Download Polyhedrons, Part 2

Polyhedrons, Part 2
Objective To provide opportunities to explore the
characteristics of prisms.
c
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Compare faces on prisms. [Geometry Goal 2]
• Identify the faces of polyhedrons. [Geometry Goal 2]
• Identify and name prisms. [Geometry Goal 2]
• Identify the faces, edges, and vertices
of prisms. [Geometry Goal 2]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Beat the Calculator
(Multiplication)
Math Journal 1, p. 156
Student Reference Book, p. 279
per group: calculator
Children practice multiplication facts.
Ongoing Assessment:
Recognizing Student Achievement
Use an Exit Slip (Math Masters,
p. 398). [Operations and Computation Goal 3]
Key Activities
Math Boxes 6 12
Children identify the bases, faces, and
vertices of various prisms. They classify
prisms according to the shapes of their bases.
Math Journal 1, p. 154
Children practice and maintain skills
through Math Box problems.
Key Vocabulary
Home Link 6 12
rectangular prism triangular prism hexagonal prism
Math Masters, p. 199
Children practice and maintain skills
through Home Link activities.
Materials
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Illustrating Prefixes
Student Reference Book, p. 103
paper
Children illustrate prefixes used to
name polygons.
ENRICHMENT
Solving Geometric Riddles
Math Masters, pp. 200 and 201
Student Reference Book, pp. 112–114
scissors slate
Children solve geometric riddles.
Math Journal 1, p. 153
Student Reference Book, p. 115
Home Link 611
pattern-block prism cereal box per group:
4 of each pattern-block shape (square,
triangle, trapezoid, hexagon), transparent
tape paper
Advance Preparation
For Part 1, place a cereal box near the Math Message. Construct a prism by taping 3 or 4 of the same
pattern-block shapes together. For the optional Enrichment activity in Part 3, copy a set of geometry
riddle cards (Math Masters, page 201) on cardstock for each small group.
Teacher’s Reference Manual, Grades 1–3 pp. 144–146
468
Unit 6
Geometry
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Getting Started
Mental Math and Reflexes
Math Message
Write decimals on the board. Children read them aloud. Encourage them to
exaggerate the th sound so that decimal numbers are not confused with whole
numbers.
What kind of shape is the
cereal box? How many faces does it
have? How many edges? How many
vertices? What is the shape of its faces?
Write your answers on paper and
discuss them with a partner.
Suggestions:
0.42 forty-two hundredths
1.34 one and thirty-four hundredths
6.09 six and nine-hundredths
0.5 five-tenths
2.4 two and four-tenths
Home Link 6 11
Follow-Up
20.50 twenty and fifty-hundredths
5.813 five and eight hundred thirteen-thousandths
45.030 forty-five and thirty thousandths
80.102 eighty and one hundred two-thousandths
Ask questions like Which digit is in the tenths place? What is the value of the digit x?
How many hundredths are there?
Have children share some of
the 3-D objects and pictures that they
brought to school. Encourage them to
use geometry vocabulary to name the
objects and pictures.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Briefly go over the answers regarding the cereal box. rectangular
prism; 6 faces; 12 edges; 8 vertices; rectangular
Identifying the Bases of a
WHOLE-CLASS
DISCUSSION
Rectangular Prism
Explain that this lesson further explores the characteristics of
prisms.
Review the characteristics of the bases of prisms:
They are flat, opposite each other, and parallel.
They are the same shape and the same size, so they are
congruent.
Have children discuss which faces are the bases of the cereal box.
Ask: Does each face have an opposite face that is parallel and
congruent to it? Yes How many pairs of parallel faces does the box
have? 3 pairs
In a rectangular prism, any pair of opposite faces can be the
bases of the prism. Choose a pair of opposite faces to be the bases.
Once you have made a choice, the other two pairs of faces are not
considered the bases.
Lesson 6 12
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Student Page
Date
6 12
䉬
Constructing Pattern-Block
Time
LESSON
Pattern-Block Prisms
SMALL-GROUP
ACTIVITY
Prisms and Tracing Their Faces
Work in a group.
