Download Intermediate Mathematics

SkillsTutor
Intermediate
Mathematics
Classroom Guide
Table of Contents
Getting Started ............................................................................................................................................ 1
Basic Skills Lessons ............................................................................................................................ 2
Quizzes ..................................................................................................................................................2
Thinking Skills Lessons ........................................................................................................................2
Tests ......................................................................................................................................................3
Worksheets ............................................................................................................................................3
Basic Skills Lesson Summaries .................................................................................................................. 5
Proportion and Percent ..........................................................................................................................7
Introduction to Algebra..........................................................................................................................8
Geometry................................................................................................................................................9
Statistics and Probability ....................................................................................................................10
Thinking Skills Lesson Summaries............................................................................................................11
About Thinking Skills..........................................................................................................................11
Lesson Content ....................................................................................................................................11
Lesson Summaries ..............................................................................................................................12
Thinking Skills Worksheets........................................................................................................................15
Assignment Sheet ...................................................................................................................................... 21
© 2004 Achievement Technologies, Inc.
All rights reserved.
All trademarks are the property of their respective owners.
Getting Started
This product is a comprehensive resource for diagnosing and remediating students’ basic
Intermediate Mathematics skills.
The SkillsTutor management system (OTS) provides several important features:
•
Tests students’ skills, providing both pretests and posttests to make initial assessments and
gauge student progress
•
Makes assignments, based on students’ pretest results
•
Monitors student scores and completion of activities
•
Produces reports for individual students
•
Provides online documentation
This guide outlines the content and activities of Intermediate Mathematics. Information on the
management system (OTS) is provided under separate cover in the SkillsTutor User’s Guide.
6 1 6
Basic Skills Lessons
Each lesson begins with one or more screens that review a concept. Lessons continue with a
number of multiple-choice questions to reinforce the student’s understanding of the topic, as
illustrated below.
These instructions will help the student take full advantage of the features of SkillsTutor lessons:
•
Use the mouse to answer questions: click on the correct answer.
•
Click Hint for help in answering a question.
•
If a question is missed, the student will be told why the answer is wrong. The student
should read the response carefully, and try again. The student cannot move to the next question until the current question is answered correctly, so reading and answering carefully will
save time.
•
The student may review the instructional material at any time during the lesson by clicking
Review. After going through the review screens, the student returns to the question that was
being answered before the review. The student may return to the question before completing
the review by clicking Resume.
•
There may be times when the student needs to exit the program before completing an activity.
To end an activity, close the activity window.
•
When the student finishes answering all of the questions in an activity, a score is displayed.
The score, expressed as a percent, is the number of questions answered correctly out of all
the questions attempted.
Quizzes
Quizzes operate similarly to lessons. However, quizzes have no introductory instructional material, and they do not require you to answer each question correctly before moving to the next
question. Detailed feedback is provided for all questions.
Thinking Skills Lessons
Each Thinking Skills lesson begins with a scenario or story that presents a problem to solve.
This is the theme that is carried through the entire lesson, and the problem is solved as the
lesson progresses.
The opening scenario or story is followed by a discussion of the thinking skill needed to solve the
problem. Step-by-step instructions and examples for using the thinking skill are provided on screen.
The problem is solved through a series of questions which require the student to use the steps
6 2 6
involved in the thinking skill. Some of the questions have only one right answer. Other
questions have more than one correct answer.
For a question of this type, read carefully and select as many of the answers as seem appropriate. To select an answer, click the box next to it to place an X in the box. If a box is marked by
mistake, click again to remove the X. Click the Hint button for help in answering a question.
Click the Check button to see feedback for answers.
At the conclusion of the lesson, a summary screen highlights the thinking skill that was used
and the problem that was solved in the lesson. Then the score for the lesson is presented. The
score is based on points accumulated, rather than the number of questions answered.
