algebra 1 concepts – 8 th grade math

Glen Ridge Public Schools – Mathematics Curriculum

Course Title: Algebra 1 Concepts

Subject: Mathematics

Grade Level: 8

Duration: one year

Prerequisite: Pre-Algebra or Pre-Algebra Advanced

Elective or Required: Required

Mathematics Mission Statement

Since Mathematics 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 manipulative, 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:

The ultimate goal of this course is to give the student a foundation for exploring and understanding algebra and geometry. Topics include the basic operations and properties of real numbers, measurement on a plane and in space, data analysis, linear equations, graphing, problem solving, functions and deductive reasoning

Author: Darleen KennedyDate Submitted : Summer 2012

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Algebra 1 Concepts – 8th grade math

Outline

Topic Number System 2 weeks

8 NS 1 - rational numbers, irrational numbers, real numbers8 NS 2 - identifying and graphing irrational numbers

Topic Expressions and Equations 3 weeks

8 EE 1 - exponents8 EE 2 - squares roots and cube roots8 EE 3 - scientific notation8 EE 4 - reading and calculating with scientific notation

Topic Understand and apply the Pythagorean Theorem 3 weeks

8 G 6 \8 G 7 Pythagorean Theorem8 G 8 /

Topic Proportional Relationships and connections to lines and linear equations 2 weeks

8 EE 5 – converting unit measurements, solving linear equations by graphing, find slope of line8 EE 6 - triangles, slope, similar figures, slope intercept

Topic Solving Linear Equations 4.5 weeks

8 EE 7 – simplifying multi-step variables on both sides and systems of equations

Topic Understand congruence and similarity using physical models, transparencies, or geometry software 3 weeks

8 G 1 - transformations8 G2 - congruence8 G 3 - dilation8 G 4 - similar figures 8 G 5 - parallel lines perpendicular line, triangles

Topic Solve real-world problems involving volume of cylinders, cones, and spheres. 2.5 weeks

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8 G 9 - volume of prisms, cylinders, cones, spheres

Topic Analyze and solve pairs of simultaneous linear equations 4 weeks

8 EE 8 - slope, graphing linear equations, systems of linear equations, writing systems of equations, special systems of equations, solving equations by graphing

Topic Investigate patterns of association in bivariate data 2 weeks

8.SP.1 - scatter plots8 SP 28 SP 3 - line of best fit8 SP 4 - patterns , 2 way tables 8 SP 5

Topic Define, evaluate, and compare functions. 4 weeks

8.F.1 - linear functions8.F.2. compare functions8.F.3. slope-intercept form

Topic Use functions to model relationships between quantities 4 weeks

8.F.4. construct function to model linear relationships and determine rate of change8.F.5. functional relationships

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Topic Number System

8.NS.1 know that numbers that are not rational are called irrational Understand that every number has a decimal expansion - that for rational numbers show

that the decimal expansion repeats eventually and converts to a decimal expansion which repeats eventually into a rational number

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

2 weeks for Unit

Essential Questions

How do you determine the difference between a rational and irrational number? Does a rational number have an expansion? What is a perfect square? How can you find decimal approximations of square roots that are irrational? How do you convert an irrational number to a decimal? How can you use a square root to describe the golden ratio?

Upon Completion of the unit students will be able to :

1. Write a rational number as the ratio of two integers. (8.NS.1)2. Identify irrational numbers (8.NS.1)3. Approximate the decimal value of an irrational number (8.NS.2)4. Understand and explain the relationship of rational, irrational, real, integers, and natural

numbers (8.NS.1)5. Locate rational, irrational, real, integers and natural numbers on a number line. (8.NS.2)6. Create the decimal expansion of a rational number (8.NS.1)7. Define square root, cube root, perfect square, radical sign, radicand, irrational number, real

numbers (8.NS.1)8. Review rules for computation of rational number (8.NS.2)9. Understand and apply the properties of addition, subtraction, division, and multiplication of

square roots (8.NS.1)

