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MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Patterns, Relationships and Functions
State Standard/Benchmarks: I.1.HS.1, I.1.HS.2
Grade Level Outcome:
PA-1 Infer and evaluate mathematical patterns.
Enabler:
1.
Analyze and generalize mathematical patterns.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
1. Write the next three numbers in each pattern.
a. 2, 4, 6, 8, _____, _____, _____
b. 30, 25, 20, 15, _____, _____, _____
c. 2, -2, 2, -2, _____, _____, _____
2. Write a rule to describe each pattern in #1.
(ans.
a) 10, 12, 14
b) 10, 5, 0
c) 2, -2, 2)
(ans. a. add 2 b. subtract 5
c. 2 and its opposite)
Vocabulary: sequence, series
0PICTORIAL (symbolic)
Which of the following is a tessellation?
a.
b.
c.
(ans. c)
Which geometric shape is used in the following tessellation?
(ans. equilateral triangle)
Vocabulary: tessellation
ABSTRACT (computational))
Make a tessellation using the following shape.
Vocabulary:
(ans.
))))
PA-1 Enabler 1 (continued)
PROBLEM SOLVING
A kitchen floor is rectangular and is 3.5 m wide and 4.2 m long. How many .5 m. by .5 m square tiles are needed to
tile the floor?
(ans. 29.5 tiles)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Patterns, Relationships and Functions
State Standard/Benchmarks: I.1.HS.3, I.1.HS.4
Grade Level Outcome:
PA-1 Infer and evaluate mathematical patterns.
Enabler:
2.
Study and interpret models of patterns.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Display the following information as ordered pairs:
Time
1 a.m.
2 a.m.
3 a.m.
4 a.m.
5 a.m.
Temp (F)
0
2
4
6
10
(ans. (1 a.m., 0) (2 a.m., 2) (3 a.m., 4) (4 a.m., 6) (5 a.m., 10))
Vocabulary:
PICTORIAL (symbolic)
Below are daily high temperatures in the first week of January recorded in Saginaw, Michigan.
What trend does the graph illustrate concerning temperatures?
Vocabulary: ordered pairs
PA-1 Enabler 2 (continued)
ABSTRACT (computational))
“Population Changes in Seven U.S. Cities”
City
New York
Los Angles
Chicago
Houston
Philadelphia
San Diego
Detroit
1970
7,896,000
2,818,000
3,369,000
1,234,000
1,950,000
697,000
1,514,000
1988
7,353,000
3,533,000
2,978,000
1,698,000
1,648,000
1,070,000
1,036,000
Which city has the largest decline in population from 1970 to 1988? How much was the decline?
(ans. New York, 543,000)
Vocabulary:
PROBLEM SOLVING
Construct a circle graph using the following information:
Yearly Spending Patterns for the Cox Family
a.
b.
c.
d.
e.
f.
Housing
Transportation $8,000
Food & Clothing
Medical
Entertainment
Miscellaneous
$6,600
$8,000
$2,000
$2,000
$6,000
(ans.)
Vocabulary: circle graph
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Patterns, Relationships and Functions
State Standard/Benchmarks: I.1.HS.5
Grade Level Outcome:
PA-1 Infer and evaluate mathematical patterns.
Enabler:
3.
Solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational))
Not Applicable
Vocabulary:
PROBLEM SOLVING
Marjorie opened a savings account with $100 at the beginning of January. The table below shows the interest earned
each month for four months.
Month
January
February
March
April
Interest
$1.00
$1.01
$1.02
$1.03
Balance
$101.00
$102.01
$103.03
$104.06
a. Describe the pattern for the values under the balance column.
b. Use the pattern to extend the table for the next four months.
(ans. a. Each month the interest increases by one penny. b. May, $1.04, $105.10; June, $1.05, 106.15 July, $1.06,
$107.21; August, $1.07, $108.28)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Patterns, Relationships and Functions
State Standard/Benchmarks: I.2.HS.1, I.2.HS.2
Grade Level Outcome:
PA-2 Investigate variability and change.
Enabler:
1.
Investigate with ordered pairs, tables, graphs, and equations and
understand rate of change.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Give the coordinates of each pt: A, D, F.
(ans. A = (0,3) D = (-3, -2
F = (-5,5))
Vocabulary:
PICTORIAL (symbolic)
Use the above graph to name the coordinates of any point:
1. in the first quadrant
2. between the 1st and 2nd quadrants.
Vocabulary: quadrants, x-axis, y-axis
(ans. 1. B (3,2) 2. A (0,3))
PA-2 Enabler 1 (continued)
ABSTRACT (computational))
Not Applicable
Vocabulary:
PROBLEM SOLVING
Graph y = 2x + 1 by completing the table and plotting the points. Then connect the points.
(ans.)
x y
x y
0
1
-1
2
-2
0
1
-1
2
-2
Vocabulary:
1
3
-1
5
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Patterns, Relationships and Functions
State Standard/Benchmarks: I.2.HS.6
Grade Level Outcome:
PA-2 Investigate variability and change.
Enabler:
2.
Solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational))
Not Applicable
Vocabulary:
PROBLEM SOLVING
Two years ago the value of a new car was $12,000. Its current value is $9,000. Predict the value of the car three
years from now if it continues to depreciate at the same rate. Use the graph to help find the solution.
(ans. the graph indicates after five
years, the car’s value is $4,500)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: I.2.HS.1, I.2.HS.2
Grade Level Outcome:
PA-3 Construct and critique geometric figures.
Enabler:
1.
Identify plane and solid geometric figures.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Where have you seen objects like these before?
What do you call them?
What geometric shape are they?
What are some objects like these that you have
seen in your home, school, and community.
(ans. will vary)
Vocabulary:
PICTORIAL (symbolic)
Make a collection of objects found in the classroom. Identify the geometric shapes that your items represent.
(ans. Example: ball = sphere, tissue box = rectangular prism)
Vocabulary:
ABSTRACT (computational))
Not Applicable
Vocabulary:
PROBLEM SOLVING
Name three real-world objects that look like:
a. spheres
b. cylinders
c. cones
d. cubes
Vocabulary:
(ans. will vary. Examples include; sun, golf ball, can,
silo, volcano, tornadoes, dice)
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.1.HS.3, II.1.HS.4
Grade Level Outcome:
PA-3 Construct and critique geometric figures.
Enabler:
2.
Draw and construct 2 and 3-dimensional figures.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Create a variety of 2 and 3-dimensional figures using mini marshmallows and toothpicks.
Vocabulary:
PICTORIAL (symbolic)
Create your own skeletal models of a cube using toothpicks and mini marshmallows.
Using graph paper, make a drawing of each of your marshmallow-toothpick figures.
Vocabulary:
ABSTRACT (computational))
Using your geometric model of a cube (with marshmallows and toothpicks), find the number of:
1. edges
2. faces
3. vertices
(ans. 1. 12 2. 6 3. 8)
Vocabulary:
PROBLEM SOLVING
Circles and rectangles can be used to create 3-dimensional models. Which of the networks (flat patterns) below
could be used to create a cylinder? Justify your conclusion.
A
B
C
D
(ans. A & C)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.1.HS.6
Grade Level Outcome:
PA-3 Construct and critique geometric figures.
Enabler:
3.
Compare and analyze shapes.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
1. Congruent figures have the same shape and size. Which figures look congruent?
A.
B.
C.
2. Similar figures have the same shape, but not necessarily the same size. Which figures are similar?
A.
B.
C.
3. Which letter(s) have a line of symmetry?
G
M
R
(ans. 1. C 2. C 3. M)
Vocabulary: congruent, similar, symmetry
PICTORIAL (symbolic)
List the pairs of equal angles in the congruent figures.
1.
f
a
b
2.
a
c
d
d
b
e
c
c
e
(ans. 1. a =  d;  b =  e;  c =  f
2.
Vocabulary: congruent, similar
ab & de , ac & df , bc & ef
f
PA-3 Enabler 3 (continued)
ABSTRACT (computational))
ABC  DEF. Find the length of AB . Use proportional thinking.
D
15
F
A
x
B
10
6
C
E
(ans. x/10 = 6/15, x =4)
Congruent figures have corresponding sides equal in length. List the pairs of equal sides in the following congruent
triangles.
A
D
(ans. AB = DE ,
Vocabulary: proportional, similar, congruent, corresponding
AC = DF , BC = EF )
PROBLEM SOLVING
A right triangle has sides with lengths 3, 4, and 5 centimeters. The smallest side of a similar right triangle has length
9. Find the lengths of the other two sides of the similar right triangle.
(ans. 3/9 = 4/x  x = 12
3/9 = 5/x  x = 15)
ABCD  EFGH. Draw two parallograms to represent this congruency. List all pairs of equal angles and equal
sides.
(ans.)
A
D
B
C
D
G
E
F
(ans. A = D
B = E
D = F
C = G
Vocabulary: similar, right triangle, congruent
AB
AD
DC
BC
= DE
DG
= GF
= EF
=
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.1.HS.2
Grade Level Outcome:
PA-3 Construct and critique geometric figures.