Tests
SkillsTutor offers content-area pretests and posttests modeled on standardized tests. Pretests and
posttests have no introductory instructional material. Like the questions for quizzes, the test
questions are presented in multiple-choice format to give students practice in answering
standardized-test questions. After each test, students have the opportunity to review the questions they missed. Feedback is provided for each missed question.
Worksheets
SkillsTutor contains reproducible worksheets for each Thinking Skills lesson. The worksheets
may be used to extend the computer activity or as a homework assignment. They are provided
in this documentation and may be printed from the online version of the documentation, or photocopied from the printed version.
6 3 6
6 4 6
Basic Skills
Lesson Summaries
Intermediate Mathematics contains 52 lessons, 8 quizzes, and 8 tests in a hierarchical arrangement designed to continually reinforce the concepts presented. On the following pages, there is
a description and example for each basic skills lesson. The lessons are arranged in the following
content areas:
•
Proportion and Percent
•
Introduction to Algebra
•
Geometry
•
Statistics and Probability
6 5 6
6 6 6
Lesson
#
Lesson
Title
Lesson Description
Example
Intermediate Mathematics: Proportion and Percent
1
Relationship of Ratios,
Percents, and Decimals
Students express ratios, fractions, decimals,
and percents in equivalent forms.
2
Ratio and Proportion
Students identify whether or not two ratios form
a proportion using the concepts of equal ratios
and cross products. They also use these concepts to find missing numbers in proportions.
4
5
The ratio 4 to 5 = --- = 0.8 = 80%.
9
3
------ 9 --12
4
(=,ú)
What is the missing number in this
proportion?
4 : y = 16 : 8
3
Using Proportions to Find Group
Prices
Students use proportions to solve money problems involving group prices.
Sugar costs 40¢ for 2 pounds. How many
pounds can you buy for $2.00?
4
Finding the Part by Using
Proportions
Students use the proportion
N : 100 = part : whole to find the part in percent
problems.
What is 20% of 60?
5
Finding the Percent by Using
Proportions
Students use the proportion
N : 100 = part : whole to find the percent in
percent problems.
15 is what percent of 45?
6
Finding the Whole by Using
Proportions
Students use the proportion
N : 100 = part : whole to find the whole in percent problems.
6% of what number is 48?
7
Finding the Part by Using
Number Sentences
Students use the equation
N × whole = part to find the part in percent
problems.
Jesse gave 25% of his models away. If he
had a total of 40 models to start, how many
did he give away?
8
Finding the Percent by Using
Number Sentences
Students use the equation
N × whole = part to find the percent in percent
problems.
Alisha started a camping trip with 24 sandwiches. She ate 6 on the first day. What percent of her sandwiches did she eat that
day?
9
Finding the Whole by Using
Number Sentences
Students use the equation
N × whole = part to find the whole in percent
problems.
Michael spent 60% of his allowance on junk
food. If he spent $1.20, how much was his
allowance?
10
Percent of Change
Students calculate the percent of increase or
decrease by dividing the amount of change by
the original amount.
If a movie cost $4.00 last year and $5.00
this year, what was the percent of increase?
11
Discounts
Students learn the terms “original price,” “discount,” “rate of discount,” and “sale price.” They
calculate amounts of discount and sale prices in
various situations.
During a sale, a used car that was regularly
$6,000 was sold for 5% off. How much was
the discount in dollars? What was the sale
price of the car?
12
Simple Interest
Students learn the meaning of “simple interest”
and the terms “principal,” “rate,” and “time.”
They calculate the amount of interest and total
amount paid (or saved) in various situations.
Asher borrowed $2,000.00 for
2 years at a rate of 8% per year. How much
interest did he pay on the loan?
SkillsTutor
2 – 21
Lesson
#
Lesson
Title
Lesson Description
Example
Intermediate Mathematics: Introduction to Algebra
1
Absolute Value
Students read and identify the absolute values
of numbers. They also practice simple computation with absolute values.
|›14| = 14
|›3| + |‹5| = 8
2
Addition and Subtraction
of Integers
Students add and subtract integers with like
and unlike signs.
