Modified 6/20/2011 1
Math, Course 3 Advanced
Radnor Middle School Course Overview
Math
Course 3
General Information Credits: N/A Length: Full Year
Weighted: N/A Format: Meets Daily
Prerequisite: N/A Grade: 7
I. Course Description The goal of this course is to develop an understanding of rational numbers and their operations and begin to apply that understanding to equations and inequalities in order to prepare for Algebra 1. These ideas will be integrated throughout the content strands of algebra, geometry, measurement, and data analysis and probability, with a focus on algebraic development. Students will also learn various problem solving strategies to solve appropriate applications within the strands listed above.
Modified 6/20/2011 2
Math, Course 3 Advanced
MARKING PERIOD: 1
Unit: Chapter 1 – Variables and Equations
Common Core Standards 7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.
7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients.
7.EE.2. Understand that rewriting an expression in different forms in a problem context can
shed light on the problem and how the quantities in it are related. For example, a + 0.05a =
1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary
of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27
1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate
can be used as a check on the exact computation.
7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for
the number of sales you need to make, and describe the solutions.
Keystone Connections: (PA Standards) M7.E.1.1-Interpret data shown in complex data displays.
M7.E.4.1-Draw conclusions and, make predictions based on data displays.
M8.E.1.1-Choose, display or interpret data (tables, charts, graphs, etc.). (Reference: 2.6.5.A,
2.6.8.E, 2.7.8.D)
M8.E.4.1-Draw conclusions, make inferences and/or evaluate hypotheses based on statistical and
data displays. (Reference: 2.6.8.C, 2.7.8.E)
M7.A.2.1-Complete calculations by applying the order of operations.
M8.A.2.1-Complete calculations by applying the order of operations. (Reference: 2.2.8.A)
2.1.7.B-Simplify equivalent numeric expressions involving four basic operations, grouping
symbols, exponents, and square roots.
MAJOR UNITS OF STUDY
Modified 6/20/2011 3
Math, Course 3 Advanced
2.2.7.A-Complete calculations by applying the order of operations.
2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers
including integers, decimal fractions, percents and proper and improper fractions.
2.2.7.F-Describe appropriate uses of scientific calculator, pencil and paper and mental math.
2.2.7.H-Check the reasonableness of an answer.
2.4.7.D-Use and explain algorithmic procedures for computing and estimating with whole
numbers, fractions, decimals and integers.
Student Objectives: In this chapter, students use bar graphs and histograms to analyze data. Students use order of
operations to evaluate numeral and variable expressions, including expressions with powers.
Students write variable expressions and write and solve equations using mental math. Students
use formulas to find unknown values.
At the conclusion of this chapter, students will successfully complete the following skills:
Use graphs to analyze data
Use order of operations to evaluate numerical expressions
Write and evaluate variable expressions
Evaluate expressions with powers
Write and solve equations
Use mental math to solve equations
Use formulas to find unknown values
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
1.1 Interpreting Graphs
1.2 Order of Operations
1.3 Variables and Expressions
1.4 Powers and Exponents
1.5 Equations and Solutions
1.6 Variables in Familiar Formulas
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Modified 6/20/2011 4
Math, Course 3 Advanced
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Bar graph, frequency table, histogram, intervals, horizontal axis, vertical axis, whole number,
sum, difference, product, quotient, numerical expression, evaluate, order of operations, verbal
model, grouping symbols, fraction bar, variable, variable expression, common words and phrases
for operations, exponent, base, power, squared, cubed, repeated multiplication, equation,
solution, solving an equation, formula, perimeter, area, distance formula, d=r·t, rate, speed
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 5
Math, Course 3 Advanced
MARKING PERIOD: 1 Unit: Chapter 2 – Integer Operations
Common Core Standards 7.NS.1.a. Describe situations in which opposite quantities combine to make 0. For example, a
hydrogen atom has 0 charge because its two constituents are oppositely charged.
7.NS.1.b. Understand p + q as the number located a distance |q| from p, in the positive or
negative direction depending on whether q is positive or negative. Show that a number and its
opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by
describing real-world contexts.
7.NS.1.c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p
+ (–q). Show that the distance between two rational numbers on the number line is the
absolute value of their difference, and apply this principle in real-world contexts.
7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world context.
7.NS.2.b. Understand that integers can be divided, provided that the divisor is not zero, and
every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers,
then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world
contexts.
7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary
of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27
1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate
can be used as a check on the exact computation.
