Glen Ridge Public Schools - Mathematics Curriculum · • Computing Compound Interest (Holt McDougal, Technology Activity 7.7, page 383) Enrichment Activities: • Practice C-level

Glen Ridge Public Schools - Mathematics Curriculum

Course Title: Advanced Pre-Algebra 7

Subject: Mathematics

Grade Level: 7th Grade

Duration: One Academic Year

Prerequisite: Final Grade of an A in Math 6, Minimum of a B on the mathematics placement test, standardized test scores in the 95th percentile & Teacher Recommendation

Elective or Required: Required Content Course

Mathematics Mission Statement:

Since Mathematical and Computational thinking are an integral part of our lives and 21st century learning, students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula will emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology.

Students will be engaged and challenged in a developmentally appropriate, student-centered learning environment. Students will communicate mathematical ideas effectively and apply those ideas by using manipulatives, computational skills, mathematical models and technology in order to solve practical problems.

To achieve these goals, students will be taught a standards-based curriculum that is aligned with the National Common Core Standards in Mathematics and the New Jersey Core Curriculum Content Standards in Technology and 21st Century Life and Careers.

Course Description:

Advanced Pre-Algebra 7 students will develop fundamental mathematical ideas and methods through a student-centered based curricula. These methods provide a strong foundation in algebraic and geometric concepts. A student selected for this course must be self-motivated and has demonstrated high mathematical ability and achievement. The student must be able to work in a fast paced atmosphere and at an abstract level. This course emphasizes problem solving, reasoning, communication, connections, representations, and technology from an in-depth perspective. Throughout the course, the following content standards will be developed: number relationships and

computation/arithmetic; algebra, patterns and functions; geometry and measurement; and data analysis, statistics, and probability. This course prepares students for Algebra I.

The students entering seventh grade Advanced Pre-Algebra have studied many of the topics in the Pre-Algebra textbook during the previous school year in sixth grade mathematics. These topics are noted with an asterisk *. Teachers may choose to refer to the noted objectives and assign selected problem as a summer assignment, or they may choose to pre-test, teach or skip according to studentsʼ abilities. This strategy is strongly suggested as the Algebra I course content is very intense and time is at a premium.

Author: Erika Taylor & Kelsey ReedDate Submitted: Summer, 2012Text: Holt McDougal Larson Pre-Algebra, Common Core Edition 2012, Larson, Boswell, Kanold, Stiff

Course Name: Pre-Algebra 7

Unit #1: Numbers & OperationsChapter 1: Variables, Expressions & Integers (1.5 - 1.7)

Chapter 2: Solving Equations (2.1 - 2.4)

Approximate Number of Weeks: 4 Weeks

Essential Questions: • How can you tell the sign of the sum of two integers?• How are adding and subtracting integers related?• How can you tell the sign of the product of two integers?• How can you tell the sign of the quotient of two integers?• How do you solve equations that involve one operation?• How can you use properties to simplify expressions?• How do you add, subtract, factor, and multiply algebraic expressions?

Common Core Standards: CC.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.

CC.7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

CC.7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

CC.7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

CC.7.EE.2: Understand that rewriting an expression in different forms in a problem context can shed light of the problem and how the quantities in it are related.

CC.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.

Upon completion of this unit students will be able to: • *Evaluate and write variable expressions.• *Use powers to describe repeated multiplication.• *Use order of operations to evaluate expressions.• *Compare and order integers.

• Add integers ((CC.7.NS.1, CC.7.NS.3, CC.7.EE.3).• Subtract integers (CC.7.NS.1).• Multiply integers (CC.7.NS.2, CC.7.EE.2).• Divide integers (CC.7.NS.2, CC.7.EE.2).

• *Identify and plot points in a coordinate plane.• *Solve equations using addition or subtraction.• *Solve equations using multiplication or division.• *Solve equations involving decimals.• Use properties of addition and multiplication (CC.7.NS.1).• Use the distributive property (CC.7.NS.1).• Simplify variable expressions (CC.7.EE.1, CC.7.EE.4).• Write equations (CC.7.EE.2, CC.7.EE.4).

