Course Syllabus-Math 7
EdOptions Course – Math 7
Course Overview
You have been studying math for years now. This course will review and build on the material
that you already know so that you can use more math in your everyday life. Your everyday life
is filled with math: at the cafeteria, your after-school job, on the field of your favorite sport, and
in your refrigerator. Understanding the math around you now will help prepare you for any
number of careers like a space scientist or doctor, or will simply make you a more aware
citizen.
In this course, you will study many parts of math. Topics for the first semester include problemsolving skills, patterns and number sense, an introduction to algebra, integers, fractions,
decimals, and ratios. Each lesson includes many real life applications with word problems.
Topics for the second semester include percents, measurement, geometry, area, Pythagorean
theorem, surface area, volume, statistics, graphing and discrete probability. Each lesson includes
many real life applications with word problems.
Tips on reading this course
Take notes! It is always important to write down what you learn. Use a notebook that is only
for math to record the new concepts taught and to review later.
Look for colors! Colors are used to highlight important parts of each lesson. Lookout for the
steps in red or green. They highlight new steps in an equation, an answer, or an important
phrase. Entire sentences, the core of the lesson, are often highlighted to guide your learning and
taking notes.
Use the glossary! Glossary links are included in each lesson. Understanding the vocabulary
for each lesson is important to understanding the math itself.
Course Structure
Algebra 1 includes 36 lessons and submissions, two midterm exams, and two semester exams.
Each lesson begins with a brief introduction. The lessons are divided into sections of content
that relate to measureable, standards-based objectives. Each section includes detailed
explanations, as well as examples that show students how to apply new concepts. Practice
problems are given throughout the lesson to give students a chance to work with new material
before moving on to other parts of the lesson.
Textbook: You will not need a textbook for this course. All of the information needed is in
each lesson.
Calculator: You may want a calculator to check your work, but it is not necessary to use one
throughout the course.
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Course Syllabus-Math 7
Materials: For this course, you will need a notebook. Other items you may need are:
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pencil
graph paper
straight edge (like a ruler or a scrap piece of paper)
Lesson Components
Objectives
Each lesson begins with objectives. They outline what the student will be able to do by the
completion of the lesson.
Course Glossary
The course includes glossary terms, which are in bold, blue font. When you click on a glossary
term, the course glossary will open in a new window. Each lesson also provides a general link
to access the glossary. This link appears at the beginning of the lesson below the objectives too.
Example Questions
Example questions are those that show the concept being taught. Each step of a problem is
clearly shown to teach the concept. There are several examples in each lesson.
Practice Problems
Practice problems give students a chance to self-check their work. At the end of each group of
practice problems, students can click on a "check answers" button to reveal solutions as well as
detailed explanations of how the answers are found.
Homework
Each lesson concludes with homework problems. Students will not have access to homework
answers; a teacher or administrator must provide students with the solutions.
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Course Syllabus-Math 7
Course Assessments
Submissions
Submissions are designed to measure the student’s mastery of lesson objectives. There is one
submission test for each lesson in a course. Submissions can include two types of assessment
questions:
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Objective questions-which are multiple choice items graded by the system.
Subjective questions-which are graded by the teacher based on an answer key or rubric
that defines the number of points to be awarded for the question.
Submissions will have approximately 25 questions.
Midterm
Midterms are designed to ensure that students are retaining what they have learned. Midterms
can include two types of assessment questions:
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Objective questions-which are multiple choice items graded by the system.
Subjective questions-which are graded by the teacher based on an answer key or rubric
that defines the number of points to be awarded for the question.
Midterms will have approximately 50 – 100 questions.
Final Exam
Final exams are designed to ensure that students have learned and retained the critical course
content. Final exams can include two types of assessment questions:
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Objective questions-which are multiple choice items graded by the system.
Subjective questions-which are graded by the teacher based on an answer key or rubric
that defines the number of points to be awarded for the question.
Final exams will have approximately 50 – 100 questions.
