Mathematics
8th Grade Math Standard 1.1
8.Math.1.1 In the real number system, rational and irrational numbers are in one to one
correspondence to points on the number line
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Define irrational numbers.
1. Why are real numbers represented by a
number line and why are the integers
2. Demonstrate informally that every number
represented by points on the number line?
has a decimal expansion.
2. Why is there no real number closest to
zero?
3. For rational numbers, show that the decimal
expansion repeats eventually.
3. What is the difference between rational and
irrational numbers?
4. Convert a decimal expansion which repeats
eventually into a rational number.
4. How can you demonstrate that every
number has a decimal expansion?
5. 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.
5. How can you convert a decimal expansion
that repeats into a rational number?
6. How can the use of rational approximations
of irrational numbers compare the size of
irrational numbers?
7. What are square roots? Cube roots?
8. How can we apply the properties of integer
exponents to generate equivalent numerical
expressions?
9. What are scientific notations and why do we
use them?
6. Apply the properties of integer exponents to
generate equivalent numerical expressions.
7. 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.
8. Evaluate square roots of small perfect
squares and cube roots of small perfect cubes.
9. Use numbers expressed in the form of a
single digit times a whole-number power of
ten to estimate very large or very small
quantities, and to express how many times as
much one is than the other.
10. Perform operations with numbers
expressed in scientific notation, including
problems where both decimal and scientific
notation are used.
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Mathematics
8th Grade Math Standard 1.1
11. Use scientific notation and choose units of
appropriate size for measurements of very
large or very small quantities.
Academic Vocabulary:
real numbers
rational numbers
irrational numbers
decimal expansion
square root
cube root
equivalent numerical expression
integer exponents
number line
estimate
expressions
approximations
scientific notation
integer
perfect square
power
base
exponent
perfect cube
law/properties of exponents
12. Interpret scientific notation that has been
generated by technology.
Assessment:
All assessments are found in the suggested
activities links, correlating with their numbers,
unless listed below.
1. Assessment can be found inside the lesson
plan at the bottom (e.g., Have students explain
the sentence: "Squaring and finding square
roots are inverse operations." They should use
models, algebra, and math vocabulary.)
2. Use the Jeopardy game as a review before
the test. Observe the students as they answer
the questions.
3. Assessment can be found in the packet.
4. Assessment can be located at the end of the
lesson in Lesson Segment Three.
5. Assessment strategies can be found at the
end of the lesson. Scroll down to bottom of the
lesson.
6. Observe individual students playing the
game to determine that they can order five out
of six cards correctly.
7. The activity score is the assessment.
8. Assessment options: 1. Students create their
own PowerPoint game (Jeopardy, 20
Questions, etc.) using links provided. 2. A link
to the exponent game is located under
extension.
9. Within the lesson, there are several
worksheet options for assessment.
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8th Grade Math Standard 1.1
10. Several worksheets located within the site
can be used as assessment.
11. Student scores can be taken as assessment.
12. Assessments are located within the
lessons. Several different lessons are located
within the site.
13. Scores from game can be used as
assessment. Teacher may observe that
students are answering questions correctly as
informal assessment.
14. This score can be used as an assessment
with Activities 3 and 4.
15. This is an interactive lesson, so the teacher
can set up students to complete the lesson on
computers or the teacher can copy problems
and put them into a PowerPoint and have
students answers questions aloud. If a CPS
system (clickers or a student response system)
is available, you can take questions and put
them into an activity using the clickers.
16. Assessment is found at the end of the
lesson; use questions #1-6.
Suggested Activities/Strategies (District):
For all activities listed below, the links are
numbered to correlate with each activity.
1. Use the Square Roots Go Rational Lesson
Plan. Students recall and model the square
root as the length of one side of a square. But
what if the square is not a perfect square? This
collection of activities explores the square
roots of not-so-perfect squares and develops
an algorithm to express the not-so-perfect
square root as a rational value.