Interdisciplinary Standards (NJCCCS.org)• Standard 5.1 – Science Practices• Standard 6.1 – U.S. History: America in the World• Standard 6.3 – Active Citizenship in the 21st Century• Standard 8.1 – Computer and Information Literacy• Standard 8.2 – Technology Education• Standard 9.1 – 21st - Century Life & Career Skills

Activities/ Technology:• Video tutors (Holt McDougal website)• Brain Game activities (Holt McDougal)• Concept activity – adding integers using a number line (Holt McDougal, page 28)• Concept activity – multiplying integers (Holt McDougal, page 41)• Concept activity – distributive property (Holt McDougal, page 77)• TI-Calculator activity – simplifying expressions (Holt McDougal, page 83)• Adding integers activities (Big Ideas, page 8)• Subtracting integers activities (Big Ideas, page 14)• Multiplying integers activities (Big Ideas, page 22)• Dividing integers activities (Big Ideas, page 28)• PowerPoint presentations (Holt McDougal)

Enrichment Activities: • Practice C-level worksheets (Holt McDougal)• Challenge worksheets (Holt McDougal)• Problem solving worksheets (Holt McDougal)• Taking math deeper problems (Big Ideas)

Methods of Assessment/Evaluation: • Entry Slips/Exit Slips• Math Chat• Notebook/Binder Quiz • K-W-L

• Journals/Open-ended Questions• EPRs• Homework • Quizzes• Chapter Test• Unit project• Alternative Assessment

Resources: • Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook by Holt McDougal• Big Ideas accelerated textbook by Holt McDougal• Selected Websites (see appendix)

Unit #2: Proportional Thinking Chapter 6: Ratio, Proportion and Probability (6.2, 6.4 - 6.5)

Chapter 7: Percents (7.5 - 7.7)


Essential Questions: • How can you use tables and equations to identify and describe proportional

relationships?• How do rates help you describe real-life problems?• How can you compare two rates graphically?• How can proportions help you decide when things are “fair”?• How can you use ratio tables and cross products to solve proportions in science?• How can you use a graph to show the relationship between to variables that vary

directly? How can you use an equation?

• How do you use percents to solve problems?• What is a percent of decrease? What is a percent of increase?• How do you find markups and discounts efficiently?• How can you find the amount of simple interest earned on a savings account? How

can you find the amount of interest owed on a loan?• What is the difference between simple interest and compound interest?

Common Core Standards: CC.7.RP.1: Compute unit rates associated with ratios of fraction, including ratios of lengths, areas and other quantities measured in like or different units.

CC.7.RP.2: Recognize and represent proportional relationships between quantities.

CC.7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

CC.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.


CC.7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

CC.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.

CC.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.

CC.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.

CC.7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from scale drawing and reproducing a scale drawing at a different scale.

Upon completion of this unit students will be able to:• * Use equivalent fractions to find ratios and unit rates.• Write and solve proportions (CC.7. RP.1, CC.7.RP.2, CC.7.NS.3).• * Apply cross products to solving proportions.• Identify similar and congruent figures (CC.7.RP.2, CC.7.NS.3, CC.7.G.1). • Apply proportional relationships to finding the unknown length of similar figures (CC.

7.RP.2, CC.7.NS.3, CC.7.G.1).

• * Use equations to solve percent problems (CC.7.RP.2, CC.7.RP.3, CC.7.EE.2, CC.7.EE.3, CC.7.EE.4).


Activities/ Technology:• Unit Rates TI Lab (Prentice Hall Mathematics, page 35)• Investigating Proportional Relationships (Holt McDougal, Concept Activity 6.2, page

283)• Comparing Two Rates Graphically (Accelerated Big Ideas, Activity 2, page 105)• Determining Proportions (Accelerated Big Ideas, Activity 1, page 110)• Problem Solving Connection (On Core Mathematics 7, page 52)• Solving a Proportion in Science (Accelerated Big Ideas, Activity 1, page 122)• The Game of Criss-Cross (Accelerate Big Ideas, Activity 2, page 123)• Math in Literature (Accelerated Big Ideas, Activity 1, page 136)• Using Percent Bar Models (Holt McDougal, Concept Activity 7.2, page 350)• Percents of Increase and Decrease (Accelerated Big Ideas, Activities 1 & 2, pages

164, 165)• Modeling Percent of Change (Holt McDougal, Concept Activity 7.5, page 367)• Percent of Change TI Lab (Prentice Hall Mathematics, page 59)