Interdisciplinary Standards

L.6.1 Language arts – learn that the prefix “it”- means not and other examples like dis-, il- , im-, in-, and un-

2.5 Physical Education - Sports – understand that a fours square court is 66 square feet and from this you can calculate the sides

5.2 Physical Science – use and understand the formula for calculating the rate a object falls.

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5-3 Life Science – understand and identify the golden ratio and the human body

Activities – including 21 st Century Technologies

Instruction Holt McDougal chapters 1-1 Rational Numbers Lab - Use calculators to find approximate values of irrational numbers Practice from On Core Mathematics chapters 1-5 – how to write any rational number as a

fraction Instruction Holt McDougal pg 128 Extension identifying and graphing irrational numbers Instruction Big Ideas lesson 6-3 irrational numbers – approximating square roots Instruction Big Ideas 6-4 Simplifying square roots Activity Big Ideas pg 244 Approximating square roots with scientific calculator

Enrichment Activities

Review of multiplying and dividing adding subtracting rational numbers with emphasis on integer rules – Holt McDougal chapter 1-2 Multiplying Rational Numbers & chapters 1-3 Dividing Rational Numbers & chapter 1-4 adding and subtracting with unlike denominators\

Holt McDougal pg 25 Focusing on Problem Solving – make sense of problems and preserve to solving them.

Instruction Holt McDougal chapters 3-7 Real Numbers Instruction Holt McDougal extension Identifying and graphing irrational numbers Big Ideas activity pg 252 constructing a golden ratio Big Ideas activity pg 253 The Golden ratio and the human body

Methods of Assessment/Evaluation:

Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment

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Group labs Warm up lesson checks Formal and informal tests and quizzes

Resources/Including Online Resources:

Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Study Island Holt McDougal Course 3 Textbook Big Ideas textbook

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Topic Expressions and Equations - exponents & scientific notation

8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

8.EE.2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108

and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

8.EE.4. 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 measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

3 weeks for Unit

Essential Questions

How can you use exponents to write numbers? How can you multiply two powers that have the same base? How can you divide two powers that have the same base? How can you define zero and negative exponents? How can you use scientific numbers to express very large or very small numbers? What are the properties of integer exponents for multiplication and division? How do you multiply or divide numbers in scientific format?


1. Write numbers with exponents (8.EE.1)2. Convert numbers to and from exponential form (8.EE.1)3. Define power, exponent, and base (8.EE.1)4. Apply exponents in real life problems (8.EE.2)5. Multiply and divide two powers with the same base (8.EE.2)6. Distribute exponential powers correctly (8.EE.2)7. Write numbers in scientific notation and standard notation (8.EE.3)8. Understand and write numbers as powers of 10 (8.EE.3)9. Create and calculate scientific notations on calculator (8.EE.4)

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10. Do calculations with scientific notation (8.EE.4)11. Identify and use correct units of measure with scientific notation (8.EE.4)


L.6.2 Language Arts – exponents expressed in poetry

S.5.4 Science – uses in astronomy and micro-biology and chemistry

2.1 Health – nutrition measurements


Instruction Holt McDougal chapters 3-1 review positive and negative exponents & powers of 10 Instruction Holt McDougal chapters 3-2 properties of exponents Instruction Holt McDougal chapters 3-3 scientific notation Instruction Holt McDougal chapters 3-4 operations with scientific notation Instruction from Big Ideas, chapter 6-1 Finding Square Roots Instruction from Big Ideas chapter 6-3 approximating square roots Instruction Holt McDougal chapters 3-5 Squares and Square roots Instruction Holt McDougal chapters 3-6 Estimating Square roots Instruction Big Ideas, chapter 9-3 quotient of powers property Instruction Big Ideas, chapter 9-4 zero and negative exponents Instruction Big Ideas, chapter 9-5 Reading scientific notation Instruction Big Ideas, chapter 9-6 Writing Scientific Notation Practice On Core 1-2 scientific notation Practice on Core 1-3 operations of scientific notation Practice On Core 1-4 square roots and cube roots Lab – Prentice Hall - pg 61 Repeating decimals Lab – Holt McDougal chapters 3-4 multiplying scientific notation Problem solving Holt McDougal chapters 3-1 to 3-4 (real life examples)