4 + ›3 = 1
›4 à ‹8 = ›12
3
Multiplication and Division of
Integers
Students multiply and divide integers with like
and unlike signs.
›6 ä ›3 = 18
›8 ã 2 = ›4
4
Exponents and Square Roots
Students read and calculate the exponential
values and square roots of numbers. There is
special emphasis on 0, 1, and negative exponents. Only perfect squares are used under the
square root symbol.
5• = 5 ä 5 ä 5 ä 5 = 625
ëØ¥ = 7
5
Scientific Notation
Students learn that scientific notation allows
them to express very large and very small numbers more simply.
4780 = 4.78 ä 10¬
0.000065 = 6.5 ä 10ʃ
6
Operations with
Exponents
Students calculate the values of exponential
expressions with terms having the same base.
7¢§ ä 7® = 7£°
8Ê™ ã 8Ê¢£ = 8§
7
Simplifying
Numerical
Expressions
Students calculate the values of numerical
expressions by following the standard order of
operations.
4 x (3 + 6) à 2£
= 4 ä (9) à 2£
= 4ä 9 à 4
= 36 à 4
= 32
8
Sequences
Students learn various common patterns used
in number sequences. They determine the rule
that describes a number sequence in order to
fill in missing numbers in the sequence.
In the number sequence
1, 3, 5, 7, 9, 11, 13, ...
the rule is to add 2 to get the next number.
9
Evaluating Variable Expressions
Students evaluate variable expressions with
one or two variables. First, they replace each
variable with its given value. Then, they use the
standard order of operations to find the value of
the expression.
If n = ›2, then î›2nï à î›4n£ï = ____.
10
Simplifying Variable
Expressions
Students simplify algebraic expressions that
include addition, subtraction, multiplication, or
division. They also learn to simplify algebraic
expressions that involve a combination of operations.
3b + 2a + 6b =____
›3y£ ã y 4 = ____
4a + 2(2a + 4b + a) = ____
11
One-Step Equations
Students solve one-step equations by isolating
variables using inverse operations.
If a + 14 = 7, then a = _____.
If 2m = ›8, then m = _____.
12
Two-Step Equations
Students solve two-step equations. First, they
isolate the term containing the variable. Then,
they isolate the variable.
If 3n + 5 = ›4, then n = _____.
Students locate points on a coordinate plane
using ordered pairs. They also use linear equations to describe lines.
(Coordinate plane with a horizontal line
drawn.) Which linear equation describes
this line?
13
2 – 22
Graphing on the Coordinate
Plane
Basic Skills Lesson Summaries
x
2
If 1 = --- à 3, then x = _____.
Lesson
#
Lesson
Title
Lesson Description
Example
14
Writing Equations from Words
Students write algebraic expressions and equations from words. First, they choose a variable
to represent the unknown number. Then, they
translate the words of the problem into an algebraic expression or equation.
Darryl is 6 years older than his little brother,
Eric. Eric is 2 years old. Write an equation
that could be used to find Darryl's age.
15
Distance-Rate-Time Problems
Students learn to solve equations using the formula d = râ t to solve word problems that
involve distance or flow, rate or speed, and
time.
Gasoline is leaking from a gas tank at the
rate of 2 gallons per minute. How long will it
take to lose 12 gallons?
Intermediate Mathematics: Geometry
1
Units of Length
Students use proportions to convert between
English units of length and between metric units
of length.
How many millimeters are in 65 centimeters? (10 mm = 1 cm)
2
Units of Weight and Capacity
Students use proportions to convert between
English units of weight, between metric units of
weight, between English units of capacity, and
between metric units of capacity.
How many pounds are in 56 ounces?
(1 lb. = 16 oz.)
3
Time Zones
Students are introduced to the concept of differences in time across time zones around the
world. Some questions require calculation of
elapsed time across time zones.