• Simple Interest (Accelerated Big Ideas, Activities 1, 2, & 3, pages 178, 179)• Computing Compound Interest (Holt McDougal, Technology Activity 7.7, page 383)


Methods of Assessment/Evaluation: • Entry Slips/Exit Slips• Math Chat• Notebook/Binder Quiz • K-W-L• Journals/Open-ended Questions• EPRs• Homework • Quizzes• Chapter Test• Unit project• Alternative Assessment

Resources: • Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook (Holt McDougal)• Big Ideas accelerated textbook (Holt McDougal)• Selected Websites (see appendix)• Teaching Middle Grades with TI Technology (Prentice Hall Mathematics)• On Core 7 (Houghton Mifflin Harcourt)

Unit #3: Data Analysis & Probability Chapter 11: Data Analysis & Probability (11.2 - 11.5, 11.9)

Chapter 6: Percents (6.7 - 6.8)


Essential Questions: • How can you use a sample to gain information about a population?• How can you use samples to make and compare predictions about a population?• How can you use measures of center and variability to compare two populations?• How can you describe the likelihood of an event?• How can you find the theoretical probability of an event?• How do you find the experimental probability of an event?• How do you find the probability of a compound event?• How can you use simulations to estimate probabilities?• How can you use a box-and-whisker plot to describe a data set?• How can you display data in a way that helps you make decisions?

Common Core Standards: CC.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.

CC.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.

CC.7.SP.3: Informally assess the degree of visual overlap of the two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

CC.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.

CC.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.

CC.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.

CC.7.SP.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model observed to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

CC.7.SP.8: Find probabilities of compound events using organized lists ,tables, tree diagrams, and simulations.

Upon completion of this unit students will be able to:• *Make stem-and-leaf plots.• *Make histograms.• *Use circle graphs to describe data.• Make and interpret box-and-whisker plots (CC.7.SP.2, CC.7.SP.3, CC.7.SP.4).• Use a graphing calculator to create a box-and-whisker plot (CC.7.SP.2, CC.7.SP.3,

CC.7.SP.4).• Choose appropriate data displays (CC.7.SP.2, CC.7.SP.4).• Access the degree of visual overlap of two data distributions (CC.7.SP.3).• Identify populations and sampling methods (CC.7.SP.1, CC.7.SP.2).• Use the multiplication principle to find probabilities (CC.7.SP.7).• Use the addition principle to find probabilities (CC.7.SP.7).• Find probabilities (CC.7.SP.5, CC.7.SP.6, CC.7.SP.7, CC.7.SP.8).• Find the probability that event A and B occur (CC.7.SP.7, CC.7.SP.8).


Activities/ Technology:• Video Tutors (Holt McDougal website)• Brain Game Activities (Holt McDougal)• TI-Calculator activity – making a histogram (Holt McDougal, page 617)• TI-Calculator activity – making a box-and-whisker plot (Holt McDougal, page 625)• Computer activity – searching for data (Holt McDougal, page 640)• Concept activity – interpreting data by investigating random samples (Holt McDougal,

page 642)• Concept activity –performing a simulation (Holt McDougal, page 667)• Independent and dependent events activities (Big Ideas, page 404)• Experimental probability activities (Big Ideas, page 398)• Samples and populations activities (Big Ideas, page 368)• Box-and-whisker plot activities (Big Ideas 8 (Blue), page 280)• Choosing a data display activities (Big Ideas 8 Blue, page 296)• Problem solving connections – happy birthday statistics activity (On Core Mathematics

7, page 149)

• Problem solving connections – fun fundraisers probability activity (On Core Mathematics 7, page 175)



Resources/Including Online Resources• Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook (Holt McDougal)• Big Ideas Accelerated textbook (Holt McDougal)• On Core 7 Mathematics (Houghton Mifflin)• Selected Websites (see appendix)

Unit #4: MeasurementChapter 10: Measurement, Area and Volume (10.5 - 10.8)

Chapter 9: Real Numbers & Right Triangles (9.5)


Essential Questions: • How can you draw three-dimensional figures?• How can you use nets to fins the surface area of a prism? Cylinder?• How do you find the surface area of a pyramid? Cone?• How do you describe the two-dimensional figures that result from slicing three-

dimensional shapes?• How do changes in dimension effect the perimeter, area and volume of a figure?• How can you use the distance and midpoint formulas to find the perimeter and areas

of figures?• How can you find the perimeter and area of polygons in a coordinate plane?

