Download Geometry and Measurement of Plane Figures Activity Set 6 Trainer

Geometry and Measurement
of Plane Figures
Activity Set 6
Trainer Guide
geometry and measurement of Plane figures—Activity Set 6 Mid_PGe_06_TG
Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
GEOMETRY AND MEASUREMENT OF Plane FIGURES
Activity Set 6
NGSSS 6.G.4.2
NGSSS 7.A.5.2
GeoJam
In this activity, participants will apply computation
skills and their understanding of plane geometry to
various problem-solving situations.
Materials
• Transparency/Page: In the Swim
• Transparency/Page: In the Swim Answer Key
• Transparency/Page: Absolutely Floored
• Transparency/Page: Absolutely Floored Answer Key A
• Transparency/Page: Absolutely Floored Answer Key B
• Transparency/Page: Angle Puzzle
• Transparency/Page: Angle Puzzle Answer Key
• calculator (1 per pair)
• blank transparency (1 per group)
Vocabulary
• area
• perimeter
• angle
Time:
30 minutes
TEACHING TIP: This activity can be modified to
address specific content skills. For example, to
focus on angles, have all participants work on the
angle puzzle.
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_TG
1
GEOMETRY AND MEASUREMENT OF Plane FIGURES
Activity Set 6
Introduce
•Tell participants that they are going to apply some of
their knowledge about area and perimeter to real-life
problem-solving situations.
in the swim
The community recreation center is building a new
swimming pool and deck area.
The deck will measure 150 feet wide and 250 feet long,
including a 3 feet wide walkway that will wrap around the
pool. The pool, which is 82 feet wide and 164 feet long, will
be centered in the deck area.
1.
How much area will the deck cover?
(including walkway)
2.
How much area will the walkway cover?
geometry and measurement of Plane figures—activity set 8
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Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: In the Swim
•Display Transparency: In the Swim and have
participants take out their matching pages.
•Tell participants that their local recreation center is
building a new pool and deck area. Participants are on
the committee to help choose the material that will
be used for the deck. Participants will need to know
how much area the deck will cover before the
material to be used can be determined.
•Tell participants that the length of the total area will
be 250 feet and the width 150 feet. In this area, a
pool, measuring 164 feet long and 82 feet wide,
will be centered.
•Ask a participant volunteer to come up and label the
transparency with the facts that are known about the
pool and deck areas.
TEACHING TIP: Emphasize that the deck includes
the walkway and that the calculations concerning the
deck should reflect this fact.
•Have a volunteer participant suggest the first step in the
solution process for question 1. (Find the area of the
total deck, including the area that the pool will cover.)
•Ask participants what the length of the area is.
(250 feet)
•Ask participants what the width of the area is.
(150 feet)
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
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2
GEOMETRY AND MEASUREMENT OF Plane FIGURES
Activity Set 6
•Ask participants how they would find the area of the
deck. (Multiply the length times the width of the
total area and subtract the area of the pool.)
Note: This is one approach. There may be others.
•Write the problem on the transparency.
(250 • 150 = __)
•Direct participants to find the total area.
(250 • 150 = 37,500 square feet)
•Fill in the correct answer to the problem on the
transparency. (37,500 square feet)
•Ask a volunteer participant to suggest the next step in
the problem. (Find the area of the pool.)
•Ask participants what the length of the pool is.
(164 feet)
•Ask participants what the width of the pool is.
(82 feet)
•Ask participants how they would find the area of the
pool. (Multiply the length times the width.)
•Write the problem on the transparency.
(164 • 82 = __)
•Direct participants to find the area of the pool.
(164 • 82 = 13,448 square feet)
•Fill in the correct answer to the problem on the
transparency. (13,448 square feet)
•Ask participants to suggest the next step in solving
the problem. (Subtract the area of the pool from the
area of the total deck.)
•Ask participants what the total area is.
(37,500 square feet)
•Ask participants what the area of the pool is.
(13,448 square feet)
•Write the problem on the transparency.
(37,500 – 13,448 = __)
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
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3
GEOMETRY AND MEASUREMENT OF Plane FIGURES
Activity Set 6
•Direct participants to solve the problem.
(total area – pool area = deck area, 24,052 square feet)
•Ask participants how they could determine the total
area of the walkway and the pool.
•Explain, if they do not mention it, that the
dimensions of the area of the walkway and the pool
together are 6 feet wider and 6 feet longer than the
dimensions of the pool alone.