Enabler:
4.
Apply necessary conditions to analyze shapes.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Which of these figures is not a parallelogram?
A
B
C
D
(ans. D)
Vocabulary: parallelogram
PICTORIAL (symbolic)
1. Draw a figure that is a parallelogram.
2. Draw figure that is not a parallelogram.
(ans. 1.
2.
)
Vocabulary:
ABSTRACT (computational))
Write an algebraic equation that can be used to define the parallelogram ABCD.
(ans. AB = CD and BC = DA)
Vocabulary:
PROBLEM SOLVING
Measure the lengths of the sides and the angles of a parallelogram. What conclusions can you draw about angles and
lengths of sides in a parallelogram?
(ans. opposite sides and opposite angles are equal)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.1.HS.7
Grade Level Outcome:
PA-3 Construct and critique geometric figures.
Enabler:
5.
Use shape properties and relationships to solve problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational))
Not Applicable
Vocabulary:
PROBLEM SOLVING
A shirt, to be given as a gift, is put into a box. The dimensions of the box are 35 cm, 22.5 cm, and 6.25 cm. What is
the least amount of wrapping paper needed to wrap the gift?
(ans. 876.25 cm2)
How much leather is needed to cover a tiny ball whose radius is 6 cm?
(ans. 452.16 cm2)
Vocabulary:
`MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.2.HS.3
Grade Level Outcome:
PA-4 Construct and predict mathematical transformations.
Enabler:
1.
Plot and describe transformations.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Identify each preimage and image as an example of translation, reflection, or rotation.
a
b
c
(ans. a. translation b. reflection c. rotation)
Vocabulary: translation, reflection, rotation
PICTORIAL (symbolic)
Draw the reflective image of ABCD and label each reflective point.
A
B
A
B
C
D
(ans.
C
D
D
B
Vocabulary: reflective
C
A
ABSTRACT (computational))
By adding 2 to the first coordinate of each ordered pair, will the pre-image ABC be translated to the right or left in
a coordinate plane?
(ans. the image will be moved 2 units to the right)
Vocabulary: translate, coordinate
PA-4 Enabler 1 (continued)
PROBLEM SOLVING
Your designer has asked you to cut a pattern for a special skirt design. Draw the arrangement of the pattern pieces
that use the least amount of fabric.
Pattern Pieces
A
B
Fabric
C
(ans. will vary)
Vocabulary: reflected over, y-axis
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.2.HS.3
Grade Level Outcome:
PA-4 Construct and predict mathematical transformations.
Enabler:
2.
Compare size change.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Create an expansion by multiplying each coordinate by 2 and graph the image. What relationship exists between
corresponding lines?
(ans. Corresponding line segments are
parallel. Image segments are twice as
long.)
Vocabulary:
PICTORIAL (symbolic)
Create a contraction by multiplying each coordinate by ½ and graph the image. What relationship exists between
corresponding lines?
(ans. Corresponding line segments are parallel
and the image has segments 1/2 the length of
the pre-image.)
Vocabulary:
ABSTRACT (computational))
Not Applicable
Vocabulary:
PA-4 Enabler 2 (continued)
PROBLEM SOLVING
Make a drawing that is similar and 2.5 times the size of the drawing below.

Hint: Student should assemble an axis, record coordinate points, then expand/contract its size.
Vocabulary: expansion, contraction
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.2.HS.5
Grade Level Outcome:
PA-4 Construct and predict mathematical transformations.
Enabler:
3.
Solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational))
Not Applicable
Vocabulary:
PROBLEM SOLVING
Polygon ABCDEFGH outlines a top view of a school building. The architect wishes to send this outline by
computer to a builder. To avoid using negative numbers, the architect slides the graph so that the images of point A
is at the origin.
The image is drawn here.
What will be the coordinates of B', C' ,D', E', F', G', and H'?
Vocabulary:
(ans.
B' = (320,0) C' = (320, 100)
D' = (220, 100) E' = (260,40)
F' = (60,40) G' = (40, 100)
H' = (0, 100))
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.2.HS.1, II.3.HS.3
Grade Level Outcome:
PA-5 Scrutinize measurement.
Enabler:
1.
Make accurate measurements.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Q: How many mm wide is the
stamp?
A: 15 mm
Vocabulary:
PICTORIAL (symbolic)
Q: Where is pt. A on the
meter stick? (cm & mm)
A: 2cm; 20mm
Vocabulary:
PA-5 Enabler 1 (continued)
PICTORIAL (symbolic) (continued)
1. Draw a 30 ° angle.
(ans. 6)
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PA-5 Enabler 1 (continued)
PROBLEM SOLVING
A. Use your folding meterstick (or metric tape or ruler) to measure these objects in your home after you first have
estimated their lengths.
Estimate
________
________
________
________
________
________
1.
2.
3.
4.
5.
6.
7.
Height of a room from floor to ceiling
Width of a doorway
Diagonal length of a TV screen.
Diagonal of a dinner plate.
Length of a fork.
Thickness of a telephone directory.
Circumference of a small pot.
B.
1.
2.
3.
4.
5.
Find something in your home that measures.
1 cm ________________________________________
5 cm ________________________________________
10 cm _______________________________________
50 cm _______________________________________
100 cm ______________________________________
Vocabulary:
Measurement
________
________
________
________
________
________
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.3.HS.2
Grade Level Outcome:
PA-5 Scrutinize measurement.
Enabler:
2.
Apply measurements.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
The perimeter of a polygon is the sum of the lengths of the sides. Find the perimeter of the following polygon.
A
7”
6”
E
B
4”
6”
D
C
(ans. 7+6+6+4+4 = 27)
4”
Area is the measure of the region inside of a two dimensional flat figure. Which of the following figures could you
find the area of using the above definition?
a
b
c
d
e
(ans. a, c, and e)
Volume measures the space inside a three dimensional figure of solid. How many cubic centimeters does this cube
have?
10 cm deep
10 cm high
(ans. 10 x 10 x 10 = 1,000 cm3)
10 cm across
Vocabulary: perimeter, area, volume
PA-5 Enabler 2 (continued)
PICTORIAL(symbolic)
For which of the following figures can you find perimeter?
A
B
C
6
6
4
6
(ans. b and d)
Draw two different polygons that could have an area of 24 square units.
6
(ans.
4
6
)
8
Give an example of an object that would represent a:
a. cube
b. rectangular solid
c. sphere
(ans. a. dice b. box c. ball)
Vocabulary: perimeter, area, polygons
ABSTRACT (computational)
Find the perimeter of a rectangle whose length is 10 cm and whose width is 6 cm.
(ans. 10 + 10 + 6 + 6 = 32 cm)
Find the area of the following figures:
6
A.
B.
8
C.
D.
10
6
6
6
6
8
10
8
12
(ans. a. 62 = 36 sq. units b. ½  6  8 = 24 sq. units c.   102 = 100  sq. units
d. ½  8  (8+12) = 80 sq. units)
PA-5 Enabler 2 (continued)
ABSTRACT (computational) (continued)
Find the volume of the following figures:
A.
B.
C.
6
3
10
6
6
3
4
(ans. A. 63 = 216 cubic units B. 3 x 4 x 10 = 120 cubic units C. 4/3    33  113.04 cubic units)
Vocabulary: perimeter, area, volume
PROBLEM SOLVING
A rectangular backyard with dimensions of 100 m by 80 m is to be enclosed with fencing. Each section of fencing is
8 m in length.
How many sections of fencing will be needed to enclose the backyard?
(ans. 100 + 100 + 80 + 80 = 360 m
360 / 8 = 45 sections needed)
Mrs. Smith wants to fertilize her rectangular yard. The dimensions are 200 m by 100 m . A bag of fertilizer will
cover 5000 sq.m. Fertilizer cost is $9.00 per bag. What would Mrs. Smith pay to fertilize her yard?
(ans. 200 x 100 = 20,000 sq. m
20,000 / 5000 = 4 bags
4 bags x $9.00 = $36.00)
The cargo space in a freezer is 19.8 cubic m. How many packages with dimensions 1 m by 1 m by 2 m could the
freezer possibly hold?
(ans. package volume =- 2 cubic meters
 9 packages could fit inside the freezer)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Geometry and Measurement
State Standard/Benchmarks: II.3.HS.6
Grade Level Outcome:
PA-5 Scrutinize measurement.
Enabler:
3.
Use measurement knowledge to solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Measure your height to the nearest cm.
Vocabulary:
PICTORIAL (symbolic)
Use the figure. a. Tell whether the angle is acute
or obtuse. b. Give the measure of the angle.
(ans. 1.  CDE a. obtuse: b. 93
2.  CDB a. acute: b. 87)
B
3. A common dimension of
camera film is:
a. 35 km
(ans. d)
b. 35 cm
c. 35 m
d. 35 mm
C
.
A.
This picture is a close up of the markings on a giraffe. a. Tell
whether the angle is acute, right, or obtuse.
