Download Mathematics Grade 8 - Pompton Lakes School District

POMPTON LAKES SCHOOL DISTRICT
Mathematics – Grade 8
COURSE OF STUDY
APRIL 2013
Submitted by
The Mathematics Department
Dr. Paul Amoroso, Superintendent
Michael Yuhas, Department Chair
BOARD MEMBERS
Mr. Jose A. Arroyo, Mrs. Traci Cioppa, Mr. Robert Cruz, Mr. Shawn Dougherty,
Mr. Garry Luciani, Mr. Carl Padula, Mr. Tom Salus, Mrs. Nancy Schwartz,
Mrs. Stephanie Shaw, Mr. Timothy Troast, Jr.
Unit Overview
Content Area:
Mathematics
Unit Title:
Unit 1- Geometry
Target Course/Grade Level: Mathematics-Grade 8
Unit Summary: Students will be able to use models to show their understanding of congruent and
similar one and two-dimensional figures.
Unit Rationale: Parallel and intersecting lines is a key concept that is also covered in Algebra. The
properties of triangles are the focus of geometry and trigonometry, as in the classification and
measurement of angles. The area of polygons and circles, as well as the transformation of these shapes
can be used in house design and landscaping.
Student Learning Objectives
1.) Utilize the properties of rotation, reflection, and translation to model and relate pre-images of
lines, line segments, and angles to their resultant image through physical representations and/or
Geometry software.
2.) Apply an effective sequence of rotations, reflections, and transitions to prove that two
dimensional figures are congruent.
3.) Use the coordinate plane to locate pre-images of two-dimensional figures and determine the
coordinates of a resultant image after applying dilations, rotations, reflections, and translations.
4.) Recognize dilation as a reduction or an enlargement of a figure and determine the scale factor.
5.) Apply an effective sequence of transformations to determine similar figures in which
corresponding angles are congruent and corresponding sides are proportional. Write similarity
statements based on such transformations.
6.) Justify facts about angles created when parallel lines are cut by a transversal.
7.) Justify facts about the exterior angles of a triangle, the sum of the measures of the interior angles
of a triangle and the angle-angle relationship used to identify similar triangles.
Selected Opportunities for Connection to Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
SLOs #2 and #5 Use a correct sequence of transformations to verify two geometric figures are similar.
3. Construct viable arguments and critique the reasoning of others.
SLOs #6 and #7 Write formal arguments to justify facts and communicate them to others.
4. Model with mathematics.
All of the SLOs in this unit will require students to use 2-D models to illustrate the relationships
geometric figures.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
SLO#3 Determine the coordinates of an image using the coordinates of its pre-image after a
Transformation.
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Code #
8.G.1
New Jersey Student Learning Standards
Verify experimentally the properties of rotations, reflections, and translations.
a) Lines are taken to lines, and line segments to line segments of the same length.
b) Angles are taken to angles of the same measure.
c) Parallel lines are taken to parallel
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.
Unit Essential Questions
Unit Enduring Understandings
 How can you use models of one and
 Congruent figures can be formed by a series of
two-dimensional figures to show
transformations.
congruent figures?
 Similar figures can be formed by a series of
 How can you use models of one and
transformations.
two-dimensional figures to show
similar figures?
 Understand angle relationships in one and two
dimensional figures.
 How are quadrilaterals used in design?

How can polygons help to find the
area of an irregular figure?
Unit Learning Targets
Students will …
1.)
2.)
3.)
4.)
Transform figures on a coordinate plane.
Use their understanding of angle relationships to find unknown angles.
Describe a sequence of transformations that will result in congruent figures.
Describe a sequence of transformations and dilations that will result in similar figures.
Evidence of Learning
Summative Assessment:
The students will be assessed with a summative unit assessment which will be modeled after the PARCC
assessment model. This model assessment will include multiple choice, constructed response and a
performance task.
Formative Assessments
 Tests and quizzes
 Discussions
 Individual practice