•Ask participants to determine the total area of the
walkway and the pool. (88 • 170 = 14,960 square feet)
absolutely Floored
The Andagans are buying new carpet for their living room,
family room, and dining room. The carpet that they have
selected costs $36.00 per square yard.
12'
Use the picture to find how much
they will have to pay for the carpet.
(Round to the nearest dollar.)
12'
20'
8'
Living Room
10'
16'
Dining Room
Family Room
•Ask participants how to use the information they
now have to find the area of the walkway alone.
•Explain, if they do not mention it, that they can
subtract the area of the pool from the area of the pool
and walkway combined.
12'
•Fill in the corresponding numbers and solve
the problem.
(14,960 – 13,448 = 1,512 square feet of walkway)
geometry and measurement of Plane figures—activity set 8
TRANS_MS_PG_08
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Absolutely Floored
angle Puzzle
Use the figure below to find the measure of each shaded
angle. (Matching hash marks indicate congruent lines.)
angle 1
angle 4
angle 2
angle 5
angle 3
3°
20° �2
Discuss and Do
•Tell participants that they will now do some problem
solving of their own.
•Have participants work in pairs or groups of three
within grade-level groups (as appropriate).
�5
•Give each pair or group a blank transparency.
125°
�3
125°
�4
�1
•Display Transparency: Absolutely Floored and
Transparency: Angle Puzzle and have participants take
out their matching pages.
geometry and measurement of Plane figures—activity set 8
TRANS_MS_PG_08
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Angle Puzzle
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
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4
GEOMETRY AND MEASUREMENT OF Plane FIGURES
Activity Set 6
•Assign each group one of the following pages:
Absolutely Floored
absolutely Floored
◆
Answer Key A
The Andagans are buying new carpet for their living room,
family room, and dining room. The carpet that they have
selected costs $36.00 per square yard.
12'
Use the picture to find how much
they will have to pay for the carpet.
(Round to the nearest dollar.)
12'
20'
8'
Living Room
10'
Dining Room
•Ask participants to use the blank transparencies to
show their step-by-step solutions to the problems.
•Give participants 5–7 minutes to work and record
their solutions.
Family Room
16'
Angle Puzzle
◆
12'
area of living room = 12 • 20 = 240 sq ft
area of dining room = 12 • 8 = 96 sq ft
area of family room = 16 (10 + 12) = (16)(22) = 352 sq ft
total area = 240 + 96 + 352 = 688 sq ft
total area in square yards = 688 ÷ 9 = 76.44 (1 sq yd = 9 sq ft)
cost = total square yards • $36.00
cost = 76.44 • $36.00 = $2,752.00
Conclude
(rounded to the nearest dollar)
geometry and measurement of Plane figures—activity set 6
TRANS_MS_PG_06
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Absolutely Floored Answer
Key A
absolutely Floored
Answer Key B
The Andagans are buying new carpet for their living room,
family room, and dining room. The carpet that they have
selected costs $36.00 per square yard.
12'
Use the picture to find how much
they will have to pay for the carpet.
(Round to the
nearest dollar.)
12'
16'
•Ask for a volunteer from a Absolutely Floored group to
share its step-by-step solution with the whole group.
•Ask if any other Absolutely Floored group had a
different solution or a different approach for solving
the problem.
20'
8'
10'
•Call the groups together.
Living Room
Dining Room
Family Room
12'
area of family and dining rooms
(including empty space) = 24 • 22 = 528 sq ft
area of empty space = 10 • 8 = 80 sq ft
area of family and dining rooms
(not including empty space) = 528 – 80 = 448 sq ft
area of living room = 12 • 20 = 240 sq ft
total area = 448 + 240 = 688 sq ft
•Have any group that had a different solution or
approach to the problem share its solution.
•Display, if participants do not suggest both solutions,
Transparencies: Absolutely Floored Answer Keys A and B
to show two approaches for solving this problem.
total area in sq yd = 688 ÷ 9 = 76.44 (1 sq yd = 9 sq ft)
cost = total sq yd • $36.00
cost = 76.44 • $36.00 = $2,752.00
(rounded to the nearest dollar)
geometry and measurement of Plane figures—activity set 8
TRANS_MS_PG_08
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Absolutely Floored Answer
Key B
•Ask participants who solved Angle Puzzle how their
problem differed from the flooring problem.
(It involved angles instead of area and perimeter.)
•Ask participants what additional knowledge they
needed to solve this problem. Some possible answers
may include:
The sum of all the angles in a triangle is 180˚.
◆
A straight angle is equal to 180˚.
◆
A right angle is equal to 90º.