(ans. d)
Vocabulary: acute, obtuse, right
(ans. A. acute
B. obtuse
C. right)
PA-5 Enabler 3 (continued)
ABSTRACT (computational)
A high school freshman might be how tall?
a. 7m
b. 1.7 m
c. 2.2 m
d. 5.6 m
(ans. b)
Name the type of angle and give the measure of the angle formed by the minute and hour hands of a watch at:
a. 1:00
b. 4:00
c. 9:00
d. 6:30 (be careful)
(ans. a. acute, 30; b. obtuse, 120; c. right, 90;
d. acute, 15)
Vocabulary:
PROBLEM SOLVING
Each edge of the cube shown at the right is 7 cm
The surface area of a cube is the sum of the areas of the faces.
a. How many faces does a cube have?
b. What is the area of one face of the cube?
c. Find the surface area of the cube. Explain
how you obtained your answer.
d. If you double the length of each edge of the
cube, does its surface area double? Explain
your reasoning.
7
cm
7 cm
7 cm
(ans.
Vocabulary:
a.
b.
c.
d.
6
49 cm2
294 cm2, 6(7cm)2
no 6(142)  2[6(72)])
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.1.HS.1
Grade Level Outcome:
PA-6 Collect, organize, and display data.
Enabler:
1.
Collect and explore data.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Survey at least 25 people to find out what their favorite subject is in school.
(ans. will vary)
Vocabulary:
PICTORIAL (symbolic)
Organize data from your survey into a frequency distribution table.
(ans.
Math
||||| |||| ||
Science
|||| ||||
Soc. Studies |||
English
|||| | )
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
For five days, keep track of the number of hours you watch TV, do homework, talk on the phone and sleep.
Organize the data in a frequency distribution table.
Pair up with another student and compare tables.
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.1.HS.2
Grade Level Outcome:
PA-6 Collect, organize, and display data.
Enabler:
2.
Interpret graphs and tables.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Number of Raisins in a ½ oz. box
40 _____
_____
36 _____
_____
32 _____
_____
28 _____
NUMBER OF
_____
RAISINS
24 _____
_____
20 _____
_____
16 _____
_____
12 _____
_____
8 _____
_____
4 _____
0
0
Chris
Reagan
Guess
Amie
Ann
Jamie
Actual Count
Use the above graph to answer the following:
1. What do the two color bars represent on the graph?
(ans. shaded bars represent guessing the number of raisins in a ½ oz box. White bars represent actual
amount of raisins in a ½ oz box.)
Vocabulary:
PA-6 Enabler 2 (continued)
PICTORIAL (symbolic)
Use the above graph to answer the following:
1. How many raisins did Ann guess were in her box of raisins?
2. How many raisins were actually in her box of raisins?
(ans. 1. 24
2. 40)
Vocabulary:
ABSTRACT (computational)
Use the above graph to answer the following:
1. What is the difference between Ann’s guess of raisins and the actual amount of raisins?
(ans. 16)
Vocabulary:
PROBLEM SOLVING
Collect three samples of graphs from the newspaper or magazines. Write a short paragraph that describes the
information found in the graph.
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.1.HS.2
Grade Level Outcome:
PA-6 Collect, organize, and display data.
Enabler:
3.
Organize data into tables, charts, and graphs.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
With a set of data (given or collected on own), organize it into tables, scatter plots, box plots, stem and leaf and
histogram.
Vocabulary: tables, scatter plots, box plots, stem and leaf, histogram
PICTORIAL (symbolic)
1. Table/Scatter Plot
2. Line Plot
Example: Sixteen students estimated how much television they
watched each week, to the nearest hour. Here are their results:
14, 16, 12, 14, 11, 20, 8, 10, 16, 15, 17, 5, 15, 10.
Show these results on a line plot.
Vocabulary: line plot
(ans.)
(ans.)
PA-6 Enabler 3 (continued)
PICTORIAL (symbolic)
3. Box Plot
The Federal Highway Administration keeps track of the average miles per gallon for vehicles driven in each
state. The table below shows the data for the Midwestern States region for 1992. Use the data to make a
box-and-whisker plot.
Average Milage in the Midwestern
States Region
State
Illinois
Indiana
Iowa
Kansas
Michigan
Minnesota
Missouri
Nebraska
North Dakota
Ohio
South Dakota
Wisconsin
Miles per Gallon
13.47
16.19
13.75
15.29
17.33
17.65
15.52
14.54
14.66
15.56
15.22
18.05
4. Histogram
Each week, Billboard 200 lists the 200 top-selling albums. It also shows how many weeks each album has been on
the Top-200 Chart. As of May 10, 1997, the top 25 albums had been on the chart these number of weeks: 1, 1, 12, 6,
24, 43, 63, 59, 1, 11, 42, 33, 69, 11, 8, 7, 2, 6, 39, 7, 45, 24, 5, 10. (Source: Billboard)
(ans.)
Show the results on a histogram.
Number of Weeks on the
Top-200 Chart (as of 5/10/97)
Number of Weeks Frequency
1-20
14
21-40
5
41-60
4
61-80
2
Vocabulary:
14
12
10
8
Frequency 6
4
2
0
1-20
21-40
41-60
Number of Weeks
61-80
PA-6 Enabler 3 (continued)
PICTORIAL (symbolic) (continued)
5. Stem and Leaf
As of 1997, the following are the ages, in chronological order, at which U.S. Presidents were inaugurated:
57, 61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, 52, 56, 46, 54, 49, 50, 47, 55, 55, 54, 42, 51, 56, 55, 51, 54,
51, 60, 62, 43, 55, 46, 61, 52, 69, 64, 46,
Use a stem-and leaf plot to help you summarize the data.
(ans.)
AGES OF US PRESIDENTS WHEN INAUGURATED
Stem
Leaves
4 2, 3, 6, 6, 7. 8. 9. 9.
5 0, 0, 1, 1, 1, 1, 2, 2, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8,
6 0, 1, 1, 1, 2, 4, 4, 5, 8, 9,
Key: 4|2 represents 42 years
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Keep track of the high and low temperatures where you live each day for a week. Organize the data in several ways
and make at least three different types of graphs using this data.
(ans. will vary)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.1.HS.4
Grade Level Outcome:
PA-6 Collect, organize, and display data.
Enabler:
4.
Model real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Using the information displayed, make a double bar graph and answer the following questions .
1.
Which cities gained in population between 1970 and 1988?
2.
What conclusion could one make from the information about population trends in this time period?
(ans. sample)
1970 Population
7,896,000
2,812,000
3,369,000
1,234,000
1,950,000
697,000
1,514,000
1988 Population
7,353,000
3,533,000
2,978,000
1,698,000
1,648,000
1,070,000
1,036,000
(ans. 1. Los Angeles, Houston, San Diego
2. Sample: Population moved toward the
Southwest.)
Vocabulary: double bar graph
10,000,000
8,000,000
6,000,000
4,000,000
2,000,000
0
N
e
Lo w Y
s or
A k
ng
el
C es
hi
ca
H go
ou
P
hi sto
la n
de
S lph
an ia
D
ie
g
D o
et
ro
it
City
New York
Los Angeles
Chicago
Houston
Philadelphia
San Diego
Detroit
1970 Population
1988 Population
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.2.HS.1
Grade Level Outcome:
PA-7 Analyze and interpret data.
Enabler:
1.
Critique data from tables, charts, and graphs.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
To display means to show. The most common ways of displaying numbers are in graphs and tables. Below, a day
in the life of a high school freshman is displayed in three different ways.
Bar Graph
9
8
7
6
5
4
3
2
1
0
Series2
E
at
S
Tr
c
an
h
sp ool
or
ta
ti o
H
n
o
S
m
ch
e
w
oo
l A ork
ct
iv
iti
R
es
el
ax
at
io
n
8
1.5
7
1
2
2
2.5
S
le
ep
Sleep
Eat
School
Transportation
Homework
School Activities
Relaxation
Number of hours
Table
Activity
Pie Chart
Relaxation
10%
School Activities
8%
Sleep
34%
Homework
8%
Transportation
4%
Eat
6%
School
30%
Vocabulary: interval
1. What is the interval of
the scale of this students
day?
2. Are the bars on this
graph horizontal or vertical?
3. The student could spend
more time on homework.
Where could the time come
from?
(ans. 1. 1 hr 2. vertical
3. relaxation time)
PA-7 Enabler 1 (continued)
PICTORIAL (symbolic)
Use the coordinate graph to the right.
1. Is the cost of insurance increasing or decreasing?
2. How much did medical insurance cost in 1980?
3. In what year did the average cost of medical
insurance exceed $200/year?
4. True or false? In 1988 medical insurance costs
hit a record high of $484 per year.
.
(ans. 1. increasing 2. $97/year 3. 1983)
Vocabulary:
PA-7 Enabler 1 (continued)
ABSTRACT (computational)
(ans.
Vocabulary:
1.
2.
3.
4.
Between 1950 & 1960
135,000,000
1960 – 1970 approx. 30,000,000
1930 – 1940 approx. 10,000,000)
PA-7 Enabler 1 (continued)
PROBLEM SOLVING
Outlined below is a miniature golf hole. All the angles are right angles. Lengths of sides are given. Suppose this outline
were graphed with A at (0,0) and H on the x-axis.