Review from Big Ideas, chapter 6-3 Challenge worksheets accompanying the textbook Practice level C worksheets


Open notebook quiz Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island

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Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment Group labs Warm up lesson checks Formal and informal tests and quizzes


Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Study Island Holt McDougal Course 3 Textbook Big Ideas textbook

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Topic Understand and apply the Pythagorean Theorem

8.G.6. Explain a proof of the Pythagorean Theorem and its converse. 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. 8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate

system.

3 weeks for Unit

Essential Questions

How can you use the Pythagorean Theorem to solve real life problems? How can you find the distance between two points on a coordinate plane using Pythagorean

Theorem? How can you find the side lengths of a right triangle if you are given two other sides? How are the lengths of the sides of a right triangle related? What is the name of the longest side in a right triangle? If the equation a2 + b2 = c2 is true, then what type of triangle is formed?


1. Solve real life problems using the Pythagorean Theorem. (8.G.6)2. Identify a right triangle by using Pythagorean Theorem and the length of the 3 sides.(8.G.6)3. Determine if three side lengths form a right triangle (8.G.7)4. Find the measurement of missing side in right triangle. (8.G.7)5. Define theorem, legs, hypotenuse, Pythagorean Theorem, Pythagorean triple (8.G.6)6. Find the distance between two points on a coordinate plane. (8.G.8)


2.5 Sports - finding distance across the baseball diamond


Activity Big Ideas pg 236-237 Discovering the Pythagorean Theorem Instruction Big Ideas 6-2 The Pythagorean Theorem Instruction Big Ideas 6-5 Using the Pythagorean Theorem Activity Big Ideas pg 258-259 Using the Pythagorean Theorem Find perimeter of right triangles, trapezoids and parallelograms where hypotenuse side is

missing. Have students work in pairs to solve real life problems using Pythagorean Theorem. Using graph paper have the student create the 3 squares and then compare area s LAB Holt McDougal pg 131 Exploring Right Triangles Instruction Holt McDougal chapters 3-8 Pythagorean Theorem

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Holt McDougal chapters 3-8 problem solving Practice On Core 5-5 Using Pythagorean Theorem Practice On Core 5-6 Proving Pythagorean Theorem LAB Holt McDougal pg 136 Exploring the Converse of the Pythagorean Theorem Instruction Holt McDougal chapters 3-9 Applying the Pythagorean Theorem and its Converse Holt McDougal chapters 3-9 problem solving Lab Prentice Hall Pythagorean Proofs pg CC8


Holt McDougal pg 143 Real World Connections – reasoning abstractly and quantitatively problem solving

Big Ideas pg T263 taking the Math Deeper Lab Prentice Hall Using the Pythagorean Theorem with three-dimensional figures pg CC16


Open notebook quiz Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment Group labs Warm up lesson checks Formal and informal tests and quizzes


Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Study Island Mathematics grade 8 by Holt McDougal Course 3 Textbook Big Ideas textbook

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Topic Proportional Relationships and connections to lines and linear equations

8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

2 weeks for Unit

Essential Questions

How can you convert one measurement system to another? How do you describe the graph of the equation y = mx + b? How can students find the slope of a line and use the slope to understand and draw graphs? How can you use rates and ratios in real life problems? How can you determine whether figures are similar? How can you find the missing dimension in similar figures? How can you use slopes and intercepts to graph linear equations?


