Download Drawing Angles

Drawing Angles
Objective To guide children as they draw angles as records
of rotations.
o
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Workshop
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Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Practicing with ×, ÷ Fact Triangles
• Use straws and twist-ties to model angles. ×, ÷ Fact Triangles
Children use Fact Triangles to practice
multiplication facts.
[Geometry Goal 1]
• Use quarter-turns to describe right angles. [Geometry Goal 1]
• Identify the vertex and sides of an angle. [Geometry Goal 2]
• Model, draw, and name angles in terms
of turns (rotations). [Measurement and Reference Frames Goal 1]
Key Activities
Children show angles with connected
straws. They record straw rotations by
drawing angles.
Key Vocabulary
rotation vertical
Ongoing Assessment:
Recognizing Student Achievement
Use an Exit Slip (Math Masters,
p. 398). [Operations and Computation Goal 3]
Math Boxes 6 7
Math Journal 1, p. 142
Children practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Differentiation Options
READINESS
Finding Right Angles
magazines scissors glue or tape index
card blank paper stapler (optional)
Children create Right Angle books.
ENRICHMENT
Making and Comparing Right Triangles
per group: paper scraps in a variety of sizes,
ruler, yardstick or meterstick
Children construct and compare a variety
of right triangles.
Home Link 6 7
Math Masters, p. 181
Children practice and maintain skills
through Home Link activities.
Materials
Math Journal 1, p. 141
Home Link 66
straws and twist-ties meterstick straightedge 4 pieces of large paper
Advance Preparation
Label and display four posters to indicate the directions north, south, east, and west. Place two 2" straws
and a twist-tie for each child in separate containers near the Math Message. Connect two 8" straws with
a twist-tie to use in a demonstration.
Teacher’s Reference Manual, Grades 1–3 pp. 133, 134
438
Unit 6
Geometry
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP5, SMP6
Content Standards
Getting Started
3.OA.7
Mental Math and Reflexes
Math Message
Have children perform turn calisthenics. Children
identify the direction they face after each turn. Have
them refer to the cardinal direction posters.
Take two straws and a twist-tie. Use them to form
an angle that shows a quarter-turn.
Face north. Do a full turn clockwise. north Do a full turn
counterclockwise. north
Face south. Do a half-turn clockwise. north Do a half-turn
counterclockwise. south
Face north. Do a half-turn clockwise. south Do a
quarter-turn counterclockwise. east Do a three-quarter
turn counterclockwise. south
Home Link 6 6 Follow-Up
Children share some of their named polygons.
Briefly review why the letters that name a polygon
cannot be repeated. Each label must be distinct so
that all parts of the polygon can be named without any confusion.
NOTE To introduce acute
1 Teaching the Lesson
and obtuse angles, go to
www.everydaymathonline.com.
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Check that children have made right angles out of their straws.
Making Angles with Straws
WHOLE-CLASS
ACTIVITY
Have children place their connected straws on their desks with
both sides touching and pointing up, like the hands of a clock
showing 12 o’clock as you demonstrate on the overhead. Have
them make angles, keeping one straw stationary while rotating
the other straw clockwise or counterclockwise. After each turn,
children return both straws to the 12 o’clock position. Use the
term rotation to describe the motion of the straws.
Adjusting the Activity
ELL
Draw these turns on the board so that children can refer to them as you
give turning directions.
left turn
counterclockwise
A U D I T O R Y
K I N E S T H E T I C
right turn
clockwise
T A C T I L E
V I S U A L
Lesson 6 7
439
Suggestions:
1
_
2
●
Show a full-turn rotation. Describe what happened. What are the
positions of the straws? They are back to where they started.
●
Make a half-turn rotation. Describe the positions of the straws.
One is pointing straight up; the other is pointing straight down.
●
Make a quarter-turn rotation, either clockwise or counterclockwise. What kind of an angle did you make? A right angle
●
Make a three-quarter turn rotation, either clockwise or
counterclockwise. What are the positions of the straws?
