Teacher Notes – Day 1
(review geometric shapes, descriptions and properties)
Activity 1 – Classify Me!
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Each student should get a copy of the page (becomes a review sheet for CST)
Work in groups of 4 students
Suggestion: let the group split up into pairs (one pair does odds, other does evens)
10 minutes to complete; 5 minutes to discuss
Note: That’s a short time limit, but make sure to have the discussion time, and let the answers come
from the students.
Activity 2 – What Are My Properties?
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Again, each student should get a copy of the page. (Don’t run the activities off front and back on
a single page; some answers to the first page are revealed on the second page.)
(5 min) Have a brief discussion with the class of what the various words mean. Let the
descriptions come from the students. Students should record a working definition in the space
provided.
(10-15 min) Let the student groups work on the table. Encourage them to draw on the examples,
or to make sketches of similar shapes on scratch paper to explore whether the property holds for
ALL examples of that kind of quadrilateral. Ask them “Are you SURE? How do you know?”
Do not re-teach material, either to the class or to that group, unless you know that NO ONE
knows anything. This is review; they should have seen it before, and need to practice recalling
prior knowledge. Questions should be aimed at jogging memories about what they know (and
mentally forming lists of what they really don’t remember)
Note: this is an opportunity for the Alg. 1A teachers to have a conversation with the Pre-algebra
teachers, even without using student performance data as evidence. There is a difference between
“covering” and “teaching for understanding”. If students learned these things last year, and don’t
remember this year, a Professional Learning Community will want to talk about what was done
and brainstorm how it might be done differently.
Activity 3 – Polygon Capture Game (IF TIME ALLOWS)
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You have an Overhead Transparency to discuss game rules with students
You have two pages of Xerox Masters that should be run off front-to-back. That should form the
cards, with the writing on both sides in the correct place. (Ideally, this would be done on
cardstock, and sets of playing cards built for use on a permanent basis.)
You have one page of Xerox Masters of what the polygon pieces are. (Ideally, this would also be
done on cardstock, with the shapes for one group put into a plastic baggie, along with the cards.
That way, you only have to distribute the bag to each pair of students.
Play on 16 sets of pieces + cards.
Suggestion: if one set is MADE, and lesson plans are choreographed so that each teacher is doing
this lesson on different days, then only one set is needed for the department.
Homework – CST Measure/Geometry 1
Classify Me!
Here is a variety of typical quadrilaterals (shapes having 4 sides):
b
f
d
a
c
g
h
i
e
For each of the following descriptions,
i) label which figures have all of those properties, and
ii) indicate the name used to describe that particular quadrilateral.
1) Has 4 sides
Opposite sides are congruent
Opposite sides are parallel
Opposite angles are congruent
2) Has 4 sides
Only 2 sides are parallel
Figures: _________________
Figures: _________________
Name: __________________
Name: __________________
3) Has 4 sides
All sides are congruent
Opposite sides are parallel
All angles are right angles
4) Has 4 sides
Has 2 pairs of congruent adjacent sides
Figures: _________________
Figures: _________________
Name: __________________
Name: __________________
5) Has 4 sides
Opposite sides are congruent
Opposite sides are parallel
All angles are right angles
6) Has 4 sides
All sides are congruent
Opposite sides are parallel
Opposite angles are congruent
Figures: _________________
Figures: _________________
Name: __________________
Name: __________________
What Are My Properties?
Here are examples of different types of quadrilaterals:
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Kite
What do the following words mean?
Congruent –
Parallel –
Right angle –
Opposite (either side or angle) –
Diagonal –
Bisect –
Perpendicular –
In the table below, put an ‘X’ in a cell if that figure has the indicated property.
Property
Diagonals bisect each other
Diagonals are congruent
Diagonals are perpendicular
Diagonals bisect angles
One diagonal forms two
congruent triangles
Both diagonals form four
congruent triangles
Parallelogram Rectangle Rhombus
Square
Trapezoid
Kite
Polygon Capture Game
To Play:
1. Player 1 turns over one card from the ANGLE deck, and
then one card from the SIDE deck. All polygons that
match both properties may be captured (removed from
play by that person).
2. If Player 1 has missed any figures, Player 2 may now
capture them.
3. Player 2 chooses a card from each deck and tries to
capture polygons.
4. If no polygons can be captured, a one-time second chance
is given -- that player may choose one more card (from
either deck). After that, the turn is over.
