications of triangles and

quadrilaterals to memory. Together, you can make a series of flash cards
with the classifications on one side of the card and definitions and/or
sketches of examples on the other side of the card.

Chapter 10 P187
 10
 




triángulo agudo Un triángulo que tiene

 tres ángulos agudos

segmento de recta Una parte de una

línea que incluye dos puntos, llamados
extremos, y los puntos que están entre
Querida familia, ellos

Durante las próximas semanas, en la clase de matemáticas triángulo obtuso Un triángulo que tiene
estudiaremos las figuras bidimensionales. Usaremos las un ángulo obtuso

definiciones para identificar y describir las características rayo Parte de una línea recta, con un
extremo y que continúa en una dirección
de esas figuras.
triángulo rectángulo Un triángulo con
Llevaré a la casa tareas con actividades para identificar un ángulo recto y dos ángulos agudos
diferentes tipos de triángulos y cuadriláteros.
Este es un ejemplo de la manera como aprenderemos a
clasificar un triángulo por sus ángulos.

Clasificar un triángulo por el tamaño de sus lados

Clasifica el triángulo KLM.


Tipos de ángulos
PASO 1 PASO 2
Los ángulos se clasifican según el
Identifica cuántos ángulos Determina la clasificación D tamaño de la abertura entre sus
son agudos. correcta. rayos. Un ángulo recto forma una

agudo Un triángulo con _

/K es ___. 3 C
esquina recta. Un ángulo agudo
mide menos que un ángulo recto.
ángulos agudos, entonces es Un ángulo obtuso mide más que
agudo
/L es ___.
acutángulo B un ángulo recto y menos que un
______. ángulo llano.
agudo .
/M es ___ Para clasificar los ángulos de
una figura, usa la esquina de una
tarjeta como modelo de ángulo
recto y compara.
Actividad © Houghton Mifflin Harcourt Publishing Company

Anime a su hijo a memorizar las clasificaciones de los triángulos y los

cuadriláteros. Puede hacer tarjetas nemotécnicas con las clasificaciones en un
lado y las definiciones y/o ejemplos visuales en el otro lado de cada tarjeta.

P188
 Lesson 10.1
Name
COMMON CORE STANDARD MACC.4.G.1.1
Lines, Rays, and Angles Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Draw and label an example of the figure.
1. obtuse /ABC

Think: An obtuse angle is greater than

A a right angle. The middle letter, B, names
the vertex of the angle.

B C
___› ___
2. GH 3. acute /JKL 4. BC

Use the figure for 5–8.

5. Name a line segment. 6. Name a right angle. % (

& '
$ )

7. Name an obtuse angle. 8. Name a ray.

+
#
"

Use the figure at the right for 9–11.

© Houghton Mifflin Harcourt Publishing Company

9. Classify /AFD. :

9
10. Classify /CFE.
;
11. Name two acute angles.
8 = <

Chapter 10 P189
Lesson Check (MACC.4.G.1.1)
1. The hands of a clock show the time 12:25. 2. Which of the following name two different
figures?
___ ___
11 12 1 A AB and BA
10 2
‹_› ‹_›
9 3 B AB and BA
8 4 _› _›
7 6 5 C AB and BA
D /ABC and /CBA
Which best describes the angle between
the hands of the clock?

A acute C obtuse
B right D straight

Spiral Review (MACC.4.NF.2.3c, MACC.4.NF.3.6, MACC.4.NF.3.7, MACC.4.MD.1.2)

3. Jan’s pencil is 8.5 cm long. Ted’s pencil 4. Kayla buys a shirt for $8.19. She pays
is longer. Which could be the length of with a $10 bill. How much change should
Ted’s pencil? (Lesson 9.7) she receive? (Lesson 9.5)
A 0.09 cm A $1.81
B 0.8 cm B $1.89
C 8.4 cm C $2.19
D 9.0 cm D $2.81

9
5. Sasha donated ____ of her class’s entire
1 2
6. Jose jumped 8__ feet. This was 2__ feet
100 3 3
can collection for the food drive. Which farther than Lila jumped. How far did Lila
9 ? (Lesson 9.2)
decimal is equivalent to ____ jump? (Lesson 7.8)
© Houghton Mifflin Harcourt Publishing Company

100
A 9 A 51__ feet
3
B 0.99 B 52__ feet
3
C 0.9 C 61__ feet
3
D 0.09
D 11 feet

P190
 Lesson 10.2
Name
COMMON CORE STANDARD MACC.4.G.1.2
Classify Triangles Draw and identify lines and angles and classify
shapes by properties of their lines and angles.
Classify each triangle. Write acute, right, or obtuse.
1. "

Think: Angles A and C are both acute.