1. Each person chooses a different pattern-block shape.
2. Each person then stacks 3 or 4 of the shapes together to make a prism. Use
(Math Journal 1, p. 153)
small pieces of tape to hold the blocks together.
3. Below, carefully trace around each face of your prism. Then trace around each
face of 2 or 3 more prisms on a separate sheet of paper. Ask someone in your
group for help if you need it. Share prisms with other people in your group.
See children’s work.
Give each group 16 pattern blocks (four each of triangles, squares,
trapezoids, and hexagons). Draw a square on the board. Ask: Why
is the drawing not a prism? The drawing is a 2-dimensional figure.
It has no thickness. Hold up a square pattern block and ask the
class why it is a prism. The pattern block is a 3-dimensional object
because it has thickness.
Hold up a pattern-block prism that you taped together. (See
Advance Preparation.) Each group will make different pattern-block
prisms by taping together 3 or 4 congruent pattern blocks. Each
child in a group should make a different prism. Children in each
group then share their pattern-block prisms to complete journal
page 153.
Discussing the Shapes of
Math Journal 1, p. 153
WHOLE-CLASS
DISCUSSION
the Faces of Prisms
(Student Reference Book, p. 115)
When most children have completed their tracings on the journal
page, discuss children’s work as a class. Ask several children to
name the shape of the bases of their prisms. Ask: What is the
shape of the faces that are not bases? rectangles
Prisms are named after the shapes of their bases. For example,
the bases of a rectangular prism are rectangles. A prism whose
bases are triangles is a triangular prism. The bases of a
hexagonal prism are hexagons.
Student Page
Geometry
Polyhedrons
A polyhedron is a solid whose surfaces are all flat and
formed by polygons. It does not have any curved surfaces.
The faces of a regular polyhedron are all formed by
copies of one regular polygon that have the same size.
Three important groups of polyhedrons are shown below.
These are pyramids, prisms, and regular polyhedrons.
Many polyhedrons do not belong to any of these groups.
Discuss the shapes on page 115 in the Student Reference Book.
Point out that pyramids, as well as prisms, are named after the
shape of their bases. Children should also notice that there are
other polyhedrons besides pyramids and prisms. Some children
might count the number of edges or vertices on the five
polyhedrons at the bottom of the page. Ask: What kind of pyramid
is the tetrahedron? Triangular pyramid
Adjusting the Activity
Pyramids
triangular
pyramids
rectangular
pyramids
pentagonal
pyramid
hexagonal
pyramid
Prisms
triangular prisms
rectangular prisms
hexagonal prism
A U D I T O R Y
Regular Polyhedrons
regular
tetrahedron
(pyramid)
(4 faces)
cube
(prism)
(6 faces)
regular
octahedron
(8 faces)
regular
dodecahedron
(12 faces)
Have children name a prism with a 5-sided base, pentagonal prism
7-sided base, heptagonal prism 8-sided base, octagonal prism 9-sided base,
nonagonal prism and 10-sided base. decagonal prism Write the names on the
board. Ask children how the names are related to the names of 2-dimensional
shapes. Pentagonal is related to pentagon, which is the shape of the base of the
pentagonal prism; heptagonal is related to heptagon, which is the shape of the
base of the heptagonal prism, and so on.
K I N E S T H E T I C
T A C T I L E
V I S U A L
regular
icosahedron
(20 faces)
Student Reference Book, p. 115
470
Unit 6 Geometry
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Student Page
2 Ongoing Learning & Practice
Playing Beat the Calculator
Date
Time
LESSON
Math Boxes
6 12
2. Draw all the lines of symmetry.
, parallel to line
1. Draw a line,
_AB
segment, CD. Draw a ray, EF
,
that intersects the ray, GH
.
A
PARTNER
ACTIVITY
B
C
(Multiplication)
D
G
E
F
There are
(Math Journal 1, p. 156; Student Reference Book, p. 279)
lines of symmetry.