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Course Syllabus-Math 7
Course Outline and Objectives
Semester 1
Lesson 1: Problem Solving 1
Objectives
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utilize the steps to solve word problems
use five problem solution strategies: work backwards, cue words, make a table,
extra facts, and simpler problem
Lesson Overview
This lesson will focus on problem-solving strategies. These strategies will be used throughout
the course to solve word problems that might be useful in your daily life. You may already
know and use certain problem solving strategies. For instance, you might already draw
diagrams, make models, or look for patterns when you work on solving a problem. The new
strategies that you learn in this lesson can be added to your problem-solving toolbox to
compliment the ones you already have.
Lesson 2: Problem Solving 2
Objectives
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decide whether estimation is appropriate or not
round and estimate with large numbers, decimals, and fractions
check problems with estimation
Lesson Overview
In the last lesson, you learned a variety of steps which help you to problem solve. Depending
on the type of problem presented, it may be useful to estimate. Estimation can be used
when you do not need to determine the exact answer, in which case you can find an
approximation. Estimating saves time and will give you a general idea of an answer without
having to work out the specifics of a problem.
For example, if you heard that a celebrity was worth $5,089,993,137, you might tell your friend
that the celebrity was worth five billion dollars. It is true that the celebrity has more money
than that, but it is unnecessary to report down to the very last dollar. Just giving your friend
an idea of how much money the celebrity is worth (by rounding) is enough in this case.
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Course Syllabus-Math 7
Lesson 3: Patterns and Number Sense 1
Objectives
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rewrite numbers in exponential form
rewrite large numbers in scientific notation
apply order of operations to word problems and to numerical problems
Lesson Overview
What does the word square mean? It has a few different meanings, as you may know. It is used
to describe a shape that has four equal sides and four equal angles. It is also used to describe a
number times itself. Why is it used to describe both of these things? They seem to have nothing
to do with each other. Understanding the relationship between these two definitions means
having a sense of numbers and their functions.
In the last lesson, you focused on gaining a better sense of large numbers by rounding and
estimating. In this lesson, large numbers will be represented in another form called
the exponential form. How to use and work with these large numbers will also be addressed in
this lesson.
Lesson 4: Patterns and Number Sense 2
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apply divisibility rules to four digit numbers
use a factor tree and step diagram to find prime factorizations of composite numbers
give the greatest common factor (GCF) of two or more whole numbers
give the least common multiple (LCM) of two or more whole numbers
Lesson Overview
Lesson 2 taught about new ways to represent numbers. For example, exponents allow repeated
multiplication of a factor to be represented by a power. Similarly, scientific notation uses
powers of ten to represent large numbers. You also learned the order of operations that spell
out the order in which computations should be done.
Throughout the rest of this course you will be focusing on many topics that require the ability
to break up numbers into even or sensible parts. Understanding fractions, decimals, and
percents requires knowledge of how to break up numbers. To make this process easier, the
focus will be on divisibility and factorization of numbers in this lesson.
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Course Syllabus-Math 7
Lesson 5: Algebra 1
Objectives
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define variable
write equations with variables
evaluate equations with one variable
evaluate equations with two variables
combine like terms
Lesson Overview
The last few lessons focused on patterns of numbers and developing a sense of numbers. In the
next lessons, we will focus on an introduction to algebra. Algebra is a form of math that could
be studied for an entire lifetime. You may have even seen some of the concepts before.
Lesson 6: Algebra 2
Objectives
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solve equations using addition and subtraction properties of equality
solve equations using multiplication and division properties of equality
Lesson Overview
Have you ever taken a long road trip? Driving different distances every day to get to your
desired destination can be fun. If you know how far away the final destination is and want to
find the distance of each leg of the journey, this lesson will be very useful.
As previously discussed, unknowns in math are often represented by a variable. This letter
stands in the place of a number needed to solve the equation. In Lesson 5, you learned to solve
equations when given the value of a variable. However, if all the other numbers in the equation
are known, it is possible to find the value of the variable by isolating it from the rest of the
numbers. In this lesson, you will focus on isolating variables by using properties of equality.
