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 21 st 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 Kennedy
Date Submitted : Summer 2012
1
Algebra 1 Concepts – 8th grade math
Outline
Topic Number System
2 weeks
8 NS 1 - rational numbers, irrational numbers, real numbers
8 NS 2 - identifying and graphing irrational numbers
Topic Expressions and Equations
8 EE 1
8 EE 2
8 EE 3
8 EE 4
3 weeks
- exponents
- squares roots and cube roots
- scientific notation
- reading and calculating with scientific notation
Topic Understand and apply the Pythagorean Theorem
3 weeks
8G6 \
8 G 7 Pythagorean Theorem
8G8 /
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 line
8 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 - transformations
8 G2 - congruence
8 G 3 - dilation
8 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
2
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 plots
8 SP 2
8 SP 3 - line of best fit
8 SP 4 - patterns , 2 way tables
8 SP 5
Topic Define, evaluate, and compare functions.
4 weeks
8.F.1 - linear functions
8.F.2. compare functions
8.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 change
8.F.5. functional relationships
3
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
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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 :
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Write a rational number as the ratio of two integers. (8.NS.1)
Identify irrational numbers (8.NS.1)
Approximate the decimal value of an irrational number (8.NS.2)
Understand and explain the relationship of rational, irrational, real, integers, and natural
numbers (8.NS.1)
Locate rational, irrational, real, integers and natural numbers on a number line. (8.NS.2)
Create the decimal expansion of a rational number (8.NS.1)
Define square root, cube root, perfect square, radical sign, radicand, irrational number, real
numbers (8.NS.1)
Review rules for computation of rational number (8.NS.2)
Understand and apply the properties of addition, subtraction, division, and multiplication of
square roots (8.NS.1)
Interdisciplinary Standards
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L.6.1 Language arts – learn that the prefix “it”- means not and other examples like dis-, il- , im-,
in-, and un2.5 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 21st Century Technologies
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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
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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:
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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
5
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Verbal Assessment
Group labs
Warm up lesson checks
Formal and informal tests and quizzes
Resources/Including Online Resources:
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Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Study Island
Holt McDougal Course 3 Textbook
Big Ideas textbook
6
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
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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?
Upon Completion of the unit students will be able to :
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8.
9.
Write numbers with exponents (8.EE.1)
Convert numbers to and from exponential form (8.EE.1)
Define power, exponent, and base (8.EE.1)
Apply exponents in real life problems (8.EE.2)
Multiply and divide two powers with the same base (8.EE.2)
Distribute exponential powers correctly (8.EE.2)
Write numbers in scientific notation and standard notation (8.EE.3)
Understand and write numbers as powers of 10 (8.EE.3)
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)
Interdisciplinary Standards
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
Activities – including 21st Century Technologies
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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)
Enrichment Activities
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Review from Big Ideas, chapter 6-3
Challenge worksheets accompanying the textbook
Practice level C worksheets
Methods of Assessment/Evaluation:
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Open notebook quiz
Ticket out the door
Interactive Smart Board quest
Open Ended Questions
Smartboard Lessons (clickers)
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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
Resources/Including Online Resources:
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Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Study Island
Holt McDougal Course 3 Textbook
Big Ideas textbook
9
Topic Understand and apply the Pythagorean Theorem
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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
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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?
Upon Completion of the unit students will be able to :
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6.
Solve real life problems using the Pythagorean Theorem. (8.G.6)
Identify a right triangle by using Pythagorean Theorem and the length of the 3 sides.(8.G.6)
Determine if three side lengths form a right triangle (8.G.7)
Find the measurement of missing side in right triangle. (8.G.7)
Define theorem, legs, hypotenuse, Pythagorean Theorem, Pythagorean triple (8.G.6)
Find the distance between two points on a coordinate plane. (8.G.8)
Interdisciplinary Standards
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2.5 Sports - finding distance across the baseball diamond
Activities – including 21st Century Technologies
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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
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Instruction Holt McDougal chapters 3-8 Pythagorean Theorem
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
Enrichment Activities
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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
Methods of Assessment/Evaluation:
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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
Resources/Including Online Resources:
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Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Study Island
11
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Mathematics grade 8 by Holt McDougal Course 3 Textbook
Big Ideas textbook
12
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
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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?