◆
The sides and angles of an equilateral triangle
are congruent.
◆
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
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5
GEOMETRY AND MEASUREMENT OF Plane FIGURES
Activity Set 6
•Ask for a volunteer from an Angle Puzzle group to
share a step-by-step solution with the whole group.
•Refer to Transparency: Angle Puzzle Answer Key to
resolve any questions.
•Display a blank transparency.
•Ask all participants to name some skills that students
need, in addition to knowledge about area, perimeter,
and angles, in order to solve real-life problems similar
to these.
•Record participant responses on the blank
transparency. Some possible answers include the
ability to
read for understanding
◆
solve multistep problems
◆
sequence information
◆
choose the correct operation
◆
use addition
◆
use subtraction
◆
use multiplication
◆
use division
◆
use rounding
◆
compute the number of square feet in a square yard
◆
End of GeoJam
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_TG
6
In the Swim
The community recreation center is building a new
swimming pool and deck area.
The deck will measure 150 feet wide and 250 feet long,
including a 3 feet wide walkway that will wrap around the
pool. The pool, which is 82 feet wide and 164 feet long, will
be centered in the deck area.
1. How much area will the deck cover?
(including walkway)
2. How much area will the walkway cover?
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_PM
In the Swim
Answer Key
The community recreation center is building a new
swimming pool and deck area.
The deck will measure 150 feet wide and 250 feet long,
including a 3 feet wide walkway that will wrap around the
pool. The pool, which is 82 feet wide and 164 feet long, will
be centered in the deck area.
1. How much area will the deck cover?
(including walkway)
deck = 150 • 250 = 37,500 square feet
pool = 82 • 164 = 13,448 square feet
deck – pool = 24,052 square feet of decking
2. How much area will the walkway cover?
walkway = 88 • 170 = 14,960 square feet
walkway – pool = 1,512 square feet of walkway
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_PM
Absolutely Floored
The Andagans are buying new carpet for their living room,
family room, and dining room. The carpet that they have
selected costs $36.00 per square yard.
12'
Use the picture to find how much
they will have to pay for the carpet.
(Round to the nearest dollar.)
12'
20'
8'
10'
16'
Living Room
Dining Room
Family Room
12'
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_PM
Absolutely Floored
Answer Key A
The Andagans are buying new carpet for their living room,
family room, and dining room. The carpet that they have
selected costs $36.00 per square yard.
12'
Use the picture to find how much
they will have to pay for the carpet.
(Round to the nearest dollar.)
12'
20'
8'
10'
16'
Living Room
Dining Room
Family Room
12'
area of living room = 12 • 20 = 240 sq ft
area of dining room = 12 • 8 = 96 sq ft
area of family room = 16 (10 + 12) = (16)(22) = 352 sq ft
total area = 240 + 96 + 352 = 688 sq ft
total area in square yards = 688 ÷ 9 = 76.44 (1 sq yd = 9 sq ft)
cost = total square yards • $36.00
cost = 76.44 • $36.00 = $2,752.00
(rounded to the nearest dollar)
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_PM
Absolutely Floored
Answer Key B
The Andagans are buying new carpet for their living room,
family room, and dining room. The carpet that they have
selected costs $36.00 per square yard.
12'
Use the picture to find how much
they will have to pay for the carpet.
(Round to the
nearest dollar.)
12'
20'
8'
10'
16'
Living Room
Dining Room
Family Room
12'
area of family and dining rooms
(including empty space) = 24 • 22 = 528 sq ft
area of empty space = 10 • 8 = 80 sq ft
rea of family and dining rooms
a
(not including empty space) = 528 – 80 = 448 sq ft
area of living room = 12 • 20 = 240 sq ft
total area = 448 + 240 = 688 sq ft
total area in sq yd = 688 ÷ 9 = 76.44 (1 sq yd = 9 sq ft)
cost = total sq yd • $36.00
cost = 76.44 • $36.00 = $2,752.00
(rounded to the nearest dollar)
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
Mid_PGe_06_PM
Angle Puzzle
Use the figure below to find the measure of each shaded
angle. (Matching hash marks indicate congruent lines.)
angle 1
angle 4
angle 2
angle 5
angle 3
3°
20° �2
125°
�3
�5
125°
�4
�1
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
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Angle Puzzle
Answer Key
Step 6
Step 4
Angle 1 and angle 2 are formed by a line
that crosses parallel lines. Therefore they
are equal to their alternate interior
angles: 20º and 35º. This means that
angle 3 is 180º – 20º – 35º = 125º.