17. Assessment is the activity score.
Resources/Technology (District):
There are several videos on Square Roots
located at the Kahn Academy website. Click
on the video for Approximating Square Roots
and look to the left to see numerous sites for
what you may need. (Teacher/Student
Resource)
Tutorial site for Rational/Irrational Numbers
below explains how to teach these numbers.
(Teacher Resource)
Homeschool site below explains what rational,
irrational numbers are. (Teacher Resource)
2. Use the Square Root Jeopardy Game for
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8th Grade Math Standard 1.1
review before a quiz or test. Teacher can
divide the class into small groups and the
groups can compete for the most points.
3. Use the Rational, Irrational Numbers
Lesson Plan to classify numbers and explore
the difference between the decimal expansions
of rational and irrational numbers.
4. Use the Representing Numbers Using
Scientific Notation Lesson Plan.
5. Use the Rational or Irrational, That is the
Question Lesson Plan. Students will
participate in an activity for discerning how
numbers are related to each other. They will
determine whether a number is rational or
irrational. Students will also be able to order
rational and irrational numbers on a number
line.
Extra practice for rational and irrational
numbers can be found at mtestprep.
Purple Math is a resource for information on
fractions to decimals, decimals to fractions,
percents, and conversions. This link includes
in-depth instruction tips and at the end of the
link, there is a table of common conversions
that may be used as an assessment.
Link to video clip for cubes and cubes roots:
Perfect cubes/cube roots.
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
6. Use the Line Up Cards Activity. This is a
very quick activity about how numbers are
related to one another. It includes how rational
and irrational numbers compare.
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
PARCC and Smarter Balance.
7. Play the Rational/Irrational Number Game.
This is a classification game and a quick check
for understanding.
Math Arizona has explanations and overviews
for how the mathematics strands progress
from one year to the next.
8. Use the The Laws of Exponents Lesson
Plan. During this activity, students will review
the laws of exponents. They will demonstrate
their knowledge by creating an interactive
computer game or a podcast.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
9. Use the Squares, Square Roots, and
Exponential Expressions Lesson. This is a
complete lesson plan with essential questions,
complete explanation, warm-ups, worksheets,
and assessment.
Achieve the Core is from Student
Achievement Partners, a nonprofit
organization that assembles educators and
researchers to design actions based in
evidence that will substantially improve
student achievement.
Balanced Assessments is a site with free
performance tasks to use in your classroom.
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Mathematics
8th Grade Math Standard 1.1
10. Use the Perfect Cubes and Cube Root
Lesson. Students will learn what perfect cubes
are and how to calculate the cube root of a
perfect cube.
11. Play the game for scientific
notation. Quick game to check for
understanding.
12. Use the Lesson Plan for higher level
students on Scientific Notation. This unit is
designed to introduce the concept of Scientific
Notation, explain how it is used for large and
small numbers, and show how to multiply and
divide using Scientific Notation. Although the
activities were written for an Algebra I course,
they could easily be adapted for other courses.
Video on Approximating Square Roots
Rational Irrational Tutor
Rational Irrational Homeschool Site
Scientific Notation Activity
Resources for Games, Worksheets, etc
Math Worksheets 4 Kids
Kahn Academy
Homework Help
Converting Decimals Link Teacher Resource
Number Types
PowerPoint for Perfect Squares and Cubes
Scientific Notation Resource
13. Play the Jeopardy Game for Scientific
Notation as a quick check for understanding.
14. Number Types from Purple Math has
true/false questions that can be used as an
opener for rational/irrational numbers.
15. Use the Scientific Notation Lesson to learn
the basic principles of Scientific Notation and
how to convert standard numbers to scientific
notation. It can be interactive or the teacher
can copy problems and use the PowerPoint.
16. Use the Math is Fun Number Line Lesson.
17. Play practice games in Math Playground
(Roots, Exponents and Scientific Notation) to
review.