Upon Completion of the unit students will be able to :
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3.
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6.
Use similar right triangles to find slope of a line (8.EE.6)
Compare proportional relationships and functions.(8.EE.5)
Interpret rates as lope of graph (8.EE.5)
Make a graph to model a situation. (8.EE.5)
Find the missing measurements in similar figures (8.EE.6)
Find the slope of a line and use the slope to understand and draw graphs (8.EE.6)
Interdisciplinary Standards
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5.2 Science – study of density
5.2 Science – energy for light patterns
Activities – including 21st Century Technologies
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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
Enrichment Activities
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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.
Methods of Assessment/Evaluation:
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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
14
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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
Project
Student Reflective Focus Writing
Resources/Including Online Resources:
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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
15
Topic Solving Linear Equations
8.EE.7. Solve linear equations in one variable.
o
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).
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
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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?
Upon Completion of the unit students will be able to :
1.
2.
3.
4.
5.
6.
7.
8.
Use the Properties of Equality to solve one-step equations. (8.EE.7)
Solve multi-step equations using the inverse operation. (8.EE.7)
Solve equations using the distributive property. (8.EE.7)
Solve multi-step equation by combining like terms. (8.EE.7)
Solve equations with variables on both sides using properties of equalities. (8.EE.7)
Solve equations that have no solution, one solution or infinitely many solutions. (8.EE.7)
Rewrite common geometric formulas. (8.EE.7)
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)
Interdisciplinary Standards
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2.1 Health Nutrition
5.2 Physical Science
Activities – including 21st Century Technologies
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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
Enrichment Activities
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Holt McDougal pg 37 Real World Connections – reasoning abstractly and quantitatively problem
solving
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
Methods of Assessment/Evaluation:
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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
Resources/Including Online Resources:




Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Holt McDougal Course 3 Textbook
Big Ideas textbook by Holt McDougal
18
Topic Understand congruence and similarity using physical models,
transparencies, or geometry software
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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 twodimensional 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 angleangle 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
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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?
Upon Completion of the unit students will be able to :
1. Identify the 4 different types of transformation. (8.G.3)
2. Identify complementary or supplementary angles. (8.G.1)
19
3.
4.
5.
6.
7.
8.
9.
10.
Differentiate between interior and exterior angles. (8.G.5)
Understand and draw transformation on a coordinate plane (8.G.1)
Understand that two dimensional figure is congruent to another (8.G.4)
Identify and describe dilation, translation, rotation and reflection and their effects on two
dimensional figures on coordinate plane. (8.G.3)
Determine congruency between transformed figures. (8.G.2)
Understand and calculate sum of interior angles in a triangle.(8.G.5)
Understand and calculate exterior angles of triangles (8.G.5)
Understand relationship of angles formed by parallel lines and a transversal. (8.G.5)
Interdisciplinary Standards
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9.3 Art – design
9.4 Building – design and construction
5.2 Physics – angle reflections
Activities – including 21st Century Technologies
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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
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Activity Big Ideas pg 212 A property of Parallel lines and Creating Parallel lines
Practice On Core 5-1Parallel lines cut by transversals
Practice On Core 5-2 Triangle angle theorem
Practice On Core 5-3 Similar triangles
Enrichment Activities
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Holt McDougal pg 181 Real World Connections – reasoning abstractly and quantitatively
problem solving
Holt McDougal pg 219 Focusing on Problem Solving – make sense of problems and preserve to
solving them.
Holt McDougal pg 245 Real World Connections – reasoning abstractly and quantitatively
problem solving
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
Methods of Assessment/Evaluation:
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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
Resources/Including Online Resources:
21
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Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Holt McDougal Course 3 Textbook
Big Ideas textbook by Holt McDougal
22
Topic Solve real-world and mathematical problems involving volume of
cylinders, cones, and spheres.
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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
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How can students find volume of cylinders, cones and spheres using given formulas?
How can students apply finding volume to real life problems?
Upon Completion of the unit students will be able to :
1.
2.
3.
4.
5.