(Map of North America w/cities highlighted
& time zones noted.) When it is 2 p.m. in
Baltimore, what time is it in San Diego?
4
Angles
Students learn the terms “straight angle,” “right
angle,” “acute angle,” and “obtuse angle.” They
use their knowledge of straight angles, right
angles, and the sum of the angles of a triangle
to find the measure of missing angles.
A right triangle has one angle that measures 40°. What is the measure of the third
angle?
5
Lines and Angles
Students identify types of angles including adjacent, vertical, and corresponding angles. They
learn to find measures of missing angles in a
drawing.
(Diagram of parallel lines with a transversal.) If angle 1 measures 120°, then angle 5
measures ____.
6
Area of Polygons
Students find the areas of parallelograms, triangles, and irregular shapes.
(Diagram of an irregular shape with base
and height labeled.) The local park has a
large, rectangular flower bed with a square
stone in the center. What is the area of just
the flower bed?
7
Circumference of Circles
Students learn that ‚ is the ratio of circumference to diameter. They use the formulas
C = ‚âd and C = 2â‚âr to find the
circumference of circles.
(Diagram of a circle with a diameter of
3.5 yds.)
What is the circumference?
8
Area of Circles
Students find the areas of circles given
the radius or the diameter of each circle. They
also find the area of irregularly shaped figures.
A circular rug has a radius of
3 meters. What is the area of this rug?
9
Surface Area
Students use the areas of triangles, squares,
rectangles, and circles to find the surface areas
of three-dimensional figures.
(Diagram of a cylinder with radius and
height labeled.) Joni is wrapping a birthday
gift. The box is a cylinder. What is the surface area that must be covered by wrapping
paper?
SkillsTutor
2 – 23
Lesson
#
Lesson
Title
10
11
Lesson Description
Example
Volume of Prisms and Cylinders
Students find the volume of triangular prisms,
rectangular prisms, and cylinders by multiplying
the area of the base by the height.
(Graphic of a frozen orange juice can with a
radius of 2 in. and height of 7 in.)
What is the volume?
Formulas in Geometry
Students build upon the skills learned in Lesson
10 and use formulas to find the volume of pyramids, cones, and spheres.
(Graphic of a rectangular pyramid with a
base of 10 m 2 and a height of 7 m.)
V = 1--- âAâh
3
What is the volume?
12
Pythagorean Theorem
Students use the Pythagorean Theorem to find
the length of the hypotenuse of a right triangle,
given the lengths of the legs. Students also find
the missing length of a leg of a right triangle.
(Diagram of a pond with dimensions on the
legs.) Joe wants to find the length of this
pond. He measures the legs of a right triangle on land. What is the length of the pond?
Intermediate Mathematics: Statistics and Probability
2 – 24
1
Pictographs
Students use the keys on pictographs to interpret and compare data. Part of the lesson is
devoted to interpreting pictographs with partial
symbols.
(Pictograph of Candy Sold at the Ace
Emporium.) How many fewer boxes of
candy were sold in March than in February?
2
Bar Graphs
Students learn to use bar graphs to compare
data. Emphasis is on reading and interpreting
bar graphs, including double and triple bar
graphs.
(Bar graph comparing wind speeds.) How
much higher was the wind speed recorded
at station U than station S?
3
Line Graphs
Students learn that line graphs are used to
show change or trends over time. Emphasis is
on reading and interpreting line graphs, including double and triple line graphs.
(Line graph showing Peaches Sold.)
What is the least amount of peaches sold in
a week?
4
Circle Graphs
Students learn that circle graphs are used to
show parts of a whole. Students interpret circle
graphs showing fractional parts of the whole
and percents of the whole.
(Circle graph showing fund-raising efforts.)
How much money did recycling raise?
5
Measures of Central Tendency
Students find the mean (average), median (middle number), and mode (most frequent number)
for a set of data.
Identify the median.