Common Core Standards: CC.7.RP.2: Recognize and represent proportional relationships between quantities.

CC.7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

CC.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.

CC.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.

CC.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.

CC.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.

CC.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.

CC.8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Upon completion of this unit students will be able to:• * Solve problems involving triangles. • * Classify polygons and quadrilaterals. • * Find the areas of parallelograms and trapezoids. • * Find the circumference and area of circles. • Find the surface areas of prisms and cylinders (CC.7.G.4, CC.7.G.6).• Find the surface area of pyramids and cones (CC.7.G.4, CC.7.G.6).• Describe two-dimensional figures that result from slicing three-dimensional figures

(CC.7.G.3). • Find the volume of prisms and cylinders (CC.7.G.4, CC.7.G.6, CC.8.G.9).• Convert areas and volumes within or between systems of measurement (CC.7.G.6).• Find the volumes of pyramids and cones (CC.7.G.4, CC.7.G.6).• Determine the effect of changes in dimensions on perimeter, area and volume (CC.

7.G.6).• Find the surface area and volume of composite solids (CC.7.G.4, CC.7.G.6).

• Use the distance and midpoint formulas (CC.7.G.6).


Activities/ Technology:• Drawing Triangles (Holt McDougal, Concept Activity 10.1, page 536A)• Investigating Area (Holt McDougal, Concept Activity 10.4, page 553)• Finding Surface Area and Volumes (Accelerated Big Ideas, Activities 1 & 2, pages

250, 251)• Nets and Surface Area (Holt McDougal, Concept Activity 10.5, page 563)• Finding Surface Area (Accelerated Big Ideas, Activities 1 & 2, page 262)• Building a Skylight (Accelerated Big Ideas, Activity 3, page 271) • Building and Sketching Solids (Holt McDougal, Concept Activity 10.7, page 576)• Surface Area and Volume (Holt McDougal, Technology Activity 10.7, page 583)• Finding and Using a Pattern (Accelerated Big Ideas, Activity 2 & 3, page 283)• Castle Problem (see appendix)



Resources: • Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook (Holt McDougal)• Big Ideas Accelerated textbook (Holt McDougal)• Selected Websites (see appendix)

Unit #5: Geometry Chapter 12: Angle Relationships & Transformations (12.1 - 12.7)


Essential Questions: • What can you conclude about the angles formed by parallel lines that are cut by a

transversal?• What can you conclude about the measures of the angles of a triangle?• How can you determine when two triangles are similar?• How can you use coordinates to describe the result of a transformation, reflection, or

rotation?• What properties of a figure are preserved under a translation, reflection, or rotation?• What is the connection between transformations and figures that have the same

shape and size?• How can you use coordinates to describe the result of a dilation?• What is the connection between transformations and similar figures?• How can you use angle pairs to solve problems?• How can you find a formula for the sum of the angle measures of any polygon?• How can you find the surface area of a composite solid?• How can you estimate the volume of a composite solid?• How can you find the area of a composite shape?

Common Core Standards:CC.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.

CC.8.G.1: Verify experimental the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same

length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines.

CC.8.G.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflection, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CC.8.G.3: Describe the effect of dilations, translations, rotations, and refections on two-dimensional figures using coordinates.

CC.8.G.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar figures two-dimensional figures, describe a sequence that exhibits the similarity between them.

CC.8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Upon completion of this unit students will be able to:• Classify special pairs of angles (CC.7.G.5, CC.8.G.1, CC.8.G.5). • Identify angles when a transversal intersects lines (CC.8.G.5).• Find measures of interior and exterior angles (CC.7.G.5, CC.8.G.1, CC.8.G.5).• Translate figures in a coordinate plane (CC.8.G.1, CC.8.G.3, CC.8.G.4).• Reflect figures and identify lines of symmetry (CC.8.G.1, CC.8.G.3, CC.8.G.4)• Rotate figures and identify rotational symmetry (CC.8.G.1, CC.8.G.3, CC.8.G.4)• Dilate figures in a coordinate plane (CC.8.G.1, CC.8.G.3, CC.8.G.4)• Copy a segment (CC.8.G.1). • Copy an angle (CC.8.G.1).• Construct the perpendicular bisector of a segment (CC.8.G.1).• Construct the angle bisector of an angle (CC.8.G.1).• Construct parallel lines through a line and a point not on the line (CC.8.G.1).• Copy a triangle (CC.8.G.1, CC.8.G.5).• Perform multiple transformations in the coordinate plane (CC.8.G.1, CC.8.G.2, CC.