Lesson 7: Algebra 3
Objectives
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solve two-step equations
solve equations with variables on both sides
solve inequalities using addition and subtraction
graph inequalities
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Course Syllabus-Math 7
Lesson Overview
In the last lesson, properties of equality were introduced. By using properties of equality you
are able to isolate a variable (the unknown) and find the value of it. In this lesson you will build
on what you have learned in order to solve equations with more terms. Then you will use
concepts from earlier lessons, such as combining like terms and defining variables, to solve even
more complex equations.
Lesson 8: Integers 1
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define integers and graph them on a number line
compare the values of opposite, positive, and negative integers on a number line
define and find absolute value
identify parts of a coordinate plane
define and graph ordered pairs
Lesson Overview
Have you ever owed anyone money? Did you ever borrow 50 cents for dessert at the school
cafeteria from a friend and promise to pay them the next day? It could be said that after you
borrowed the money and bought the dessert, you had negative 50 cents. The next day, you
bring a dollar to school. Fifty cents of that is your friend's, though, so you actually only have 50
cents, not a full dollar.
Understanding and visualizing negative numbers will be the focus of this lesson. How do they
relate to each other and how do they relate to other numbers? Use what you know from
Lesson 7, about graphing numbers on number lines, to graph negative numbers in this lesson.
Lesson 9: Integers 2
Objectives
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add, subtract, multiply, and divide integers
derive rules for multiplying and dividing integers without the use of a number line
identify and apply the commutative, identity, associative, and distributive properties
Lesson Overview
In the last lesson you looked at the concept of integers and how positive and negative numbers
relate to each other. In this lesson you will continue to explore integers. You will derive, or
make up, rules for how integers combine using the four operations (addition, subtraction,
multiplication, and division). You will also look at the properties that govern mathematic
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Course Syllabus-Math 7
equations and see how they apply to equations. These concepts will be useful when solving
algebraic equations.
Lesson 10: Integers 3
Objectives
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create transformations using ordered pairs
summarize patterns found in tessellations and transformations
Lesson Overview
In the last two lessons, you learned about integers, and you figured out how to put numbers on
a number line. You also learned what happens when negative numbers are added, subtracted,
multiplied, and divided by themselves and by positive numbers. These concepts will continue to
be used. The background knowledge you have will be necessary in order to learn about
geometry and how figures, or shapes, move and shift indifferent ways. This lesson also includes
the concept of coordinate planes as discussed in Lesson 8.
Lesson 11: Fractions 1
Objectives
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write decimals and fractions on the same number line
find equivalent fractions
define improper fractions and mixed numbers
convert improper fractions to mixed numbers
distinguish between rational and irrational numbers
write rational numbers as fractions
Lesson Overview
In the past, you have looked at number lines in relation to whole numbers. Now focus on the
placement of decimal numbers and fractions on a number line. To do this, you need to take a
magnified look at the number line and find where these decimal and fractional values belong.
Using knowledge of integers, both positive and negative fractions and decimals will be explored.
Lesson 12: Fractions 2
Objectives
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estimate addition and subtraction of fractions
add fractions and mixed numbers
subtract fractions and mixed numbers
multiply fractions and mixed numbers
divide fractions and mixed numbers
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Course Syllabus-Math 7
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use the identity property with fractions
Lesson Overview
The last lesson was spent determining how fractions are formed as well as comparing them to
other fractions and decimals. These skills will prove useful now that you will be estimating,
adding, subtracting, multiplying, and dividing all the numbers that you have been learning about.
Lesson 13: Fractions 3
Objectives
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write fractions as decimals
write decimals as fractions
compare and order decimals, fractions, mixed numbers, and improper fractions
Lesson Overview
The last two lessons concentrated on computations with fractions. This lesson will focus on
comparing parts of a whole that are represented in various ways. Two ways to represent parts
of a whole are through the use of fractions and decimals. To compare numbers, they have to be
written in like terms. In other words, the numbers have to be expressed in the same form.