122 123
100 101
4. Write the numerals.
3. Number of days for one revolution
around the sun:
Children develop automaticity with multiplication facts by playing
Beat the Calculator. Have children keep a record of the facts for
which they get the product first when playing the role of the Brain
by making a check mark on their Fact Power Table, journal page
156. For Fact Power Table directions, see Lesson 4-5. For game
directions, see page 279 in the Student Reference Book. Remind
children to fill in the product on their Fact Power Table when they
have 3 check marks for a fact.
Which planet
takes the fewest
days to revolve
around the sun?
Mercury
88
Venus
225
Earth
365
Mars
687
A. Mercury
C. Venus
B. Earth
D. Mars
Exit Slip
5
_
or 0.05
_ or 0.3
five-hundredths 100
3
10
three-tenths
3
_
three-hundredths 100
33 34
6. Divide.
triangle. Label the points.
5
3
30 ÷ 6 =
B
12 ÷ 4 =
4
20 ÷ 5 =
A
2
3
C
C
or 0.03
79
5. Connect 3 points to make a right
Sample
answer:
5
_
10 or 0.5
five-tenths
Fill in the circle for the best answer.
Which letter names
the right angle?
Ongoing Assessment:
Recognizing Student Achievement
5
H
106 107
= 14 ÷ 7
=9÷3
52 53
Math Journal 1, p. 154
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Use an Exit Slip (Math Masters, page 398) to assess children’s progress toward
demonstrating automaticity with multiplication facts through 10 × 10. Children
record the facts from the Fact Power Table for which they recorded at least
one check mark. Children are making adequate progress if they record all of
the facts from the unshaded portion of the table. Some children may record
additional facts from the shaded portion.
1/18/11 3:31 PM
NOTE For practice identifying
congruent figures, go to
www.everydaymathonline.com.
[Operations and Computation Goal 3]
Math Boxes 6 12
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 154)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-10. The skill in Problem 6
previews Unit 7 content.
Home Link Master
Name
HOME LINK
6 12
Family
Note
Home Link 6 12
INDEPENDENT
ACTIVITY
(Math Masters, p. 199)
Date
Time
Making a Solid Shape
Our class has been exploring the characteristics and parts of various 3-dimensional shapes—
especially prisms. The pattern on this page can be used to make one type of prism. Prisms
are named for the shapes of their bases.
117
Please return this Home Link to school tomorrow.
Cut on the dashed lines. Fold on the dotted lines. Tape or paste each
TAB inside or outside the shape.
Discuss the following questions with someone at home:
pentagonal prism
pentagon
What is the shape of the bases?
rectangle
What is the shape of the other faces?
15 edges
How many edges does the shape have?
10 vertices
How many vertices does the shape have?
1. What is this 3-D shape called?
Home Connection Children cut out a pattern and make a
pentagonal prism. Then they talk about the shape with
someone at home.
2.
3.
4.
5.
B
TA
TAB
TAB
TAB
TA
B
TAB
TAB
TA
B
TAB
Math Masters, p. 199
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Lesson 6 12
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3 Differentiation Options
PARTNER
ACTIVITY
READINESS
Illustrating Prefixes
15–30 Min
(Student Reference Book, p. 103)
To explore polygon names, have children discuss prefixes used to
name polygons and relate the prefixes to other words they know.
Children refer to the chart of prefixes on page 103 in the Student
Reference Book. They fold a blank page into 4 boxes and illustrate
4 or more (use the back of the page) of the prefixes with pictures
that will help them remember the prefix meanings.
Examples:
Tricycles have three wheels like a triangle has three angles
and sides.
A dollar is made of four quarters like a quadrangle is made of
four angles and sides.
The Pentagon building in Washington, D.C. is in the shape
of a pentagon.
The x in hexa- is like the x in six.
An octopus has eight legs like an octagon has eight sides.
The Ns in nona- are like the Ns in nine.
Decades are made of 10 years like decagons are made of 10
angles and sides.