Subtract angle 4 and 125º from 180º to find
the remaining angle (5) of this triangle.
180º – 125º – 33º = 22º
20° �2
3°
�5
Step 2
Angle b is equal to 180º – 90º – 3º.
(A triangle has 180º, so subtract the
known angles to find the unknown.)
�3
125°
125°
�4
b
a
c �1
Step 1
Angle a is part of an
equilateral triangle—all angles
are equal. So, angle a equals 60º.
Step 5
180º – 125º – 20º = 35º
(The angles of a
triangle sum to 180º.)
Step 3
Angle a plus angle b plus angle 4 = 180º—a straight line.
180º – a – b = angle 4
180º – 60º – 87º = 33º
geometry and measurement of Plane figures—Activity Set 6 Copyright© by the McGraw-Hill Companies—McGraw-Hill Professional Development
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Glossary
Geometry and Measurement of Plane Figures
acute angle An angle with a measure less than 90degrees (°).
angle A geometric figure composed of two rays or line segments that share
the same endpoint, called a vertex.
area The number of square units in a region.
circle The set of all points in a plane that are the same distance from a
fixed point (the center of the circle).
circumference The perimeter of (distance around) a circle. The
circumference can be found using the formula C = 2πr, where C is
the circumference of the circle and r is the radius of the circle.
congruent figures Two figures that have identical size and shape so that
when one is placed over the other, they coincide exactly.
coordinate pair An ordered pair of numbers that indicates the position of
a point on a plane. The first number of a coordinate pair gives the
point’s location in relation to the x-axis. The second number in a
coordinate pair gives the point’s location in relation to the y-axis.
coordinate plane A plane containing an x-axis and a y-axis. Every point
on the plane can be described using a coordinate pair.
degree (°) A unit of measure for angles. 1° is
around a point.
1
360
of a complete revolution
equilateral The property of having equal, or congruent, sides.
equilateral triangle A three-sided polygon with all sides and with all
angles congruent.
hexagon A six-sided polygon.
irregular polygon A polygon in which not all the sides are congruent
and not all the angles have the same measure.
geometry and
and measurement
measurement of
of Plane
Plane figures—activity
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Glossary
(continued)
isosceles triangle A triangle that has two congruent sides and two
congruent angles.
line The set of all contiguous (touching) points that form a straight path
extending indefinitely in two directions opposite each other.
line segment A part of a straight line that has two end points and a
fixed length; a straight line segment marks the shortest distance
between two points.
linear unit A unit of measure for elements of a single dimension—length.
obtuse angle An angle with a measure greater than 90° and less than 180°.
parallel lines Lines that do not intersect and that are everywhere
equidistant from each other.
parallelogram A quadrilateral in which both pairs of opposite sides
are parallel.
pentagon A five-sided polygon.
perimeter The distance around the outside of a plane shape or figure.
perpendicular At right angles to. Two lines are perpendicular if their
intersection creates right angles.
pi (π) The ratio of the circumference of any circle to its diameter
(3.141592653. . .). Pi is usually represented by the Greek letter, π.
plane A flat surface that extends forever in all directions.
plane figure A figure that lies entirely in one plane.
point A location in space.
polygon A simple, closed plane shape composed of a minimum of three
straight-line segments.
geometry and
and measurement
measurement of
of Plane
Plane figures—activity
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Glossary
(continued)
quadrilateral A four-sided polygon.
radius A segment connecting the center of a circle to any point on the
circle; the length of the radius.
ray A subset of a line that includes one endpoint and that extends infinitely
from that endpoint in one direction.
rectangle A quadrilateral that includes four interior right angles.
regular polygon A polygon in which all the sides are congruent and all the
angles have the same measure.
rhombus A parallelogram in which all sides are congruent.
right angle An angle with a measure of 90°.
right triangle A triangle with one right angle.
scalene triangle A triangle in which no sides are congruent and no angles
have the same measure.
similar figures Figures that have congruent corresponding angles and in
which corresponding sides are proportional.
square A quadrilateral in which all sides and all angles are congruent.
square unit A unit of measure used to describe the surface (area) of figures
of two dimensions—length and width.
straight angle An angle with a measure of 180°.
trapezoid A quadrilateral in which only one pair of sides is parallel.
triangle A three-sided polygon.
vertex (pl. vertices) The intersection point shared by two sides of a
polygon or the two sides (rays) of an angle. Also the intersection point
shared by three or more edges of a polyhedron.
geometry and
and measurement
measurement of
of Plane
Plane figures—activity
figures—Activityset
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