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

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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. �

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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.

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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 �� 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.

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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.

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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.

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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.

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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.

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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.

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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.

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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).

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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.

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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.

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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.

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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.

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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 148 Project Ten – Electronic Quiz - Part 4 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.

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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.

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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.

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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.

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Take off on the right path for Seventh Grade Math!

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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,�1747.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,�172b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

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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.

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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,�1747.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,�175The 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.

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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,�168c. 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,�168d. Apply properties of operations as strategies to add and subtract rational numbers.

15,�16,�17,�20,�21,�22,�28,�30,�1687.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.

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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,�168c. Apply properties of operations as strategies to multiply and divide rational numbers. 18,�20,�21,�22,�28,�29,�96,�98,�99,�

100,�101,�102,�168d. 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

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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.

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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.

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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?

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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.

79�82

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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

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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

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STUDENT MANUAL MATH — LESSON — 177–1

Lesson 177Review – 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.

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5. Imagine the shape of a stop sign. Is this shape concave or convex?

6. Name each of the following shapes.

a.

b.

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c.

d.

e.

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Lesson: 178Review: Congruence and Similarity

Create a review presentation from Lessons 130-150. Your presentation must include the vocabulary from those Lessons and sample problems from the section. Use the 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?

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Determine if the shapes below are similar.

5.

6.

7.

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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

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Lesson 179Review: Perimeter, Area, and Surface Area

Create a review presentation from Lessons 130-150. 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: Memorize the measurement equations for area, perimeter, and surface area.

Find the perimeter.

1.

2.

3.

12

8

8

44

33

8

61

4

5

20

15

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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

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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

126

8.5

8

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STUDENT MANUAL GRADE 7 MATH — LESSON — 180–2

Lesson 180Writing 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 friendFocus 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

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Lesson 180Assessment

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

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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.

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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

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