Objectives
To guide the exploration of reflections; and to
provide practice identifying lines of reflection.
1
materials
Teaching the Lesson
Key Activities
Students play games that involve reflections, such as the Dart Game and the PocketBilliards Game. They explore finding the line of reflection of a reflected image.
Key Concepts and Skills
• Describe properties of congruent figures, right angles, and perpendicular lines.
[Geometry Goal 2]
ⵧ Math Journal 2, p. 276 and
Activity Sheets 7 and 8
ⵧ Study Link 10 1
䉬
ⵧ 1 transparent mirror per partnership
ⵧ ruler
ⵧ slate
• Explore lines of reflection and reflected images. [Geometry Goal 3]
• Solve problems involving spatial visualization. [Geometry Goal 3]
Key Vocabulary reflection • line of reflection
Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes.
[Number and Numeration Goal 6]
2
materials
Ongoing Learning & Practice
Students play Angle Tangle to practice estimating the measures of angles and
measuring angles.
Students practice and maintain skills through Math Boxes and Study Link activities.
Ongoing Assessment: Informing Instruction See page 802.
ⵧ Math Journal 2, p. 277
ⵧ Student Reference Book, p. 230
ⵧ Study Link Master (Math Masters,
p. 307)
ⵧ Game Master (Math Masters, p. 457)
ⵧ Geometry Template; protractor
3
materials
Differentiation Options
READINESS
Students create
reflections by
painting on
half-sheets of paper
and then folding the
paper.
ENRICHMENT
Students solve
paper-folding
puzzles.
ENRICHMENT
Students use
technology to
investigate the
mirror as a virtual
manipulative.
ELL SUPPORT
Students add
reflection to their
Math Word Banks.
ⵧ Teaching Master (Math Masters,
p. 308)
ⵧ Teaching Aid Master (Math Masters,
p. 389)
ⵧ Differentiation Handbook
ⵧ large sheets of paper; paints,
brushes, and dark marker; computer
with Internet access; scissors
See Advance Preparation
Additional Information
Advance Preparation For the optional Readiness activity in Part 3, students will need
supplies and space for painting.
Technology
Assessment Management System
Mental Math and Reflexes
See the iTLG.
See the Web site on page 804.
Lesson 10 2
䉬
799
Getting Started
Mental Math and Reflexes
夹
Study Link 10 1 Follow-Up
䉬
Have students name and explain the strategy for finding
the greater fraction in each fraction pair. Suggestions:
3
1 3
or 4 4
4
5
2 5
or 8
8 8
6
6 6
or 9
7 7
2
1 2
or 3
2 3
4
1 4
or 6
2 6
3
1 1
or 9
2 2
8
5 8
or 9
6 9
6
4 6
or 7
5 7
1
2 2
or 7
8 8
Students place Study Link 10-1 and their sketch
side by side on their desks. They compare the
preimage and the image. Students should note that
the image is the opposite or reverse of the preimage.
Math Message
Have you ever played darts or pocket billiards? Discuss
the object of each game and some of the rules with a friend.
preimage
image
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and Reflexes
夹
Use Mental Math and Reflexes to assess students’ ability to compare
fractions. Students are making adequate progress if they are able to solve the
problems, which involve like numerators or like denominators, and the
1
problems, which involve comparing fractions to the benchmark 2. Some
students may be able to solve the
problems and write about their strategies.
[Number and Numeration Goal 6]
1 Teaching the Lesson
䉴 Math Message Follow-Up
Student Page
Date
Time
LESSON
10 2
䉬
Finding Lines of Reflection
106
Dart Game
Practice before you play the game on Activity Sheet 7. One partner chooses Dart A
and the other partner Dart B. Try to hit the target with your own dart, using the
transparent mirror. Do not practice with your partner’s dart.
Now play the game with your partner.
Directions
Take turns. When it is your turn, use the other dart—the one you did not use for
practice. Try to hit the target by placing the transparent mirror on the page, but do not
look through the mirror. Then both you and your partner look through the mirror to
see where the dart hit the target. Keep score.
Pocket-Billiards Game
Practice before you play the game on Activity Sheet 8. Choose a ball (1, 2, 3, or 4)
and a pocket (A, B, C, D, E, or F). Try to get the ball into the pocket, using
the transparent mirror.
WHOLE-CLASS
DISCUSSION
Students briefly share the object and some of the rules of each
game with the class. Some students may mention that another
name for pocket billiards is pool.
NOTE It is not essential that students know the rules or have played these
games to understand these activities. However, displaying a dartboard or a
picture of a pool table would be helpful to students unfamiliar with the games.
䉴 Playing Games that Involve
PARTNER
ACTIVITY
Reflections
Now play the game with a partner.