Explanation of examples
Daily homework assignments
Notes
Lesson Plans
Lesson
Lesson #1:
Translations/Quiz #1
Timeframe
2 days
Lesson #2:
Rotations/Quiz #2
4days
Lesson #3:
Reflections/Quiz #3
4 days
Lesson #4:
Dilations
3 days
Lesson #5:
Symmetry/Quiz #4
6 days
Lesson #6:
Congruence and Similarity/Quiz #5
7 days
Lesson #7:
Special Pairs of Angles/Quiz #6
8 days
Review and Unit Assessment
3 days
Teacher Notes:
7 days allocated for formative/summative assessments
Curriculum Development Resources:
http://www.khanacademy.org
Pearson Connected Math 2
 Symmetry and Transformations.
Glencoe Pre-Algebra 2006
Smartboard Smart Exchange
Senteo response system
Unit Overview
Content Area:
Mathematics
Unit Title:
Unit 2 – The Number System
Target Course/Grade Level: Mathematics-Grade 8
Unit Summary: In this unit, students will explore reasoning with real numbers and know that there are
numbers that are not rational, and approximate them by using rational numbers.
Unit Rationale: Understand informally that every number has a decimal expansion; the rational numbers
are those with decimal expansions that terminate in zeros or eventually repeat. Know that the other
numbers are called irrational.
Student Learning Objectives
1.) Compare rational and irrational numbers to demonstrate that the decimal expansion of irrational
numbers do not repeat; show that every rational number has a decimal expansion which eventually
repeats and covert such decimals into rational numbers.
2.) Use rational numbers to approximate and locate irrational numbers on a number line and estimate
the value of expressions involving irrational numbers.
3.) Apply the properties of integer exponents to simplify and write equivalent numerical expressions.
4.) Use scientific notation to estimate and express the values of very large or very small numbers and
compare their values (how many times larger/smaller is one than the other).
5.) Perform operations using numbers expressed in scientific notation, including problems where both
decimals and scientific notation are used (interpret scientific notation generated when technology
has been used for calculations).
6.) In real-world problem solving situations choose units of appropriate size for measurement of very
small and very large quantities.
Selected Opportunities for Connection to Mathematical Practices
1. Make sense of problems and persevere in solving them.
SLO #6 Use problems that describe complex real-world problems.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
SLO #6 Determine appropriate sized units for a given context.
7. Look for and make use of structure.
SLO#3 Examine the form of expressions involving integer exponents and apply the correct property
of exponents to create equivalent expressions.
8. Look for and express regularity in repeated reasoning.
SLO#1 Explain orally or in written language the difference between a rational number and an irrational
Number.
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Code #
New Jersey Student Learning Standards
8.NS.1
Know that numbers that are not rational are called irrational. Understand informally that
every number has a decimal expansion; for rational numbers show that the decimal
expansion repeats eventually, and convert a decimal expansion which repeats eventually
into a rational number.
8.NS.2
Use rational approximations of irrational numbers to compare the size of irrational
numbers, locate them approximately on a number line diagram, and estimate the value of
expressions. For example, by truncating the decimal expansion of the square root of 2,
show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain
how to continue on to get better approximations.
8.EE.1
Know and apply the properties of integer exponents to generate equivalent numerical
expressions.
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 radicals can also be solutions
and that √2 is irrational.
8.EE.3
Use numbers expressed in the form of a single digit times an integer power of 10 estimate
very large or very small quantities, and to express how many times as much one is than the
8
other. For example, estimate the population of the United States as 3 × 10 and the
9
population of the world as7 × 10 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 decimals decimal and scientific notation are used. Use scientific notation and
choose units of appropriate size for measurements of very large or very small quantities.
Interpret scientific notation that has been generated by technology.
Unit Essential Questions
Unit Enduring Understandings
 What are the number types that make up the
 The Real Number system includes rational and
Real number systems?
irrational numbers, integers, whole numbers and
natural numbers.
 How can I estimate the square root of a number?
 Estimating and ordering rational and irrational
 How can I find the length of something without
numbers.
directly measuring it?
 Estimate the values of square roots of whole
 How will scientific notation help when writing
numbers.
numbers and equations?
 Locate irrational numbers on a number line.
 How is scientific notation used in real world
 Scientific notation will help demonstrate very large
application problems?
and very small numbers when solving real world
 How are numbers compared and manipulated
application problems.
using scientific notation?
 Numbers can be represented in scientific notation
and still be manipulated using operations such as
addition, subtraction, multiplication, and division.
Unit Learning Targets
Students will ...
1. Be able to find the squares and square roots of both rational and irrational numbers.
2. Learn to reason with real numbers and perform numerical operations with them.