5. A player may challenge the opponent’s capture. If the
piece was incorrectly chosen, it is put back in play.
6. If the WILD CARD comes up, you may choose any side
property, and use that to capture polygons.
7. If the STEAL CARD comes up, do not turn over a second
card. Pick one side property and one angle property, and
steal all polygons from your opponent that have those two
properties.
6. Play until only two (or less) polygons remain. If you run
out of cards, reshuffle the deck. The player with the most
polygons wins.
Playing Cards (front side)
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
ANGLE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
SIDE
Playing Cards (back side)
All angles are
right angles.
At least one angle
is obtuse.
No angle is a
right angle.
At least one angle
is a right angle
At least two angles
are acute
All angles have the
same measure
At least one angle
is less than 90
STEAL CARD Select
properties; steal those
Throw away (extra)
No pair of sides
are parallel
All sides are of
equal length
Only one pair of
sides is parallel
All pairs of opposite
sides are parallel
It is a quadrilateral
All pairs of opposite
sides have equal lengths
At least one pair
of sides is perpendicular
WILD CARD Pick
your own side property
Throw away (extra)
All angles are
right angles.
At least one angle
is obtuse.
No angle is a
right angle.
At least one angle
is a right angle
At least two angles
are acute
All angles have the
same measure
At least one angle
is less than 90
STEAL CARD Select
properties; steal those
Throw away (extra)
No pair of sides
are parallel
All sides are of
equal length
Only one pair of
sides is parallel
All pairs of opposite
sides are parallel
It is a quadrilateral
All pairs of opposite
sides have equal lengths
At least one pair
of sides is perpendicular
WILD CARD Pick
your own side property
Throw away (extra)
Polygon Shapes
CST Measure/Geometry 1
I. Sketch a shape that fits each of the following descriptions; be sure to label important things.
1. isosceles right
triangle ABC with sides
AB and AC equal in
length and A the right
angle.
2. quadrilateral PQRS
with adjacent sides
PQ = QR and RS = SP
3. quadrilateral WXYZ
with all 4 sides having
different lengths
4. parallelogram ABCD
with AB about 3 times
as long as BC and A
around 60
5. trapezoid JKLM with
sides JK and LM the
parallel bases and with
side JM half the length
of side KL
6. two circles having the
same center, with the
radius of one being
twice the radius of the
other
II. Pick the correct answer from the ones that have been provided. Be prepared to defend your
choice in class tomorrow!
7. Of the following, which is NOT true for all rectangles?
A) The opposite sides are parallel
B) The opposite sides are equal
C) All angles are right angles
D) The diagonals are equal
E) The diagonals are perpendicular
8. Which of these quadrilaterals has exactly one pair of opposite sides that are parallel?
A) rectangle
b) rhombus
C) trapezoid
D) parallelogram
9. Which angle in the figure
shown at right has a measure
closest to 45?
A) p
B) q
C) r
D) s
(OVER)
10. In a quadrilateral, each of two angles has a measure of 115. If the measure of a third angle
is 70, what is the measure of the remaining angle?
A) 60
B) 70
C) 130
D) 140
E) none of the others
11. Carl drew the triangles shown below:
Carl concludes that all isosceles triangles are obtuse. Which of the triangles below could be used
to prove that Carl is incorrect?
A)
B)
C)
D)
Teacher Notes – Day 2
(focus on measurements, units, conversions, estimation)
Activity 1 – Metric Models
 Students could pair up, or work individually. They should begin working on this while
you check last night’s HW.
When checking the HW, look over the sketches quickly, but critically, and comment on
individual ones if there is something specific that needs to be corrected.
Discuss the multiple choice questions as a class; be sure to ask them for reasons WHY
they have a particular answer marked.
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When discussing the activity responses with the class, be sure to make explicit the
appropriate units that go with the types of quantities specified (weight, distance, volume,
temperature, etc.)
Activity 2 – Tools of the Trade
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This activity could be done in pairs, or in groups of 3-4 students. They will need access
to a protractor and a ruler with both inch and centimeter scales.
Have one group demonstrate their calculations for Question 1, with other student groups
verifying the work done. (Or have several groups contribute answers to one part of the
question.)
For question 2, make sure that the part b) question is discussed thoroughly. (There was a
HW question from the previous night that required the knowledge that angles in a
quadrilateral always add up to 360.)