Angle B is obtuse.

# $

obtuse
2. ' 3. ( + 4. - /

.
% & )

5. Use figure ABCD below. Draw a line 6. Use figure ABCD below. Draw a line
segment from point B to point D. Name segment from point A to point C. Name
and classify the triangles formed. and classify the triangles formed.

A B A B
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D C D C

Chapter 10 P191
Lesson Check (MACC.4.G.1.2)
1. Stephen drew this triangle. How many 2. Joan was asked to draw a right triangle.
obtuse angles does the triangle have? How many right angles are in a right
triangle?
A 0
B 1
C 2
D 3
A 0 C 2
B 1 D 3

Spiral Review (MACC.4.OA.2.4, MACC.4.NBT.2.5, MACC.4.NF.3.5, MACC.4.G.1.1)

3. Oliver drew the figure below to show light 1 8
4. Armon added ___ and ____. Which is the
10 100
traveling from the sun to Earth. Name the correct sum? (Lesson 9.6)
figure he drew. (Lesson 10.1) 18
A ___
4 10
9
B ___
& 10
9
C ____
100
18
A segment SE C line SE D ____
100
B ray SE D ray ES

5. Sam counted out loud by 6s. Jorge 6. A basketball team averaged 105 points
counted out loud by 8s. What are the per game. How many points did the team
first three numbers both students said? score in 6 games? (Lesson 2.10)
(Lesson 5.4)
A 605 points
© Houghton Mifflin Harcourt Publishing Company

A 8, 16, 24
B 630 points
B 14, 28, 42 C 900 points
C 24, 48, 72
D 6,030 points
D 48, 96, 144

P192
 Lesson 10.3
Name
COMMON CORE STANDARD MACC.4.G.1.1
Parallel Lines and Draw and identify lines and angles, and classify
Perpendicular Lines shapes by properties of their lines and angles.

Use the figure for 1–3.

1. Name a pair of lines that appear to be perpendicular.

Think: Perpendicular lines form right angles. 8 :

‹___› ‹___›

‹___› ‹__›
AB and EF appear to form right angles.

AB and EF < =
9 ;
2. Name a pair of lines that appear to be parallel.

3. Name another pair of lines that appear to be perpendicular.

Draw and label the figure described.

‹____› ‹___› ‹___› ‹___› ‹___› T ‹___›
4. MN and PQ intersecting 5. WX || YZ 6. FH JK
at point R

Use the street map for 7–8.

© Houghton Mifflin Harcourt Publishing Company

7. Name two streets that intersect but do not appear

Maple
to be perpendicular.

Birch
Oa
k
Elm

8. Name two streets that appear to be parallel to

each other.

Chapter 10 P193
Lesson Check (MACC.4.G.1.1)
1. Which capital letter appears to have 2. In the figure, which pair of line segments
perpendicular line segments? appear to be parallel?
A N F G
B O
C T
J H
D V
___ ___
A FG and GH
__ ___
B FJ and GH
___ ___
C FG and JH
___ __
D JH and FJ

Spiral Review (MACC.4.NBT.2.5, MACC.4.NBT.2.6, MACC.4.NF.1.2, MACC.4.G.1.2)

3. Nolan drew a right triangle. How many 4. Mike drank more than half the juice in
acute angles did he draw? (Lesson 10.2) his glass. What fraction of the juice could
A 0 Mike have drunk? (Lesson 6.6)
A 1__
B 1 3
C 2 B 2__
5
D 3 C 3 __
6
D 5__
8

5. A school principal ordered 1,000 pencils. 6. A carton of juice contains 64 ounces.

He gave an equal number to each of Ms. Wilson bought 6 cartons of juice.
7 teachers until he had given out as many How many ounces of juice did she buy?
© Houghton Mifflin Harcourt Publishing Company

as possible. How many pencils were left? (Lesson 2.10)

(Lesson 4.11)
A 364 ounces
A 2 B 370 ounces
B 4 C 384 ounces
C 6 D 402 ounces
D 142

P194
 Lesson 10.4
Name
COMMON CORE STANDARD MACC.4.G.1.2
Classify Quadrilaterals Draw and identify lines and angles and classify
shapes by properties of their lines and angles.
Classify each figure as many ways as possible. Write
quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

1. Think: 2 pairs of parallel sides

4 sides of equal length
0 right angles

quadrilateral, parallelogram,
rhombus
2. 3. 4.

5. 6. 7.
© Houghton Mifflin Harcourt Publishing Company

8. Alan drew a polygon with four sides and 9. Teresa drew a quadrilateral with 2 pairs
four angles. All four sides are equal. None of parallel sides and 4 right angles. What
of the angles are right angles. What figure quadrilateral could she have drawn?
did Alan draw?