43, 39, 81, 50, 62
6
Simple Probability
Students learn that probability is a ratio of the
number of favorable outcomes to the total number of possible outcomes. This ratio can be
expressed as a fraction, decimal, or percent.
There are 12 slips of paper in a bag, each
one naming a different month of the year.
What is the probability of picking “May” out
of the bag?
7
Counting Outcomes
Students read word problems involving 2 or 3
decisions. They learn to determine the total
number of possible outcomes by finding all the
possible combinations of the choices.
You have 4 different colored t-shirts. You
also have black shorts, blue shorts, and
green shorts. How many combinations of
shirts and shorts are possible?
8
Predicting Outcomes
Students learn that by multiplying the probability
of an event by the number of attempts, they can
predict the number of favorable outcomes.
If you flip a coin 50 times, about how many
times can you expect the coin to land on
“heads”?
Basic Skills Lesson Summaries
Thinking Skills
Lesson Summaries
About Thinking Skills
To complement the efforts of teachers and programs focused on incorporating thinking skills (or
skills labeled as “higher order thinking,” “critical thinking,” “creative thinking,” “reasoning,” or
“problem-solving”), Intermediate Mathematics includes thinking skills lessons as an integral
part of its instruction. Each Thinking Skills lesson provides students with direct instruction in a
specific thinking skill. Several different thinking skills are addressed and are repeated across
different content areas. The lessons instruct students in a step-by-step thinking process they can
use each time they are faced with a problem that requires them to use that thinking skill. We
have chosen to group the Intermediate Mathematics thinking skills in two broad categories:
1. Extending Knowledge
Comparison
2. Drawing Conclusions
Prediction
Problem Solving
Decision Making
Lesson Content
Each lesson begins by placing one of the thinking skills in the context of a problem or scenario
that ties the lesson together. After instruction in the thinking skill, students answer questions
related to the opening scenario that combine the targeted thinking skill as well as basic skills
learned in previous lessons. By the end of each lesson, students have practiced basic skills content and a thinking skill while solving a “real life” problem.
As you introduce your students to these lessons, you might find it helpful to point out the following features:
1. After the title screen, a problem or scenario is presented. This is the theme of the entire lesson and is solved as the lesson progresses.
2. The opening problem is followed by direct instruction in a specific thinking skill. A step-bystep process is presented to help students focus on the thinking skill that will be used to
respond to the opening problem. If students wish to reread any part of the scenario or steps,
they can return to these screens from any of the questions by selecting Review.
3. A set of questions walks the students through the steps of the thinking process introduced in
the instruction. Through this sequence of questions, students apply their basic skills knowl6 11 6
edge to solve the opening problem. Unlike the rest of the SkillsTutor lessons, many of the
questions in these lessons have more than one correct response to a multiple-choice question. Students should read carefully and mark as many of the boxes as seem appropriate to
answer each question.
4. At the conclusion of the questions, a summary screen highlights again the thinking skill that
was used and the problem that was solved in the lesson. Students then see their score for the
lesson, based on points accumulated rather than just the number of questions answered. This
scoring procedure tallies a point for each correct response given to a single question.
Lesson Summaries
On the following pages you will find a lesson summary and strategy or example for each of the
Intermediate Mathematics Thinking Skills lessons. For teachers who want to focus on a particular thinking skill with one or more students, this chart makes it easy to locate related lessons.
Group discussion is always encouraged as a means of improving metacognition, or getting students to think about their thinking processes.
You will find a reproducible worksheet for each Thinking Skills lesson. The worksheet may be
used by students at the completion of the computer lesson or as a homework assignment. Each
worksheet concludes with a “Write Idea” which is a suggested writing activity that should help
students think through the process learned in the lesson and apply it to a new situation. Answer
keys are not provided for the worksheets since many of the activities are open-ended and do not
lend themselves to single “correct” answers. Encourage students to verbalize the thinking
processes they use on these worksheet questions. You might also have students discuss their
worksheet answers in small groups and correct each other’s papers.