(Math Journal 2, p. 276 and Activity Sheets 7 and 8)
Directions
Take turns. When it is your turn, say which ball and which pocket you have picked: for
example, “Ball 2 to go into Pocket D.” Try to get the ball into the pocket by placing the
transparent mirror on the billiard table, but do not look through the mirror. Then both
you and your partner look through the mirror to check whether the ball has gone into
the pocket.
Tell students that in this lesson they will experiment with
transparent mirrors and reflections by playing two games.
1. How could measuring distances with a ruler help you place the mirror so that the ball goes
into the pocket? For example, exactly where can you put the mirror so that Ball 2 will go
into Pocket D?
Since the image and the preimage are equal distances from the
mirror, I can measure the distance between the ball and the
pocket and place the mirror halfway between the two.
276
Math Journal 2, p. 276
800
Unit 10 Reflections and Symmetry
Dart Game
Activity Sheet 7 contains two darts, labeled A and B, and a target.
The object is to “hit” the target by reflecting one of the darts with
the transparent mirror.
Student Page
Date
Students first practice hitting the target. One partner uses Dart A,
and the other uses Dart B. Students look through the mirror and
move it around until the image of the dart hits the target.
Time
LESSON
10 2
䉬
Dart Game
Scoreboard 1
Player 1
After a little practice, students begin the game. Players switch
darts—that is, if they practiced with Dart A, they play the game
with Dart B (and vice versa). Now students must place the mirror
on the master without looking through the mirror. (There would
not be much of a game if they could look through the mirror—it
would be easy to hit the bull’s eye every time.) Only after placing
the mirror on the master may the player look through it to find
the score.
Player 2
200
Scoreboard 2
100
Player 1
Player 2
50
25
Scoreboard 3
Player 1
Pocket-Billiards Game
Activity Sheet 8 shows the top of a pocket-billiards table. There are
six pockets, labeled A–F, and four billiard balls, labeled 1–4. The
object is to “sink” a ball into one of the pockets by reflecting the
ball with the transparent mirror. As with the Dart Game, students
practice by looking at the image of a billiard ball through the mirror.
Then partners play the game without looking through the mirror.
Players should look through the mirror only to check results.
B
Player 2
A
A i i
Sh
7
Math Journal 2, Activity Sheet 7
After students have played the game several times, ask them to
answer the question at the bottom of journal page 276.
Adjusting the Activity
Have partners devise their own scoring system for the game. It might be
as simple as scoring 1 point for each time a ball is sunk into a pocket. Or
perhaps each partner gets three tries at sinking a ball into a designated pocket,
scoring 5 points if the ball goes in on the first try, 3 points if it goes in on the
second try, or 1 point if it goes in on the last try.
A U D I T O R Y
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
V I S U A L
Student Page
䉴 Introducing the Concept
WHOLE-CLASS
DISCUSSION
Date
Time
LESSON
10 2
䉬
Pocket-Billiards Game
of Reflection
Start the discussion by asking the following question:
●
A
In Lesson 10-1, the clown hats were upside down. What would
happen if they were drawn right-side up? After being moved to
the clown’s head, the hats would be upside down.
Introduce the word reflection—a flipping motion that makes the
image appear to be the “opposite” of the original object. Point out
that in a reflection in a mirror, everything is reversed. Explain
that the line along the recessed edge of a transparent mirror is
called the line of reflection.
B
2
1
C
D
4
3
E
image
F
ction
f refle
line o
preimage
A i i
Sh
8
Math Journal 2, Activity Sheet 8
Lesson 10 2
䉬
801
Student Page
Date
Time
LESSON
Have students share their strategies for locating the line of
reflection on the pocket-billiards table. Help them see that the
mirror must be placed about halfway between the ball and the
pocket and that it should be perpendicular (at a right angle) to
the invisible line connecting the ball and the pocket. This method
works because a reflected object is the same distance from the line
of reflection as the original object.
Math Boxes
10 2
䉬
1. Complete the table with equivalent names.
Fraction
Decimal
Percent
29
100
30
100
0.29
29%
0.30
8
10
0.8
0.90
30%
80%
90
100
2. Insert the decimal point in each quotient.
a.
2 8•2
84.6 3
b. 91.6 4 c.
2 2•9
2 1• 4 128.4 6
d. 265.6 8 3 3•2
90%
22 23
61 62
3. The fourth-grade students at Lighthouse School voted on their favorite season.
Favorite Season
winter: 30 students
Seasons
spring: 20 students
summer: 35 students
fall: 15 students
A
fall
summer
spring
winter
2
0
Use this data to create a bar graph.
1
5 10 15 20 25 30 35 40
Number of Students
C
76
plotted on the coordinate grid.
4 , 2)
B(2 , 2)
C (0 , 0)
D (1 , 4)
E(2 , 5)
a.
E
5
4
c.
B
2
1
0
b.
D
3
A
d.