1. Use similar right triangles to find slope of a line (8.EE.6)2. Compare proportional relationships and functions.(8.EE.5)3. Interpret rates as lope of graph (8.EE.5) 4. Make a graph to model a situation. (8.EE.5)5. Find the missing measurements in similar figures (8.EE.6)6. Find the slope of a line and use the slope to understand and draw graphs (8.EE.6)


5.2 Science – study of density 5.2 Science – energy for light patterns


Instruction Holt McDougal chapters 2-3 Interpreting Graphs Lab Holt McDougal pg 58 graphing points on graphing calculator Instruction Holt McDougal chapters 4-1 ratios, rates and unit rates LAB Holt McDougal pg 168-169 Explore Similarity Instruction Holt McDougal chapters 4-3 Similar Figures Instruction Holt McDougal 8-1 Graphing Linear Equations

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LAB Holt McDougal pg 343 Explore Slope Instruction Holt McDougal chapters 8-2 Slope of Line Instruction Holt McDougal chapters 8-3 Using Slopes and Intercepts LAB Holt McDougal pg 355 Graph Equations in Slope Intercept Form on Graphing Calculator Instruction Holt McDougal chapters 8-4 Point Slope Form Instruction Big Ideas 1-5 Converting Units of Measure Activity Big Ideas pg 30 Converting Units of Measure Instruction Big Ideas 2-2 Slope of a Line Instruction Big Ideas 2-2b Triangles and Slope Instruction Big Ideas 3-3 Writing equations using two points Instruction Big Ideas 4-4b Comparing Rates Activity Big Ideas pg 173 Comparing Proportional Relationships Instruction Big Ideas 2-3 Graphing Linear Equations in Slope Intercept form Slope of a Line Instruction Big Ideas 2-4 Graphing Linear Equations in Standard Form Instruction Big Ideas 3-1 Writing Equations in Slope Intercept form Instruction Big Ideas 3-2 Writing Equations using a Slope and a point Instruction Big Ideas 3-4 Solving Real Life Problems Practice On Core 2-3 Rate of Change Practice On Core 2-4 Slope Intercept form Practice On Core 5-4 similar Triangles and Slope


Review Holt McDougal chapters 1-5 solving equations with rational numbers Review Holt McDougal chapter 4-2 Solving Problems Review ordered pairs and graphing on coordinate plane Holt McDougal chapters 2-1 and 2-2 Holt McDougal pg 65 Focusing on Problem Solving – make sense of problems and preserve to

solving them. Holt McDougal pg 361 Focusing on Problem Solving – make sense of problems and preserve to

solving them.


Open notebook quiz Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards

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Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment Group labs Warm up lesson checks Formal and informal tests and quizzes Project Student Reflective Focus Writing


Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Study Island Holt McDougal Course 3 Textbook Big Ideas textbook by Holt McDougal

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Topic Solving Linear Equations

8.EE.7. Solve linear equations in one variable.

o Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. 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).

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

3 weeks for Unit

Essential Questions

How can you use inductive reason to discover rules in mathematics? How can you test rules you discover inductively? How can you solve a multi-step equation? How can you check the reasonableness of a solution? How can you solve an equation that has variables on both sides? How can you use a formula for one measurement to write a formula for a different

measurement? How can you write, solve and graph one-step linear inequalities? How can you write, solve and graph multi-step linear inequalities? How can you use and inequality to describe a real-life statement? How can you use addition or subtraction to solve an inequality? How can you use multiplication and division to solve an inequality? How can you use an inequality to describe the area and perimeter of a composite figure?


1. Use the Properties of Equality to solve one-step equations. (8.EE.7)2. Solve multi-step equations using the inverse operation. (8.EE.7)3. Solve equations using the distributive property. (8.EE.7)4. Solve multi-step equation by combining like terms. (8.EE.7)5. Solve equations with variables on both sides using properties of equalities. (8.EE.7)6. Solve equations that have no solution, one solution or infinitely many solutions. (8.EE.7)7. Rewrite common geometric formulas. (8.EE.7)8. Translate inequalities from words to symbols and check to see if a value is a solution of the

inequality. (8.EE.7)

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9. Solve inequalities and equations using addition and subtraction properties of inequality. (8.EE.7)