Activity 3 – Building the Great Pyramid*
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Work can be done in groups, but each student should make their own pyramid. They can
share scissors, rulers, etc.
Students will need to prepare the net first, then take additional measurements and
calculate the surface area and volume of the pyramid, before taping the model into a 3-D
pyramid.
The question of interpreting the surface area formula should prove interesting; make sure
students see the expressions in terms of the geometric shapes they work with.
If they run out of time, the calculations can be part of their HW assignment.
Homework – CST Measure/Geometry 2
Metric Models
Directions: Each item in Column A will have a best answer from the measurements given in
column B. Put the letter that identifies the best measurement in the space provided.
Column A
Column B
1. _____ weight of a nickel
A) 1 mm
2. _____ thickness of a dime
B) 1 cm
3. _____ a little more than a quart
C) 1 dm
4. _____ a little more than 2 pounds
D) 1 m
5. _____ height of a doorknob (measured from floor)
E) 1 km
6. _____ size of a piece of toast
F) 1 dm2
7. _____ width of a small fingernail
G) 1 m2
8. _____ weight of a paper clip
H) 1 cm3 (or 1 cc)
9. _____ width of a clenched fist
I) 15 mL
10. _____ a little longer than 1/2 mile
J) 1 L
11. _____ a little larger than the top of a card table
K) 1 mg
12. _____ capacity of a tablespoon
L) 1 g
13. _____ weight of a little more than a quart of water
M) 1 kg
14. _____ capacity of a measuring cup
N) 0C
15. _____ around 20 short city blocks in size
O) 20C
16. _____ weight of a few grains of sand
P) 40C
17. _____ normal room temperature
18. _____ normal body temperature
19. _____ width of an adult’s handspan
20. _____ weight of a newborn baby
21. _____ temperature during a record-setting heat wave
22. _____ size of a man’s handkerchief
23. _____ freezing point of water
24. _____ capacity of an eye dropper
Symbol Key
1st letter
m: millic: centid: decik: kilo2nd letter (or only letter)
m – meter
m2: squares having unit length
m3: cubes having unit length
L: liters
g: grams
C: Celsius temperature scale
Tools of the Trade
Directions: You will need a ruler and a protractor to complete this activity. Be sure to answer
all of the questions.
a) The map, shown at right,
uses a scale in which 1 cm
represents 10 km on the land.
a) On the map, what is the
distance between Melville
and Foley in inches?
b) Knowing that 1 inch equals
2.54 cm, convert your answer
from part a) into cm.
c) Now, using the map scale, convert your answer from part b) into km. How many kilometers
actually separate the towns of Melville and Foley?
C
a) Robert measured the sides and angles of the
quadrilateral shown at right. Here are his measurements:
AB = 7.2 cm
BC = 6.0 cm
CD = 4.0 cm
AD = 7.8 cm
B
mA = 62
mB = 90
mC = 90
mA = 138
a) Robert made two incorrect measurements.
What are they?
*b) Just looking at his angle measurements, how can
you tell that a mistake was made somewhere?
D
A
Building the Great Pyramid*
(* If you build it, it’s gotta be great, right?)
Preparation Steps
1. Fold one corner of the 8½” x 11” paper to the
opposite corner. Cut off the extra rectangle.
The result is a square with sides of length 8½”.
(See figure 1 at right.)
2. Fold the paper in half lengthwise, then in
half again widthwise. Open the paper out and
mark the midpoint on each side. Draw a line
connecting opposite center points.
(See figure 2 at right.)
3. Measure 3¼” away from the center on each
of the four lines. Draw a red line from each
corner of the paper to each point you just marked.
Cut along these red lines to see what to throw
away. (See figure 3 at right.)
Figure 1
Figure 2
Figure 3
4. Draw blue lines as shown in figure 4 at right.
5. Put your name at the base of one of the sides
of your pyramid.
Figure 4
6. When the back side is finished, fold up and
tape into a pyramid shape. (See figure 5 at right).