1. Square Roots Go Rational Lesson Plan
2. Square Root Jeopardy
3. Rational, Irrational Lesson Plan
4. Scientific Notation Lesson Plan
5. Rational, Irrational, That is the Question
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Mathematics
8th Grade Math Standard 1.1
Lesson Plan
6. Line Up Cards Activity
7. Rational/Irrational Number Game
8. Laws of Exponents Lesson Plan
8. PowerPoints with Exponents
9. Squares, Square Roots, and Exponential
Expressions
10. Perfect Cubes and Cube Roots Lesson
11. Game for Scientific Notation
12. Higher Level Student Lesson on Scientific
Notation
13. Jeopardy Game
14. Number Types
15. Scientific Notation Lesson Plan
16. Number Line Lesson
17. Math Playground
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Mathematics
8th Grade Math Standard 2.1
8.Math.2.1 Linear functions model situations with a constant rate of change and can be
represented numerically, algebraically, and graphically
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Describe the connections between
proportional relationships, lines, and linear
1. How can different representations of linear
patterns present different perspectives of
equations.
situations?
2. Graph proportional relationships,
2. How can a relationship be analyzed with
interpreting the unit rate as the slope of the
graph.
tables, graphs, and equations?
3. Why is one variable dependent upon the
other in relationships?
3. Compare two different proportional
relationships represented in different ways.
4. What are ways to describe the connections
between proportional relationships, lines, and
linear equations?
4. 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.
5. How can you compare two different
proportional relationships represented in
different ways?
6. Why do you use the equation y=mx and the
equation y=mx + b?
Academic Vocabulary:
Y intercept
slope intercept form
independent variable
dependent variable
horizontal axis
constant rate of change
proportional relationships
linear equations
unit rate
slope
similar triangles
non-vertical line
coordinate plane
equation
intercepting
vertical axis
5. 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.
Assessment:
All assessments are found in the suggested
activities links, correlating with their
numbers, unless listed below.
1. Assessment is located toward the bottom of
the lesson. There is also a rubric to use. For
example, as a journal response, have students
answer the Key Questions in the lesson. Then
require students to present their solutions to
the class and demonstrate that their answers
are correct (e.g., If a student says that Barbie
can jump safely from a height of 400 cm with
12 rubber bands, then they should demonstrate
that Barbie will not hit the ground when 12
rubber bands are used.)
2. Assessment is located toward the bottom of
the lesson plan. You can also use student
answers to the questions within the lesson to
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Mathematics
8th Grade Math Standard 2.1
determine skill knowledge.
3. Assessment is located toward the bottom of
the lesson plan. An example would be to have
students summarize the activity on a poster or
in a PowerPoint presentation by showing
how trendlines and equations represent a path.
They should include a scatterplot and an
analysis of three areas, one with average slope,
one with extreme upward slope, and another
with extreme downward slope.
4. The T-chart is your assessment.
5. Assessment can be any worksheet from the
lesson.
6. Assessment is found at the bottom of lesson
plan.
7. Assessment is built into lesson plan.
8. Several worksheets located at the bottom of
lesson plan can be for used as formal or
informal assessment.
Suggested Activities/Strategies:
For all activities listed below, the links are
numbered to correlate with each activity.
1. Use the Barbie Bungee Lesson Plan to
examine linear functions.
2. Use the Amazing Profit Lesson Plan. This
is designed for students who already know
how to determine linear equations from a
coordinate graph. Its purpose is to illustrate an
application of understanding relationships and
9. Assessment is teacher observation of
student graphs. An alternate assessment might
be for students to plot a graph with pencil and
paper. Teacher and students can use the
website to assess the created graphs.
Resources/Technology:
Virtual Nerd is a free site for Educators with
numerous tutorial videos for students that need
extra help. It is a great source for re-teaching
as well as for ideas to begin a lesson. Go in
and sign up for your free membership.
purplemath.com is a site that can help students
gain understanding and self-confidence in
Algebra. Look for Slope Intercept.
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Mathematics
8th Grade Math Standard 2.1
trends.
3. Use the The Line Runner Lesson Plan for
studying linear equations and exploring the
concept of slope.
4. Use the Graphing Linear Equations with a
T-chart link.