10. Solve inequalities and equations using multiplication and division properties of inequality. (8.EE.7)

11. Solve and graph multi-step inequalities. (8.EE.7)


2.1 Health Nutrition 5.2 Physical Science


LAB Holt McDougal pg 30 Model Two Step Equations Instruction Holt McDougal chapters 1-6 Solving two-step Equations Instruction Holt McDougal chapters 7-2 Solving Multi-step Equations LAB Holt McDougal pg 308 Model Equations with variables on Both Sides Holt McDougal Extension pg 314 Possible Solutions of One-variable Equations Instruction Holt McDougal chapter 7-3 solving equations with variables on both sides Instruction Big Ideas 1-1 Solving Simple equations Activity Big Ideas pg 2-3 Sum of the angles of a triangle Instruction Big Ideas 1-2 Solving Multi-step equations Activity Big Ideas pg 10-11 Solving the angles of a triangle Instruction Big Ideas 1-3 Solving Equations with variables on both sides Activity Big Ideas pg 16-17 Perimeter and Area equations Instruction Big Ideas 1-3b Solutions of linear equations Instruction Big Ideas 1-4 Rewriting equations and Formulas Activity Big Ideas pg 24-25 Using Perimeter and area formulas Instruction Big Ideas 8-1 Writing and graphing Inequalities Activity Big Ideas pg 312-313 Writing and graphing inequalities Instruction Big Ideas 8-2 Solving Inequalities Using Addition or Subtraction Activity Big Ideas pg 318-319 Quarterback Passing efficiency Instruction Big Ideas 8-3 Solving Inequalities Using Multiplication or Division Activity Big Ideas pg 326-327 Using a table to solve and inequality Instruction Big Ideas 8-4 Solving Multi-step inequalities Activity Big Ideas pg 334-335 Areas and perimeters of Composite figures Practice On Core 3-1 Solving equations Practice On Core 3-2 Analyzing Solutions


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Review Simplifying Algebraic Equations Holt McDougal 7-1 Holt McDougal pg 317 Focusing on Problem Solving – make sense of problems and preserve to

solving them. Big Ideas pg T15 Taking Math Deeper – problem solving algebraically in sports Big Ideas pg T29 Taking Math Deeper – circles and percents




Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Holt McDougal Course 3 Textbook Big Ideas textbook by Holt McDougal

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Topic Understand congruence and similarity using physical models, transparencies, or geometry software

8.G.1. Verify experimentally the properties of rotations, reflections, and translations: o a. Lines are taken to lines, and line segments to line segments of the same length.o b. Angles are taken to angles of the same measure.o c. Parallel lines are taken to parallel lines.

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, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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

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 two-dimensional figures, describe a sequence that exhibits the similarity between them.

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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

3 weeks for Unit

Essential Questions

What are transformations? How do you identify rotation, reflection and translation of 2 dimensional figures? How can you classify two angles as complementary or supplementary? How do you calculate the sum of interior angles in a polygon? How do you calculate the exterior angles of a triangle and other polygons? How can you determine congruence by a sequence of rotations, reflections, or translations? How can you identify similar figures on a coordinate plane using dilations, rotations, reflections

or translations? How do you classify triangles by their angles? How can you find a formula for the sum of the angle measures in any polygon? Which properties of triangles make them special among all other types of polygons? How can you use similar triangles to find a missing measurement? How can you use the properties of parallel lines to solve real life problems? How do parallel lines and a transversal create corresponding angles?


1. Identify the 4 different types of transformation. (8.G.3)2. Identify complementary or supplementary angles. (8.G.1)

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3. Differentiate between interior and exterior angles. (8.G.5)4. Understand and draw transformation on a coordinate plane (8.G.1)5. Understand that two dimensional figure is congruent to another (8.G.4)6. Identify and describe dilation, translation, rotation and reflection and their effects on two

dimensional figures on coordinate plane. (8.G.3)7. Determine congruency between transformed figures. (8.G.2)8. Understand and calculate sum of interior angles in a triangle.(8.G.5)9. Understand and calculate exterior angles of triangles (8.G.5)10. Understand relationship of angles formed by parallel lines and a transversal. (8.G.5)