Therefore, before comparing numbers, you will practice converting fractions to decimals and
decimals to fractions.
Lesson 14: Decimals 1
Objectives
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name place value of decimals through the thousandths
place decimals on a number line and compare their values
estimate sums and differences of decimals
estimate products and quotients of decimals
add and subtract decimals to find exact amounts
round decimals to the nearest tenth, hundredth, and thousandth
Lesson Overview
The past three lessons have focused mainly on fractions. Decimals have also been discussed, but
not as thoroughly. The next few lessons will focus on decimals. You use decimals everyday.
Dollars are divided into 100 cents, so the decimal system in this case shows a part of a dollar
(cents). Notice that fractions are never used with money. For instance, have you ever gone to a
video store and seen a sign that says, "Two night rental for $4 99/100"? It is not likely. In this
lesson, you will focus on estimating with decimals as well as performing addition and
subtraction equations with decimals. It will be important to review both rounding and place
value. This is where you will start.
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Course Syllabus-Math 7
Lesson 15: Decimals 2
Objectives
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multiply integers by decimals
multiply decimals by decimals
express integers and decimals in scientific notation using positive and negative
exponents
Lesson Overview
Since Lesson 14 focused on adding and subtracting decimals, it is a natural jump to start
multiplying decimals. Remember, multiplication is simply a form of repeated addition. Learning
how to multiply decimals will be done in two parts in this lesson. First, you will multiply
decimals by integers. Then you will focus on multiplying decimals by other decimals.
Lesson 16: Decimals 3
Objectives
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divide decimals by integers
divide integers by decimals
divide decimals by decimals
Lesson Overview
The last lesson focused on multiplication with decimals. This lesson covers division. Dividing
decimals is basically like dividing a part of a whole into more parts. You will have the
opportunity to practice dividing a part of a whole by wholes and a part of a whole by other
parts of a whole. In addition, wholes will be divided by a part of a whole. In order to truly
understand these concepts, keep reading.
Lesson 17: Ratios 1
Objectives
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define ratio, rate, and unit rate
write ratios
simplify ratios to make proportions
write rates and unit rates
distinguish between rates and unit rates
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Course Syllabus-Math 7
Lesson Overview
In the last several lessons, decimals have been explored. A decimal is a part of a whole, as is a
fraction. This lesson will discuss different types of fractions such as ratios, which are fractions,
and proportions, which compare ratios. A rate is a special type of ratio, and a unit rate is a
special kind of rate. These terms will be discussed throughout the next two lessons. Learning
about these concepts will make you a better consumer. A consumer is someone who purchases
things. So the next time you go to the store, use what you will learn about ratios,
proportions, rates, and unit rates from this lesson.
Lesson 18: Ratios 2
Objectives
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solve proportions and apply the property of proportion
use ratios and proportions with a scale
use models to find missing dimensions of similar figures
Lesson Overview
This lesson will build on what was taught in the last lesson. That lesson focused on ratios, rates,
and proportions. In this lesson, proportions will be presented with part of the ratio missing,
such as in the example above. You will then solve the proportion for the missing measurement.
In addition, the concept of proportions will be applied to maps and scales.
Semester 2
Lesson 19: Percent 1
Objectives
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write equivalent forms of percents, decimals, and fractions
estimate percentages when given a fraction
estimate percentages of numbers
use proportions to find the percentage of a number
find exact percentages of numbers using decimals
Lesson Overview
Fractions and decimals have been covered in one form or another in every single lesson thus
far. Percents are another way of showing parts of a whole. Finding percents using decimals,
fractions, and proportions is the purpose of this lesson.