Student Page
Geometry
Polygons are named after the number of their sides.
The prefix for a name tells the number of sides.
Prefixes
triangle
quadrangle or
quadrilateral
pentagon
hexagon
heptagon
octagon
tri-
3
quad-
4
penta-
5
hexa-
6
hepta-
7
octa-
8
nona-
9
deca-
10
dodeca-
12
The flag of Nepal is the
only flag in the world with
5 sides. All other flags
have 4 sides. The flag of
Switzerland has a white
cross with an edge that is
a dodecagon (12 sides).
nonagon
flag of Nepal
flag of
Switzerland
1. Name the polygon.
a. 6 sides
b. 4 sides
d. 8 sides
e. 12 sides
c. 10 sides
2. Draw a pentagon whose sides are not all the same length.
Check your answers on page 339.
Student Reference Book, p. 103
472
Unit 6 Geometry
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SMALL-GROUP
ACTIVITY
ENRICHMENT
Solving Geometric Riddles
15–30 Min
(Math Masters, pp. 200 and 201; Student Reference
Book, pp. 112–114)
To apply children’s knowledge of geometric solid attributes, have
them solve geometry riddles. Directions are found on Math
Masters, page 200. Children may refer to the Geometric Solids
pages in the Student Reference Book as needed.
Planning Ahead
Make the prism from Home Link 6 12 for the Home Link
Lesson 6 13 Follow-Up.
Have children keep Math Journal 1 accessible throughout Unit 7
as they will need to cut out the remaining Fact Triangles on
Activity Sheets 3 and 4 for Lesson 7-2. Children also need to copy
the Length of Day graph on journal page 125 to the graph on
journal page 279. They need the data from the National
High/Low Temperatures Project on journal page 43 for
Lesson 7-8. Have children copy their body measures from journal
page 251. They will revisit their body measures in Lesson 10-7.
Teaching Master
Name
LESSON
6 12
Date
Teaching Master
Time
Name
Geometry Riddles
Date
Time
LESSON
6 12 Geometry Riddles Cards
1. Work in teams of 2 to 4.
112–119
2. Cut out the Geometry Riddles cards from Math Masters, page 201
and place them facedown on the playing surface.
3. The team of readers chooses a card and silently reads all the clues.
They write the answer to the riddle on a slate without showing it to
the other team, the guessers. Then they read only the first clue
aloud to the guessers. The guessers discuss the clue and guess
the shape. If their guess is correct, the turn is over. If it is not
correct, the readers read the second clue. Continue until the
guessers name the shape on the card. Then switch roles.
4. Readers assign one tally mark for every clue needed. Record the
tallies on the chart below.
5. If teams disagree on an answer to a riddle, they may use the Student
1. I am a geometric solid.
2. I have 2 surfaces.
2. I have only 1 surface.
3. My base is formed by a circle.
3. My 1 surface is curved.
4. I have a point at the top.
4. I have no base.
What am I?
What am I?
A cone
A sphere
1. I am a polyhedron.
1. I am a polyhedron.
2. I have 2 triangular bases.
2. I have the fewest number of
3. I have 3 other faces.
Reference Book section on Geometric Solids, pages 112–119.
4. My other faces are rectangles.
6. Teams switch roles. The game ends when all the cards have been
What am I?
used. The team with the fewest tally marks wins.
Names of Team Members
1. I am a geometric solid.
A triangular prism
Points
4. I come to a point at the top.
What am I?
A triangular pyramid
Team 1:
Team 2:
Math Masters, p. 200
EM3MM_G3_U06_167-205.indd 200
faces of all the polyhedrons.
3. All of my faces are triangles.
1. I am a polyhedron.
1. I am a polyhedron.
2. I have 5 faces.
2. I have 6 faces.
3. Four of my faces are triangles.
3. All of my faces are congruent.
4. My base is a square.
4. All of my faces are squares.
What am I?
What am I?
A rectangular pyramid
A rectangular prism or cube
Math Masters, p. 201
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2/10/10
Lesson 6 12
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