(ans. a. B (0,10) C (6,10) D (6,4) E (9,4) G (15,10) H (15, 0) b. (12,10) c. (3,7))
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.2.HS.2
Grade Level Outcome:
PA-7 Analyze and interpret data.
Enabler:
2.
Determine the measures of central tendency.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
A student scores 89, 72, 99, 93, and 81 on five tests. Give the range, median, mean, and mode of this set of
numbers.
(ans. The range is the difference of the largest and smallest numbers. 99 – 72 = 27. The range is 27. The median is
the middle number is the numbers are in numerical order. So order the numbers: 72, 81, 89, 93, 99. The middle
number is 89, the median. No number appears more often than the others. Therefore, this set of numbers has no
mode.
Mean: The mean is the average of the given numbers. First add the five scores and then divide by four.
(89  72  99  93  81)
5
mean = 86.8
Vocabulary: range, median, mean, mode
PICTORIAL (symbolic)
Below are the state sales tax rates charged on restaurant meals in the 50 states.





























  



   
|
|
|
|
|
|
0
1
2
3
4
5
A.
B.
C.
D.




|
6


|
7
percent
How many states charge 4% or less?
How many states use tax rates that involve a fraction of a percent?
Find the mode for the data.
Find the mean for the data.
(ans. A. 33 states, B. 6 states, C. 4%, D. 3.44%)
Vocabulary:
PA-7 Enabler 2 (continued)
ABSTRACT (computational)
The school board reported the average teacher salary was $44,000. The teacher association stated that the most
frequent salary earned was $41,000. The Saginaw News stated that the middle salary was $43,000.
State which measure of central tendency each group is using.
(ans. school board: mean, teacher association: mode, Saginaw News: median)
Vocabulary: central tendency
PROBLEM SOLVING
In ten basketball games, Kim scored 9, 12, 11, 8, 11, 15, 15, 16, 15, and 19 points. To the nearest tenth of a point,
find the mean, the median, the mode, and the range.
(ans.
Vocabulary:
Mean: 13.1
Median: 13.5
Mode: 15
Range: 11)
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.2.HS.5
Grade Level Outcome:
PA-7 Analyze and interpret data.
Enabler:
3.
Solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Graph the following temperatures and find the mode, median, and the range for the average monthly temperatures
given in degrees Celsius: -1.5, -2, -1, 5, 24.5, 28, 33.5, 34, 28.5, 18.5, 6, 1.5.
(ans.)
Mean:  14.58
Median: 12.25
Mode: None
Range: 36
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PA-7 Enabler 3 (continued)
PROBLEM SOLVING
Each student will develop a graph (bar/circle/coordinated) by gathering data from a school related activity. After
plotting the graph the student will analyze and interpret the data in the form of writing related questions to be
answered by their peers.
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.3.HS.1
Grade Level Outcome:
PA-8 Draw conclusions and make predictions.
Enabler:
1.
Make and test hypotheses.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
The science teacher lost five test papers, and of course, mine was one of them. He found a summary of the missing
scores which said that the mode of the scores was 90, the median was 85, and the mean was 83. This summary
sounds pretty good! How bad could my score be? The grades were whole numbers between 0 and 100. What is the
lowest possible score I might have gotten?
(ans. 66 Explanation:
Mode:
90
7
90
7
85
2
85
1
??
??
These scores total 17 above the mean. To make the average of the scores come out to 83, the missing score must be
17 below the mean: 83 – 17 = 66.)
Vocabulary:
PA-8 Enabler 1 (continued)
PROBLEM SOLVING
A hypothesis is an educated guess. To find if a hypothesis is true, you must test it.
A
5
3
B
6
C
9
10
15
1. Write a hypothesis about the ratio of the perimeters and areas of two similar figures.
2. Make a table with entries for base, height, perimeter, and area and find this information for similar figures A,
B, and C.
3. Use the information in your chart for figures B and C to answer the following questions. Write all fractions in
lowest terms.
a. What is the ratio of the heights?
b. What is the ratio of the bases?
c. What is the ratio of the perimeters?
d. What is the ratio of the areas?
4. Do you need to revise your hypothesis? Do so, if necessary. Test it on figures A and C.
5. Predict the ratio of the perimeters and areas of two triangles if the ratio of their heights is 5/8.
(ans. 1. may vary
b
h
p
2. a
A
5
3
16
15
B
10
6
32
60
C
15
9
48
135
3. a. 2/3 b. 2/3 c. 2/3 d. 4/9
4. A possible response: Square of heights equal ratio of areas.
5. 5/8, 25/64
Vocabulary: hypotheses, ratio
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Data Analysis and Statistics
State Standard/Benchmarks: III.3.HS.2, III.3.HS.5
Grade Level Outcome:
PA-8 Draw conclusions and make predictions.
Enabler:
2.
Design experiments to model and solve problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Collect Data
The school bookstore plans to stock sweatshirts, hats, and jackets. It is important not to overstock. The store
manager asks you to determine the number, color, and size of each item to order.
1. Write a survey questionnaire to find out student interest. Design the questionnaire so that you can
estimate the sales by color and size of each item.
2. Who will you survey? Will a random survey suit your purposes or will selecting survey groups from
each grade level be a more accurate method of determining your market?
3. Where will you conduct the survey? Will verbal responses be as helpful as written responses?
4. Conduct the survey.
Analyze Data
5. Calculate the number of expected sales for each item by color and size.
6. In collecting data, was interest expressed in items not on your list? Do you need to expand your
choices and do another survey?
Make Decisions
7. Decide if you will order exactly the number of items you have found to be your expected sales. Should
you order more? Less? Explain your decision.
8. Contact a supplier to find the wholesale cost of each item. Determine what price you will set for each
item.
9. Present your results to the school bookstore or to some other group for a fund-raising project.
(ans. will vary)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.1.HS.1
Grade Level Outcome:
PA-9 Analyze and apply properties of real numbers.
Enabler:
1.
Develop an understanding of the properties of real numbers.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Match each property with its general form.
1.
4+3=3+4
2.
7(2+3)=72+73
3.
4x1/4=1
4.
(4+2)+3=4+(2+3)
5.
7+0=7
6.
-6+6=0
7.
121=12
8.
2/3=12/18
a.
b.
c.
d.
e.
f.
g.
h.
Multiplicative Identity
Commutative Property of Addition
Property of Opposites
Distributive Property
Additive Identity
Property of Reciprocals
Associative Property of Addition
Means and Extremes Property
(ans. 1b, 2d, 3f, 4g, 5e, 6c, 7a, 8h)
Vocabulary
PICTORIAL (symbolic)
Write the math equation that is pictured for each of the properties listed below.
1.
ASSOCIATIVE PROPERTY
DATE
DEPOSIT WITHDRAWAL
24-Oct $150.00
27-Oct
$70.00
31-Oct $100.00
1-Nov
$40.00
3-Nov
$60.00
6-Nov
$50.00
(ans. (150+-70)+(100+-40)+-(60+50)=130)
2. COMMUTATIVE PROPERTY
(ans. 3 x 5 = 5 x 3)
Vocabulary: associative property, commutative property
PA-9 Enabler 1 (continued)
PICTORIAL (symbolic)
3.
DISTRIBUTIVE PROPERTY
8X20
8X3
(ans.)
8 23 = 8(20+3)
= (820) + (83)
= 160+24
= 184)
23
4.
ADDITIVE IDENTITY
|
-3
|
-2
|
-1
5.
|
0
MULTIPLICATIVE IDENTITY
1=
(ans. n  1 = n)
(ans. –3 + 0 = -3)
PROPERTY OF RECIPROCAL
4X
=
(ans. 4  1/4 = 1)
PROPERTY OF OPPOSITES
$5 in wallet
-$5 out of wallet
=
$0 left in wallet
(ans. 5 + -5 = 0)
MEANS AND EXTREMES PROPERTY
A
B
D
C
E
F
(ans.
AB
AC
=
)
DE
DF
Vocabulary: additive identity, property of reciprocal, property of opposites, means and extremes property,
distributive property, multiplicative identity
PA-9 Enabler 1 (continued)
ABSTRACT (computational)
Complete:
Associative Property:
Commutative Property
Distributive Property
Additive Identify
Multiplicative Identity
Property of Reciprocal
Property of Opposites
Means and Extremes Property
(4 + 2) + 3 =  + (2 + 3)
4+3=+4
7(2 + x) = 7   + 7  
7+=7
12   = 12
¼=1
-6 +  = 0
AB = AC
DE
DF
Vocabulary:
PROBLEM SOLVING
Means and Extremes Property:
1.
Suppose six bags of wheat cost 11 silver pieces. How much should 10 bags cost?
(ans.
11 P
=
; P = 18 1/3)
6 10
Distributive Property:
2.