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Course Syllabus-Math 7
Lesson 20: Percent 2
Objectives
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find percent change
use percent change to solve problems
compose a circle graph from a data table by using percent change and include equivalent
fractions in the circle graph
Lesson Overview
Both the last lesson and this one focus on percents. Percents are just another way to represent
parts of a whole. Leaders in a variety of positions such as principals, mayors, and presidents
have to look at information all of the time. With this information, they compare numbers in
order to make decisions. Percents are often used to show these comparisons. For instance,
instead of making a speech concerning 147,867,067 Americans, the President of the United
States might choose to talk about 50% of Americans. When the population grows, the
President would not typically refer to the new 592,023 citizens, but instead note the change in
percent of the population. Understanding and being able to use percents is very important. This
lesson addresses how to use percents and percent change in order to understand data. How to
display that data and how to buy things more efficiently is also covered in this lesson.
Lesson 21: Percent 3
Objectives
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use knowledge of variables, decimals, and algebra to solve problems involving simple
interest
find the sale price of items
select the best sale items to save the most money when shopping
Lesson Overview
Have you ever noticed how much junk mail your parents get at your home address? A lot of
that junk mail consists of credit card deals. Credit cards allow people to borrow money, buy
things, and then pay the lender back later. The trick is that the lender usually charges interest.
The longer someone takes to pay back the initial amount, the more that person has to pay!
Understanding interest can save you a lot of money. This lesson will give you valuable tips in
order to save money, both in terms of interest and in terms of calculating sale prices on items
you might find in a store.
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Course Syllabus-Math 7
Lesson 22: Measurement
Objectives
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choose the most appropriate unit to measure length, volume, and weight of everyday
objects and distances, using both the metric and customary systems
convert measurements of length, volume, and mass within the same system of
measurement
Lesson Overview
Measuring takes place every day all around us. On the street, signs tell you how far you are
allowed to go in a certain time (15 miles per hour in most school zones) or how far it is until
the next exit on the highway (George Washington Parkway 1.5 miles). Off the top of your
head, you know that a pint of ice cream is much smaller than a gallon of milk and that
centimeters and liters measure totally different things. This lesson explores the mathematics
behind measurements.
Throughout the lesson, look for the shaded column of tables called In Your Life. This column will
help you relate the information in the table to your life in some way, giving the information
presented something called context. The exact information given in In Your Life will not be in the
practice problems or homework; however, it will be important to learn this so that you know
how all of the measurements studied in this lesson relate to your life.
Lesson 23: Geometry 1
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identify a point, line, ray, and line segment
use rays, points, and lines to make acute, right, obtuse, and straight angles
identify parallel, perpendicular, and intersecting lines, as well as the angles formed by
lines
identify polygons and their names using their number of sides
find the sum of the interior angles of polygons
determine the measure of an angle by using knowledge of complementary,
supplementary, and vertical angles
Lesson Overview
Have you ever designed anything? A new plan for your room? A new route to school? A poster
for a class election or a lost dog? Chances are you used geometry in your designs. Learning
about the various aspects of geometry will allow you to see the world in a whole new way.
Notice what is taught in geometry, including the names of angles, the different aspects of lines,
and the names of shapes. See how all parts of geometry interact with each other, and in the
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Course Syllabus-Math 7
meantime, think about how geometry is involved in your daily life. To do this, just look out the
window, on your desk, or at a piece of furniture in the room. Geometry is all around you. This
lesson is an introduction to geometry.
Lesson 24: Geometry 2
Objectives
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differentiate between polygons and non-polygons
identify quadrilaterals and triangles according to sides and angles
find the perimeter of polygons
find the perimeter of polygons using ratios and similar figures
Lesson Overview
Polygons are everywhere, from artwork to city planning, from the desk you are sitting at to the
parts of the computer that you are working on. Finding polygons in your daily life is the first
way to get to know them better. You need to know what you are looking at. What makes a
shape a polygon? When is a shape not a polygon? What is the difference between various types
of polygons? Are there many types of polygons? As you work through this lesson, note that the
names of shapes are very general, based only on the number of sides. Among other things, we
are going to explore the differences and similarities of some types of polygons in this lesson.