3. Understand irrational numbers as non-terminating, non-repeating decimals.
4. Understand calculations with irrational numbers and approximate reasonable solutions.
5. Express numbers using scientific notation.
6. Recognize the difference between scientific notation and standard form.
7. Distinguish the difference between different numbers written in scientific notation.
8. Solve equations with addition, subtraction, multiplication, and division using numbers in scientific
notation.
Evidence of Learning
Summative Assessment: The students will be assessed with a summative unit assessment which will be
modeled after the PARCC assessment model. This model assessment will include multiple choice,
constructed response and a performance task.
Formative Assessments
 Tests and quizzes
 Explanation of examples
 Discussions
 Daily homework assignments
 Individual practice
 Notes
Lesson Plans
Lesson
Lesson #1:
Purpose of Scientific Notation/Quiz #1
Lesson #2:
How to Write Numbers in Scientific Notation
Lesson #3:
How to convert between Scientific Notation and
Standard Form/ Quiz #2
Lesson #4:
Comparing Numbers in Scientific Notation/Quiz
#3
Lesson #5:
Multiply and Divide with Scientific Notation
Lesson #6:
Addition and Subtraction with Scientific
Notation/Quiz #4
Mid Unit Review and Assessment
Lesson #7:
Squares, Square Roots and Perfect Squares
Lesson #8:
Simplifying Perfect Square Radical Expressions/
Quiz #5
Lesson #9:
Approximating Square Roots
Lesson #10:
Rational & Irrational Numbers/Quiz #6
Lesson #11:
Radical Expressions Containing Variables
Lesson #12:
Simplifying Non-Perfect Square Radicands
Lesson #13:
Simplifying Roots of Variables/Quiz #7
Lesson #14:
Properties of Exponents
Lesson #15:
Solving Equations with Perfect Square & Cube
Roots/Quiz #8
Unit Review and Assessment
Teacher Notes:
10 days allocated for formative/summative assessments
Curriculum Development Resources
http://www.khanacademy.org
Pearson Connected Math 2
 Looking for Pythagoras, Growing, Growing, Growing
Glencoe Pre-Algebra 2006
Smartboard slideshow introduction to rational numbers
Rational number game
Timeframe
2 days
2 days
3 days
3 days
2-1/2 days
3-1/2 days
2 days
1 day
3 days
1 day
3 days
2 days
2 days
2 days
2 days
2 days
3 days
Unit Overview
Content Area:
Mathematics
Unit Title:
Unit 3 – Functions
Target Course/Grade Level: Mathematics-Grade 8
Unit Summary: Recognizing linear and nonlinear patterns in tables and graphs and describing those
patterns using words and equations. Writing equations to express patterns appearing in tables, graphs, and
“stories”. Solve linear equations.
Unit Rationale: Students will learn that a function is a special type of relation and that a linear equation is
one of many ways to represent a function. They will learn to write linear equations and use them to solve
real world problems.
Student Learning Objectives
1.) Define linear functions as a rule that assigns one output to each input and determine if data
represented as a graph or in a table is a function.
2.) Compare two functions each represented in a different way (numerically, verbally, graphically,
and algebraically) and draw conclusions about their properties (rate of change and intercepts).
3.) Utilize equations, graphs, and tables to classify functions as linear or non-linear, recognizing that
y = mx + b is linear with a constant rate of change.
4.) Using a linear equation to model real life problems then solve it by interpreting the meaning of the
slope and the intercept.
5.) Construct and interpret scatter plots for bivariate measurement data and identify and interpret data
patterns (clustering, outliers, positive or negative association, possible lines of best fit, and
nonlinear association).
6.) Construct frequency/relative frequency tables to analyze and describe possible associations
between two variables.
Selected Opportunities for Connection to Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
SLO#2 Use functions that are represented in different ways to identify and compare the rates of change
and the intercepts of each.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
SLOs #4, #5 and #6 Use equations, scatter plots, and frequency tables to model relationships between
real-world quantities.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
SLO#2 Identify the rate of change and the intercepts of functions represented in different ways.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Code #
8.F.1
8.F.2
New Jersey Student Learning Standards
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.
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;
2
give examples of functions that are not linear. For example, the function A = s giving the
area of a square as a function of its side lengths is not linear because its graph contains
the points (1, 1), (2, 4), and (3, 9) which are not on a straight line.
8.SP.1
Construct and interpret scatter plot 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 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 the patterns of association can also be seen in bivariate categorical data by
displaying the 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?
Unit Essential Questions:
Unit Enduring Understandings:
 What are the key variables in this
 Recognize linear and nonlinear patterns from
situation?
verbal descriptions, tables, and graphs and
describe those patterns using words and
 What is the pattern relating the variables?
equations.
 What is a function?
 Write equations to express linear patterns
 How are functions represented?
appearing in tables, graphs and verbal
 What can a relationship between numbers
context.
tell about a problem?