7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for
the number of sales you need to make, and describe the solutions.
Keystone Connections: (PA Standards) M7.A.1.2-Compare quantities and/or magnitudes of numbers.
M7.A.2.1-Complete calculations by applying the order of operations.
M7.A.2.2-Solve problems using ratios, proportions, percents and/or rates.
Modified 6/20/2011 6
Math, Course 3 Advanced
M7.A.3.2-Compute accurately with and without use of a calculator.
M7.D.1.1-Recognize, reproduce, extend and/or describe patterns, sequences and relationships.
M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M8.A.2.1-Complete calculations by applying the order of operations. (Reference: 2.2.8.A)
M8.A.2.2-Represent or solve problems using rates, ratios, proportions and/or percents.
(Reference: 2.1.8.D, 2.3.8.B)
M8.A.3.3-Compute and/or explain operations with integers, fractions and/or decimals.
(Reference: 2.2.8.B)
M8.D.1.1-Analyze, extend or develop descriptions of patterns or functions. (Reference: 2.8.8.B,
2.8.8.G, 2.11.8.C)
M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality
and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)
2.2.7.A-Complete calculations by applying the order of operations.
2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers
including integers, decimal fractions, percents and proper and improper fractions.
2.4.7.B-Develop numeric relationship expressions to arrive at a conclusion. (e.g. commutative,
associative, distributive, and transitive properties, substitution, and numerical patterns)
identify
Student Objectives: In this chapter, students use a number line to explore integers and absolute value and they add,
subtract, multiply, and divide integers. Students find the mean of a data set. Students use the
commutative, associate, and distributive properties to evaluate expressions. Students also find
and plot points in the coordinate plane.
At the conclusion of this chapter, students will successfully complete the following skills:
Use integers to represent life situations
Add, subtract, multiply, and divide integers
Find the mean of a set of integers
Use properties to evaluate expressions
Use the distribute to simplify expressions
Identify and plot points on a coordinate plane
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
2.1 Integers
2.2 Adding Integers
Modified 6/20/2011 7
Math, Course 3 Advanced
2.3 Subtracting Integers
2.4 Multiplying Integers
2.5 Dividing Integers
2.6 Number Properties
2.7 The Distributive Property
2.8 The Coordinate Plane
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Integers, negative integers, positive integers, zero, absolute value, opposites, opposite numbers,
number line, variable, variable expression, perimeter, area, identity property of addition, inverse
property of addition, sum, signs +/-, rules for addition of integers, opposite, difference, rules for
subtraction of integers, identity property of multiplication, product, rules for multiplying
integers, multiplication property of zero, multiplicative identity, commutative property,
associative property, distributive property, terms, like terms, coefficient, constant term,
coordinate plane, x-axis, y-axis, origin, quadrants, ordered pairs, x-coordinate, y-coordinate
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 8
Math, Course 3 Advanced
MARKING PERIOD: 1 Unit: Chapter 3 – Solving Equations and Inequalities
Common Core Standards 7.RP.2.c. Represent proportional relationships by equations. For example, if total cost t is
proportional to the number n of items purchased at a constant price p, the relationship
between the total cost and the number of items can be expressed as t = pn.
7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.
7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients.
7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary
of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27
1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate
can be used as a check on the exact computation.
7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for
the number of sales you need to make, and describe the solutions.
Keystone Connections: (PA Standards) M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M7.D.2.2-Create and/or interpret expressions, equations or inequalities that model problem
situations.
M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality
and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)
M8.D.2.2-Create and/or interpret expressions, equations or inequalities that model problem
situations. (Reference: 2.8.8.C)
2.1.7.E-Simplify algebraic expressions involving like terms and use algebraic expressions to
model real world situations.
2.1.7.G-Solve one and two-step equations and inequalities to solve real world problems.
2.8.7.C-Create and interpret expressions that model problem situations and create and solve
equations and equalities that model problem situations.
2.8.7.D-Represent algebraic expressions using concrete models (tiles, blocks).
2.8.7.E-Solve one and two-step equations and inequalities.
2.5.7.A-Invent, select, use, and justify the appropriate methods, materials and strategies used to
Modified 6/20/2011 9
Math, Course 3 Advanced
solve problems.
2.5.7.B-Verify and interpret results using precise mathematical language, notation, and
representations, including numerical tables and equations, simple algebraic equations and
formulas, charts, graphs and diagrams.
2.5.7.C-Justify strategies and defend approaches used and conclusions reached.