One is pointing straight up; the other is pointing at 3:00 or 9:00.
What kind of angle did you make? A 270° angle
●
Make less than a half-turn but more than a quarter-turn
counterclockwise.
●
Make less than a quarter-turn clockwise.
●
Make more than a half-turn but less than a three-quarter turn
clockwise.
turn
1 full turn
3
_
4
1
_
4
turn
turn
Drawing Angles to
WHOLE-CLASS
ACTIVITY
Record Rotations
(Math Journal 1, p. 141)
Ask a child to assist you in demonstrating how to draw an angle to
record a turn, or rotation.
Less than
Less than _12
turn but more
than _14 turn
1
_
4
turn
1. Draw a dot on the board. Label it A. Explain
that it is called Point A.
A
2. Place the connected straws so that the vertex
is on Point A with both straws pointing
to 12 o’clock.
A
3. Keeping one straw stationary, rotate the
other straw clockwise a quarter-turn.
More than _12
turn but less
3
than _4 turn
4. Ask your assistant to draw a dot to represent
a point at the tip of each straw.
5. Using a meterstick, draw two rays: one
from the vertex through each point. Draw
a curved arrow to show the direction of the
rotation. Call children’s attention to the
sides of the angle. The sides of angles are
rays with common endpoints at the vertex
of the angle.
A
A
NOTE A point is an exact location in space and has no size. Dots, which do
have size, are not really points; they are used to represent points. Points are
usually named with capital letters.
Journal page 141 provides additional practice with drawing
angles. Each exercise is done twice (partners trade roles so that
work is done in both journals).
440
Unit 6 Geometry
Student Page
Part 1
Date
LESSON
6 7
䉬
Present the following directions:
Time
Drawing Angles
Draw each angle as directed by your teacher.
Record the direction of each turn with a curved arrow.
1. Each dot on the journal page represents a point, the vertex of
an angle. Place the connected straws so the vertex is on point
A with both straws pointing to 12 o’clock.
Part 1
2. While one partner keeps the left straw stationary, the other
partner rotates the other straw less than a quarter-turn
clockwise.
Sample answers:
B
A
C
Part 2
3. One partner marks points along both straws.
S
4. Put the straws aside. Using a straightedge, draw a ray from
the vertex through each point. Then draw a curved arrow to
show the direction of the turn.
R
Present similar directions for angles B and C. For example:
Draw an angle that shows more than a half-turn counter
clockwise but less than a three-quarter turn.
Draw an angle that shows more than a quarter-turn clockwise
but less than a half-turn.
T
Math Journal 1, p. 141
Part 2
Present directions for drawing angles R, S, and T using the
routine outlined above. This time the fixed straw should not be
pointing to 12 o’clock. For example:
Draw an angle that shows a quarter-turn clockwise.
Draw an angle that shows more than a quarter-turn
counterclockwise but less than a half-turn.
Draw an angle that shows a half-turn clockwise.
After children have completed the journal page, emphasize the
following ideas:
Angle size is determined by the amount of the turn.
Neither side needs to be vertical (upright).
To record a rotation correctly, draw a curved arrow showing
which direction one side was rotated.
Adjusting the Activity
ELL
Model and discuss the meaning of the word vertical. Have children
stand in a vertical position, raise their arms in a vertical position, and find vertical
line segments in the classroom.
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
V I S U A L
Lesson 6 7
441
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Math Boxes
67
57
_
1. The grid is ONE. Shade 100 of
2. Circle the pairs of lines that intersect.
the grid.
Practicing with ×, ÷
Fact Triangles
Write the decimal that tells how
much of the grid is shaded.
0.57
99
34
Have children sort their 18 Fact Triangles into 2 piles–
multiplication facts they know and multiplication facts they
still need to practice. Have them work independently or with a
partner to review the facts they still need to practice.
4. Draw a ray,
. Draw a line
_SO
3. Draw an angle that is less than
1
a_
4 turn.