You own a small business that has three employees. You pay one employee $1800 a month, the second
$1500 a month, and the third $1300 a month.
a. Write an algebraic model that represents how much you pay all three employees in the year.
b. Use the model in part a to determine how much you pay your employees in a year.
(ans.
a. 12(1800 + 1500 + 1300)
b. (21600 + 18000 + 15600) = 55200)
Commutative & Associative Properties:
1.
On November 1, a person has $400 in a savings account. Below are the transactions for the next two
weeks.
Date
Deposit Withdrawal
3-Nov
$ 102.00
5-Nov
$
35.00
8-Nov
$
75.00
11-Nov $ 40.00
12-Nov
$
200.00
Using commutative and associative properties, calculate the amount in the account at the end of the day
on November 12.
(ans. $232.00)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.1HS.4
Grade Level Outcome:
PA-9 Analyze and apply properties of real numbers.
Enabler:
2.
Apply knowledge of properties to real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
The Smith family drove 230 miles the first day and 185 miles the second day. If they reversed the driving distance
by driving 185 miles the first day and 230 miles the second day, what would be the results. Name the appropriate
property used to solve the problem.
(ans. Commutative Property, 415 miles)
There are eight people who received a check for $23.00. What property would allow each person to receive a $20
bill and 3 ones? 8 x 23 = 8(20 + 3)
(ans. Distributive Property)
Suppose a dozen cookies cost $6.60. How much will 2 cookies cost? Name the property used to solve the problem.
(ans. Means and Extremes Property, $1.10)
Three friends went to the bulk food store. Sally bought $3.00, Tom bought $2.50, and Pat bought $7.25 worth of
candy. They also all bought trail mix. Sally bought $7.25, Tom bought $3.00, and Pat bought $2.50 worth. Was the
total dollars spent on candy more than the total spent on trail mix? What property does this show?
(ans. Total dollars are the same, 3.00 + 2.50 + 7.25 = 7.25 +
3.00 + 2.50. Shows the commutative property)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.2.HS.1
Grade Level Outcome:
PA-10 Analyze the representations and use of numbers.
Enabler:
1.
Recognize and generate equivalent representations of a number.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
If 1/2 = .5 = 50% and 1/4 = .25 = 25% then 1/2 + 1/4 = __________ or __________ or __________.
a. fraction
b. decimal
c. percent
(ans. a. 3/4 b. .75 c. 75%)
********************
Fill in the missing letter with the correct answer.
Power of 10
Word Name
Written as a decimal
101
__________A
10
102
hundred
100
103
thousand
1000
106
million
__________B
_____C
billion
1,000,000,000
_____D
trillion
__________E
1015
quadrillion
1,000,000,000,000,000
Answer the following:
Decimal Notation
340.67
2.380,000,000
__________B
Scientific Notation
3.4067 x 102
__________A
6 x 1013
***********************
(ans. A. ten
B. 1,000,000
C. 109
D. 1012
E. 1,000,000,000,000)
(ans. A. 2.38 x 109
B. 60 trillion)
The square of 25 is 625. Twenty-five is called the square root of 625. Which of the following numbers have square
roots that are integers?
a. 25 b. 30 c. 144 d. 200
(ans. a, c)
Vocabulary: square root, integers
PA-10 Enabler 1 (continued)
PICTORIAL (symbolic)
Given the following information, find the fraction
and percent equivalent.
Decimal: 0.9
Word name: nine tenths
Fraction: ______________
Percent: ______________
Decimal: 0.64
Word name: sixty-four hundredths
Fraction: __________________
Percent: ___________________
(ans. a) 9/10, 90% b) 64/100, 64%
******************
Would you rather have $100 a day for 30 days or 2¢ on Day 1, 4¢ on Day 2, 8¢ on Day 3 and so on?
(ans. 100 a day for 30 = $3000, daily totaled each day = $10,737,418.24)
********************
Between what two consecutive whole numbers is
Vocabulary:
ABSTRACT (computational)
Find the missing numbers:
Fraction
Decimal
a. 1/2
.5
b. _____
.75
c. 1/100
_____
d. _____
.05
40
(ans. 6 and 7)
Percent
_____%
75%
1%
5%
(ans. a. 50%,
b. 75/100 or 3/4,
c..01, 5/100 or 1/20)
********************
Solve:
25 + 16 b. 100  44 c.
a.
(ans. a. 9; b. 12; c. 3, d. 17)
Vocabulary:
36 x
4 / 16
d. (
17 )
PA-10-Enabler 1 (continued)
PROBLEM SOLVING
The probability of a single birth being a boy is about .52. Convert this number to a percent. (ans. 52%)
********************
The distance from Earth to the Sun is about 150,000,000 km. Write this number in scientific notation.
Solution: First, move the decimal point to get a number between 1 ans 10. In this case, the number is 1/5 and this
tells you the answer will look like this:
1/5 x 10exponent
The exponent of 10 is the number of places you must move the decimal in 1/5 to the right in order to get
150,000,000. You must move it 8 places, so the answer is
1.5 x 108
********************
The area of a square shaped deck is 196 square feet. How long is each side of the deck?
(ans.
Vocabulary: exponent
196 = 14 ft.)
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.2.HS.4
Grade Level Outcome:
PA-10 Analyze the representations and use of numbers.
Enabler:
2.
Apply and refine strategies for estimating quantities.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Drawing pencils are sold in packages of 10. If a teacher needs one pencil for each student in a class of 32, how many
boxes must be bought?
(ans. 4 boxes)
Vocabulary:
PICTORIAL (symbolic)
The area of a room is 90.25 sq.m. If carpet is sold at $3.00 of sq.m. and you have $300.00, will you be able to carpet
the room? Estimate your answer.
(ans. yes)
Vocabulary:
ABSTRACT (computational)
If small cans of grapefruit juice are 5 for $1.69, estimate how many cans can be bought for $10.00?
(ans. 30 cans)
Vocabulary:
PROBLEM SOLVING
A town’s population, rounded to the nearest hundred, is 800. What is the smallest possible actual population?
(ans. 750)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.2.HS.5
Grade Level Outcome:
PA-10 Analyze the representations and use of numbers.
Enabler:
3.
Use knowledge of number systems to solve problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PA-10 Enabler 3 (continued)
PROBLEM SOLVING
An electron microscope can magnify an object 105 times. The length of a poliomyelitis virus is 1.2 x 10 -8 cm.
Multiply this length by 105 to find how many meters long the virus would appear to be when viewed through this
microscope.
(ans. .12 cm)
It rains or snows on about 42% of the days of the year in Seattle, Washington. About how many days per year is
this?
(ans. 153)
The population of the world passed 5.3 billion in 1990. This number is 5,300,000,000 and has too many digits for
most calculators. Write it in scientific notation so that it can be entered into a calculator and used.
(ans.
Since 1 billion = 109, 5.3 billion = 5.3 x 109
So, the number is 5.3 x 109 in scientific notation.)
You are making a comic book that is 11.5 cm by 16 cm. Each page of the comic book has a bottom and a top
margin of 1.7 cm and a left and right margin of .6 cm.
a. What is the perimeter of the page.
b. What are the dimensions of the printed portion of the page?
(ans. a. 55 cm
b. 10.3 cm x 12.6 cm)
Write and equation and solve.
A 13-meter extension ladder is placed 5 meters away from a building. How high will it reach? (Use h for height.)
a. equation
b. solution
13 m
5m
Vocabulary:
(ans. a. 52 + h2 = 132
b. 12)
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.2.HS.1
Grade Level Outcome:
PA-11 Compare number relationships.
Enabler:
1.
Compare and order real numbers.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Order the following numbers from lowest to greatest.
0 -3 2 1/2 -0.25
(ans. –3 -0.25 0 1/2 2)
Vocabulary:
PICTORIAL (symbolic)
The thermometers pictured at the right show Joanne’s body
temperature on three consecutive days of a cold.
Put the three numbers into one sentence connected by
inequality symbols.
(ans. 100.4 > 99.8 > 99.2)
Vocabulary: inequality symbols
ABSTRACT (computational)
Draw a real-number line. Put the following on the real-number line.
(ans.)
Vocabulary:
-1/2 0 7 1 1/4 -2 1/3 -4
PA-11 Enabler 1 (continued)
PROBLEM SOLVING
Sam and Amy had two equal sized pizzas. Sam cut his pizza into three equal parts. Amy cut her pizza into eight
equal parts. Sam ate two of the three pieces of a small pizza. Amy ate five of the eight pieces of the same size.
Compare 2/3 and 5/8 to find out who ate more.
(ans. 2/3. Sam ate more)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Number Sense and Numeration
State Standard/Benchmarks: IV.2.HS.2, IV.3.HS.3
Grade Level Outcome:
PA-11 Compare number relationships.
Enabler:
2.
Express numeric relationships.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
A prime number has only two factors: itself and one. Example: 7 x 1 = 7
A composite number has three or more factors.