2.5.7.D-Determine pertinent information in problem situations and whether any further
information is needed for solution.
Student Objectives: In this chapter, students will solve one and two step equations and inequalities. Students will
write and solve each type of equation and inequality to solve real life problems. Students solve
equations and find dimensions using formulas for perimeter and area.
At the conclusion of this chapter, students will successfully complete the following skills:
Solve one step equations using inverse operations of addition, subtraction, multiplication,
and division
Solve two step equations using inverse operations of addition, subtraction, multiplication,
and division
Translate verbal expressions/equations into variable expressions/equations
Use formulas to solve problems for perimeter and area
Solve one step inequalities using inverse operations of addition, subtraction,
multiplication, and division
Solve two step inequalities using inverse operations of addition, subtraction,
multiplication, and division
Graph solutions to inequalities
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
3.1 Solving Equations Using Addition or Subtraction
3.2 Solving Equations Using Multiplication or Division
3.3 Solving Two-Step Equations
3.4 Writing Equations
3.5 Geometric Formulas
3.6 One-Step Inequalities
3.7 More Inequalities
ASSIGNMENTS
Modified 6/20/2011 10
Math, Course 3 Advanced
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Variable, equation, solution, opposite, like terms, coefficient, equivalent equations, inverse
operations, subtraction property of equality, addition property of equality, multiplication
property of equality, division property of equality, two-step equation, verbal model, algebraic
model, base, height, perimeter, area, area formula for a triangle, area formula for a rectangle,
perimeter formula for a rectangle, inequality, solution of an inequality, equivalent inequalities,
symbols of inequalities, addition property of inequality, subtraction property of inequality, graph
of an inequality, multiplication property of inequality, division property of inequality
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 11
Math, Course 3 Advanced
MARKING PERIOD: 2 Unit: Chapter 4 – Factors, Fractions, and Exponents
Common Core Standards 7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.2.b. Understand that integers can be divided, provided that the divisor is not zero, and
every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers,
then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world
contexts.
7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.
7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients.
7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary
of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27
1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate
can be used as a check on the exact computation.
Keystone Connections: (PA Standards) M7.A.1.1-Express numbers in equivalent forms.
M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B)
M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B)
M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality
and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)
Student Objectives: In this chapter, students use factorization trees to write the prime factorization of numbers and
also factor monomials. Students find the greatest common factor and least common multiple of
numbers and monomials. They use these quantities to simplify, compare, and order fractions and
mixed numbers. Students multiply and divide expressions with exponents and simplify
expressions with negative exponents. Students also read and write numbers in scientific notation
and use scientific notation in real world problems.
At the conclusion of this chapter, students will successfully complete the following skills:
Write the prime factorization of numbers
Find the greatest common factor of two or more numbers/monomials
Simplify fractions
Modified 6/20/2011 12
Math, Course 3 Advanced
Find the least common multiple of two or more numbers/monomials
Compare and order fractions and mixed numbers
Multiply and divide expressions with exponents
Read and write numbers using scientific notation
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
4.1 Factors and Prime Factorization
4.2 Greatest Common Factor
4.3 Simplifying Fractions
4.4 Least Common Multiple
4.5 Comparing Fractions and Mixed numbers
4.6 Rules of Exponents
4.8 Scientific Notation
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Prime number, composite number, factor, prime factorization, factor tree, monomial, common
factor, greatest common factor (GCF), relatively prime, simplest form, equivalent fractions,
multiple, common multiple, least common multiple (LCM), least common denominator (LCD),
exponent, power, base, product of powers property, quotient of powers property, rule for
negative exponents, rule for zero exponents, scientific notation, standard form, product form
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
Modified 6/20/2011 13
Math, Course 3 Advanced
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 14
Math, Course 3 Advanced
MARKING PERIOD: 2 Unit: Chapter 5 – Rational Number Operations
Common Core Standards 7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2.d. Convert a rational number to a decimal using long division; know that the decimal
form of a rational number terminates in 0s or eventually repeats.
7.NS.3. Solve real-world and mathematical problems involving the four operations with
rational number.
7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients
7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary
of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27
1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate
can be used as a check on the exact computation.
Keystone Connections: (PA Standards) M7.A.3.2-Compute accurately with and without use of a calculator.
M8.A.3.3-Compute and/or explain operations with integers, fractions and/or decimals.
(Reference: 2.2.8.B)
M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality
and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)
2.2.7.A-Complete calculations by applying the order of operations.