The definition of a function and what its
 Are properties of functions and graphs the
graph represents.
same for all functions?
 Properties of functions and their graphs are
 How can information from a problem be
similar but not identical.
represented in a way to see a pattern or a

Slope-intercept form is an easy way of
frequency?
graphing functions.
 What is a line of best fit and how can it
 Scatter plots, line of best fit, and frequencies
simply a conclusion?
all help interpret data within a problem.
 Are interpretation and predication an

Patterns can be modeled using different
accurate conclusion for a problem?
graphs.
 Straight lines are widely used to model
relationships.
Unit Learning Targets
Students will ...
1. Understand what a function is and its corresponding graph.
2. Compare properties of different functions and relate the information to real world situations.
3. Graph slope-intercept form of a line.
4. Construct a function and determine the rate of change and initial value.
5. Describe a functional relationship by examining a graph.
6. Be able to graph scatter plots.
7.
8.
9.
10.
Interpret and examine data to come to a conclusion.
Know about line of best fit and two variable data relationships.
Understand patterns of association in bivariate categorical data.
Use frequency to solve real life problems and make predictions for future ones.
Evidence of Learning
Summative Assessment: The students will be assessed with a summative unit assessment which will be
modeled after the PARCC assessment model. This model assessment will include multiple choice,
constructed response and a performance task.
Formative Assessments
 Tests and quizzes
 Explanation of examples
 Discussions
 Daily homework assignments
 Individual practice
 Notes
Lesson Plans
Lesson
Timeframe
Lesson #1:
Relationships and Functions
2 days
Lesson #2:
Domain and Range/Quiz #1
3 days
Lesson #3:
Vertical Line Test/Quiz #2
3 days
Lesson #4:
Linear Vs. Non-Linear Functions/Quiz #3
3 days
Lesson #5:
Interpreting with Functions
3 days
Lesson #6:
Analyzing a Graph
3 days
Lesson #7:
Comparing Different Representations of
3 days
Functions/Quiz #4
Mid Unit review and assessment
2 days
Lesson #8:
Two Variable Data/Quiz #5
3 days
Lesson #9:
Line of Best Fit/Quiz #6
3 days
Lesson #10:
Determining the Prediction Equation/Quiz #7
4 days
Lesson #11:
Two Way Table
3 days
Review and Unit Test
2 days
Teacher Notes:
9 days allocated for formative/summative assessments
Curriculum Development Resources
http://www.khanacademy.org
Pearson Connected Math 2
 Thinking with Mathematical Models, Growing, Growing, Growing, Shapes of Algebra, Say it with
Symbols. Samples and Populations.
Glencoe Pre-Algebra 2006
Smartboard Smart Exchange
Senteo response system
Unit Overview
Content Area:
Mathematics
Unit Title:
Unit 4-Expressions and Equations
Target Course/Grade Level: Mathematics-Grade 8
Unit Summary: This unit explores linear equations. Students learn to solve equations starting from one
step equations and progressing to more complex equations. The unit concludes with using the skills to
transform formulas so that they are solved for a named variable. The unit covers how to graph linear
equations and different forms the equations can be written in. Students will also learn how write the
equation of a line with given qualities. The relationships between parallel lines and perpendicular lines
will be covered. This unit also uses graphing, elimination, and substitution to solve systems of equations.
Situations will be modeled with systems and solved.
Unit Rationale: Equations help describe quantitative relationships among certain quantities. Linear
equations can be used to solve problems in every facet of life from planning a garden, to investigating
trends in data, to making wise career choices. One of the most frequent uses of linear equations is solving
problems involving mixtures or motion.
Student Learning Objectives
1.) Graph and analyze the different representations of proportional relationships and interpret the unit
rate as the slope of the graph which indicates the rate of change.
2.) Derive the equation of a line (y = mx for a line through the origin and the equation y = mx +b for a
line intercepting the vertical axis at b) and use similar triangles to explain why the slope (m) is the
same between any two points on a non-vertical line in the coordinate plane.
3.) Solve linear equations in one variable with rational number coefficients that might require
expanding expressions using the distributive property and/or combining like terms, including
examples with one solution, infinite solutions, or no solution.
4.) Solve systems of linear equations in two variables by inspection, algebraically, and/or graphically
(estimate solutions) to demonstrate solutions correspond to points of intersection of their graphs,
because points of intersection satisfy both equations simultaneously.
5.) Construct a function to model the linear relationship between two variables and determine the rate
of change and initial value of the real world data it represents from either graphs or tabulated
values.
6.) Sketch a graph of a function from a qualitative description and give a qualitative description of a
graph of a function.
Selected Opportunities for Connection to Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
SLO#1 Describe the relationship between the slope of a graph and the rate of change in proportional
Relationships.
3. Construct viable arguments and critique the reasoning of others.
SLOs #3 and #4 Determine and justify the steps to the solutions to equations.
4. Model with mathematics.
SLO #6 Create a graph from a description of a real-world condition and give a real-world context for
a graphic display.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Code #
8.EE.5
New Jersey Student Learning Standards
Graph proportional relationships, interpreting the unit rate as the slope of a 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.
8.EE.7
Solve linear equations in one variable.
a) 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).
b) Solve linear equations with rational number coefficients, including equations
whose solutions require expanding expressions using the distributive property and
collecting like terms.
8.EE.8
Analyze and solve pairs of simultaneous linear equations.
a. Understand the 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.
b. Solve systems of two linear equations in two variables algebraically, and estimate
solutions by graphing the equations. Solve simple cases by inspection.
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.
Unit Essential Questions
 How can the value of an unknown variable
be found?