Determine whether each number is prime or composite.
a) 11 b) 12 c) 15 d) 53
(ans. a) prime b) composite c) composite d) prime)
A factor is a number that divides another number exactly. Which of the following is a factor of 20?
a) 7 b) 15 c) 3 d) 5
(ans. D)
The first five multiples of ten are 10, 20, 30, 40, and 50. List the first three multiples of eight.
(ans. 8, 16, 24)
The ratio of boys to girls in Mr. Smith’s class is 2 to 3. If there are 30 students in the class, how many girls are
there?
(ans. 18 girls)
Rates are usually expressed using the word per. If Tom made $400 in 8 hrs. of work express his rate of income in
dollars per hour.
(ans. 400/8 = $50 per hr.)
Reciprocals are two numbers whose product is one. Six is the reciprocal of one-sixth. Which of the following pairs
of numbers are reciprocals?
a) 10, 1/10 b) 4/3, 3/4 c) 4, 4/1
(ans. a & b)
Vocabulary: prime, composite, factor, multiple, reciprocal, ratio, rate
PA-11 Enabler 2 (continued)
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
List all prime numbers between 30 and 50.
(ans. 31, 37, 41, 43, 47)
List all composite numbers between 30 and 50.
(ans. 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46,
48, 49)
List the factors of 24 and 60. Then state the greatest common factor.
(ans. F24 = 1, 2 ,3, 4, 6, 8, 12, 24,
F60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
GCF = 12)
Find the least common multiple of 12 and 15.
(ans. 60)
Determine whether the quotient is a rate or a ratio and then simplfy.
16 yards/2 jumps
(ans. rate 8 yd/jump)
28 points/4 quarters
(ans. rate 7pt/qt)
2 animals/20 animals
(ans. ratio 1/10)
4 feet/10 seconds
(ans. rate .4 ft/sec)
Find the reciprocals of the following numbers.
a. 3 b. 0.5 c. 2 1/2 d. –3 e. 3/5
(ans. a. 1/3 b. 2 c. 2/5 d. –1/3 e. 5/3)
Vocabulary:
PA-11 Enabler 2 (continued)
PROBLEM SOLVING
Tell whether the following numbers are prime or composite.
a. The number of liters in a kiloliter.
b. The number of months in year.
c. The number of days in a week.
d. The number of sides in a hexagon.
e. The number of sides in a pentagon.
(ans. a. composite (4), b. composite (12), c. prime
(7), d. composite (6), e. prime (5))
A physical education teacher has class sizes of 48, 60, 54, 48, and 36. The teacher wants to form equivalent
basketball teams in each of his classes. How many students could be placed on each team, so that they have the same
number of participants.
(ans. 6)
If two out of every five voters intend to vote Republican in a recent survey, how many votes should a Republican
candidate expect to receive from 20,000 votes cast.
(ans. 8,000)
A 1200 mile trip to Panama City took 20 hours. Find the mean speed for the entire trip.
(ans. 60 mph)
A large cake was bought for a party. First the cake was cut into 20 pieces. These pieces were too large, so each was
cut into two smaller pieces. Kris at one of the smaller pieces. What part of the cake did she eat?
(ans. 1/40)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations
State Standard/Benchmarks: IV.3.HS.5
Grade Level Outcome:
PA-11 Compare number relationships.
Enabler:
3.
Use number relationships to solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
At the end of the 1989-1990 season, hockey player Wayne Gretsky had scored 691 goals in 853 games in his career. At
this rate, in what game would he score his 1000th goal? Give several methods for finding the solution and justify your
answer in writing.
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.1.HS.1
Grade Level Outcome:
PA-12 Assess algebraic operations and their properties.
Enabler:
1.
Present symbolic models for real numbers.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Each student will be given a package of M & Ms candies. Use the candies to form an algebraic equation based on
color.
Example: 2r + 3b = 5
Vocabulary:
PICTORIAL (symbolic)
At Saturday’s Middle School Pizza Party, each student was given a whole small pizza. The students cut and ate what
they wanted. At the end of the party these pizzas were left on a table. How much of each pizza did each student eat?
Order the amount eaten from greatest to least.
(ans. 0, 5/8, 3/4)
Vocabulary:
ABSTRACT (computational)
Nina’s car can reach 60 mph in 30 sec. Luann’s truck can reach 85 mph in 1 minute. Who would receive the
handicap (seconds spotted to a slower driver) and how many seconds would it be?
(ans. Luann; 12.5 seconds)
Vocabulary:
PROBLEM SOLVING
You have a baby-sitting job. You work after school for three hours on Wednesday, Thursday, and Friday, and nine
hours on Saturday. You earn x dollars an hour.
a. Write an expression that represents your weekly earnings.
b. Suppose you earn $3.25 an hour. How much money would you earn?
(ans. a. 3(3x) + 9x or 18x
Vocabulary:
b. $58.50)
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.1.HS.2
Grade Level Outcome:
PA-12 Assess algebraic operations and their properties.
Enabler:
2.
Compute with real numbers.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Draw a number line to find each sum.
a. -4 + 3
b. 6 + (-2)
c. 2 + (-7)
(ans.
)
Vocabulary:
PICTORIAL (symbolic)
Use +/;- counters to model 4 + (-2).
(ans.
)
Vocabulary:
ABSTRACT (computational)
Solve:
1) -15 + -3
2) 68 + -25
3) -3 – (-7)
4) –5 – 6
5) 8(-6)
6) -21(-8)
7) -6/-2
8) 28 ÷ (-4)
Vocabulary:
(ans.
(-18)
(43)
(4)
(-11)
(-48)
(168)
(3)
(-7) )
))))
PA-12 Enabler 2 (continued)
PROBLEM SOLVING
Finding a Temperature
The thermometers at the right show the temperatures
(in degrees Celsius) at 1 p.m., 2 p.m., and 3 p.m.
a. Use the thermometers to approximate the temperatures.
b. Write an addition equation that relates the temperatures
at 1 p.m. and 2 p.m.
c. Write an equation that relates the temperatures
at 2 p.m. and 3 p.m.
(ans. a. 1 p.m. the temperature is 20C. 2 p.m. the temperature is
10C. 3 p.m. the temperature is 15C.
b. From 1 p.m. to 2 p.m. the temperature dropped 10 degrees.
This can be represented by adding –10 degrees to the 1 p.m. temperature.
1 p.m. temperature + temperature drop of 10 = 2 p.m. temperature
20 + (-10) = 10
c. From 2 p.m. to 3 p.m. the temperature rose 5 degrees. This can be represented by adding 5 degrees to the 2
p.m. temperature.
2 p.m. temperature + temperature rise of 5 = 3 p.m. temperature.
10 + 5 = 15
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.1.HS.2
Grade Level Outcome:
PA-12 Assess algebraic operations and their properties.
Enabler:
3.
Evaluate numerical and algebraic expressions.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Numerical expressions use only numbers. Example: 3 + 5
Algebraic expressions use number and/or variables. Example: 3x + 5
Tell whether each is a numerical expression or an algebraic expression.
a. b + 6
b. 9x
c. 80 ÷ 8
(ans. a. algebraic b. algebraic c. numerical
Vocabulary:
PICTORIAL (symbolic)
Just as we use models to stand for integers, we can use models for variable expressions. Use rectangles for variables.
Expression
Model
2x
3x + 3
Choose a variable and write a variable expression for each model.
a.
+
b.
-
c.
÷
(ans. a. 2x + 2 b. 3 – x c. 3x ÷ 2, student may use any variable)
Vocabulary: variable, expression
ABSTRACT (computational)
Evaluate for x = 16.
1) x + 7
2) 20 – x
3) 3x
4) x/8
(ans. 1. 23 2. 4 3. 48 4. 2)
Vocabulary:
PA-12 Enabler 3 (continued)
PROBLEM SOLVING
Jeans sell for $25 and T-shirts sell for $12.
a. Write a numerical expression for the selling price of two pairs of jeans and four T-shirts.
b. Write a algebraic expression for the selling price of j pairs of jeans and t T-shirts.
(ans. a. (2 x 25) + (4 x 12) b. 25j + 12 t)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.1.HS.3
Grade Level Outcome:
PA-12 Assess algebraic operations and their properties.
Enabler:
4.
Describe the properties of operations and give examples of their
use.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
State which property is show below.
1. A + B = B + A
2. A(BC) = (AB)C
3. A(B + C) = AB + BC
(ans.
1. commutative property of addition
2. associative property of multiplication
3. distributive property)
List the correct order of operations.
A÷4+2x6
Vocabulary:
(ans.
PICTORIAL (symbolic)
State which property is shown below.
1. A = A
2. (5 + x) + y = 5 + (x + y)
3. 2  = 2 + 2
Division, multiplication, addition)
(ans.
1. commutative property of multiplication
2. associative property of addition
3. distributive property)
Vocabulary:
ABSTRACT (computational)
Match each equation with the property illustrated.
1. x + y = y + x
2. (6x)y = 6(xy)
3. (6 + 5) + x = 6 + (5 + x)
4. ab = ba
a.
b.
c.
d.
commutative property of addition
commutative property of multiplication
associative property of addition
associative property of multiplication.