2.2.7.B-Add, subtract, multiply and divide different kinds and forms of rational numbers
including integers, decimal fractions, percents and proper and improper fractions.
Student Objectives: In this chapter, students add, subtract, multiply, and divide fractions and mixed numbers.
Students write fractions and mixed numbers as decimals and vice versa. Students add, subtract,
multiply, and divide decimals. Students estimate answers to decimal operations. They use
operations with fractions and decimals to solve real world problems. Students find the mean,
median, mode, and range of a data set.
At the conclusion of this chapter, students will successfully complete the following skills:
Modified 6/20/2011 15
Math, Course 3 Advanced
Add and subtract fractions with common denominators
Add and subtract fractions with different denominators
Multiply and divide fractions and mixed numbers
Convert between fractions and decimals
Identify rational numbers
Add, subtract, multiply, and divide decimals
Solve equations with fractions and decimals
Describe data sets using mean, median, mode, and range
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
5.1 Fractions with Common Denominators
5.2 Fractions with Different Denominators
5.3 Multiplying Fractions
5.4 Dividing Fractions
5.5 Fractions and Decimals
5.6 Adding and Subtracting Decimals
5.7 Multiplying and Dividing Decimals
5.8 Mean, Median, and Mode
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Like terms, simplest form, LCD, improper fraction, mixed number, numerator, denominator,
reciprocal, multiplicative inverse, rational number, terminating decimal, repeating decimal, front-
end estimation, mean, median, mode, range
Modified 6/20/2011 16
Math, Course 3 Advanced
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 17
Math, Course 3 Advanced
MARKING PERIOD: 3 Unit: Chapter 6 – Multi-Step Equations and Inequalities
Common Core Standards 7.G.4. Know the formulas for the area and circumference of a circle and use them to solve
problems; give an informal derivation of the relationship between the circumference and area
of a circle.
Keystone Connections: (PA Standards) M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M7.B.2.1-Develop, use and/or describe measures of length, perimeter, circumference, area or
volume.
M8.B.2.2-Use, describe and/or develop procedures to determine measures of perimeter,
circumference, area, surface area and/or volume. Reference: 2.3.8.A, 2.3.8.D
2.3.7.A-Apply formulas to determine perimeter and area of polygons and circles, and volume of
prisms, pyramids, spheres, cylinders, and cones.
2.9.7.G-Approximate the value of (pi) through experimentation.
Student Objectives: In this chapter, students solve equations involving the circumference of a circle.
At the conclusion of this chapter, students will successfully complete the following skills:
Solve equations involving the circumference of a circle
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
6-4 Solving Equations Involving Circumference
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Modified 6/20/2011 18
Math, Course 3 Advanced
Chapter Tests
Terminology Circle, center, radius, diameter, chord, circumference, pi (π), formulas for circumference
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 19
Math, Course 3 Advanced
MARKING PERIOD: 3 Unit: Chapter 7 – Ratios, Proportions, and Percents
Common Core Standards 7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas and other quantities measured in like or different units. For example, if a person walks
1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per
hour, equivalently 2 miles per hour.
7.RP.2.a. Decide whether two quantities are in a proportional relationship, e.g., by testing for
equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph
is a straight line through the origin.
7.RP.3. Use proportional relationships to solve multistep ratio and percent problems.
Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error.
7.NS. 2.a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.EE.2. Understand that rewriting an expression in different forms in a problem context can
shed light on the problem and how the quantities in it are related. For example, a + 0.05a =
1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary
of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27
1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate
can be used as a check on the exact computation.
7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for
the number of sales you need to make, and describe the solutions.
Keystone Connections: (PA Standards) M7.A.2.1-Complete calculations by applying the order of operations.
M7.A.2.2-Solve problems using ratios, proportions, percents and/or rates.
M7.B.1.1-Add or convert measurements.
M7.B.2.2-Construct, interpret and/or use scale drawings to solve real-world problems.
Modified 6/20/2011 20
Math, Course 3 Advanced
M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M8.A.2.2-Represent or solve problems using rates, ratios, proportions and/or percents.
(Reference: 2.1.8.D, 2.3.8.B)
M8.B.1.1-Convert measurements. (Reference: 2.3.5.D)
M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality
and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)
2.1.7.D-Distinguish between ratios and rates and solve proportions that represent real world
problems.
2.2.7.C-Create and solve word problems involving ratios, proportions, and percents including
determining percentage, rate, and base.
2.11.7.B-Compute and compare unit rates, ratios and slopes in real world situations.
2.3.7.D-Recognize use and appropriate measures of distance, rate, capacity, are, weight, mass
and angles in degrees in real-life situations.
2.3.7.F-Use scale measurements to interpret maps and scale drawings.
2.3.7.G-Create and use scale drawings and models.
Student Objectives: In this chapter, students find ratios and unit rates and write and then solve proportions. Students
solve percent problems by using proportions and the percent equation. Students convert among
fractions, decimals, and percents. Students use circle graphs. Students apply percents to solve
discount, markup, and other price problems. Students find the probability of simple events.
At the conclusion of this chapter, students will successfully complete the following skills:
Find ratios and unit rates
Write and solve proportions
Solve percent problems using proportions
Convert between fractions, decimals, and percents
Solve problems with percent of increase or decrease
Solve percent application problems
Solve percent problems using the percent equation
Find probabilities of events
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
7.1 Ratios and Rates
7.2 Writing and Solving Proportions
7.3 Solving Percent Problems
Modified 6/20/2011 21
Math, Course 3 Advanced
7.4 Fractions, Decimals, and Percents
7.5 Percentage Change
7.6 Percent Applications
7.7 Using the Percent Equation
7.8 Simple Probability
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Ratio, equivalent, rate, unit rate, proportion, cross products, scale, scale model, percent, base,
part, whole, rules for changing between fractions, decimals, percents, percent of change, percent
of increase, percent of decrease, percent change formula, markup, discount, retail price,
wholesale price, interest, principal, annual interest rate, simple interest formula, percent
equation, outcome, event, favorable outcome, probability of an event, theoretical probability,
experimental probability, formula for theoretical probability
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 22
Math, Course 3 Advanced
MARKING PERIOD: 3 Unit: Chapter 8 – Polygons and Transformations
Common Core Standards 7.RP.2.b. Identify the constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for
the number of sales you need to make, and describe the solutions.
7.G.1. Solve problems involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale drawing at a different
scale.
7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with
given conditions. Focus on constructing triangles from three measures of angles or sides,
noticing when the conditions determine a unique triangle, more than one triangle, or no
triangle.
7.G.3. Describe the two-dimensional figures that result from slicing three dimensional figures,
as in plane sections of right rectangular prisms and right rectangular pyramids.
7.G.4. Know the formulas for the area and circumference of a circle and use them to solve
problems; given an informal derivation of then relationship between the circumference and
area of a circle.
7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-
step problem to write and solve simple equations for an unknown angle in a figure.
7.G.6. Solve real-world and mathematical problems involving area, volume and surface area
of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes,
and right prisms.
Keystone Connections: (PA Standards) M7.C.1.1-Define and/or apply basic properties of two- and three-dimensional geometric shapes.
M8.B.2.1-Determine the measurement of a missing side(s) or angle(s) in a polygon. (Reference:
2.3.8.C, 2.9.8.D)
M8.C.1.1-Identify, use, and/or describe properties of angles, triangles, quadrilaterals, circles,
pyramids, cubes, prisms, spheres, cones and/or cylinders. (Reference: 2.9.8.D)
2.9.7.A-Draw, construct and label figures incorporating perpendicular and parallel lines,
perpendicular bisector of a line segment and angle bisector using a protractor and compass.
2.9.7.B-Identify, draw, label, measure, and list the properties of complementary, supplementary,
vertical, and adjacent angles and use properties to determine missing angles.
2.9.7.C-Draw, label, and classify polygons as regular or irregular up to decagon. 2.9.7.E-
Construct parallel lines, draw a transversal, measure and compare angles formed such as
Modified 6/20/2011 23
Math, Course 3 Advanced
alternate interior and exterior angles.
2.3.7.C-Measure and construct angles using a protractor.
Student Objectives: In this chapter, students solve equations to find angle measures involving supplementary and
complementary angles and angles formed by a line intersecting parallel lines. Students classify
angles, triangles, and quadrilaterals, and they find angle measures in polygons. Students identify
and name congruent polygons and use the special rules for identifying congruent triangles.
Students identify reflective figures and their lines of symmetry. They reflect, translate, and rotate
figures in a coordinate plane. Students also use similar polygons to find missing measures.
At the conclusion of this chapter, students will successfully complete the following skills:
Solve equations to find angle measures
Classify angles and triangles
Classify quadrilaterals
Find angle measures in polygons
Identify and name congruent polygons
Reflect figures and identify lines of symmetry
Translate and rotate figures in a coordinate plane
Use similar polygons to find missing measures
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
8.1 Angle Pairs
8.2 Angles and Triangles
8.3 Quadrilaterals
8.4 Polygons and Angles
8.5 Congruent Polygons
8.6 Reflections and Symmetry
8.7 Translations and Rotations
8.8 Similar Polygons
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Modified 6/20/2011 24
Math, Course 3 Advanced
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Point, line, ray, plane, angle, vertex, degree, straight angle, right angle, supplementary,
complementary, vertical angles, perpendicular lines, parallel lines, transversal, alternate interior
angles, alternate exterior angles, corresponding angles, angle symbols (m∠, ∠, right angle), acute
angle, right angle, obtuse angle, acute triangle, right triangle, obtuse triangle, equilateral triangle,
isosceles triangle, scalene triangle, tick marks, arc marks, sum of angles in a triangle,
quadrilateral, parallelogram, rhombus, trapezoid, sum of angles in a quadrilateral, diagonals,
parallel symbol, polygon, regular polygon, hexagon, heptagon, octagon, sum of angle measures,
formula, measure of one angle formula, congruent, congruent angles, corresponding parts,
congruence symbol (≅), SSS, SAS, ASA, naming polygons, congruence statement,
transformation, reflection, image, pre-image, line of symmetry, x-axis, y-axis, line of reflection,
rules for reflections, translation, rotation, translation rules, rotation rules, clockwise, counter-
clockwise, coordinate notation, prime, similar polygons, similarity symbol (∼), similarity
notation, proportional side lengths, scale factor
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 25
Math, Course 3 Advanced
MARKING PERIOD: 4 Unit: Chapter 9 – Real Numbers and Right Triangles
Common Core Standards 7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world contexts.
Keystone Connections: (PA Standards) M7.A.1.1-Express numbers in equivalent forms.
M7.A.3.1-Apply estimation strategies to a variety of problems.
M8.A.1.1-Represent numbers in equivalent forms. (Reference: 2.1.8.A, 2.1.8.B)
M8.A.3.1-Determine the appropriateness of overestimating, underestimating or calculating an
exact answer in problem-solving situations. (Reference: 2.2.8.F)
M8.C.1.2-Compute measures of sides of right triangles using Pythagorean Theorem. (Reference:
2.10.8.A)
2.1.7.C-Distinguish between and order rational and irrational numbers.
2.2.7.D-Identify and distinguish between rational and irrational numbers (e.g. (pi), square roots).
2.10.7.A-State the Pythagorean Theorem and apply it to real world problems.
Student Objectives: In this chapter, students find and approximate square roots and classify real numbers as rational
or irrational. Students solve real world problems involving square roots including problems that
use the Pythagorean Theorem and problems that involve special right triangles.
At the conclusion of this chapter, students will successfully complete the following skills:
Find and approximate square roots of numbers
Identify real numbers as rational or irrational
Use the Pythagorean Theorem to solve problems including real world problems
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
9.1 Square Roots
9.2 Rational and Irrational Numbers (Click to see note)
9.3 The Pythagorean Theorem
9.4 Using the Pythagorean Theorem
Modified 6/20/2011 26
Math, Course 3 Advanced
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Right angle, isosceles triangle, scalene triangle, equilateral triangle, square root, radical
expression, perfect square, radical sign, negative square root, positive-or-negative or plus-or-
minus symbol (±), irrational number, real number, rational number, integer, whole number, leg,
hypotenuse, Pythagorean Theorem, converse, Pythagorean triple
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 27
Math, Course 3 Advanced
MARKING PERIOD: 4 Unit: Chapter 10 – Measurement, Area, and Volume
Common Core Standards 7.NS.2.a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the
distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying
signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.EE.4.a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
7.EE.4.b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for
the number of sales you need to make, and describe the solutions.
7.G.1. Solve problems involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale drawing at a different
scale.
7.G.6. Solve real-world and mathematical problems involving area, volume and surface area
of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes,
and right prisms.
Keystone Connections: (PA Standards) M7.B.2.1-Develop, use and/or describe measures of length, perimeter, circumference, area or
volume.
M7.D.2.1-Select and/or use appropriate strategies to solve or represent equations or expressions.
M8.B.2.2-Use, describe and/or develop procedures to determine measures of perimeter,
circumference, area, surface area and/or volume. Reference: 2.3.8.A, 2.3.8.D
M8.C.1.1-Identify, use, and/or describe properties of angles, triangles, quadrilaterals, circles,
pyramids, cubes, prisms, spheres, cones and/or cylinders. (Reference: 2.9.8.D)
M8.D.2.1-Select and/or use a strategy to simplify an expression, solve an equation or inequality
and/or check the solution for accuracy. (Reference: 2.8.8.C, 2.8.8.E)
2.3.7.A-Apply formulas to determine perimeter and area of polygons and circles, and volume of
prisms, pyramids, spheres, cylinders, and cones.
2.3.7.E-Compare and analyze perimeters, areas, volumes of similar figures.
2.9.7.D-Identify, name, draw, and list all properties of spheres, prisms, cylinders, and cones.
2.9.7.G-Approximate the value of (pi) through experimentation.
Student Objectives: In this chapter, students find the areas of parallelograms, trapezoids, and circles. Students
identify solids. Students draw nets of prisms, pyramids, cylinders, and cones and use them to
find surface areas. Students also use formulas to find the volumes of solids.
Modified 6/20/2011 28
Math, Course 3 Advanced
At the conclusion of this chapter, students will successfully complete the following skills:
Find the areas of parallelograms and trapezoids
Find the areas of circles
Classify and sketch solids
Find surface areas of prisms, cylinders, pyramids, and cones.
Find volume of prisms, cylinders, pyramids, and cones.
Materials &Texts Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
10.1 Areas of Parallelograms and Trapezoids
10.2 Areas of Circles
10.3 Three-Dimensional Figures
10.4 Surface Areas of Prisms and Cylinders
10.5 Surface Areas of Pyramids and Cones
10.6 Volumes of Prisms and Cylinders
10.7 Volumes of Pyramids and Cones
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Area, base, height, circle, radius, diameter, pi (π), trapezoid, parallelogram, rhombus, base of a
parallelogram, height of a parallelogram, base of a trapezoid, height of a trapezoid, formula for
area of a parallelogram, formula for area of a trapezoid, circumference, area formula for circles,
circumference formula for circles, solid, polyhedron, face, prism, pyramid, cylinder, cone,
sphere, edge, vertex, net, surface area, formula for surface area of a prism, formula for surface
area of a cylinder, slant height, formula for surface area of pyramid, formula for surface area of a
Modified 6/20/2011 29
Math, Course 3 Advanced
cone, volume, formula for volume of a prism, formula for volume of a cylinder, formula for
volume of pyramid, formula for volume of cone
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator
Modified 6/20/2011 30
Math, Course 3 Advanced
MARKING PERIOD: 4 Unit: Chapter 12 – Data Analysis and Probability
Common Core Standards 7.SP.1. Understand that statistics can be used to gain information about a population by
examining a sample of the population; generalizations about a population from a sample are
valid only if the sample is representative of that population. Understand that random sampling
tends to produce representative samples and support valid inferences.
7.SP.2. Use data from a random sample to draw inferences about a population with an
unknown characteristic of interest. Generate multiple samples (or simulated samples) of the
same size to gauge the variation in estimates or predictions. For example, estimate the mean
word length in a book by randomly sampling words from the book; predict the winner of a
school election based on randomly sampled survey data. Gauge how far off the estimate or
prediction might be.
7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with
similar variabilities, measuring the difference between the centers by expressing it as a
multiple of a measure of variability. For example, the mean height of players on the basketball
team is 10 cm greater than the mean height of players on the soccer team, about twice the
variability (mean absolute deviation) on either team; on a dot plot, the separation between the
two distributions of heights is noticeable.
7.SP.4. Use measures of center and measures of variability for numerical data from random
samples to draw informal comparative inferences about two populations. For example, decide
whether the words in a chapter of a seventh-grade science book are generally longer than the
words in a chapter of a fourth-grade science book.
7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that
expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A
probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that
is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7.SP.6. Approximate the probability of a chance event by collecting data on the chance
process that produces it and observing its long-run relative frequency, and predict the
approximate relative frequency given the probability. For example, when rolling a number
cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not
exactly 200 times.
7.SP.7.a. Develop a uniform probability model by assigning equal probability to all outcomes,
and use the model to determine probabilities of events. For example, if a student is selected at
random from a class, find the probability that Jane will be selected and the probability that a
girl will be selected.
7.SP.7.b. Develop a probability model (which may not be uniform) by observing frequencies
in data generated from a chance process. For example, find the approximate probability that a
spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the
outcomes for the spinning penny appear to be equally likely based on the observed
frequencies?
7.SP.8.a. Understand that, just as with simple events, the probability of a compound event is
the fraction of outcomes in the sample space for which the compound event occurs.
7.SP.8.b. Represent sample spaces for compound events using methods such as organized
lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling
Modified 6/20/2011 31
Math, Course 3 Advanced
double sixes”), identify the outcomes in the sample space which compose the event.
7.SP.8.c. Design and use a simulation to generate frequencies for compound events. For
example, use random digits as a simulation tool to approximate the answer to the question: If
40% of donors have type A blood, what is the probability that it will take at least 4 donors to
find one with type A blood?
Keystone Connections: M7.E.1.1-Interpret data shown in complex data displays.
M7.E.2.1-Describe, compare and/or contrast data using measures of mean, median, mode or
range.
M7.E.3.1-Determine or calculate theoretical or experimental probability.
M7.E.4.1-Draw conclusions and, make predictions based on data displays.
M8.E.1.1-Choose, display or interpret data (tables, charts, graphs, etc.). (Reference: 2.6.5.A,
2.6.8.E, 2.7.8.D)
M8.E.3.1-Calculate the probability of an event. (Reference: 2.7.8.E)
M8.E.4.1-Draw conclusions, make inferences and/or evaluate hypotheses based on statistical and
data displays. (Reference: 2.6.8.C, 2.7.8.E)
2.6.7.E-Collect and represent data using stem and-leaf plot and box-and-whisker plots.
2.6.7.F-Explain data displayed on a spreadsheet.
2.6.7.G-Examine examples of valid and invalid surveys and the sample used.
2.7.7.B-Design and conduct an experiment with dependent and independent events and
determine the probability of each.
2.7.7.C-Write and solve a problem situation requiring probability in a real-world event.
2.7.7.D-Conduct an experiment and discuss the differences between the experimental and
theoretical probabilities.
Student Objectives: In this chapter, students make-and-interpret stem and leaf plots, box-and-whisker plots, circle
graphs, and line graphs. Students decide which graph or plot is most appropriate for a data set.
Students use tree diagrams, the counting principle, permutations, and combinations to count
choices or possibilities. Students apply these counting methods to find the probability and odds
of simple events. Students also learn to distinguish between and find the probabilities of
independent and dependent events.
At the conclusion of this chapter, students will successfully complete the following skills:
Make and interpret stem-and-leaf plots
Make and interpret box-and-whisker plots
Organize data using circle graphs and line graphs
Use counting methods to determine the number of choices
Use permutations to count possibilities
Use combinations to count possibilities
Find the odds in favor of events
Classify events as independent or dependent and then find their probabilities
Materials &Texts
Modified 6/20/2011 32
Math, Course 3 Advanced
Larson, R., Boswell, L., Kanold, T., & Stiff, L. (2007). Math Course 3. Evanston, II: McDougal
Littell.
Lesson Practice Sheets B
Study Guides (optional)
Lesson Note Taking Guides (optional)
Activities, Assignments, & Assessments ACTIVITIES
12.1 Stem-and-Leaf Plots
12.2 Box-and-Whisker Plots
12.3 Using Data Displays
12.4 Counting Methods
12.5 Permutations
12.6 Combinations
12.7 Probability and Odds
12.8 Independent and Dependent Events
ASSIGNMENTS
Lesson Practice Sheets B
Associated Chapter exercises
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In
addition, teachers may use homework, group activities, and/or projects for grading purposes. The
Radnor Middle School grading system and scale will be used to determine letter grades.
Lesson Assessment/Quizzes
Chapter Tests
Terminology Data, mean, median, range, outcome, probability of an event, stem-and-leaf plot, box-and-
whisker plot, lower quartile, upper quartile, lower extreme, upper extreme, inter quartile range,
circle graph, line graph, protractor, horizontal and vertical scales, tree diagram, counting
principle, probability, permutation, factorial, counting principle, permutation formula,
combination, combination formula, complementary events, complementary formula, unfavorable
outcomes, odds, probability, find probability of an event, find odds using probability, compound
events, independent events, dependent events
Media, Technology, Web Resources
McDougal Littell Course 3 Easy Planner DVD ROM
McDougal Littell Course 3 Power Presentations DVD ROM
McDougal Littell Classzone.com resources
Teacher developed smart-board documents
Scientific Calculator