Lesson 25: Area 1
Objectives
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find the area of a rectangle
find the area of a triangle
find the area of a parallelogram
Lesson Overview
A small family lives in a three bedroom house. The parents have the master bedroom, and the
son has one of the other bedrooms. When the parents bring their new baby home from the
hospital, she will live in the third bedroom. The son wants the baby's bedroom and asks his
parents if he can switch with the baby. They say, "Give us one good reason." To prove that the
baby's room is bigger, he has to take measurements. He finds the size of both rooms, or the
area, and argues that he deserves the bigger room.
Knowing how to find the size of spaces can be very beneficial to you. Finding the outside
measurement, or perimeter, and the different shapes that exist is discussed in Lesson 24. In this
lesson, that knowledge will be used to find the inside measurement, or how much space a shape
takes up. This is known as area.
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Course Syllabus-Math 7
Lesson 26: Area 2
Objectives
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find the area of a trapezoid
find the area of irregular polygons
Lesson Overview
When it comes to area, not all shapes are as predictable as triangles and rectangles as shown in
Lesson 25. Finding the area of a parallelogram started with splitting it up into two triangles. You
will use that same strategy in this lesson as you divide trapezoids and irregular polygons into
shapes such as triangles and rectangles in order to find the area.
Lesson 27: Pythagorean Theorem and Circles
Objectives
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use the Pythagorean Theorem
find the circumference of a circle to the nearest tenth
find the area of a circle
Lesson Overview
Over the last four lessons, different aspects of geometry have been discussed. Certain parts
have been left out to be discussed separately. This lesson discusses those parts. Right triangles
and their perimeters, and circles and their perimeters and areas have special formulas and
numbers associated with them. Learn these ideas separately from the rest of geometry and
then use all of what you have learned to find the area of several everyday objects.
Lesson 28: Surface Area
Objectives
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name the parts of three-dimensional figures
find the surface area of a rectangular prism
find the surface area of a cube
find the surface area of a cylinder
Lesson Overview
What is the difference between a soda can and a picture of the same soda can? What is the
difference between drawings in a picture book and drawings in a pop-up picture book? The
difference is the third dimension.
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Course Syllabus-Math 7
So far we have only addressed two dimensions. The lines discussed in Lesson 23 only have
length. The polygons discussed in Lessons 24-26 only have length and height. These objects are
all on a plane. In this lesson, a third dimension will be added and the properties of the new
shapes will be explored.
Lesson 29: Volume
Objectives
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find the volume of a rectangular prism
find the volume of a cylinder
Lesson Overview
In the last lesson, surface area was measured. Surface area measures what fits on the outside of
three dimensional shapes. Volume measures how much can fit inside three dimensional shapes.
Lesson 30: Statistics 1
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solve problems by organizing data into a table
create and interpret stem-and-leaf plots and box and whisker plots
find the measures of central tendency for a set of numbers
identify population and random samples
Lesson Overview
How many communities are you a part of? Start with where you live. If you live with another
person, the two (or four or five) of you form a living community in your home. Now, keep
expanding out from your house. If you live in an apartment complex, all of the people in that
building form a community as well. If you live in a neighborhood of houses, there might be a
neighborhood community watch. The neighborhood is a community. If you live in a small town,
it probably has a village within the town. The village is a community and so is the town. The
county and state that your town is in is also a community as is the union of all of the states: the
United States of America.
Leaders in communities that are more relevant to your life like bosses, student council
members, and team captains want to know what you are thinking about issues that arise in the
communities they lead (like work, school, and your soccer team). As a member of these
communities your opinion of the leader and of the community matters. Leaders also want to
show you what other people in your shared community are thinking to try to sway your ideas
to benefit themselves or the greater community. Citizens of a community, any community, need
to know how to interpret information that is presented to them. Most times, that information
comes in the form of a graph based on a survey.