.
segment, LA. Draw a line, TI
Sample answer:
S
L
O
A
T
I
167 168
100
5. Circle the regular polygons.
6. Complete.
⫻10
104
Ongoing Assessment:
Recognizing Student Achievement
⫼5
1
10
2
20
80
8
40
4
200 201
142
Exit Slip
Use an Exit Slip (Math Masters, page 398) to assess children’s progress toward
demonstrating automaticity with multiplication facts through 10 × 10. Have
children record the facts they know from their Fact Triangles. Children are
making adequate progress if they record most of the facts represented on the
Fact Triangles. Some children may be able to record all of the facts.
Math Journal 1, p. 142
EM3MJ1_G3_U06_128-155.indd
SMALL-GROUP
ACTIVITY
2/10/10
1:48 PM
[Operations and Computation Goal 3]
Math Boxes 6 7
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 142)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-5. The skill in Problem 6
previews Unit 7 content.
Writing/Reasoning Have children write an answer to the
following: Look at the polygons in Problem 5. Draw a
different regular polygon and explain why it is regular.
Sample answer: The polygon is regular because all of its sides are
the same length and all of its angles are the same size.
Home Link Master
Name
Date
HOME LINK
Time
Turns
67
Family
Note
Home Link 6 7
If your child needs help with the following problems, consider
putting up signs in a room in your home to indicate the directions
north, south, east, and west. Do the turns with your child.
Please return this Home Link to school tomorrow.
left turn
counterclockwise
right turn
clockwise
INDEPENDENT
ACTIVITY
(Math Masters, p. 181)
Make the turns described below. Show which way you face after each turn.
Draw a dot on the circle.
Label the dot with a letter.
E
Example: Face north.
1
turn counterclockwise.
Do a _
2
West
On the circle, mark the direction
you are facing with the letter A.
E, F, and G are
sample answers.
1
_
1. Face north. Do a 4 turn clockwise.
Mark the direction you are facing
with the letter B.
1
_
F
D
B
You
East
A
South
3
_
2. Face north. Do a 4 turn clockwise.
Mark the direction you are facing
with the letter C.
1
_
3. Face east. Do a 4 turn
4. Face west. Make less than a 4 turn
5. Face north. Make a clockwise turn
6. Face north. Make a
p
counterclockwise. Mark the direction
you are facing with the letter D.
1
that is more than a _
turn, but less
2
3
than a _
turn. Mark the direction
4
you are facing with the letter F.
py g
g
C
G
Home Connection Children determine which direction
they are facing after making certain turns. They record
the results on a circle by drawing and labeling a point.
North
clockwise. Mark the direction you
are facing with the letter E.
counterclockwise turn that is less
1
than a _
turn, but more than a
2
1
_
turn. Mark the direction you are
4
facing with the letter G.
Math Masters, p. 181
EM3MM_G3_U06_167-205.indd
442
181
2/10/10
Unit 6 Geometry
1:45 PM
3 Differentiation Options
READINESS
Finding Right Angles
SMALL-GROUP
ACTIVITY
15–30 Min
To provide experience identifying right angles, have children look
through magazines for pictures of objects that have right angles.
They can verify the angle measurements with the corner of an
index card. Children cut out the pictures and tape or glue them on
paper. They may staple their papers together to make a Right
Angle book.
ENRICHMENT
Making and Comparing
SMALL-GROUP
ACTIVITY
15–30 Min
Right Triangles
To apply children’s understanding that an angle remains the same
size regardless of its orientation and the length of its sides, have
children make and compare right triangles.
First, each child in the group chooses three or more paper scraps
and traces the square corner of an index card onto each scrap of
paper.
Children use rulers or yardsticks to extend the sides of their right
angles in order to make right triangles of varying sizes. Encourage
the group to make many different looking triangles. They cut out
the triangles and display them in a variety of orientations.
Using the corners of the index cards, children verify that the right
angles match, or are congruent, regardless of the other properties
of the triangles. Children share their findings with the class.
Lesson 6 7
443