8.G.3, CC.8.G.4)


Activities – include 21st Century Technologies: • Video tutors (Holt McDougal website)• Brain Game activities (Holt McDougal)• Concept activity – angle relationships (Holt McDougal, page 691)• Concept activity –finding sums of angle measures of polygons (Holt McDougal, page

697)• TI-Calculator activity –reflecting a line (Holt McDougal, page 715)• Concept activity –rotating a segment (Holt McDougal, page 716)• Dilations Concept activity – rotations and symmetry (Holt McDougal, page 722)• Hands-on Lab – Identifying combined transformations (Holt McDougal Mathematics 8,

page 237)• Hands-on Lab – Exploring congruence (Holt McDougal Mathematics 8, page 220)• Translations activities (Big Ideas, page 220)• Reflections activities (Big Ideas, page 226)• Rotations activities (Big Ideas, page 232) • Classifying angles activities (Big Ideas, page 464)

• Angles and sides of triangle activities (Big Ideas, page 470)• Angles of polygons activities (Big Ideas, page 476)• Parallel lines and transversals activities (Big Ideas, page 492)• Surface area of composite solids activities (Big Ideas, page 282)• Volume of composite solids activities (Big Ideas, page 324)• Surface area and volumes of similar solids activities (Big Ideas, page 330)• Review game – finding the missing angle measure in a triangle (Big Ideas, page 502) • Problem Solving Connections – stitch perfect transformation activity (On Core

Mathematics 8, page 105)



Resources/Including Online Resources• Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook by Holt McDougal• Big Ideas Accelerated textbook by Holt McDougal• Mathematics 8 by Holt McDougal• NJ ASK Coach book Grade 8• On Core Mathematics Grade 8 Workbook• Selected Websites (see appendix)

Unit #6: Exponents & Their ApplicationsChapter 4: Factors, Fractions and Exponents (4.5 - 4.7)

Chapter 9: Real Numbers and Right Triangles (9.2 - 9.4, EXT)


Essential Questions: • How can you find the side length of a square when you are given the area of the

square? • How are the sides of a right triangle related?• How can you find decimal approximations of square roots that are irrational?• How can you use the Pythagorean Theorem to solve real-life problems?

Common Core Standards: CC.8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

CC.8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

CC.8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

CC.8.EE.3: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurement of very large or very small quantities. Interpret scientific notation that has been generated by technology.

CC.8.G.6: Explain a proof of the Pythagorean Theorem and its converse.

CC.8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CC.8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Upon completion of this unit students will be able to:• * Identify prime and composite numbers. • * Find the GCF of two or more whole numbers. • * Write equivalent fractions. • * Find the LCM of two numbers. • Multiply and divide powers (CC.8.NS.1, CC.8.NS.2, CC.8.EE.1).

• Work with negative and zero exponents (CC.8.NS.1, CC.8.NS.2, CC.8.EE.1).• Write numbers using scientific notation (CC.8.EE.1, CC.8.EE.3).

• * Find and approximate square roots of numbers. • Simplify radical expressions (CC.8.NS.2). • Use the Pythagorean Theorem to solve problems (CC.8.G.6, CC.8.G.7, CC.8.G.8). • Compare and order real numbers (CC.8.NS.2).