9.3 Art – design 9.4 Building – design and construction 5.2 Physics – angle reflections


Instruction holt McDougal chapters 4-4 Dilations LAB Holt McDougal pg 174 Explore Dilations LAB Holt McDougal pg 201 Bisect Figures Instruction Holt McDougal chapters 5-1 Angle Relationships Instruction Holt McDougal chapters 5-2 Parallel and Perpendicular Lines Instruction Holt McDougal chapters 5-3 Triangles LAB Holt McDougal pg 212 Exterior Angles of Polygons Instruction Holt McDougal chapters 5-4 Coordinate Geometry LAB Holt McDougal pg 220 Explore Congruence Instruction Holt McDougal chapters 5-5 Congruence Instruction Holt McDougal chapters 5-6 Transformations Instruction Holt McDougal chapters 5-7 Similarity and Congruence Transformations LAB Holt McDougal pg 237 Combine Transformations Instruction Holt McDougal chapters 5-8 Identifying Combined Transformations Instruction Big Ideas Topic 1 pg 398-401 Transformation on coordinate plane Instruction Big Ideas 5-1 Classifying Angles Activity Big Ideas pg 184 Identifying complementary and supplementary angles Instruction Big Ideas 5-2 Angles and Sides of Triangles Activity Big Ideas pg 190 Exploring the angles of a Triangle Instruction Big Ideas 5-3 Angles of Polygons Activity Big Ideas pg 196 The sum of the angle measure of a polygon Instruction Big Ideas 5-4 Using Similar Triangles Activity Big Ideas pg 206 Angles of Similar triangles Instruction Big Ideas 5-5 Parallel Lines and Transversals Activity Big Ideas pg 212 A property of Parallel lines and Creating Parallel lines

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Practice On Core 5-1Parallel lines cut by transversals Practice On Core 5-2 Triangle angle theorem Practice On Core 5-3 Similar triangles





Big Ideas pg T189 Taking Math Deeper – vertical angles Activity Big Ideas pg T195 Taking Math Deeper – exploring angles Big Ideas pg T203 Taking Math Deeper – comparison of linear and non-linear functions Big Ideas pg T219 Taking Math Deeper – use reflective property




Online Textbook- my.hrw.com Userid and password to be determined

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Teacher webpage Holt McDougal Course 3 Textbook Big Ideas textbook by Holt McDougal

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Topic Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

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

2 weeks for Unit

Essential Questions

How can students find volume of cylinders, cones and spheres using given formulas? How can students apply finding volume to real life problems?


1. Find Volume of cylinders.(8.G.9)2. Find Volume of cones.(8.G.9)3. Find Volume of spheres.(8.G.9)4. Find volume of compound figures.(8.G.9)5. Apply formulas for finding volume to real life problems.(8.G.9)


5.2 Physical Science 5.2 Earth Systems Science


LAB Holt McDougal pg 266 Find Volume of Prisms and Cylinders Instruction Holt McDougal chapters 6-2 Volume of Prisms and Cylinders LAB Holt McDougal pg 274 Find Volume of Pyramids and Cones Practice On Core 5-7 Instruction Holt McDougal chapters 6-3 Volume of Pyramids and Cones Instruction Holt McDougal chapters 6-4 Spheres Instruction Big Ideas Topic 2 Volume pg 402


Review of Circles Holt McDougal 6-1 circles Holt McDougal pg 273 Focusing on Problem Solving – make sense of problems and preserve to

solving them. Holt McDougal pg 287 Real World Connections – reasoning abstractly and quantitatively

problem solving

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Topic Analyze and solve pairs of simultaneous linear equations

8.EE.8. Analyze and solve pairs of simultaneous linear equations.

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

o Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

o Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

2 weeks for Unit

Essential Questions

How can you recognize a linear equation? How can you draw a graph of a linear equation? How can you solve a system of linear equations? Can a system of linear equations have no solution? Can a system of linear equations have many solutions? How can you use a system of linear equations to solve an equation that has variable on both

sides? How can you use a system of linear equations to model and solve a real-life problem?


1. Graph Linear equations using a table of values. (8.EE.8.)2. Solving systems of linear equations using three different techniques. (8.EE.8.)3. Identify the 3 types of solutions for systems of linear equations (no solution, one solution, and

infinitely many solutions). (8.EE.8.)4. Solve equations with variables on both sides by using two techniques.(graphing or solving

algebraically) (8.EE.8.)


2.5 Sports 5.2 Physical Science


Instruction Holt McDougal chapters 7-4 Systems of Equations

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Instruction Holt McDougal chapters 8-6 Solving Systems of Linear Equations by graphing Instruction Big Ideas 2-1 Graphing Linear equations Activity Big Ideas pg 48 Graphing a linear equation Instruction Big Ideas 2-5 Systems of Linear equations Activity Big Ideas pg 76 Writing a System of Linear Equations Instruction Big Ideas 2-6 Special Systems of Linear equations Activity Big Ideas pg 82-83 Writing a System of Linear Equations using a table Instruction Big Ideas 2-7 Solving equations by graphing Activity Big Ideas pg 88-89 Solving a system of linear equations using a graphing calculator Instruction Big Ideas 3-5 Writing Systems of Linear equations




Big Ideas pg T81 Taking Math Deeper – using 3 methods to solve systems of linear equations Big Ideas pg T87 Taking Math Deeper – comparisons of systems of linear equations



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Topic Investigate patterns of association in bivariate data.

8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.SP.3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

2 weeks for Unit

Essential Questions

Determine and describe how changes in data values impact measures of central tendency. How can you use the measures of central tendency to distribute an amount evenly among a

group of people? What is the impact of removing an outlier on the measures of central tendency? How can you use a box-and-whisker plot to describe a population? How can you use data to predict an event?


1. Construct, read, and interpret a box-and-whisker plot. (8.SP.1)2. Write an equation of the line of best fit. (8.SP.2)3. Draw line of best fit (8.SP.2)4. Understand the purpose of the line of best fit and the resulting equation. (8.SP.3)


5.3 Science - Biology – animal studies


Instruction Holt McDougal chapters 9-1 Scatter Plots Instruction Holt McDougal chapters 9-2 Linear Best Fit Models

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LAB Holt McDougal pg 394 Create a Scatter Plot on graphing calculator Instruction Big Ideas 7-1 Measures of Central Tendency Big Ideas Activity pg 274-275 Exploring Mean, Median, Mode and Line Plots Instruction Big Ideas 7-2 Box and Whiskers Plots (mean, median, mode) Big Ideas Activity pg 280 Drawing a Box and Whisker Plot Instruction Big Ideas 7-3 Scatter Plots and Lines of Best Fit Big Ideas Activity pg 288-289 Representing Data by a Linear Equation Practice On Core 6-1 Scatter plots and Associations Practice On Core 6-2 scatter plots and predictions Practice On Core 6-3 Two way tables Instruction Holt McDougal Extension Patterns in Two Way Tables Instruction Big Ideas 7-3b Two Way Tables Instruction and Activity Prentice Hall Pearson pg CC18 Exploring Bivariate Data



Big Ideas pg T279 Taking Math Deeper Big Ideas pg T285 Taking Math Deeper – box-and-whisker benefits and limitations Big Ideas pg T295 Taking Math Deeper – Proportions of a Man


Open notebook quiz Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment Group labs Warm up lesson checks

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Formal and informal tests and quizzes


Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Holt McDougal Course 3 Textbook Big Ideas textbook by Holt McDougal Prentice Hall Pearson Course 3 Mathematics textbook

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Topic Define, evaluate, and compare functions.

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.1

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

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. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line

3 weeks for Unit

Essential Questions

How can you find the domain and range of a function? How can you decide whether the domain of a function is discrete or continuous? How can you use a linear function to describe a linear pattern? ????? How can you recognize when a pattern in real life is linear or nonlinear? ?????