6 12 6
6 13 6
6 14 6
Name:
Date:
Proportion and Percent: Thinking Skills Lesson 2
Student Activity
Comparison: Movie House Management
STEPS: 1.
2.
3.
4.
Identify the items you are comparing.
List features of the items you are comparing.
Decide how items are similar or different for each
feature.
Summarize what you have learned.
Here is the problem that appeared in the lesson:
In the lesson, you considered opening a movie theater. Your problem was not knowing what to charge for
tickets. You compared profits for three different ticket prices.
Directions: Now try a price of $7 per ticket and assume only 50 people come at that price. For this new
price, compute the same features:
INCOME = TICKET PRICE x NUMBER in CROWD
COSTS = 20% of INCOME + $150
PROFIT = INCOME – COSTS
PROFIT RATIO = PROFIT ÷ INCOME
Then compare the results with this table from the lesson:
Tickets
Crowd
Income
Costs
Profit
Profit Ratio
Option A
$ 3.00
90
$270.00
$204.00
$ 66.00
24.4%
Option B
$ 4.50
75
$337.50
$217.50
$120.00
35.6%
Option C
$ 5.00
60
$300.00
$210.00
$ 90.00
30%
In the lesson, you concluded that $4.50 was the best ticket price to use. Do you still agree with this
conclusion? What other situations would you test if you were really going to open the movie house?
Write Idea: Social scientists study information about people. They use comparison to examine similar
information about different population groups such as recent immigrants. They might study population
size, education levels, or life expectancy. In this way, they can see what needs improvement. Write about
something you think needs improvement. What kind of information would you need to compare to prove
your case?
Portions of this product are based on materials copyrighted by Mattel, Inc.
Proportion and Percent Lessons 1-12
Name:
Date:
Introduction to Algebra: Thinking Skills Lesson 1
Student Activity
Prediction: Number Sequence Puzzles
STEPS:
1.
2.
3.
4.
5.
Identify the facts that you know.
Look for patterns in the information.
Make a general statement that explains the
patterns you have observed.
Based on your conclusions, predict the next
event (or number).
Make more observations to see if you have
predicted correctly.
In the lesson, you explained the patterns for and predicted numbers in these sequences:
Sequence:
Pattern:
0, 1, 1, 2, 3, 5, ...
Each number is the sum of the previous two numbers.
Sequence:
Pattern:
-15°C, -11°C, -7°C, -3°C, +1°C, +5°C, +9°C, ...
The temperature gets 4° warmer every two hours.
Sequence:
Pattern:
2, 4, 8, 16, 32, 64, ...
t = 2n
Sequence:
Pattern:
0.000025, 0.0025, 0.25, 25.00, ...
Each new number is the previous number multiplied by 102.
Directions: Now apply your prediction skills to this number sequencing problem. Your friend is saving
for a new radio. It costs $36.50. She started with a quarter. Now she saves the same amount from her
allowance each week. Here is how the savings account is growing:
Week
Amount
1
2
3
4
$0.25
$1.50
$2.75
$4.00
Predict how many weeks it will take to reach
the goal of $36.50.
Write Idea: Scientists use the prediction process to warn people about natural disasters. Imagine this
situation. A river is 72 inches deep. Rain is causing the river to rise at a rate of two inches per hour. The
river will flood at 96 inches. Write a paragraph about how scientists could use the prediction process and
number sequences to predict how many hours of rain will cause the river to flood.
Portions of this product are based on materials copyrighted by Mattel, Inc.
Introduction to Algebra Lessons 1-8
Name:
Date:
Introduction to Algebra: Thinking Skills Lesson 2
Student Activity
Decision Making: Buying a House
STEPS:
1.
2.
3.
4.
5.
Identify the decision you need to make.
List all the choices available to you.
Identify the important information that you
must consider when making your decision.
Determine the outcome of each choice.