Activities/ Technology:• Finding Rules of Exponents (Holt McDougal, Concept Activity 4.5, page 195)• Writing Numbers Using Powers of 10 (Holt McDougal, Focus on Numbers, page

205A)• Operations with Scientific Notation (Holt McDougal, Focus on Operations, page 210A)• Using Scientific Notation (Holt McDougal, Technology Activity, page 211)• Performing Operations on Square Roots (Holt McDougal, Focus on Operations, page

486)• Investigating Right Triangles (Holt McDougal, Concept Activity 9.3, page 488)• Proving the Pythagorean Theorem and its Converse (Holt McDougal, Concept Activity

9.3, page 493A)• Angles of a Triangle (Holt McDougal, Focus on Geometry, page 494)• Pythagorean Theorem TI-84 Lab (Prentice Hall Mathematics, page 53)• Scientific Notation TI-84 Lab (Prentice Hall Mathematics, page 49)• Problem Solving Connections: Living on the Moon! (Houghton Mifflin Harcourt, On

Core 8, page 28)• Finding Square Roots (Accelerated Big Ideas, Activity 1, page 510)• Discovering the Pythagorean Theorem (Accelerated Big Ideas, Activity 1, page 516)• Approximating Square Roots Geometrically (Accelerated Big Ideas, Activity 2, page

525)• The Golden Ratio and the Human Body (Accelerated Big Ideas, Activity 2, page 533)• Using the Pythagorean Theorem (Accelerated Big Ideas, Activities 1 - 4, pages 538 -

539)• “I have... Who has? Square Roots” (The Middle School Mathematician, page 84)



Resources: • Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook (Holt McDougal)• Big Ideas Accelerated textbook (Holt McDougal)• On Core 7 (Houghton Mifflin Harcourt)• On Core 8 (Houghton Mifflin Harcourt)• The Middle School Mathematician (Terri Breedan and Kathryn Dillard)• Selected Websites (see appendix)

Unit #7: Solving EquationsChapter 5: Rational Numbers and Equations (5.6 - 5.7)

Chapter 3: Multi-Step Equations and Inequalities (3.1 - 3.6)


Essential Questions: • How do you write rational numbers as decimals and as fractions?• What step is performed first in a two-step equation?• How do you solve equations that contain multiple operations?• How do you solve equations by combining like terms and multiplying expressions?• How do you solve inequalities that involve one operation?• How do you solve inequalities that involve multiple operations?• How can you solve problems by using expressions, equations, and inequalities?• How can you give examples of equations with a given number of solutions?

Common Core Standards:


CC.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.

CC.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.

CC.8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

CC.8.EE.7: Solve linear equation in one variable.a. Give examples of linear equations in one variable with one solution, infinitely

many solutions, or no solution. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Upon completion of this unit students will be able to:• * Write fractions as decimals and decimals as fractions.• * Add and subtract fractions and mixed numbers.• * Multiply fractions and mixed numbers.• * Divide fractions and mixed numbers.• Solve two-step equations (CC.7.NS.2, CC.8.EE.7). • Use multiplicative inverses to solve equations (CC.7.NS.2, CC.7.NS.2, CC.8.EE.7).• Use the LCD to solve equations and inequalities (CC.7.EE.3, CC.7.EE.4). • Solve equations using the distributive property (CC.8.EE.7).• Solve equations with variables on both sides (CC.8.EE.7).• Solve inequalities using addition or subtraction (CC.8.EE.7).• Solve multi-step inequalities (CC.8.EE.7).

Interdisciplinary Standards (njcccs.org)• Standard 5.1 – Science Practices• Standard 6.1 – U.S. History: America in the World• Standard 6.3 – Active Citizenship in the 21st Century• Standard 8.1 – Computer and Information Literacy• Standard 8.2 – Technology Education• Standard 9.1 – 21st - Century Life & Career Skills

Activities – include 21st Century Technologies: • Video tutors (Holt McDougal website)• Brain Game activities (Holt McDougal)• Modeling activity – modeling two-step equations (Holt McDougal, page 119)• Modeling activity – modeling equations with variables on both sides (Holt McDougal,

page 130)• TI Calculator activity – solving equations (Holt McDougal, page 136)• Concept activity – multiplication and division properties of inequality (Holt McDougal,

page 145)• Solving two-step equations activities (Big Ideas, page 82)• Solving multi-step equations activities (Big Ideas, page 422)• Solving multi-step inequalities (Big Ideas 8 (Blue), page 334)• Solving equations with variables on both sides activities (Big Ideas, page 428)• Solving equations using tables and graphs activities (Big Ideas, page 434)• Problem Solving Connection – to buy or not to buy solving and evaluating activity (On

Core Mathematics 7, page 81)



Resources/Including Online Resources• Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook by Holt McDougal• Big Ideas Accelerated textbook by Holt McDougal• Big Ideas Blue-level textbook by Holt McDougal