Figure 5
Calculations
1) Calculating the surface area of a pyramid involves these steps:
a) The area of a triangle is found by using the formula: A = ½ bh. Measure and record the
base and height of one of your triangles; then calculate the area in units of sq. in.
b) You have four of those triangles. What would be the total area of all four triangles?
c) You also have to include the area of the base. In this case, it is a square. What is its area?
d) What is the total surface area of the pyramid? (Add together answers from parts b and c)
e) Here is the formula for finding the surface area of a pyramid: SA = 2sl + s2, where s is
the side length of the square (bottom) and l is the distance from the tip of the pyramid straight
down to the edge of the bottom along one of the four triangular walls (also called the slant
height). Where are the expressions ‘2sl’ and ‘s2’ actually calculating?
2. Calculating the volume of a pyramid uses the formula: V = (1/3)Bh, where B is the area of
the base, and h is the distance straight down from the tip of the pyramid to the center of the floor
below (called the height of the pyramid).
a) Fold two flaps of your net to form half of the pyramid. Now, measure and record the
height of your pyramid.
b) Now, calculate the volume of your pyramid. (Show your work!)
CST Measure/Geometry 2
I. For each of the following situations, indicate whether the specified measurement is likely to
be accurate (reasonable size, or can find an example in the real world) or unlikely. Indicate your
answer by checking the appropriate column. Be ready to defend your answers tomorrow!!!
Likely
Unlikely
Situation
1. My cousin, an NBA basketball player, is 3 m tall.
2. She ran 1 km in a minute.
3. A bicycle can travel at 12 km/hr
4. He planted a tulip in 1 cm3 of dirt.
5. He bought a meter of milk at the grocery store.
6. They made ice cream in a freezer at 10C.
7. A professional football player weighs 120 kg.
8. A top of a card table was covered with 1 m2 of cloth.
9. The temperature dropped to 25F and it began to snow.
10. She found a pencil which was 1 mm long.
11. His hand span (from the end of thumb to end of little
finger) measures 10 decimeters.
12. The area of a regular postage stamp is 20 cm
13. A gram is the same as a milliliter.
14. A ml is the same as a cc.
II. Use your ruler to help you solve this problem.
15. Janice rode her bicycle from Echo to Rapids,
and then from Rapids to Grant. About how many
miles did she ride? (1 mile = 1.6 km)
Map Scale: 1 cm = 1 km
(OVER)
16. What units would be best to use to measure the weight (mass) of an egg?
A) centimeters
B) milliliters
C) grams
D) kilograms
17. How many millimeters are in 20 centimeters?
A) 0.02 millimeters
B) 0.2 millimeters
C) 200 millimeters
D) 20,000 millimeters
18. How many seconds are in an hour?
A) 1/60 second
B) 60 seconds
D) 86,400 seconds
C) 3600 seconds
19. If the string in the diagram below is pulled straight, which of these answers is closest to the
length of the string?
A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
20. Which of the cubes below could be made
by folding the net figure shown at right?
Teacher Notes – Day 3
(review factor-label, converting units, area/perimeter)
Warmup –
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Ask students if they have seen the type of setup shown in Question 1. If necessary,
discuss
o what determines the first entry,
o how the rest of the rates are positioned into the calculation so that the units change
o how to double check what units the answer will have, and
o how to actually calculate the answer.
While students work on the warm-up questions, check students’ HW progress.
When reviewing last night’s HW, solicit responses and explanations from part I (#1-14),
and the multiple choice questions on the back side. Question 15 is more aligned with
today’s focus; spend time setting up the calculation using factor-label method:
1 km
1 mi
= answer (in miles)

1 in
1.6 km
Question 18 can also be set up using factor-label method:
______ cm 

1 hr 
60 min

1 hr
60 sec
1 min
= answer (in sec)
Activity 1 – Paving the Patio
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This is an assessment task. Take the opportunity to find out how well students can
actually do something of this nature when working in groups (recommend 3-4), as well as
what they remember about converting units and calculating area and perimeter. Make a
note of what skills need further review.
Encourage students to write out the steps they took, to show all the calculations (even if
using a calculator), and to convince you that the answer is correct. Each student should
have their own copy, but maybe an extra one could be provided to be turned in by the
group as their “final answer”.
It will be okay to clarify WHAT the task is asking the students to do, if they have read the
problem and don’t know what to do. It is also okay to coach students into drawing
geometric shapes, and asking them what the area would be or how they would find the
area.
Homework – CST Measure/Geometry 3
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The first several problems take a little setup work. If the previous activity is finished
fairly quickly, and there is time left in the class period, let the students discuss the
problems and how to do the setup work.