1. Develop an understanding of domain and range by exploring similar problems. (8.F.1)2. Identify domain and range from a graph or table of values (8.F.2)3. Write an equation in function form. (8.F.3)4. Develop an understanding of discrete and continuous domains. (8.F.1)5. Graph functions and determine if the domain is discrete or continuous. (8.F.1)6. Develop an understanding of linear patterns in tables and graphs to write linear equations.

(8.F.3)7. Describe four ways to represent a function. (8.F.3)8. Compare and identify tables and graphs of linear and nonlinear functions. (8.F.2)9. Compare and identify proportional relationships and functions (8.F.3)


Biology – spiders rates of decent Psychics – rates of change History – population studies Astronomy

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Instruction Holt McDougal chapters 2-4 Functions Instruction Holt McDougal chapters 2-5 Equations Tables and graphs Instruction Big Ideas 4-1 Domain and Range of a Function Activity Big Ideas pg 148-149 The Domain and Range of a function Practice On Core 2-1 Functions tables and graphs Practice On Core 2-5 writing equations to describe a function Instruction Big Ideas 4-2 Discrete and Continuous Domains Activity Big Ideas pg 154-155 Discrete or Continuous Domains Instruction Big Ideas 4-3 Linear Function Patterns Activity Big Ideas pg 162-163 Finding Linear Patterns Instruction Big Ideas 4-4 Comparing Linear and Nonlinear Functions Activity Big Ideas pg 168-169 Finding Patterns for Similar Figures Instruction Big Ideas 4-4b Comparing Rates Instruction Holt McDougal chapters 9-3 Linear Functions Instruction Holt McDougal chapters 9-4 Comparing Multiple Representations





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Topic Use functions to model relationships between quantities.

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 from a table 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.

8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

3 weeks for Unit

Essential Questions

How can you write an equation of line when you are given the slope and the y-intercept of the line?

How can you write an equation of a line when you are given two points on the line? How can you use a linear equation in two variables to model and solve a real-life problem? How can you use a linear function to describe a linear pattern? How can you recognize when a pattern in real life is linear or nonlinear? How can you identify and write a linear function?


1. Write, solve and graph two step linear equations. (8.F.4)2. Write an equation in slope-intercept form when given the slope and the y intercept. (8.F.4)3. Write an equation when given two points on the line. (8.F.4)4. Calculate the slope from two points (not graphed). (8.F.4)5. Solve real life problems using linear equations. (8.F.4)6. Write a linear equation for a graphed function. (8.F.5)7. Write linear functions by recognizing patters in graphical and tabular information. (8.F.6)


Physics – rate of falling Chemistry – tracking chemical changes


Instruction Big Ideas 3-2 Writing equations using a slope and point (repeat from (8.EE.6) Activity Big Ideas pg 112 Writing equations of lines. Instruction Big Ideas 3-3 Writing equations using two points

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Activity Big Ideas pg 118-119 Writing equations of lines Instruction Big Ideas 3-4 Solving Real Life Problems (repeat from (8.EE.6) Activity Big Ideas pg 126-127 Writing a Story / drawing graphs Instruction Big Ideas 4-3 Linear Function Patterns (repeat from (8.F.3) Practice On Core 2-6 comparing functions Practice On Core 2-7 analyzing graphs Activity Big Ideas pg 162-163 Find Linear Patters Instruction Big Ideas 4-4 Comparing Linear and Nonlinear Functions (repeat from (8.F.3) Instruction Holt McDougal chapters 8-5 Direct Variation (8.f.5) Instruction Holt McDougal chapters 9-3 Linear Functions


Instruction Holt McDougal chapters 2-5 Equations, tables and graphs (review from 8.F.1) Big Ideas pg T117 Taking Math Deeper tracking biology information Big Ideas pg T123 Taking Math Deeper real life problems Big Ideas pg T131 Taking Math Deeper business problems




Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage

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Holt McDougal Course 3 Textbook Big Ideas textbook by Holt McDougal

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algebra 1 concepts – 8 th grade math

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