Unit #8: Linear Functions Chapter 8: Linear Functions (8.1 - 8.9)


Essential Questions: • How can you convert temperatures between the Fahrenheit an Celsius scales?• How do you represent relationships algebraically?• How can you use tables and graphs to solve equations?• How can the slope of a line be used to describe the line?• How do you represent functions?• How can you describe the graph of an equation of the form y = mx + b?• How can you use the properties of equality to support your solution to a linear

equation?• How do you justify the solution to a linear inequality?• How do you graph the solutions to a linear equation in two variables?• How do you graph the solutions to a linear inequality in two variables?• How do you approximate the solution of a system of linear equation by graphing? By

substitution? By linear combination (elimination)?

Common Core Standards: CC.8.EE.8: Analyze and solve pairs of simultaneous linear equations.

a. Understand that solutions to a system of two linear equations in two variables correspond to points on intersection of their graphs, because points of intersection satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

c. Solve real-world and mathematical problems leading to two linear equations in two variables.

CC.8.F.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

CC.8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

CC.8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

CC.8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these tables or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Upon completion of this unit students will be able to:• Use graphs to represent relations and functions (CC.8.F.1, CC.8.F.2• Find solutions of equations in two variables (CC.8.F.4). • Use x- and y-intercepts to graph linear equations (CC.8.F.3). • Find and interpret slopes of lines (CC.8.F.3). • Graph linear equations in slope-intercept form (CC.8.F.3). • Write linear equations (CC.8.F.4). • Use function notation (CC.8.F.4). • Graph and solve systems of linear equations (CC.8.EE.8).• Graph inequalities in two variables (CC.8.EE.8).


Activities/ Technology:• Converting Temperatures (Accelerated Big Ideas, Activities 1 - 3, pages 422, 423)• Linear and Nonlinear Functions (Holt McDougal, Focus on Functions, page 412A)• Graphing Linear Equations (Holt McDougal, Technology Activity, page 413)• Planning Your Own Business (Accelerated Big Ideas, Activity 2, page 435)• Investigating Slope (Holt McDougal, Concept Activity 8.4, page 419)• Inductive Reasoning - Slope (Accelerated Big Ideas, page 443)• Real-World Graphs (Holt McDougal, Focus on Graphing, page 426)• Understanding Slopes (Holt McDougal, Concept Activity 8.5, page 429A)• Inductive Reasoning - Slope-Intercept Form (Accelerated Big Ideas, page 449)• Graphs of Direct Variation (Holt McDougal, Focus on Graphing, page 436)• Fitting Lines to Data (Holt McDougal, Focus on Functions, page 437A)• Finding Best-Fitting Lines (Holt McDougal, Technology Activity, page 445)• Domain and Range of a Function (Holt McDougal, Focus on Functions, page 446)• Interpreting Scatter Plots (Holt McDougal, Focus on Functions, page 447A)• Modeling a Linear System (Holt McDougal, Concept Activity 8.8, page 453)• Properties of Functions (Holt McDougal, Focus on Functions, page 453A)• Solving Systems of Equations (Holt McDougal, Focus on Functions, page 458A)• Using Tables to Solve a Systems (Holt McDougal, Technology Activity, page 459)• Focus on Modeling - Modeling with Functions (On Core Algebra, page 29)• Focus on Modeling - Modeling with One-Variable (On Core Algebra, page 51)• Focus on Modeling - Modeling with Two-Variables (On Core Algebra, page 79)

Enrichment Activities: • Practice C-level worksheets (Holt McDougal)• Challenge worksheets (Holt McDougal)

• Problem solving worksheets (Holt McDougal)• Taking math deeper problems (Big Ideas)


Resources: • Online textbook information: my.hrw.com• Teacher webpage• Pre-Algebra textbook by Holt McDougal• Big Ideas Accelerated textbook by Holt McDougal• Big Ideas Blue-level textbook by Holt McDougal

Appendix

Advanced Pre-Algebra 7 Textbook Sequence

Summer Assignment & Review

Unit 1: Numbers & Operations - MP1

" 1.5: Adding Integers" 1.6: Subtracting Integers" 1.7: Multiplying & Dividing Integers" 2.1: Properties & Operations" 2.2: The Distributive Property " 2.3: Simplifying Variable Expressions" 2.4: Variables & Equations