Rate These Problems
1) Gina works 6 hours per day and is paid $3.50 per
hour. If she works for 5 days, how much will she earn?
5 days 
6 hrs
1 day

$3.50 = ?
1 hr
The method shown above is called “Factor-Label” or
“Unit Analysis”. Set up the next problem in a similar
manner, and then solve it.
2) Robert is inviting 100 people to a party. He wants
to serve shrimp and hopes that each person will eat
only four shrimp. There are 20 medium-sized shrimp
to a pound, and shrimp costs $3.75 per pound. How
many pounds of shrimp should Robert order, and
what will it cost him?
Paving the Patio
(Balanced Assessment Program)
1. You have just been given the job of providing the measurement specifications for an
advertising circular that the HandyHome Company is going to produce. It is very
important that your specifications be accurate. Fill in the missing data on the
following sketch of one of the ads:
1 patio block covers _______ sq. ft.
______ round patio blocks cover 100 sq. ft.
_____ stepping stones cover 12 sq. ft.
_______ patio blocks cover 100 sq. ft.
2. A customer calls your HandyHotLine and wants to know what is the most
economical block to use to pave a 12 ft.  15 ft. patio. What would you advise? Be
sure to justify your answer clearly.
3. What would be the additional cost
if the customer decides to use these
border bricks around the perimeter
of the 12 ft. x 15 ft. patio?
CST Measure/Geometry 3
3 in.
1) You are going to put tile down on a square floor which is 10 ft.  10 ft.
The tile pattern is shown at right, and cost $0.30 each. How much will you
have to spend on tile?
3 in.
2) Lucille makes copper bracelets to sell at the local crafts show. Each bracelet requires a
rectangular strip of hammered copper that is 5”  7”. She buys the copper in rectangular sheets
that measure 21”  24”. What is the maximum number of bracelets that she can get from a
single sheet of copper?
3) Jones High School is constructing a circular ice skating rink. They want to design the rink so
that 15 trips around the outside rail will equal exactly one mile. (1 mile = 5280 feet) To the
nearest foot, what should the radius be? (Remember the formula: Circumference = 2r)
4) The front face of a rectangular box is a rectangle with area of 96 in2. The top face of the box
is a rectangle with area of 72 in2. The side face is also a rectangle, but only has an area of 48 in2.
What would the length, width and height of the box have to be?
A) 16  8  6
B) 12  8  6
C) 12  9  8
D) 12  6  4
5) A runner ran 9000 ft. in exactly 8 minutes. What was his average speed in feet per second?
A) 11.25
B) 18.75
C) 48.0
D) 112.5
E) 187.5
6) The chart shown at right describes the
speed of four desktop printers. Which
printer is the fastest?
A) Roboprint
B) Voltronn
C) Vantek Plus
D) DLS Pro
Printer
Roboprint
Voltronn
Vantek Plus
DLS Pro
Description
Prints 2 pages per second
Prints 1 page every 2 seconds
Prints 160 pages in 2 minutes
Prints 100 pages per minute
Teacher Notes – Day 4
(review area of regular and irregular-shaped objects)
Activity 1 – Islands
 Students could pair up, or work individually. They should begin working on this while

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


you check last night’s HW.
Ask students to explain how they determined areas for the last 4 islands, in particular.
(There may be more than one method used by students; let them all be discussed.)
Ask students to explain clearly how they found the perimeter of the triangle.
Ask students to explain what the difference is between perimeter and area as
mathematical concepts.
If students get done with the activity early, ask them to post a solution to Questions 1-3
from the previous night’s HW, but they must show all their work and explain
themselves clearly. (The multiple-choice questions are probably not necessary to
discuss completely; simply report the answers for those.)
Between working out the answers, discussing them, and discussing the previous night’s
HW, this should take about 15-20 minutes.
Activity 2 – County Concerns


This is another performance task, and students should be fairly well-prepared to do this
on their own. Provide as little support as possible, but encourage them to use factor-label
analysis to set up and solve Questions 2-4.
Allow some students to present their solutions and methods; let the other students in the
class critically examine their work. Be the authority only if needed.
Homework – CST Measure/Geometry 4
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
Mixture of problem types and demands. Some formulas are given, and others are not
provided deliberately. Some are calculations, some are thinking/process questions, and
an occasional problem solving question included.
The multiple choice format is to provide students the answers to help them check their
work. Make sure to have students present answers and discuss how they got them, and
how they know it’s correct.