C
0
1
2
3
4
D
5. Write five names for 12.
4. Write the ordered pair for each point
A(
B
5
e.
144
5.1 (6.9)
6 (6)
4 ⴱ (3)
13 1
12 (24)
Sample answers
4
3
E
F
60
277
Math Journal 2, p. 277
Links to the Future
This is as far as you need to go with this topic for now. With additional
experience, students will learn that when an object is reflected, corresponding
points on the object and on its reflection are the same distance from the line
of reflection.
2 Ongoing Learning & Practice
䉴 Playing Angle Tangle
PARTNER
ACTIVITY
(Student Reference Book, p. 230; Math Masters, p. 457)
Students play Angle Tangle to practice estimating and measuring
angles. See Lesson 6-8 for additional information.
䉴 Math Boxes 10 2
䉬
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 277)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 10-5. The skill in Problem 5
previews Unit 11 content.
Ongoing Assessment: Informing Instruction
Watch for students who have difficulty labeling the horizontal axis of the
graph in Problem 3 because there is not enough space provided to label it
by ones. Encourage them to look at the data and find a common factor to use
as the interval.
802
Unit 10 Reflections and Symmetry
Study Link Master
䉴 Study Link 10 2
INDEPENDENT
ACTIVITY
䉬
(Math Masters, p. 307)
Name
Date
STUDY LINK
10 2
䉬
Time
Lines of Reflection
106
For each preimage and image, draw the line of reflection.
1.
Home Connection Students draw lines of reflection
between preimages and images. For given preimages,
they use the Geometry Template to draw the image on
the other side of the line of reflection.
2.
3.
preimage
image
preimage
image
preimage
image
For each preimage, use your Geometry Template to draw the
image on the other side of the line of reflection.
4.
5.
preimage
3 Differentiation Options
READINESS
䉴 Creating a Paint Reflection
preimage
INDEPENDENT
ACTIVITY
6.
7.
preimage
Create one of your own.
preimage
15–30 Min
(Math Masters, p. 389)
Sample
answer
Art Link To explore the concept of reflection, have
students create a paint reflection. Students fold a large
sheet of paper in half and then unfold it. They paint a
simple design, using several colors if they wish, on half of
the sheet without touching the fold line. Before the paint
has dried, students refold the paper and unfold it again. The
result will be a reflection of the painted design on the other half of
the paper.
Math Masters, p. 307
line of reflection
Have students use a dark marker to highlight the fold line and
label it as the line of reflection. In addition, have students label
the preimage and image.
preimage
image
Simple design with reflection
Ask students to answer questions such as the following on an
Exit Slip:
●
What do you notice about your design?
●
How are the designs on both sides of the fold alike? How are
they different?
●
What does the fold represent?
●
How would you describe a reflection to someone who did not
know what it was?
Lesson 10 2
䉬
803
Teaching Master
Name
Date
LESSON
Time
ENRICHMENT
Paper-Folding Puzzles
10 2
䉬
䉴 Solving Paper-Folding
For each design, circle the pieces that could be unfolded to match it.
For some problems, there is more than one correct answer.
The dashed lines represent folds. The pieces in Problems 3 and 4
have been folded two times.
A
B
C
D
E
INDEPENDENT
ACTIVITY
5–15 Min
Puzzles
1.
(Math Masters, p. 308)
A
B
C
D
E
A
B
C
D
E
A
B
C
D
E
2.
3.
4.
To apply students’ understanding of lines of reflection and
reflected images, have them match folded and unfolded designs.
Ask students to describe how they used lines of reflection to help
them match the designs. Some students may choose to sketch the
folded designs and cut them out to check their work. Encourage
students to make up their own paper-folding puzzles.
ENRICHMENT
Try This
Match the folded piece to the correct unfolded design. Circle it.
A
B
C
D
E
5.
䉴 Exploring Reflections and
INDEPENDENT
ACTIVITY
15–30 Min
Lines of Reflection
Math Masters, p. 308
Technology Link To apply students’ understanding of
reflections and lines of reflection, have them investigate
the use of a mirror as a virtual manipulative. See the Web site
at http://nlvm.usu.edu/en/nav/frames_asid_297_g_2_t_
3.html?openactivities. The site is part of the National Library
of Virtual Manipulatives for Interactive Mathematics developed
by Utah State University. See http://nlvm.usu.edu.
ELL SUPPORT
䉴 Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook)
To provide language support for transformations, have students
use the Word Bank Template found in the Differentiation
Handbook. Ask students to write the term reflection, draw a
picture representing the term, and write other related words.
See the Differentiation Handbook for more information.
Planning Ahead
Begin collecting pictures of symmetric objects, such as the front
view of an automobile, a table, a window, and a fork. These will
be used in an optional ELL Support activity in Lesson 10-4 to
start a Line Symmetry Museum.
804
Unit 10 Reflections and Symmetry