What is meant by the slope of a line, and
how can knowing a line’s slope help to
graph a line and find parallel and
perpendicular lines?

How can real world situations be modeled
by systems? How can solutions be found
to a system?
Unit Enduring Understandings
 How to solve an equation in one variable be
solved for that variable.
 How to solve an equation for a variable in
the equation.
 Various methods can be used to solve
equations and the solution to an equation can
be checked by substituting into the original
equation.
 The point at which lines intersect is the
solution to the system with those lines.
Unit Learning Targets
Students will ...
1.
2.
3.
4.
5.
6.
7.
8.
Be able to solve equations.
Be able transform a formula to a different form of that equation.
Be able to graph a line given different forms of the equation.
Be able to identify parallel and perpendicular lines from their slopes.
Be able to describe how slope relates to horizontal and vertical lines.
Be able to graph systems of linear equations or to find a solution.
Be able to translate real world problem into a system.
Be able to solve a system of equations by using substitution and elimination
Evidence of Learning
Summative Assessment:
The students will be assessed with a summative unit assessment which will be modeled after the PARCC
assessment model. This model assessment will include multiple choice, constructed response and a
performance task.
Formative Assessments
 Tests and quizzes

Explanation of examples

Discussions

Daily homework assignments

Individual practice

Notes
Lesson Plans
Lesson
Lesson #1:
Tables/Quiz #1
Lesson #2:
Slope & Y-Intercept
Lesson #3:
Defining Slope on the Coordinate Plane
Lesson #4:
Tables & Slope/Quiz #2
Lesson #5:
Slope Formula/Quiz #3
Lesson #6:
Slope Intercept Form/Quiz #4
Lesson #7:
Rate of Change
Lesson #8:
Proportional Relationships and Graphing
Lesson #9:
Slope and Similar Triangles/Quiz #5
Lesson #10:
Parallel and Perpendicular Lines/Quiz #6
Timeframe
2 days
2 days
2 days
2 days
2 days
2 days
1 day
1 day
3 days
3 days
Lesson #11:
Solve Systems by Graphing
Lesson #12:
Solve Systems by Substitution
Lesson #13:
Solve Systems by Elimination
Lesson #14:
Choosing Your Strategy/Quiz #7
Lesson #15:
Writing Systems to Model Situations
Mid Unit review and Assessment
Lesson #16:
Inverse Operations
Lesson #17:
One Step Equations
Lesson #18:
Two Step Equations
Quiz #8
Lesson #19:
Multi-Step Equations
Lesson #20:
More Equations
Lesson #21:
Transforming Formulas
Quiz #9
Review and Unit Test
Teacher Notes:
1 day
2 days
2 days
2.5 days
2 days
2 days
2 days
2 days
2 days
1 day
2 days
2 days
2 days
1 day
2 days
6 days allocated for formative/summative assessments
Curriculum Development Resources:
http://www.khanacademy.org
Pearson Connected Math 2
 The Shapes of Algebra, Say it with Symbols, Thinking with Mathematical Models.
Glencoe Pre-Algebra 2006
Smartboard Smart Exchange
Senteo response system
Unit Overview
Content Area:
Mathematics
Unit Title:
Unit 5 – Geometry
Target Course/Grade Level: Mathematics-Grade 8
Unit Summary: This unit will provide a deeper understanding of the Pythagorean Theorem and its
converse for students. They will apply the theorem to problems involving right triangles that model real
world problems. They will also find distances and midpoints between two points. Students will learn
about 3-dimensional solids and how to calculate their volume. They will also use these formulas to solve
real world problems.
Unit Rationale: The basics of trigonometry and the study of triangles are explored in this chapter. These
basics will be applied to deeper studies of triangles in later mathematics courses. Many of these concepts
are used in construction and engineering. Three dimensional figures have special characteristics. These
characteristics are important when architects are designing buildings and other three-dimensional
structures.
Student Learning Objectives
1.) Evaluate square roots and cubic roots of small perfect squares and cubes respectively and use