Chapter 10 P195
Lesson Check (MACC.4.G.1.2)
1. Joey is asked to name a quadrilateral that 2. Which quadrilateral has exactly one pair
is also a rhombus. What should be his of parallel sides?
answer? A square
A square
B rhombus
B rectangle C parallelogram
C parallelogram
D trapezoid
D trapezoid

Spiral Review (MACC.4.OA.2.4, MACC.4.OA.3.5, MACC.4.NF.2.3d, MACC.4.G.1.1)

3. Terrence has 24 eggs to divide into 4. In a line of students, Jenna is number 8.
equal groups. What are all the possible The teacher says that a rule for a number
numbers of eggs that Terence could put pattern is add 4. The first student in
in each group? (Lesson 5.2) line says the first term, 7. What number
A 1, 2, 3, 4 should Jenna say? (Lesson 5.6)
A 31
B 2, 4, 6, 8, 12
C 1, 2, 3, 4, 6, 8, 12, 24 B 35
C 39
D 24, 48, 72, 96
D 43

6
5. Lou eats __ of a pizza. What fraction of the 6. Which capital letter appears to have
8
pizza is left over? (Lesson 7.5) parallel lines? (Lesson 10.3)

A 1__ A D
8
B L
B 1__
4
© Houghton Mifflin Harcourt Publishing Company

C N
C 1 __
2 D T
D 3 __
4

P196
 Lesson 10.5
Name
COMMON CORE STANDARD MACC.4.G.1.3
Line Symmetry Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
Tell if the dashed line appears to be a line of symmetry.
Write yes or no.

1. 2. 3. 4.

yes
__ __ __ __
5. 6. 7. 8.

__ __ __ __

Complete the design by reflecting over the line of symmetry.

9. 10.
© Houghton Mifflin Harcourt Publishing Company

11. Kara uses the pattern at the right to make

paper dolls. The dashed line represents a
line of symmetry. A complete doll includes
the reflection of the pattern over the line
of symmetry. Complete the design to show
what one of Kara’s paper dolls looks like.

Chapter 10 P197
Lesson Check (MACC.4.G.1.3)
1. Which best describes the line of 2. Which shape has a correctly drawn
symmetry in the letter D? line of symmetry?

D
A horizontal
A C

B D
B vertical
C diagonal
D half turn

Spiral Review (MACC.4.NBT.2.5, MACC.4.NBT.2.6, MACC.4.NF.1.2, MACC.4.NF.2.4c)

3. The class has 360 unit cubes in a bag. 4. There are 5,280 feet in one mile. How
Johnnie divides the unit cubes equally many feet are there in 6 miles? (Lesson 2.11)
among 8 groups. How many unit cubes
A 30,680
will each group get? (Lesson 4.11)
B 31,260
A 40
C 31,608
B 44
D 31,680
C 45
D 48

5. Sue has 4 pieces of wood. The lengths 6. Alice has _15 as many miniature cars as
of her pieces of wood are _13 foot, 2_5 foot, Sylvester has. Sylvester has 35 miniature
__
3
foot, and 1_ foot. Which piece of wood cars. How many miniature cars does
10 4
is the shortest? (Lesson 6.7) Alice have? (Lesson 8.5)
© Houghton Mifflin Harcourt Publishing Company

A the 1__-foot piece A 7

3
B the 2__-foot piece B 9
5
3 -foot piece
C the ___ C 40
10
D 175
D the 1__-foot piece
4

P198
 Lesson 10.6
Name
COMMON CORE STANDARD MACC.4.G.1.3
Find and Draw Lines of Symmetry Draw and identify lines and angles, and classify
Tell whether the shape appears to have zero shapes by properties of their lines and angles.

lines, 1 line, or more than 1 line of symmetry.

Write zero, 1, or more than 1.
1. 2. 3. 4.

1
Does the design have line symmetry? Write yes or no.
If your answer is yes, draw all lines of symmetry.
5. 6. 7. 8.

Draw a shape for the statement. Draw the line or lines of symmetry.
9. zero lines of symmetry 10. 1 line of symmetry 11. 2 lines of symmetry
© Houghton Mifflin Harcourt Publishing Company

Use the chart for 12–13. 12. Which number or numbers appear to have
only 1 line of symmetry?

_______

13. Which number or numbers appear to have

2 lines of symmetry?
_______

Chapter 10 P199
Lesson Check (MACC.4.G.1.3)
1. How many lines of symmetry does this 2. Which of the following shapes appears
shape appear to have? to have exactly 1 line of symmetry?