Unit 2: Proportional Thinking - MP1"" 6.2: Writing & Solving Proportions" 6.4: Similar & Congruent Figures" 6.5: Similarity & Measurement" 7.5: Percent of Change" 7.6: Percent Application" 7.7: Simple & Compound Interest

Unit 3: Data Analysis & Probability - MP2

" 11.2: Box-and-Whisker Plots (add Line Plots)" 11.3: Using Data Displays" 11.4: Collecting Data" 11.5: Interpreting Data" 6.8: The Multiplication Principle" 6.7: Probability (& Odds)" 11.9: Independent & Dependent Events

Unit 4: Measurement, Area & Volume - MP2"" 10.5: Surface Areas of Prisms & Cylinders" 10.6: Surface Areas of Pyramids & Cones" 10.7: Volumes of Prisms & Cylinders" 10.8: Volumes of Pyramids & Cones" ADD: Polygons in the Coordinate Plane" 9.5: The Distance & Midpoint Formula

Unit 5: Angle Relationships & Transformations - MP3"

" 12.1: Angle Relationships" 12.2: Angles & Parallel Lines" Add: Constructions" 12.3: Angles & Polygons" 12.4: Translations" 12.5: Reflections & Symmetry" 12.6: Rotations & Symmetry " 12.7: Dilations" EXT: " Compound Figures" " Compound Volume & Surface Area" " Combine Transformations

Unit 6: Exponents & Their Applications - MP3

" 4.5: Rules of Exponents" 4.6: Negative & Zero Exponents" 4.7: Scientific Notation" 9.2: Simplifying Square Roots" 9.3: The Pythagorean Theorem " 9.4: Real Numbers" EXT: Converse & Pythagorean Triples

Unit 7: Solving Equations" "" 5.6: Using Multiplicative Inverses to Solving Equations" 5.7: Equations & Inequalities with Rational Numbers " 3.1: Solving Two-Step Equations" 3.2: Solving Equations Having Like Terms & Parentheses" 3.3: Solving Equations with Variables on Both Sides" 3.4: Solving Inequalities Using Addition & Subtraction " 3.5: Solving Inequalities Using Multiplication & Division " 3.6: Solving Multi-Step Inequalities"Unit 8: Linear Functions"" 8.1: Relations & Functions " 8.2: Linear Equations in Two Variables" 8.3: Using Intercepts" 8.4: The Slope of a Line" 8.5: Slope-Intercept Form" 8.6: Writing Linear Equations" 8.7: Function Notation" 8.8: Systems of Linear Equations" ADD: Graphing Linear Inequalities " 8.9: Graphs of Linear Inequalities

Selected Websites Math Game Websites:

http://www.slidermath.com/

http://www.math-play.com

http://www.mathisfun.com

http://www.mathplayground.com

http://www.mathwire.com/

http://www.mathwarehouse.com

http://themathgames.com/our-games/

http://www.arcademicskillbuilders.com/games/

http://www.shodor.org/interactivate/activities

http://www.bbc.co.uk/education/mathsfile/index.shtml

Online Math Resources:

http://www.mathbits.com

http://www.quia.com

http://www.brainpop.com

http://illuminations.nctm.org/Activities.aspx?grade=all

http://www.regentsprep.org/Regents/math/ALGEBRA/math-ALGEBRA.htm

http://www.superteachertools.com - Website that offers tools for teachers such as random name chooser, group makers, seating charts, timers, jeopardy, who wants to be a millionaire, plus other flash games to use for review, plus search pre-made review games to use in the classroom!

http://www.mathopenref.com/constructions.html - Website that offers animation of many geometric constructions

http://www.scribd.com/doc/64213488/Castle-Problem - A complex castle problem where students have to find composite lateral area and volume of a castle.























http://www.quia.com

http://www.quia.com







http://www.superteachertools.com

http://www.superteachertools.com

http://www.mathopenref.com/constructions.html

http://www.mathopenref.com/constructions.html

http://www.scribd.com/doc/64213488/Castle-Problem

http://www.scribd.com/doc/64213488/Castle-Problem

Documents

Glen Ridge Public Schools - Mathematics Curriculum · • Computing Compound Interest (Holt McDougal, Technology Activity 7.7, page 383) Enrichment Activities: • Practice C-level