(ans. 1. a 2. d 3. c 4. b )
Vocabulary:
PA-12 Enabler 4 (continued)
PROBLEM SOLVING
ACME
PLUMBING
918-467-9823
25 + 4 x 30
25 + 120
From the desk
of:
Toni & John
25 + 4 x 30
29 x 30
$870.00
$145
John and Toni White called a plumber to repair a leaking pipe in the kitchen of their home. The plumber charges a
service charge of $25 plus $30 an hour. The two bills shown above show how the plumber and the Whites computed
the cost for four hours of work. Who computed the cost correctly? Justify your answer.
(ans. Following correct order of operations: multiply before addition
Acme Plumbing Co. is correct.)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.1.HS.4
Grade Level Outcome:
PA-12 Assess algebraic operations and their properties.
Enabler:
5.
Apply operations with real-numbers to real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Solve:
You go to the mall to shop for school clothes. You purchase two pairs of jeans for $25 each, three shirts for $20
each, and two pairs of shoes for $25 each. Write an expression that represents your total cost. How much money did
you spend?
(ans. 2($25) + 3($20) + 2($25) = $160)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.2.HS.1
Grade Level Outcome:
PA-13 Formulate and solve linear equations and inequalities.
Enabler:
1.
Translate words into algebraic expressions.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Translate into algebraic expressions:
1. eight less than five times a number
2. six divided by a number
3. a number multiplied by four
4. the sum of x and y
(ans.
5n – 8
6/x
4y
x + y)
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Give three possible English expressions for the algebraic expression:
1. x + 10
2. 2 – y
(ans.
1. 10 more than a number
a number plus 10
a number increased by 10
2. 2 less a number
2 decreased by a number
2 minus a number)
Vocabulary:
PROBLEM SOLVING
1. Sylvia earned $45 by washing cars. How much money will she have when she earns d dollars more?
(ans. (45 + d) dollars)
2. Karl has saved x dollars. Carlos has saved three times a much. How much has Carlos saved?
(ans. 3x dollars)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.2.HS.3
Grade Level Outcome:
PA-13 Formulate and solve linear equations and inequalities.
Enabler:
2.
Solve linear equations and inequalities.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Tom bought a shirt for $25, two pairs of pants costing x dollars each, and a pair of shoes selling for y dollars. Write
an equation that represents Tom’s total cost. Use c for the cost.
(ans. c = 2x + y + 25)
Vocabulary: linear equations, inequalities
PICTORIAL (symbolic)
Analyze the graph and give the cost of an eleven ounce first class letter. The costs of mailing a first-class letter in
1990 are in the table below. At right the pairs of numbers – the weight and cost are graphed.
(ans. $2.25)
Vocabulary:
ABSTRACT (computational)
Solve each equation:
a. x + 4 = -10
b. 2x + 40 = 120
c. 8x – 10 = 6x + 30
d. 2(3x + 4) = 4x + 4
(ans. a. x = -14; b. x = 40; c. x = 20; d. x = -2)
Vocabulary:
PA-13 Enabler 2 (continued)
PROBLEM SOLVING
The cost for mailing a first class letter in 1990 was found by using the formula c = 20W + 5, where c is the cost in
cents and w is weight in ounces. The post office round weights up! If a letter weighed 8.7 ounces, what would the
cost be?
(ans. (20 x 9) + 5 = $1.85)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Numerical and Algebraic Operations and Analytical Thinking
State Standard/Benchmarks: V.2.HS.5
Grade Level Outcome:
PA-13 Formulate and solve linear equations and inequalities.
Enabler:
3.
Solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Today there are 400 packages of duplicating paper at a school. Each week about 12 packages are used. Using L for
packages left and w for weeks, write an equation representing the use of paper.
(ans. L = 400 – 12w)
Vocabulary:
PICTORIAL (symbolic)
Under a lease plan, a new car costs $1,000 down plus $200 per month. Write an equation for the amount paid after n
months. Use P for the amount paid.
(ans. P = 1000 + 200 n)
Vocabulary:
ABSTRACT (computational)
In PIN, the measure of angle N is 4x + 36 The measure of angle P is 10x. If the measure of angle N equals the
measure of angle P, find the measures of all three angles. (Hint: write an equation to find the solution.)
(ans.
4x + 36 = 10x
N = 60
P = 60
I = 60)
Vocabulary:
PROBLEM SOLVING
Peggy is spending money while Vanna is saving it. At present, Peggy has $65 but spends $2 more than her
allowance each week. Vanna has $40 but saves $3 a week. Solving what equation will give the exact time when the
two will have them same amount? Use w to represent weeks.
(ans. 65 – 2w = 40 + 3w)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Probability and Discrete Mathematics
State Standard/Benchmarks: VI.1.HS.1, VI.2.HS.2, VI.1.HS.4
Grade Level Outcome:
PA-14 Investigate probability.
Enabler:
1.
Describe chance situations using language of probability.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
You roll a die once.
a. How many possible outcomes are there?
b. What are your chances of rolling a 5?
c. What is the probability of rolling a 5?
(ans. a. 6 (1, 2, 3, 4, 5, 6) b. 1/6 c. 1/6)
Vocabulary:
PICTORIAL (symbolic)
An ice cream stand offers two flavors of ice cream, two topping options, and two container options. How many
possible combinations of flavors, containers, and toppings are there? Assume all possibilities will have toppings.
Make a tree diagram to show all of the possible combinations (outcomes) in the sample space.
Flavor
Container
cup
Topping
rainbow
chocolate
Outcome
chocolate cup with rainbow sprinkles
chocolate cup with chocolate sprinkles
rainbow
chocolate
chocolate cone with rainbow sprinkles
chocolate cone with chocolate sprinkles
rainbow
chocolate
vanilla cup with rainbow sprinkles
vanilla cup with chocolate sprinkles
rainbow
chocolate
vanilla cone with rainbow sprinkles
vanilla cone with chocolate sprinkles
chocolate
cone
cup
vanilla
cone
FLAVORS
TOPPINGS
(sprinkles)
Vocabulary:
CONTAINERS
PA-14 Enabler 1 (continued)
ABSTRACT (computational)
Estimate the probabilities for these problems.
One thousand golf balls, some white, some green, and some yellow, are put into a barrel. As they are drawn out,
their colors are tallied. Using the tally shown, find the probability that the next ball will be this color?
1. green
2. white
3. yellow
4. white or yellow
5. yellow or green
6. green or white
Green
White
Yellow
Tally
||||| ||||| |||||
||||| ||||| ||||| |||||
||||| |||||
7. Of the 1000 golf balls described above, about how many are white?
8. Of the 1000 golf balls described above, about how many are yellow?
(ans. 1. .32 2. .46 3. .22 4. .68 5. .54 6 .78 7. 460 8. 220)
Vocabulary:
PROBLEM SOLVING
A factory turns out 5000 digital calculators a day. To control quality, a daily random sample of 200 is taken and
tested. Of these 6 are found defective.
a. Find the probability that a randomly chosen calculator will be defective.
b. How many calculators in a day’s output are likely to be defective?
(ans. a. 6/200 = .03 b. 150)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Probability and Discrete Mathematics
State Standard/Benchmarks: VI.1.HS.3
Grade Level Outcome:
PA-14 Investigate probability.
Enabler:
2.
Illustrate the difference between dependent and independent
events.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Are events A and B dependent or independent?
1. A coin is tossed twice.
a. Heads come up on the first toss.
b. Heads come up on the second toss.
2. A bag contains 1 red marble and 2 blue marbles. A marble is drawn and not replaced.
a. The first marble is red.
b. The second marble is blue.
(ans. a. independent; b. dependent)
Vocabulary: probabilty
PICTORIAL (symbolic)
A coin is tossed and a die is rolled. List the 12 possible outcomes.
(ans. H-1, H-2, H-3, H-4, H-5, H-6
T-1, T-2, T-3, T-4, T-5, T-6)
Vocabulary:
ABSTRACT (computational)
A bag contains two red and three blue marbles. A marble is drawn and is not replaced. A second marble is drawn.
Find the probability of these events.
a. The first marble is red, and the second one is blue.
b. Both marbles are red.
c. Both marbles are blue.
(ans. a. 3/10 b. 1/10 c. 3/10)
Vocabulary:
PA-14 Enabler 2 (continued)
PROBLEM SOLVING
Suppose you are playing a Scrabble game, and these 8 tiles are left. If you choose two tiles at random, what is the
probability you will choose a Q, then another Q?
S
V
U
Q
T
O
F
Q
(ans. Since choosing one Q changes the number of times and the number of Qs that are left to choose from, the two
choices are dependent events.
P(Q, then Q) = P(Q) x P(Q, given Q)
number of Qs
number of tiles
2
8
1
x 7
= 1/28
number of Qs left after the first pick
number of tiles left after the first pick
So, the probability that you choose a Q, then another Q is 1/28, 030357…., or about 3.6%.)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Probability and Discrete Mathematics
State Standard/Benchmarks: VI.1.HS.5
Grade Level Outcome:
PA-14 Investigate probability.