Islands
Directions: Find the area of each of the following man-made islands. All measurements are in
miles.
1) Rectangle
2) Square
3) Zig-Zag
4
6
4
1
1
3
3
3
1
4
4
3
Answer: ___________ mi2
Answer: ___________ mi2
Answer: ___________ mi2
4) Chair
5) “H”
6) Triangle
2
2
6
2
3
3
2
2
2
8
1
8
12
2
3
2
2
2
2
5
Answer: ___________ mi2
Answer: ___________ mi2
Answer: ___________ mi2
Directions: If you had to walk all the way around the outermost part of each island, how far
would you travel? (In other words, what is the perimeter of each island?)
7) Rectangle: _________ mi
8) Square: __________ mi
9) Zig-Zag: __________ mi
10) Chair: __________ mi
11) “H”: ___________ mi
12) Triangle: __________ mi
County Concerns
The Jackson County Executive Board is considering a proposal to conduct aerial spraying of
insecticides to control the mosquito population. An agricultural organization supports the plan
because mosquitoes cause crop damage. An environmental group opposes the plan because of
possible food contamination and other medical risks.




Here are some facts about the case:
A map of Jackson County is shown at right.
All county boundaries are on a north-south
line or an east-west line.
The estimated annual cost of aerial spraying
12 miles
is $29 per acre.
There are 640 acres in 1 square mile.
Plan supporters cite a study stating that for
every $1 spent on insecticides, farmers would
gain $4 through increased agricultural production.
14 miles
Jackson County
3 miles
18 miles
1) What is the area of Jackson County in square miles?
2) How many acres are in the county altogether?
3) What would the proposed spraying program cost Jackson County?
4) According to plan supporters, how much money would the farmers gain from the spraying
program?
CST Measure/Geometry 4
1) Tracy is going to paint the outside of a box (with lid) to give as a gift. The box is 3 in. long, 4
in. wide, and 5 in. tall.
a) What is the surface area of the box in sq. in.?
b) What is the volume of the box in cubic in.?
2) The picture at right is a famous puzzle called
the Rubik’s cube. Suppose you painted the
outside completely purple. Then, after the
paint had dried, you took apart the puzzle,
producing 27 little cubes.
a) How many of the little cubes would have purple paint on 3 faces?
b) How many of them would have purple paint on only 2 faces?
c) How many of them would have purple paint on only 1 face?
3) Which of the two rectangles shown below has the greater area? How do you know?
Rectangle #1
Rectangle #2
5 units
4 units
(OVER)
4) Which has the greater area – the rectangle or the triangle? How do you know?
T riangle
Rectangle #1
5 units
T riangle
8 units
Directions: Only one correct answer for each of these.
Be prepared to explain your answers in class tomorrow!
5) Look at the circle shown at right. What is the circumference
of the circle? Round the answer to the nearest inch.
A) 3,142
B) 6,283
C) 3,141,593
D) 12,566,371
2,000 in.
6) The formula for the perimeter (P) of a rectangle is: P = 2l + 2w, where l represents the length
and w represents the width. What is the perimeter of a rectangle that has a length of 7 cm. and a
width of 4 cm.?
A) 11 cm
B) 18 cm
C) 22 cm
D) 28 cm
7) In the figure shown at right, the radius of the inscribed
circle is 6 inches (in.). What is the perimeter of square ABCD?
A) 12 in
B) 36
C) 24 in
D) 48 in
8) A right triangle is removed from a rectangle,
as shown in the figure at right. Find the area
of the remaining part of the rectangle.
(Area of a triangle = ½bh).
A) 40 in2
B) 44 in2
2
C) 48 in
D) 52 in2
9) A rectangular garden that is next to a building has a
path around the other three sides, as shown.
What is the area of the path?
A) 144 m2
B) 64 m2
C) 44 m2
D) 16 m2
Teacher Notes – Day 5
(review similarity, effect of size transformation on perimeter, area)
Warmup – Bulletin Board
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Let students work individually on this problem while you check last night’s HW. Monitor
the questions that give students particular difficulty; have students present solutions to those
problems. Discuss the BIG mathematical ideas behind those problems, or remind them
where that mathematics was studied last year.