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Course Syllabus-Math 7
Surveys are used to collect people's ideas for just about everything: traffic patterns, cafeteria
food, rules at a dog park, or what to eat for dinner. Then the information collected is presented
to the community. In this lesson, you will learn how to interpret the information and some of
the different ways it is presented.
Lesson 31: Statistics 2
Objectives
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read a bar graph and line graph
display data from a table on bar and line graphs
evaluate the effectiveness of a graph
make predictions when reading bar, circle, and line graphs
revise existing misleading graphs
Lesson Overview
The last lesson focused on collecting data and organizing it. Once it is organized, what do you
do with it? Most people use the data to prove a point, to show a new idea, or to find a pattern
by making a graph. The people making the graph pick the data that best proves their point, or
shows the new idea or pattern. The person making the graph has a lot of control over what is
presented to the reader. The person looking at the graph did not create the survey and collect
and organize the data, but is looking at the final product. It is her job to decide what it all
means. This lesson will focus on creating two types of graphs and deciphering ones that have
already been made.
Lesson 32: Graphing 1
Objectives
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solve multi-step equations with all integers
solve and graph inequalities with all integers
write and graph inequalities with all integers
Lesson Overview
For the last two lessons, you have been learning about statistics, reading graphs, and
understanding trends in graphs so that you can tell the difference between an effective graph
and an ineffective one. Now that you understand what you are looking at when you see a graph,
you are going to shift gears and make your own graphs. These graphs will not be from data
gathered through polls or by counting items. Instead, these graphs will be visual representations
of algebra. Way back in Lesson 7, you began this process by solving and graphing one and twostep inequalities on number lines. These skills will be reviewed and built upon in this lesson in
order to prepare you for more complicated graphing in the next few lessons.
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Course Syllabus-Math 7
Lesson 33: Graphing 2
Objectives
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solve equations with two variables
graph equations using function tables
identify functions in sequences
find patterns to complete sequences using tables
Lesson Overview
The algebra taught throughout this course will be used during this lesson to graph. Being able to
see the algebra on a graph will help to visualize what unknowns represent. These graphs are
used not only by mathematicians to find new ideas, but also scientists, architects, and engineers.
Lesson 34: Graphing 3
Objectives
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identify the parts of a linear function
graph linear equations
define and determine the slope of a line
Lesson Overview
In the last lesson many functions were graphed. Sometimes the points reflected over the y-axis
and sometimes the points formed a pattern that looked like a line. This lesson focuses on the
functions that make lines. What makes a function form a line? What are the parts of that
function? What can you tell about a line from its function? All of these questions and more will
be discussed in this lesson.
Lesson 35: Discrete Math and Probability 1
Objectives
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•
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determine the likelihood of an event
find experimental and theoretical probability
use counting methods to determine combination outcomes
Lesson Overview
Have you ever flipped a coin to decide an argument? Have you ever entered a raffle? Have you
ever rolled dice while playing a board game? Each of these activities involves mathematical
probability. Probability is based on how likely it is that an event will occur. An experiment, such
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Course Syllabus-Math 7
as flipping a coin, has an outcome, like getting "heads" as opposed to "tails." You can judge how
likely an event is to happen, or the odds of the event occurring, based on the number of
possible outcomes. Flipping a coin only has two possible outcomes, but other experiments can
have many different outcomes. Probability helps us understand these outcomes.
Lesson 36: Discrete Math and Probability 2
Objectives
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•
distinguish between independent and dependent events
find the probability of combinations of events
Lesson Overview
Lesson 35 focused on finding the probability of events in which the occurrence of one event
does not affect the outcome of another. Most of the examples were fairly straightforward
examples of relatively simple probability problems. This lesson will explore more complex
probability problems where events depend on previous occurrences. For example, instead of
simply determining what color a marble might be when it is chosen from a bag, you will now be
asked to determine the probability of various colors being chosen after your first selection. The
second marble selection depends on what happens the first time.
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