A C

B D
A 0 C 6
B 2 D 10

Spiral Review (MACC.4.NF.1.1, MACC.4.NF.2.4b, MACC.4.NF.3.6, MACC.4.G.1.2)

3. Richard practiced each of 3 piano solos 4. Which of the following decimals is
5 hour. How long did he practice in
for ___ equivalent to three and ten hundredths?
12
all? (Lesson 8.3) (Lesson 9.2)

A 2 hour
__ A 0.30
3
1
__ B 0.31
B 14 hours
C 3.01
C 11
__ hours
3
5 hours D 3.1
D 1___
12

3 1
5. Lynne used __ cup of flour and __ cup of 6. Kevin draws a figure that has four sides.
8 3
sugar in a recipe. Which number below All sides have the same length. His figure
3 and __
is a common denominator for __ 1? has no right angles. What figure does
8 3
(Lesson 6.4) Kevin draw? (Lesson 10.4)
A 8 A square © Houghton Mifflin Harcourt Publishing Company

B 12 B trapezoid
C 16 C rhombus
D 24 D rectangle

P200
 PROBLEM SOLVING
Name
Lesson 10.7
HE8B;CÃEBL?D=ÃÄÃ>7F;Ã7JJ;HDI
COMMON CORE STANDARD MACC.4.OA.3.5

Generate and analyze patterns.

Solve each problem.

1. Marta is using this pattern to decorate a picture frame.

Describe the pattern. Draw what might be the next
three figures in the pattern.

Possible
______ answer: the pattern repeats:
one triangle followed by two squares.
______

2. Describe the pattern. Draw what might be the next

three figures in the pattern. How many circles are
in the sixth figure in the pattern?

________

________

3. Larry stencils this pattern to make a border at the top of

his bedroom walls. Describe the pattern. Draw what might
© Houghton Mifflin Harcourt Publishing Company

be the missing figure in the pattern.

________

________

Chapter 10 P201
Lesson Check (MACC.4.OA.3.5)
1. What might be the next three figures in 2. Which might be the missing figure in the
this pattern? following pattern?

A C A C

B D B D

Spiral Review (MACC.4.OA.2.4, MACC.4.NF.2.3d, MACC.4.NF.2.4a, MACC.4.NF.3.7)

3. Chad has two pieces of wood. One 4. Olivia finished a race in 40.64 seconds.
piece is __
7
12 foot long. The second piece Patty finished the race in 40.39 seconds.
is __
5
foot longer than the first piece. How
12 Miguel finished the race in 41.44 seconds.
long is the second piece? (Lesson 7.5) Chad finished the race in 40.46 seconds.
2
A ___ foot Who finished the race in the least time?
12 (Lesson 9.7)
1
B __ foot A Olivia
2
C 12
___ foot B Patty
18
C Miguel
D 1 foot
D Chad

5. Justin bought 6 ribbons for an art project. 6. Kyle and Andrea were asked to make
Each ribbon is 1_ yard long. How many
4
a list of prime numbers.
yards of ribbon did Justin buy? (Lesson 8.1) Kyle: 1, 3, 7, 19, 23
Andrea: 2, 3, 5, 7, 11
© Houghton Mifflin Harcourt Publishing Company

A _23 yard
Whose list is correct? (Lesson 5.5)
B 1 1_4 yards
A Only Kyle’s list
C 1 _12 yards B Only Andrea’s list
D 1 3_4 yards C Both lists are correct.
D Neither list is correct.

P202
 COMMON CORE STANDARDS MACC.4.OA.3.5,
MACC.4.G.1.1, MACC.4.G.1.2, MACC.4.G.1.3
Name

Chapter 10 Extra Practice

Lesson 10.1
Draw and label an example of the figure.
___
1. acute /MNP 2. QR 3. TS

Lesson 10.2
Classify each triangle. Write acute, right, or obtuse.
1. 2. 3.

Lesson 10.3
Use the streeet map for 1–2.
1. Name two streets that appear to be parallel.
0BL
.
1BSL

BJO

2. Name two streets that appear to be perpendicular. &MN

Lesson 10.4
© Houghton Mifflin Harcourt Publishing Company

Classify each figure as many ways as possible. Write

quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.
1. 2.

Chapter 10 P203
Lesson 10.5
Tell if the dashed line appears to be a line of symmetry.
Write yes or no.
1. 2. 3.

Lesson 10.6
Does the design have line symmetry? Write yes or no.
If your answer is yes, draw all lines of symmetry.
1. 2. 3.

Lesson 10.7
1. Sonia made a pattern. The first nine 2. Leo makes a pattern with triangles.
shapes are shown below. Describe the Draw what might be the next figure in
pattern. Draw what might be the next three the pattern. How can you describe the
shapes in Sonia’s pattern. pattern?

© Houghton Mifflin Harcourt Publishing Company

P204