When you discuss the warmup problem, remind students that there is another way to
calculate the answer besides finding the missing length. The scale factor (comparing the
size of the big rectangle to the size of the little one) is 2.5, so the perimeter of the big
rectangle must also be 2.5 times bigger than the perimeter of the little one. Therefore, the
answer is (19)(2.5).
While discussing how perimeter changes with size transformations, ask how the area would
be affected. The small rectangle’s area is 15, and the big one would be (2.5)2 times bigger.
Activity 1 – Washington’s Shadow
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This is a group activity (recommend 3-4 people per group). The students may not recognize
that triangles are involved, and they might not know that the triangles will be similar, since
the sun’s light rays are essentially parallel. If necessary, provide that information for the
students’ benefit, but let them set up the proportion and solve the problem.
Have 1-2 student groups present their solutions, especially if you see that there is more than
one method for finding the answer used by the student groups.
In a brief post-activity discussion, remind students that both the WU and the Activity used
similar shapes. Ask them what that means, what would be true of the shapes, and how to
proceed solving problems when you know the shapes are similar.
Activity 2 – Paving a Playground
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This is also a group activity (probably keep the same groups as before). This should be a
more familiar activity by the end of the week, especially the calculations of area and the use
of rates to solve problems.
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You might consider this activity as an actual assessment, and see what your students are
capable of doing on a task like that. 
HW – CST Measure/Geometry 5
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Students can begin working on this when their group is finished with Activity 2.
This is also a hodge-podge of problems, many coming from the CAHSEE sample test or
support materials. Monitor student difficulties with the problems, and provide additional
instruction and practice problems as appropriate.
Bulletin Board
In the pictures below, the larger bulletin board is
similar to the smaller one.
2 ft
5 ft
7.5 ft
Note: These figures are not drawn to scale.
What is the perimeter of the larger bulletin board?
Round your answer to the nearest foot.
Washington’s Shadow
Dion is standing next to the Washington Monument. He is 5’10” tall.
His shadow is 16 inches long. The shadow of the Washington Monument
is 127 feet long, as shown in the diagram at right and below.
Find the approximate height of the Washington Monument.
Use mathematics to explain how you determined your answer.
510
16 in.
127 ft.
Paving a Playground
You work for a paving company and need to give a school a cost estimate for paving the
playground and putting a concrete border around its perimeter. A scale drawing of the
playground is shown below.
The cost (labor and materials) for the pavement is $54 per square yard.
The cost (labor and materials) for the concrete border is $18 per linear foot.
What is your estimate for the total cost of the project?
CST Measure/Geometry 5
1) Look at the figure to the right.
What is the value of x?
O
x
A
5
12
T
42
H
2) The figure at right shows a shaded rectangle
inside a parallelogram. What is the area of
the shaded region?
For the remaining questions, there is only one correct answer. Be prepared to discuss your
answer with the class tomorrow.
3) The largest possible circle is to be cut from a 10-foot
square board. What will be the approximate area, in
square feet, of the remaining board (shaded region)?
(Hints: A = r2 and   3.14)
A) 20 B) 30 C) 50 D) 80
4) Bonnie had two similar rectangular
boxes. The dimensions of Box 1 are
twice that of Box 2. How many times
greater is the volume of Box 1 than the
volume of Box 2?
A) 3
B) 6
C) 8
D) 9
P
5) The short stairway shown at right is made
of solid concrete. The height and width of
each step is 10 in. (inches). The length is 20 in.
What is the volume, in cubic inches, of the
concrete used to create these steps?
A) 3000
B) 4000
C) 6000
D) 8000
6) The figure at right represents two
similar triangles. The triangles are not
drawn to scale.
In triangle ABC, what is the length of side BC?
A) 3.5 cm
B) 4.5 cm
C) 5 cm
D) 5.5 cm
E) 8 cm
7) The rectangle shown at right is twice
as long as it is wide.
What is the ratio of the width of the rectangle
to its perimeter?
A) 1/2
B) 1/3
C) 1/4
D) 1/6
8) Cherie cut four congruent triangles off the
corners of a rectangle to make an octagon, as
shown at right.
What is the area of the shaded region?
A) 128 cm2
B) 136 cm2
2
C) 140 cm
D) 152 cm2
9) In the figure shown at right, D is the
midpoint of AC , and BD is perpendicular
to AC .
What is the length of BD ?
A) 15 cm
B) 16 cm
C) 18 cm
D) 20 cm