Find Volume of cylinders.(8.G.9)
Find Volume of cones.(8.G.9)
Find Volume of spheres.(8.G.9)
Find volume of compound figures.(8.G.9)
Apply formulas for finding volume to real life problems.(8.G.9)
Interdisciplinary Standards
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5.2 Physical Science
5.2 Earth Systems Science
Activities – including 21st Century Technologies
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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
Enrichment Activities
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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
23
Methods of Assessment/Evaluation:
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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
Resources/Including Online Resources:

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Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Holt McDougal Course 3 Textbook
Big Ideas textbook by Holt McDougal
24
Topic Analyze and solve pairs of simultaneous linear equations
8.EE.8. Analyze and solve pairs of simultaneous linear equations.
o
o
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.
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.
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
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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?
Upon Completion of the unit students will be able to :
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.)
Interdisciplinary Standards
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2.5 Sports
5.2 Physical Science
Activities – including 21st Century Technologies
25
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Instruction Holt McDougal chapters 7-4 Systems of Equations
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
Enrichment Activities
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Holt McDougal pg 323 Real World Connections – reasoning abstractly and quantitatively
problem solving
Holt McDougal pg 373 Real World Connections – reasoning abstractly and quantitatively
problem solving
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
Methods of Assessment/Evaluation:
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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
26
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Formal and informal tests and quizzes
Resources/Including Online Resources:
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Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
Holt McDougal Course 3 Textbook
Big Ideas textbook by Holt McDougal
27
Topic Investigate patterns of association in bivariate data.
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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
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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?
Upon Completion of the unit students will be able to :
1.
2.
3.
4.
Construct, read, and interpret a box-and-whisker plot. (8.SP.1)
Write an equation of the line of best fit. (8.SP.2)
Draw line of best fit (8.SP.2)
Understand the purpose of the line of best fit and the resulting equation. (8.SP.3)
Interdisciplinary Standards
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5.3 Science - Biology – animal studies
Activities – including 21st Century Technologies
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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
Enrichment Activities
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Holt McDougal pg 399 Focusing on Problem Solving – make sense of problems and preserve to
solving them.
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
Methods of Assessment/Evaluation:
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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
29
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Warm up lesson checks
Formal and informal tests and quizzes
Resources/Including Online Resources:
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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
30
Topic Define, evaluate, and compare functions.
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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
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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? ?????
Upon Completion of the unit students will be able to :
1.
2.
3.
4.
5.
6.
Develop an understanding of domain and range by exploring similar problems. (8.F.1)
Identify domain and range from a graph or table of values (8.F.2)
Write an equation in function form. (8.F.3)
Develop an understanding of discrete and continuous domains. (8.F.1)
Graph functions and determine if the domain is discrete or continuous. (8.F.1)
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)
Interdisciplinary Standards
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Biology – spiders rates of decent
Psychics – rates of change
History – population studies
Astronomy
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Activities – including 21st Century Technologies
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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
Enrichment Activities
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Holt McDougal pg 409 Real World Connections – reasoning abstractly and quantitatively
problem solving
Methods of Assessment/Evaluation:
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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
32
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
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
Holt McDougal Course 3 Textbook
Big Ideas textbook by Holt McDougal
33
Topic Use functions to model relationships between quantities.
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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
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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?
Upon Completion of the unit students will be able to :
1.
2.
3.
4.
5.
6.
7.
Write, solve and graph two step linear equations. (8.F.4)
Write an equation in slope-intercept form when given the slope and the y intercept. (8.F.4)
Write an equation when given two points on the line. (8.F.4)
Calculate the slope from two points (not graphed). (8.F.4)
Solve real life problems using linear equations. (8.F.4)
Write a linear equation for a graphed function. (8.F.5)
Write linear functions by recognizing patters in graphical and tabular information. (8.F.6)
Interdisciplinary Standards
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Physics – rate of falling
Chemistry – tracking chemical changes
Activities – including 21st Century Technologies
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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
Activity Big Ideas pg 118-119 Writing equations of lines
34
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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
Enrichment Activities
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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
Methods of Assessment/Evaluation:
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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
Resources/Including Online Resources:


Online Textbook- my.hrw.com Userid and password to be determined
Teacher webpage
35
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
Holt McDougal Course 3 Textbook
Big Ideas textbook by Holt McDougal
36