Evaluate your choices and summarize what
you have learned. Then make your decision.
Here is the problem that appeared in the lesson:
You have a very important decision to make. You would like to buy a house. You want the tax deduction
that a house provides. You would also enjoy remodeling and decorating your own place. You know that
buying a house is not something to rush into. There are many facts to consider when making this
decision.
• The price of one house you like is $70,000.
• The price of another house you like is $95,000.
• Your income is $24,000 a year.
You have to decide if you can buy one of these houses.
Directions: You have just gotten a big promotion at work. Your salary was raised to $30,000 a year. You
determine that the monthly payment for the $95,000 house is $771.28 including property taxes.
Remember, the bank will lend you the money if 30% of your monthly income is greater than or equal to
your monthly payment. Write an equation that will determine whether your monthly salary is greater than
or equal to the payment for the $95,000 house. Will the bank lend you the money for the more expensive
house?
Write Idea: Determing whether or not to buy a house is one of the most important decisions a person can
make. Think of another important decision that does not involve buying something, maybe taking one class
versus another, or choosing one job over the other. After stating the decision, list the possible choices, the
outcome of each choice, and then summarize what you’ve learned.
Portions of this product are based on materials copyrighted by Mattel, Inc.
Introduction to Algebra Lessons 9-15
Name:
Date:
Geometry: Thinking Skills Lesson 2
Student Activity
Problem Solving: Building a Sandbox
STEPS:
1.
2.
3.
4.
5.
Identify your goal.
Identify limiting conditions.
Identify ways to meet the limiting conditions.
Identify and try possible solutions.
Evaluate your possible solutions.
Here is the problem that appeared in the lesson:
Your neighborhood has collected $200 to build a sandbox for the playground. You are in charge of the
project. The land available for the sandbox is 8 feet by 5 feet with a tree in the corner. You want to make
the sandbox as large as possible, but you have a limited amount of space available. The tree cannot be
inside the sandbox. Volunteers will build the sandbox, but they can only build simple 90º corners. Since
you are in charge of the project, it’s up to you to solve these problems and produce a sandbox.
Directions: You solved the sandbox problem. Now the committee has asked you to research adding a
circular sand pit around the sliding board. The major limiting condition is the space allowed for the
sliding board and sand pit, so you must find the area of the circle. Use these dimensions to find the area of
the circular sand pit:
• The sliding board ladder is 6 feet tall.
• The sliding board is 10 feet long.
• The ladder forms a 90º angle with the ground.
• The sand should extend 3 feet beyond the end of the sliding board and 3 feet beyond the ladder.
Hint: First, use the Pythagorean Theorem to find the length between the sliding board and the ladder.
Then, add 3 feet on each side to find the diameter of the circle.
Write Idea: Another problem that has come up in relation to the playground is children getting hurt
while playing. Describe a possible solution to this problem? Are there limiting conditions to your
solution? If so, how would you meet those limiting conditions?
Portions of this product are based on materials copyrighted by Mattel, Inc.
Geometry Lessons 6-12
Name:
Date:
Statistics and Probability: Thinking Skills Lesson 2
Student Activity
Prediction: The Real Cost of Living
STEPS:
1.
2.
3.
4.
5.
Identify the facts that you know.
Look for patterns in the information.
Make a general statement that explains the patterns
you have observed.
Based on your conclusions, predict what might
happen in a new situation.
Make more observations to see if you predicted
correctly.
In the lesson, you used the prediction process to complete this table:
Savings
Expenses
Income
5 years
ago
$47
$781
$785
Present
$50
$890
$892
% of
change
6%
14%
13.6%
Change/
year
1.2%
2.8%
2.7%
You predicted that your salary needed to increase 3% a year for you to meet expenses and increase your
savings.
Directions: Now apply your prediction skills to this problem. You are in charge of fund raising at your
local high school. This graph shows the results of fund-raising efforts at the school for each of the past
five years.