Enabler:
3.
Use concepts of probability to solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Toss a dime, a nickel, and a penny once. Record the eight possible outcomes.
(ans. HHH, HTH, HHT, THH, TTT, THT, TTH, HTT)
Vocabulary:
PICTORIAL (symbolic)
Perform an experiment to determine the probability that a thumb-tack will land up when dropped.
(ans.
One student found eight thumbtacks. He decided to drop all of them ten times, for a total of 80 dropped tacks. Here
are the results.
Experiment
UP
On Edge
1
5
3
2
3
5
3
3
5
4
4
4
5
5
3
6
7
1
7
1
7
8
5
3
9
5
3
10
4
4
Adding the numbers that landed up, a total of 42 tacks landed up. The tacks in the other 38 tosses landed on edge.
The relative frequency of a tack landing up was 42/80. We might pick that number as the probability. However,
42/80 = .525, which is closer to .5. We might take the probability to be 1/2.)
Vocabulary: relative frequency
ABSTRACT (computational)
In a survey of a neighborhood, 60% of those surveyed expressed a need for greater police protection.
a. If 100 were surveyed, how many said they needed more police protection?
b. If 500 people were surveyed, how many said they needed more police protection?
c. If 5 people were surveyed, how many said they need more police protection?
(ans. a. 60 people; b. 300 people; c. 3 people)
Vocabulary:
PA-14 Enabler 3 (continued)
PROBLEM SOLVING
Consider the following:
A tire company tests 50 tires to see how long they last under typical road
conditions. The results are shown below:
Mileage until worn out
10,000-14,999
15,000-19,999
20,000-24,999
25,000-29,999
30,000-34,999
35,000-39,999
40,000 or more
Number of tires
1
3
6
15
14
7
4
a. What is the relative frequency of a tire lasting less than 25,000 miles?
b. What is the relative frequency of a tire lasting more than 10,000 miles?
(ans. a. 10/50 = 1/5; b. 1)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Probability and Discrete Mathematics
State Standard/Benchmarks: VI.2.MS.3
Grade Level Outcome:
PA-15 Examine discrete mathematics.
Enabler:
1.
Solve network problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
After school, Vilma plans to go to the music store and then to the pool. She can take any of 3 routes from school to
the music store and then take either of two routes from the store to the pool. In how many ways can Vilma go from
school to the pool?
(ans. 6)
Vocabulary:
PICTORIAL (symbolic)
How many different ways can you travel from one city to another?
a. Ames to Plainview
b. Carthage to Dutton
c. Cathage toWeston
d. Ames to Dutton
(ans. a. 6 ways; b. 6 ways; c. 16 ways; d. 12 ways)
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Contact a travel agency to find all the possible pathways from MBS International Airport to Orlando, Florida. Draw
a network that show the pathways. Which one would you prefer and why?
(ans. will vary)
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Probability and Discrete Mathematics
State Standard/Benchmarks: VI.2.HS.5
Grade Level Outcome:
PA-15 Examine discrete mathematics.
Enabler:
2.
Describe and analyze efficient algorithms to accomplish a task or
solve a problem in a variety of contexts.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Consider the vowels A, E, I, O, and U. Make two-letter monograms with these vowels like AO, UE, II, How many
two-letter monograms are there? (Hint: Make an organized list.
AA
AE
AI
AO
AU
EA
EE
EI
EO
EU
Vocabulary: efficient algotithms
IA
IE
II
IO
IU
OA
OE
OI
OO
OU
UA
UE
UI
UO
UU
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Probability and Discrete Mathematics
State Standard/Benchmarks: VI.2.HS.6
Grade Level Outcome:
PA-15 Examine discrete mathematics.
Enabler:
3.
Solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Not Applicable
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
In Wilson Hall, a person may enter through entrances A, B, C, or D. When leaving, they may use either exit C or D.
How many different ways could a person enter and exit Wilson Hall?
C
A
(ans. 8)
D
Vocabulary:
B
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Technology
State Standard/Benchmarks:
Grade Level Outcome:
PA-16 Use, transfer, and apply appropriate technology.
Enabler:
1.
Use scientific calculators to perform basic functions and solve
real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Write the problem that matches the key sequence.
(ans.)
25
5987 + 6545
3.73 + 46.298
437 + -1764
(3.2 x 103)  (4.5 x 105)
57
5
Vocabulary:
PICTORIAL (symbolic)
Do the following key sequence on your calculator.
(ans. 6 x 17.95 + 5 x 17.95 = 197.45)
Vocabulary:
ABSTRACT (computational)
Write the key sequence for the following problems.
-676 ÷ 13
8.8128 ÷ 2.04
Vocabulary:
PA-16 Enabler 1 (continued)
PROBLEM SOLVING
Use this information and your calculator. Jeffrey is saving money each week to buy presents for his family. He wants to
save $150. How much must he save each week if he saves for the given amount of time?
(ans.)
a. 3 weeks
a. $50
b. 5 weeks
b. $30
c. 8 weeks
c. $18.75
d. 12 weeks
d. $12.50
e. 20 weeks
e. $7.50
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Technology
State Standard/Benchmarks:
Grade Level Outcome:
PA-16 Use, transfer, and apply appropriate technology
Enabler:
2.
Use computer spreadsheets to solve real-world problems.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Here is a sample spreadsheet for a school store.
A
1
2
3
4
5
6
7
8
9
10
11
12
Item
Gym Shorts
Shirts
Sweatshirts
Tablets
Pencils
Folders
B
C
January Sales
D
Unit Price Number Sold Total Sales
$
$
$
$
$
$
6.00
8.00
12.00
0.60
0.10
0.50
15
24
32
38
123
21
Monthly Sales
1. What is a spreadsheet?
2. What is displayed in the given cell locations of the spreadsheet? a) C5 b) A10 c) B8?
3. Give the heading for row 7.
(ans. 1. Table made up of columns and rows. 2. a)15 b) folders c) .60 3. Sweatshirts)
Vocabulary:
PA-16 Enabler 2 (continued)
PICTORIAL (symbolic)
1
2
3
4
5
6
7
Name
John
Paul
George
James
Student
Test 1
Grades
Test 2
86
55
97
23
Av erage
78
80
94
18
=(b11+c11)/2)
1. Write the formula that calculates John’s test average, and name the cell in which the formula is entered.
2. What formula should be entered in cell B7 to calculate the group’s average on Test 1?
3. a. In which cell will the formula used to calculate the group’s average on Test 2 be entered?
b. What formula should be entered here?
(ans. 1. =(b3+c3)/2 in cell d3
2. =(b3+b4+b5+b6)/4
3. a. c7 b. =(c3+c4+c5+c6)/4)
Vocabulary:
ABSTRACT (computational)
A
B
1
X
2
2
4
3
3
9
4
5
25
C
D
E
8
27
125
16
81
625
32
243
3125
(ans.
a. x2
b. x3
c. x4
d. x5)
Give a heading for each column.
B C D E
Vocabulary:
PROBLEM SOLVING
Create a spreadsheet that lists times and costs for a phone call to Nigeria if the cost is $1.19 for the first minute and
79¢ for each additional minute.
a. What is the formula that should
be placed in Bs and copied into
the rest of the B column?
b. What will it cost for a 27
minute phone call?
(ans. a. (A2 – 1).79 + 1.19
Vocabulary:
1
2
3
4
b. $21.73)
A
Minutes
1
2
3
B
Cost
1.19
1.98
2.77
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Employability/Career Skills
State Standard/Benchmarks:
Grade Level Outcome:
PA-17 Explore careers.
Enabler:
1.
Explore professions.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
The teacher brings in the following career professionals and the students will describe/write three ways that two of
the following professions use mathematics.
1. Accountant
2. Banker
3. Sales
4. Artist
5. Architect
6. Mathematician
Vocabulary:
PICTORIAL (symbolic)
Not Applicable
Vocabulary:
ABSTRACT (computational)
Students will research and write a one page paper on one of the following occupations:
1. Accountant
2. Banker
3. Sales
4. Artist
5. Architect
6. Mathematician
Vocabulary:
PROBLEM SOLVING
Students will set up and interview a business person. Include applications of mathematics in this occupation.
Vocabulary:
MATHEMATICS ACTIVITIES
Pre-Algebra
Framework/Strands:
Employability/Career Skills
State Standard/Benchmarks:
Grade Level Outcome:
PA-18 Demonstrate employability skills.
Enabler:
1.
Work cooperatively with all team members.
LEARNING ACTIVITY
CONCRETE (conceptualizing)
Working in teams, students will keep track for five days of time spent in the following activities:
1. Sleeping
2. Eating
3. School
4. Leisure time
5. Homework/study time
6. Extra curricular (i.e., sports, practice times)
Vocabulary:
PICTORIAL (symbolic)
Organize above information in a chart and graph all team members results.
(ans. will vary)
Vocabulary:
ABSTRACT (computational)
Not Applicable
Vocabulary:
PROBLEM SOLVING
Students will open a bank account and maintain it for one semester.
Vocabulary: