7th Grade Homeschool Curriculum - Seventh Grade Math - Best Homeschool Curriculum - Cheap Homeschool Curriculum (Affordable)!

Acknowledgments
Complete Curriculum’s K-12 curriculum has been team-developed by a consortium
of teachers, administrators, educational and subject matter specialists, graphic artists
and editors.
In a collaborative environment, each professional participant contributed to ensuring the quality,
integrity and effectiveness of each Compete Curriculum resource was commensurate with the
required educational benchmarks and contemporary standards Complete Curriculum had set
forth at the onset of this publishing program.
SAM
PLE
10-15

TABLE OF CONTENTS AND OBJECTIVES SEVENTH GRADE MATH
Lesson 1
Measures of Central Tendency
Objective: Student will be able to find the mode, mean, median and range
of a given set of data.
Lesson 2
Stem-and-Leaf Plots and Line Plots
Objective: Student will be able to create a Stem-and-Leaf Plot and a Line Plot
for any given data set.
Lesson 3
Box-and-Whisker Plots
Objective: The student will be able to find the upper quartile, the median and the lower
quartile. Using this information, the student will be able to construct a Box-and-Whisker Plot.
Lesson 4
Lessons 1-3 Review – Central Tendency and Plots
Objective: The student will review the concepts introduced in Lessons 1-3.
Lesson 5
Bar Graphs and Double Bar Graphs
Objective: Students will be able to create graphs bar graphs for different sets of data,
and interpret bar graphs.
Lesson 6
Line Graphs and Double Line Graphs
Objective: Student will be able to create line graphs and double line
graphs for appropriate sets of data.
Lesson 7
Writing Assignment I - Central Tendency Applications
Objective: Students will carefully choose words that explain the importance and the
relevance of learning measures of central tendency.
Lesson 8
Frequency Tables and Histograms
Objective: Student will be able to create a frequency table and a histogram.
Lesson 9
Scatter Plots
Objective: Student will be able to create a scatter plot and determine the trend in the graph.
Lesson 10
Review: Lessons 1-9 – Basic Data Analysis Techniques
Objective: Student will practice Basic Data Analysis Techniques learned in Lessons 1-9.
Lesson 11
Project One – Graphical Analysis
Objective: The student will collect, organize, analyze and graph data gathered from a
survey created and conducted independently.
SAM
PLE
10-15

Lesson 12
Assessment One – Central Tendencies
and Graphical Analysis
Objective: The student will be assessed on his understanding of Central Tendencies
and Graphical Analysis.
Lesson 13
Integers and Absolute Value
Objective: The student will be able to put integers in order and compare them,
and find the absolute value of integers.
Lesson 14
Numeric Groupings and Properties
Objective: The student will be able to identify and use the associative property, the
commutative property, the inverse property of BEEJUJPO
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multiplication and the distributive property.
Lesson 15
Adding Positive and Negative Integers
Objective: The student will be able to add positive and negative numbers.
Lesson 16
Subtracting Positive and Negative Integers
Objective: The student will subtract positive and negative numbers.
Lesson 17
Review: Lessons 13-16
Grouping and Properties of Positive and Negative Integers
Objective: Student will review addition and subtraction of integers, as well as the
properties learned in the previous Lessons.
Lesson 18
Multiplication of Integers
Objective: The student will be able to multiply integers.
Lesson 19
Division of Integers
Objective: The student will be able to divide positive and negative integers.
Lesson 20
Order of Operations
Objective: The student will be able to use the order of operations to correctly solve
problems involving two or more operations.
Lesson 21
Writing Assignment Two - Order of Operations
Objective: The student will explain the order of operations, in writing, to a friend.
Lesson 22
Review: Absolute Value, Positive & Negative
Numbers, Order of Operations
Objective: The student will use the skills learned in Lessons 13-21 to solve problems
and answer questions to include absolute values, and positive and negative numbers for
multiplication, division, subtraction, and addition.
SAM
PLE
10-15
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Lesson 23
Graphing Integers on the Coordinate Plane
Objective: The student will be able to graph integers on the coordinate plane.
Lesson 24
Powers and Exponents
Objective: The student will be able to evaluate exponents.
Lesson 25
Scientific Notation
Objective: The student will be able to convert very large numbers into scientific notation,
and vice versa.
Lesson 26
Scientific Notation Using Negative Exponents
Objective: The student will be able to apply knowledge of scientific notation to work
with very small numbers using negative exponents.
Lesson 27
Project Two - Integers and a Real World Picture Tour
Objective: The student will collect pictures that show how integers are used in everyday
life. She will then present them using presentation software.
Lesson 28
Review: The World of Integers, Very Large and
Very Small Numbers
Objective: The student will apply the knowledge and skills learned in Lessons 23-27 to
solve problems.
Lesson 29
Project Three – Understanding Integers
Objective: The student will create a business and keep track of costs and profit
for a given period of time.
Lesson 30
Assessment Two – Understanding Integers
Objective: The student will display his or her understanding of working with integers.
Lesson 31
Formulas and Variables
Objective: The student will be able to use familiar and unfamiliar formulas to solve problems.
Lesson 32
Algebraic Expressions
Objective: The student will be able to evaluate algebraic expressions.
Lesson 33
Equations
Objective: The student will be able to solve simple equations.
SAM
PLE
10-15

Lesson 34
Writing Expressions
Objective: The student will be able to convert verbal expressions into written expressions
using variables and operations.
Lesson 35
Using Adding and Subtracting to Solve Equations
Objective: The student will be able to solve equations by using addition and subtraction.
Lesson 36
Solving Multiplication and Division Equations
Objective: Student will be able to use multiplication and division to solve equations.
Lesson 37
Writing Assignment Three - Solving an Equation
Objective: Student will explain the steps in his own words to describe how
to solve an equation.
Lesson 38
Review: Lessons 31-37 – Solving Equations
Objective: The student will use the skills learned in Lessons 31-37 to solve
equations problems.
Lesson 39
Solving Two-Step Equations Part 1
Objective: The student will be able to solve two-step equations, with variables
having coefficients.
Lesson 40
Solving Two-Step Equations Part 2
Objective: The student will be able to solve two-step equations, whereby the coefficients
are an applied reciprocal.
Lesson 41
Solving Inequalities
Objective: The student will use number lines to graph inequalities.
Lesson 42
Writing Assignment Four - Inequality Equations
Objective: The student will be able to complete a writing assignment that will explain
how to solve an inequality.
Lesson 43
Project Four – Solving for Equations
Objective: Student will practice problems that review the skills learned in Solving
for Equations.
Lesson 44
Review: Lessons 31-41 – Solving for Equations
Objective: The student will practice the skills acquired in Lessons 31-41, Solving for Equations.
Lesson 45
Assessment Three – Solving for Equations
Objective: The student will complete a formal Assessment of their Solving for Equations skills.
SAM
PLE
10-15

Lesson 46
Equations and Linear Relationships
Objective: The student will use a real life example of a linear relationship as an
introduction to Equations and Linear Relationships.
Lesson 47
Two-Variable Relationships
Objective: The student will complete “input/output tables” for two-variable relationships.
Lesson 48
Writing the Rules
Objective: The student will examine tables to find the rule that relates x and y in a two
variable relationship.
Lesson 49
Solutions of Two-Variable Equations
Objective: Student will determine if an ordered pair is a solution to a two-variable
equation. Student will also find solutions for two-variable equations.
Lesson 50
Graphing Two-Variable Relationships - Part 1
Objective: The student will use solutions for two-variable equations (ordered pairs) to
graph linear relationships.
Lesson 51
Graphing Two-Variable Equations - Part 2
Objective: The student will write an explanation in her own words to describe how to
graph a two-variable equation.
Lesson 52
Review: Lessons 46-51 – Two Variable
Relationships and Equations
Objective: The student will apply the skills learned in Lessons 46 to 51 to solve
two-variable or linear equation problems.
Lesson 53
Slope 1 – Determining Positive, Negative
or Zero Slopes
Objective: The student will be able to determine if the slope of a line is positive,
negative, zero or if it has no slope.
Lesson 54
Slope 2 - Finding the Slope of a Graphed Line
Objective: The student will be able to find the slope of a graphed line.
Lesson 55
Slope Formula and Slope Intercept Form
Objective: To find the slope using the slope formula and the slope intercept form.
Lesson 56
x-intercept and y-intercept
Objective: The student will be able to find the x and y-intercepts.
SAM
PLE
10-15

Lesson 57
Writing Assignment Five – Slope
Objective: The student will express an understanding of slope in a writing assignment.
Lesson 58
Project Five – Linear Equalities and Slopes
Objective: The student will use what has been learned thus far to discover real world
applications for linear equalities and slope.
Lesson 59
Review: Lessons 46-56 – Linear Graphs and Slopes
Objective: The student will be able to answer questions based on the information learned
in previous Lessons regarding linear graphs and slopes.
Lesson 60
Assessment Four – Linear Equations Slopes
and Intercepts
Objective: The student will be formally assessed on Linear equations.
Lesson 61
Ratios
Objective: The student will be able to write ratios and estimate ratios from pictures and data.
Lesson 62
Rates
Objective: The student will be able to determine rates and unit rates.
Lesson 63
Equal Ratios and Proportions
Objective: Student will be able to find equal ratios and proportions.
Lesson 64
Review: Lessons 61-63 – Ratios, Rates, Proportions
Objective: Student will review skills learned to determine and understand Ratios, Rates,
and Proportions.
Lesson 65
Writing Assignment Six - Creating a Study Guide
for Rates and Ratios
Objective: The student will create a study guide that explains how to write rates and
ratios, determine the unit rate, and determine if ratios are proportional.
Lesson 66
Relating Proportions and Slope
Objective: The student will be able to determine the rate of change based on a table,
or the slope of a graph.
Lesson 67
Converting Customary Units
Objective: Student will be able to change units in the customary system.
SAM
PLE
10-15

Lesson 68
Converting Rates
Objective: Student will be able to convert rates.
Lesson 69
Review: Lessons 66-68 – Conversions,
Proportion vs. Slope
Objective: Student will review skills learned in computing unit conversions, and
comparing proportions and slope.
Lesson 70
Writing Assignment Seven - Converting Units
Objective: The student will determine the real world use for converting units and explain
in writing how to convert units.
Lesson 71
Solving Proportions
Objective: Student will solve proportions using cross multiplication.
Lesson 72
Solving Proportions: Word Problems Part I
Objective: Student will be able to take real life situations and use proportions to solve for
missing numbers.
Lesson 73
Solving Proportions: Word Problems Part II
Objective: Student will be able to take real life situations, and use proportions to solve
for missing numbers.
Lesson 74
Writing Assignment Eight - Understanding
Proportions
Objective: Student will continue with taking real life situations to use proportions to solve
for missing numbers.
Lesson 75
Review: Lessons 71-74 – Proportions
Objective: Student will review the Proportions skills learned in Lessons 71-74.
Lesson 76
Scale Drawings: Maps
Objective: Use the scale on a map to determine actual distances.
Lesson 77
Scale Drawing and Models
Objective: Student will be able to create scale drawings, and determine actual
dimensions based on scales drawings and models.
Lesson 78
Integrating Scale Drawings and Models
Objective: Review the skills learned in Lessons 76 - 77 for scale drawings, maps,
and models.
SAM
PLE
10-15

Lesson 79
Project Six – Shopping Mall Design – Part 1
Objective: The student will apply the skills learned in previous Scale Drawing Lessons to
create a real-world project.
Lesson 80
Project Six – Shopping Mall Design – Part 2
Objective: Pull the skills learned in previous Scale Drawing Lessons together to create a
real world project.
Key Vocabulary Needed: Scale drawing
Lesson 81
Review: Lessons 61-78 – Ratios, Rates,
Proportions, Conversions
Objective: Student will review the skills learned in Lessons 61-80 starting with Ratios,
Rates, Proportions, Slope, Conversions, and Scaling.
Lesson 82
Assessment Five – Ratios, Rates, Proportion,
Scale, Unit Rate
Objective: Student will be assessed on the skills learned in previous Lessons starting
from Lesson 61 on Ratios.
Lesson 83
Understanding Percents
Objective: Student will be able to convert percents into fractions and decimals.
Lesson 84
Using Percents
Objective: Student will be able to solve common problems using percents.
Lesson 85
Increased Percents
Objective: Student will be able to determine the amount a percent was increased.
Lesson 86
Writing Assignment Nine - Understanding Percents
Objective: The student will be able to express her understanding of percents by
explaining a problem.
Lesson 87
Decreased Percent
Objective: Student will be able to find decreased percents.
Lesson 88
Review: Lessons 83-87 – Percents
Objective: Student will review the skills learned in previous Lessons about Percents.
Lesson 89
Project Seven - Percents
Objective: Student will be able use percents to figure out real life problems.
SAM
PLE
10-15

Lesson 90
Assessment Six - Percents
Objective: Student will be able to use the skills he has learned in previous Lessons about
Percents to answer the questions below.
Lesson 91
Prime Factorization
Objective: The student will be able to determine if numbers are prime or composite, and
will be able to find the prime factorization of a number.
Lesson 92
Greatest Common Factors
Objective: The student will be able to identify the GCF (Greatest Common Factor) of a
number.
Lesson 93
Least Common Multiples
Objective: The student will be able to identify the Least Common Multiples of two or
more numbers.
Lesson 94
Writing Assignment Ten - LCM and GCF
Objective: The student will demonstrate an understanding of LCM and GCF through writing.
Lesson 95
Review: Lessons 91-94 – Prime Factorization, GCF, LCM
Objective: The student will review the skills learned in Lessons 91-95 for Prime
Factorization, GCF, and LCM.
Lesson 96
Rational Numbers
Objective: The student will be able to identify rational numbers and compare them.
Lesson 97
Adding and Subtracting Rational Numbers (Decimals)
Objective: Student will be able to add and subtract rational numbers (decimals).
Lesson 98
Adding and Subtracting Rational Numbers (Fractions)
Objective: The student will be able to add and subtract rational numbers (fractions).
Lesson 99
Multiplying and Dividing Rational Numbers (Decimals)
Objective: The student will be able to multiply and divide rational numbers (decimals).
Key Vocabulary Needed: Rational numbers
Lesson 100
Multiplying and Dividing Rational Numbers
(Fractions)
Objective: The student will continue to learn to multiply and divide
rational numbers (fractions).
SAM
PLE
10-15

Lesson 101
Writing Assignment Eleven -
Multiplying and Dividing Rational Numbers
Objective: Student will be able to explain through writing how to multiply and divide
rational numbers.
Lesson 102
Review: Lessons 96-101 – Rational Numbers
Objective: The student will review the Rational Numbers skills learned and practiced in
Lessons 96-101.
Lesson 103
Perfect Squares
Objective: The student will be able to identify perfect squares.
Lesson 104
Square Roots
Objective: The student will be able to find the square root of numbers.
Lesson 105
Irrational Numbers and Square Roots
Objective: Student will be able to identify if square roots are rational numbers or
irrational numbers.
Lesson 106
Review: Lessons 103-105 Review – Square Roots
Objective: Student will be able to use the skills learned in the previous Lessons about
Square Roots to solve problems.
Lesson 107
Solving Equations with Square Roots:
Leading Up To Pythagorean Theorem
Objective: The student will learn the background information needed to solve problems
using the Pythagorean Theorem.
Lesson 108
Pythagorean Theorem
Objective: The student will be able to use the Pythagorean Theorem to solve problems.
Lesson 109
Review: Lessons 107-108 - Pythagorean Theorem
Objective: The student will continue to work with the Pythagorean Theorem.
Lesson 110
Writing Assignment Twelve - Pythagorean Theorem
Objective: Student will be able to explain in writing how to use the Pythagorean Theorem.
Lesson 111
Project Eight - Number Hunt
Objective: The student will identify rational and irrational numbers in the real world.
The student will use the examples to create a slide show presentation.
SAM
PLE
10-15

Lesson 112
Review: Lessons 91-111
LCD, LCM, PM, RN, Squares, Square Roots - Part 1
Objective: The student will use the skills learned in the previous Lessons to include LCD,
LCM, PM, RN Squares, and Square Roots to answer the questions below.
Lesson 113
Review: Lessons 91- 111
LCD, LCM, PM, RN, Squares, Square Roots - Part 2
Objective: The student will practice and apply the Rational and Irrational numbers
principles and skills taught and practiced in Lessons 91-111.
Lesson 114
Assessment Seven – GCF, LCM, PT, RN’s, SR’s, IR’s
Objective: The student will show mastery of the skills learned in Lessons 91-111 by
completing the Assessment.
Lesson 115
Angles – Part 1
Objective: The student will be able to draw and measure angles.
Lesson 116
Angles Part 2
Objective: The student will be able to classify angles, based on their measure and
also be able to identify complementary and supplementary angles.
Lesson 117
Perpendicular and Parallel Lines
Objective: The student will be able to identify parallel and perpendicular lines.
Lesson 118
Writing Assignment Thirteen - Angles
Objective: The student will be able to explain the qualities of angles in their writing.
Lesson 119
Review: Lessons 115 to 118 - Angles
Objective: The student will be able to use the skills from the previous Lessons on
Angles to solve the problems below.
Lesson 120
Project Nine – Everyday Applications of Angles
Objective: The student will be able to apply knowledge of angles she has gained and
practiced to everyday life.
Lesson 121
Triangles – The Missing Angle
Objective: The student will be able to determine the missing angle measurement
of a triangle.
SAM
PLE
10-15

Lesson 122
Triangles-Side Lengths
Objective: The student will be able to determine side lengths based on her knowledge of
isosceles, equilateral, and scalene triangles.
Lesson 123
Classifying Polygons
Objective: The student will be able to classify and identify regular and irregular polygons.
Lesson 124
Angle Measures of Polygons
Objective: The student will be able to determine the sum of the interior angles of
different polygons.
Lesson 125
Quadrilaterals
Objective: The student will be able to recognize the different types of quadrilaterals.
Lesson 126
Review: Lessons 121-125 - Polygons and Angles
Objective: The student will review the skills and concepts learned in the previous Lessons
covering Polygons, Triangles, Quadrilaterals, and measuring their angles.
Lesson 127
Writing Assignment Fourteen - Geometry
Objective: The student will be able to use his acquired knowledge to explain problems
concerning geometric figures in writing.
Lesson 128
Applied Geometry In Action
Objective: The student will be able to find and identify polygons in and around their
surroundings.
Lesson 129
Assessment Eight - Polygons
Objective: The student will use the knowledge gained from studying Polygons to
complete this assessment.
Lesson 130
Congruent Polygons
Objective: The student will be able to identify congruent polygons.
Lesson 131
Similar Polygons
Objective: The student will be able to determine if polygons are similar.
Lesson 132
Congruent Triangles
Objective: The student will be able to use side lengths and angle measures to determine if
two triangles are congruent.
SAM
PLE
10-15

Lesson 133
Rules for Congruent Triangles
Objective: The student will create posters that will help identify and remember the
triangle congruence rules.
Lesson 134
Review: Lessons 130-133 – Polygons and Triangles
Congruency and Similarity
Objective: The student will review the skills and information learned in previous Lessons
pertaining to Congruency for Polygons, and Triangles.
Lesson 135
Writing Assignment Fifteen - Similarity and
Congruence
Objective: The student will be able to describe in writing the importance of congruent
polygons.
Lesson 136
Measuring with Similar Triangles
Objective: Student will be able to use similar triangles to find missing measurements.
Lesson 137
Transformations, Reflections, Rotations,
and Translations
Objective: The student will be able to recognize and perform translations,
reflections, and rotations.
Lesson 138
Transformations with Similarities
Objective: The student will be able to translate similar figures using scale factor.
Lesson 139
Symmetry
Objective: The student will be able to identify the different types of symmetry.
Lesson 140
Review: Lessons 136-139 Review - Transformation,
Reflections, Rotations, Symmetry
Objective: The student will review the skills and knowledge learned in the previous
Lessons pertaining to Transformations, Reflections, Rotations, and Symmetry.
Lesson 141
Tessellations
Objective: The student will be able to describe and identify tessellations.
Lesson 142
Creating a Tessellation
Objective: Student will learn to create unique designs that will form tessellations.
Lesson 143
Writing Assignment Sixteen - Transformations
Objective: Student will be able to express his understanding of transformations in writing.
SAM
PLE
10-15

Lesson 144
Review: Lessons 130-142 – Similarity, Congruence,
and Transformations
Objective: The student will review the information learned in Lessons 130-142.
Lesson 145
Project Ten – Electronic Quiz - Part 1
Objective: The student will be able to apply knowledge of similarity, congruence and
transformations to create a slide show quiz.
Lesson 146
Lesson 147
Lesson 148
Objective: The student will share and practice the review presentations.
Lesson 149
Assessment Nine: Practical Applications Part 1
Objective: The student will demonstrate an understanding of the concepts
learned in this unit.
Lesson 150
Assessment Nine: Practical Applications Part 2
Objective: The student will be able to answer questions about similarity, congruence,
symmetry, and tessellation.
Lesson 151
Perimeter
Objective: The student will be able to find the perimeter of different polygons.
Lesson 152
Area
Objective: The student will be able to find the area of polygons.
Lesson 153
Scale: Area and Perimeter
Objective: The student will be able to apply scale factor and determine the new area and
perimeter based on the scale factor.
Lesson 154
Review: Lessons 151-153 – Area, Perimeter
Objective: The student will review area, perimeter, and scale.
SAM
PLE
10-15

Lesson 155
Writing Assignment Seventeen –
Area, Perimeter, Scale
Objective: The student will be able to show a deep understanding of scale, area and
perimeter by explaining these concepts in writing.
Lesson 156
Project 11 – Area, Perimeter Part 1
Objective: The student will be able to apply what they have learned about area,
perimeter, and scale to create a real world project.
Lesson 157
Project Eleven – Area, Perimeter Part 2
Objective: The student will apply what has been learned thus far about area, perimeter,
and scale to a real world based project.
Lesson 158
Piece of PI (Circles)
Objective: The students will be able to find the area and circumference of a circle.
Lesson 159
Surface Area of Prisms
Objective: The student will be able to determine the surface area of a prism by analyzing
the shape and exploring the areas of the faces of the shape.
Lesson 160
Surface Area of Cylinders
Objective: The student will be able to find the surface area of a cylinder.
Lesson 161
Lessons: 158-160 Review – Pi, Surface Areas of
Cylinders, Prisms
Objective: The student will demonstrate an understanding of the concepts introduced in
Lessons 158-160.
Lesson 162
Writing Assignment Eighteen - Surface Area
Objective: The student will be able to demonstrate a clear understanding of surface area.
Lesson 163
Project Twelve – Surface Area Measurement
and Buildings Part 1
Objective: The student will be able to apply an understanding of surface area to a
real life situation.
Lesson 164
Project Twelve – Surface Area Measurement
and Buildings Part 2
Objective: The student will continue to apply understanding of surface area
to a real life situation.
SAM
PLE
10-15

Lesson 165
Review Assessment – Polygon Measurement
Objective: The student will review the Polygon measurement skills and information
learned thus far.
Lesson 166
Assessment Ten - Measurement
Objective: The student will demonstrate knowledge and understanding of the
measurement concepts introduced, reviewed and practiced in previous Lessons.
Lesson 167
Review - Central Tendency
Objective: Students will review the information that they learned in Lessons 1-12 on
Central Tendency.
Lesson 168
Review - Integers
Objective: The student will review the information on Integers introduced in Lessons 13-30.
Lesson 169
Review – Equations Part 1
Objective: The student will review the information on Equations taught in Lessons 31-45.
Lesson 170
Review - Equations Part 2
Objective: The review of equations will be extended by applying knowledge learned to a
new situation.
Lesson 171
Review - Graphing Equations
Objective: The student will review the Graphing Equations material covered in Lessons 46-60.
Lesson 172
Review - Rate, Ratio, and Proportions
Objective: The student will review Rate, Ratio and Proportions originally presented in
Lessons 61-82.
Lesson 173
Sports Statistic Project- Collecting and
Graphing Data
Objective: The student will understand how equations, ratios and proportions relate and
apply to sports statistics.
Lesson 174
Sports Statistic Project – Equations, Ratios
and Proportions
Objective: The student will complete the project begun in Lesson 173 and understand
how equations, ratios and proportions relate and apply to sports statistics.
Lesson 175
Review: Percents
Objective: The student will review Percents originally covered in Lessons 83-90.
SAM
PLE
10-15

Lesson 176
Review - Number Theory
Objective: The student will review the skills presented in Lessons 91-114.
Lesson 177
Review - Polygons
Objective: The student will review the Polygon skills presented in Lessons 115-129.
Lesson: 178
Review: Congruence and Similarity
Objective: The student will review Congruence and Similarity taught in Lessons 130 to 150.
Lesson 179
Review: Perimeter, Area, and Surface Area
Objective: The student will review the Perimeter, Area and Surface area covered in
Lessons 151-166.
Lesson 180
Writing Assignment Nineteen – Seventh Grade
Math to a Sixth Grader
Objective: The student will be able to demonstrate an understanding of problem solving
the main ideas learned in 7th Grade Math.
SAM
PLE
10-15

Take off on the right path
for Seventh Grade Math!
70
SAM
PLE
10-15

Standard Complete Curriculum Lesson
Ratios and Proportional Relationships
--Analyze proportional relationships and use them to solve real-world and
mathematical problems.
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.
61, 64, 65, 81, 82, 172, 173, 174
7.RP.2 Recognize and represent proportional relationships between quantities.
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.
48, 49, 50, 51, 59, 60, 64, 65, 81, 82,
171, 172
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
48, 49, 50, 51, 59, 60, 64, 65, 81, 82,
171, 172, 173, 174
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.
62, 63, 64, 65, 67, 68, 69, 70, 72, 73,
74, 75, 81, 82, 172, 173, 174
d. Explain what a point (x, y) on the graph of a proportional relationship means in
terms of the situation, with special attention to the points (0, 0) and (1, r) where r is
the unit rate. 66, 69, 70, 81, 82, 172, 173, 174
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.
85, 86, 87, 88, 89, 90, 175
The Number System
--Apply and extend previous understandings of operations with fractions to add,
subtract, multiply, and divide rational numbers.
7.NS.1 Apply and extend previous understandings of addition and subtraction to
add and subtract rational numbers; represent addition and subtraction on a
horizontal or vertical number line diagram.
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.
15
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. 15, 17, 22, 28, 97, 168
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.
15, 16, 17, 20, 21, 22, 28, 30, 97, 168
d. Apply properties of operations as strategies to add and subtract rational numbers.
15, 16, 17, 20, 21, 22, 28, 30, 168
7.NS.2 Apply and extend previous understandings of multiplication and division and
of fractions to multiply and divide rational numbers.
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.
18, 20, 21, 22, 28, 30, 100, 101, 102,
168
SAM
PLE
10-15

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. 19, 20, 21, 22, 28, 30, 99, 100, 101,
102, 168
c. Apply properties of operations as strategies to multiply and divide rational
numbers. 18, 20, 21, 22, 28, 29, 96, 98, 99,
100, 101, 102, 168
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.
25, 83, 102
7.NS.3 Solve real-world and mathematical problems involving the four operations
with rational numbers.1
18, 20, 21, 22, 28, 29, 96, 98, 99,
100, 101, 102, 168
Expressions and Equations
--Use properties of operations to generate equivalent expressions.
7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients.
31, 32, 35, 38, 39, 40, 44, 45, 169,
170
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.”
*35, 36
--Solve real-life and mathematical problems using numerical and algebraic
expressions and equations.
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 ½
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.
33, 37, 38, 44, 45, 169, 170
7.EE.4 Use variables to represent quantities in a real-world or mathematical
problem, and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
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?
34, 37, 38, 44, 45, 169, 170
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
41, 42, 46,
Geometry
--Draw, construct, and describe geometrical figures and describe the relationships
between them.
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.
79Ͳ82
SAM
PLE
10-15

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.
122
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.
159
--Solve real-life and mathematical problems involving angle measure, area, surface
area, and volume.
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.
158
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.
116, 121
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.
152, 153, 154, 155, 157, 159, 162,
163, 164
--Solve real-life and mathematical problems involving volume of cylinders, cones,
and spheres.
Statistics and Probability
--Use random sampling to draw inferences about a population.
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.
11, 173
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.
1, 7, 8, 9, 10
--Draw informal comparative inferences about two populations.
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.
6
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.
4
--Investigate chance processes and develop, use, and evaluate probability models.
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.
72
SAM
PLE
10-15

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.
8, 72
7.SP.7 Develop a probability model and use it to find probabilities of events.
Compare probabilities from a model to observed frequencies; if the agreement is not
good, explain possible sources of the discrepancy.
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.
72
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
lik l b d th b d f i ?
72
7.SP.8 Find probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
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.
72
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 double sixes”), identify the outcomes in the sample space
which compose the event.
72
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?
72
SAM
PLE
10-15

STUDENT MANUAL MATH — LESSON — 177–1
Lesson 177
Review – Polygons
Create a review presentation from Lessons 115-129. Your presentation must include
the vocabulary from those Lessons and sample problems from the section. Use the
presentation you create to help you answer the Assessment questions.
Lesson Wrap-Up: Share with your teacher how well you have grasped knowledge of
basic geometric ﬁgures like polygons.
1. What is the measure of one interior angle of a regular pentagon?
2. What is the measure of the sum of the interior angles of a decagon (10 sides)?
3. What is the sum of the interior angles of a triangle?
4. Jill says that she has a rhombus. Sam says it is a quadrilateral. Peter is pretty sure that it
is a parallelogram. Explain who is correct and why.
SAM
PLE
10-15

5. Imagine the shape of a stop sign. Is this shape concave or convex?
6. Name each of the following shapes.
a.
b.
SAM
PLE
10-15

c.
d.
e.
SAM
PLE
10-15
Print Form

Lesson: 178
Review: Congruence and Similarity
presentation to help you answer the Assessment questions.
Lesson Wrap-Up: Similarity and congruence are part of everyday activity. Become familiar
with their relation to your world.
1. What is similarity?
2. What is congruence?
3. What is symmetry?
4. What is a tessellation?
SAM
PLE
10-15

Determine if the shapes below are similar.
5.
6.
7.
SAM
PLE
10-15

Determine if the shapes below are congruent
8.
9.
10. Nick noticed a very tall building, and he wanted to know how tall it was. He stood so
that his shadow and the building’s shadow ended at the same point, creating similar
triangle. The shadow of the building was 100 feet long. If Nick is 6 feet tall, and his
shadow is 14 feet long, how tall is the building?
10
10 10
8
8 8
88
2
2
66
SAM
PLE
10-15
Print Form

Lesson 179
Review: Perimeter, Area, and Surface Area
presentation you create to help you answer the Assessment questions.
Lesson Wrap-Up: Memorize the measurement equations for area, perimeter,
and surface area.
Find the perimeter.
1.
2.
3.
12
8
8
4
4
3
3
8
61
4
5
20
15
88
SAM
PLE
10-15

Find the area.
4.
5.
6. A rectangle has a perimeter of 20 cm and an area of 25 cm squared. If it is enlarged by
a scale factor of 4, what would the new perimeter and area be?
7. Find the area and circumference of the circle pictured below.
12
6
6
2
10
4
12
SAM
PLE
10-15

8. Find the area and circumference of the circle pictured below.
9. Find the surface area of the prism below.
10. Find the surface area of the prism below.
5
3
3
8
12
6
8.5
8
SAM
PLE
10-15
In order to draw on this document goto--> Tools in
the Menu Bar--> Click Comments & Markup--->
Click Show Comments & Markups Toolbar at the
bottom of list.
Print Form

STUDENT MANUAL GRADE 7 MATH — LESSON — 180–2
Lesson 180
Writing Assignment Nineteen – Seventh Grade
Math to a Sixth Grader
In this final lesson, you will show – in writing – your overall accomplishments
in 7th Grade Math.
Purpose: To write to a 6th Grade friend to explain what he or she will learn in
7th Grade math and to give them problem-solving advice.
Writer’s Role: You will be writing as yourself.
Audience: A 6th Grade friend
Focus Areas: 1. Use math terms correctly.
2. Explain some of the main concepts that you learned in math.
3. Explain at least one problem solving strategy.
Refer to the Grading Rubric below to understand how you can receive full credit, and meet
all of the requirements.
Lesson Wrap Up: If you carefully describe the math expectations to a 6th grader you will
essentially remind yourself of what you have learned this year.
Grading Rubric
Math Terms (10) Spelled/Used correctly 10
Main concepts (10)
Some main concepts from the year
explained in detail
10
Problem solving (10)
At least one problem solving strategy
explained in detail
10
SAM
PLE
10-15

Lesson 180
Assessment
Name the operation that should be done first in each situation.
1. 3 x 4 – 7
2. (10 – 4) x 3
3 (10 -5) + 35
Solve using the order of operations.
4. 4 – 2 + 5 (7)
5. 10 + 2 x 18 (46)
6 21 ÷ 7 – 3 x 1 (0)
Graph the ordered pairs to determine if the graphs are linear.
7.
y
0
(Not Linear. All points do not
lie on a straight Line)
x y
1 1
2 4
3 9
4 16
SAM
PLE
10-15

Lesson 180
Assessment
Use the skills and knowledge you have obtained about Percents to answer the questions below.
Write the percent as a fraction and a decimal.
8. 25% (25/100 and 0.25)
Measure the angles.
9.
10.
SAM
PLE
10-15

Lesson 180
Assessment
Determine if the shapes below are congruent. (Answers will vary)
11. Draw two decagons that are congruent.
Multiply or Divide
12. -3 6 ÷ (-6 )
13. -7 (-7 )
14.
4(-7)
15 Find the surface area of the prism belo w. )
3
3
9
SAM
PLE
10-15

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