1. Identify the mean, median, and mode of the
fund-raising dollars for the past five years.
2. You want to set a goal for year 6 that is based
on a reasonable prediction. If the upward trend
from years 3-5 continues, what is your prediction for dollars to be raised in year 6? Describe
your procedure for arriving at this prediction.
Write Idea: Air pollution is increasing. Scientists know that if it continues to increase at high rates, our
air will become toxic. Science has the numbers it needs. What is needed is a plan for predicting. Write a
plan for scientists to predict how many years it will take our air to become toxic. Remember the steps of
the prediction process.
Portions of this product are based on materials copyrighted by Mattel, Inc.
Statistics and Probability Lessons 1-8
6 20 6
Assignment Sheet
This appendix contains an assignment sheet for all the activities in Intermediate Mathematics.
The assignment sheet lists the available lessons and tests. The SkillsTutor management system
will track the lessons and tests your students complete. However, it may be helpful to photocopy
an assignment sheet to help you plan lesson assignments or to help your students keep track of
the lessons and tests they complete.
6 21 6
6 22 6
Assignment Sheets: Intermediate Mathematics Series
Activity
Date Assigned
Proportion and Percent
•
Pretest on Proportion and Percent
1
Relationship of Ratios, Percents, and Decimals
2
Ratios and Proportion
3
Using Proportions to Find Group Prices
4
Finding the Part by Using Proportions
5
Finding the Percent by Using Proportions
6
Finding the Whole by Using Proportions
Q1
Quiz on Lessons 1 through 6
7
Finding the Part by Using Number Sequences
8
Finding the Percent by Using Number Sentences
9
Finding the Whole by Using Number Sentences
10
Percent of Change
11
Discounts
12
Simple Interest
Q2
Quiz on Lessons 7 through 12
TS
Comparison: Movie House Management
•
Posttest on Proportion and Percent
Date Completed
Score/Progress
Assignment Sheets: Intermediate Mathematics Series
Activity
Date Assigned
Introduction to Algebra
•
Pretest on Introduction to Algebra
1
Absolute Value
2
Addition and Subtraction of Integers
3
Multiplication and Division of Integers
4
Exponents and Square Roots
5
Scientific Notation
6
Operations with Exponents
7
Simplifying Numerical Expressions
8
Sequences
Q1
Quiz on Lessons 1 through 8
TS
Prediction: Number Sequence Puzzles
9
Evaluating Variable Expressions
10
Simplifying Variable Expressions
11
One-Step Equations
12
Two-Step Equations
13
Graphing on the Coordinate Plane
14
Writing Equations from Words
15
Distance-Rate-Time Problems
Q2
Quiz on Lessons 9 through 15
TS
Decision Making: Buying a House
•
Posttest on Introduction to Algebra
Date Completed
Score/Progress
Assignment Sheets: Intermediate Mathematics Series
Activity
Date Assigned
Geometry
•
Pretest on Geometry
1
Units of Length
2
Units of Weight and Capacity
3
Time Zones
4
Angles
5
Lines and Angles
Q1
Quiz on Lessons 1 through 5
6
Area of Polygons
7
Circumference of Circles
8
Area of Circles
9
Surface Area
10
Volume of Prisms and Cylinders
11
Formulas in Geometry
12
Pythagorean Theorem
Q2
Quiz on Lessons 6 through 12
TS
Problem Solving: Building a Sandbox
•
Posttest on Geometry
Statistics and Probability
•
Pretest on Statistics and Probability
1
Pictographs
2
Bar Graphs
3
Line Graphs
4
Circle Graphs
5
Measures of Central Tendency
Q1
Quiz on Lessons 1 through 5
6
Simple Probability
7
Counting Outcomes
8
Predicting Outcomes
Q2
Quiz on Lessons 6 through 8
TS
Prediction: The Real Cost of Living
•
Posttest on Statistics and Probability
Date Completed
Score/Progress