square and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p
where p is a positive rational number.
2.) Identify √2 as irrational.
3.) Explain a proof of the Pythagorean Theorem and its converse.
4.) Utilize the Pythagorean Theorem to determine unknown side lengths of right triangles in two and
three dimensions to solve real-world and mathematical problems.
5.) Use the Pythagorean Theorem to determine the distance between two points in the coordinate
plane.
6.) Know and apply the appropriate formula for the volume of a cone, a cylinder, or a sphere to solve
real-world and mathematical problems.
Selected Opportunities for Connection to Mathematical Practices
1. Make sense of problems and persevere in solving them.
SLO#6 Involve problems that must be constructed and deconstructed in order to solve.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
SLO #3 Explain the difference between the Pythagorean Theorem and its converse. Listen to or read
the explanation of others and pose questions that will clarify or improve the explanations.
4. Model with mathematics.
SLO #5 Use the coordinates of a figure represented on a coordinate plane to determine the length of
the missing side.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Code #
8.EE.2
New Jersey Student Learning Standards
Use square root and cube root symbols to represent solutions to equations of the form x =
8.G.6
p and x = p where p is a positive rational number. Evaluate square roots of small perfect
squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.
Explain a proof of the Pythagorean Theorem and its converse.
2
3
8.G.7
8.G.8
8.G.9
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in
real-world and mathematical problems in two or three dimensions.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate
system.
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve
real-world and mathematical problems.
Unit Essential Questions
 How does the Pythagorean Theorem help
solve real world problems?
 How do we compute the distance and
midpoint within problems?
 What is a 3-dimensional figure?
 How can I find the volume of a 3dimensional figure?
 How can the volume of a 3-dimensional
figure help me solve real world problems?
Unit Enduring Understandings
 The Pythagorean Theorem can be used to
solve real world problems.
 The Pythagorean Theorem aids in solving
problems involving right triangles.
 There are different formulas that can be used
when solving for the volume of a 3dimensional figure.
Unit Learning Targets
Students will ...
1.)
2.)
3.)
4.)
5.)
6.)
7.)
Identify what a 3-dimensional figure is.
Use a formula to find the volume of a prism and cylinder.
Use a formula to find the volume of pyramids, cones and spheres.
Be able to explain the proof of the Pythagorean Theorem.
Find unknown side lengths using the Pythagorean Theorem.
Use the Pythagorean Theorem to solve problems involving distance and midpoints.
Solve real world application problems using the Pythagorean Theorem.
Evidence of Learning
Summative Assessment:
The students will be assessed with a summative unit assessment which will be modeled after the PARCC
assessment model. This model assessment will include multiple choice, constructed response and a
performance task.
Formative Assessments
 Tests and quizzes
 Discussions
 Individual practice



Explanation of examples
Daily homework assignments
Notes
Lesson Plans
Lesson
Lesson #1:
Pythagorean Theorem/Quiz #1
Lesson #2:
Distance Formula
Lesson #3:
Midpoints/Quiz #2
Timeframe
14 days
5 days
6 days
Review and Unit Test
Lesson #4:
3-Dimensional Solids/Quiz #3
Lesson #5:
Volume-Prisms and Cylinders
Lesson #6:
Volume-Pyramids, Cones & Spheres/Quiz #4
Review and Unit Test
Teacher Notes:
6 days allocated for formative/summative assessments
Curriculum Development Resources:
http://www.khanacademy.org
Pearson Connected Math 2
 Looking for Pythagoras
Glencoe Pre-Algebra 2006
Smartboard Smart Exchange
Senteo response system
2 days
4 days
6 days
4 days
3 days