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
5. Drill and Practice with worksheets
(with/without peer check.) Students complete
problems on their own and then check answers
with a partner. If the answers don't agree, both
students must rework problem and figure out
who was wrong and where the mistake was.
Two links for worksheets can be found below.
icoachmath is a site that has numerous practice
worksheets for 6th, 7th, and 8th grade math.
math.com is a site that allows you to generate
your own worksheets. The link is named Math
Worksheet Generator.
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
PARCC and Smarter Balance.
6. Use the Yo-Yo Linear Activity for students
to explore linear patterns, write a pattern in
symbolic form, and solve linear equations
using algebra tiles, symbolic manipulation,
and the graphing calculator.
Achieve the Core is from Student
Achievement Partners, a nonprofit
organization that assembles educators and
researchers to design actions based in
evidence that will substantially improve
student achievement.
7. Use the Proportional Reasoning Lesson
where students will extend their understanding
of ratios and proportional relationships, and
work with situations involving constant rates
of change.
8. Use the Linear Graphs Lesson to graph
proportional relationships and to identify the
unit rate as the slope of the related line.
9. Use the Line of Best Fit Lesson. This
activity allows the user to enter a data set, plot
the data on a coordinate grid, and determine
the equation for a line of best fit. (InteractiveRequires Java.)
10. If you have a SmartBoard or Airliner, go
Math Arizona has explanations and overviews
for how the mathematics strands progress
from one year to the next.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
Balanced Assessments is a site with free
performance tasks to use in your classroom.
Virtual Nerd
Slope of a Straight Line
Functioning Graph Resource
Link to Linear Video
Multiple PowerPoints for Triangles
Proportional Relationships PowerPoints
Multiple Lessons on Linear Equations
Examples of Linear Equations
Game on Linear Equations
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Mathematics
8th Grade Math Standard 2.1
to Smart Exchange and search for lessons on
linear equations.
1. Barbie Bungee Lesson Plan
2. Amazing Profit Lesson Plan
3. The Line Runner Lesson Plan
4. Graphing Using a T-chart
5. I Coach Math Worksheets
5. Math Worksheet Generator
6. Yo-Yo Activity
7. Proportional Reasoning Lesson
8. Linear Graphs Lesson
9. Line of Best Fit Lesson
10. Smart Exchange Link
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Mathematics
8th Grade Math Standard 2.2
8.Math.2.2 Properties of algebra and equality are used to solve linear equations and systems
of equations
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Solve linear equations in one variable.
1. What makes a solution strategy both
efficient and effective?
2. Give examples of linear equations in one
variable with one solution, infinitely many
2. How is it determined whether multiple
solutions, or no solutions.
solutions to an equation are valid?
3. Solve linear equations with rational number
3. How does the context of the problem affect
coefficients, including equations whose
solutions require expanding expressions using
the reasonableness of a solution?
the distributive property and collecting like
4. Why can two equations be added together to terms.
get another true equation?
4. Analyze and solve pairs of simultaneous
linear equations.
5. How can you use the properties of algebra
and equality to solve linear equations?
5. Explain that solutions to a system of two
Systems of equations?
linear equations in two variables correspond to
points of intersection of their graphs, because
6. How can you solve linear equations in one
points of intersection satisfy both equations
variable?
simultaneously.
7. How can you use the distributive property
6. Solve systems of two linear equations in
to solve linear equations with rational number
two variables algebraically, and estimate
coefficients?
solutions by graphing the equations. Solve
simple cases by inspection.
Academic Vocabulary:
equality
linear equations
systems of equations
variable
rational number
coefficients
points of intersection
solution of an equation
expression
equation
7. Solve real-world and mathematical
problems leading to two linear equations in
two variables.
Assessment:
All assessments are found in the suggested
activities links, correlating with their
numbers, unless listed below.
1. Assessment is located under the Procedures
for Teachers Tab. Scroll all the way to the
bottom of the page and look at the culminating
activity/assessment.
2. Go to the Lesson Plan and scroll down to
the Performance Task section for assessment.
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Mathematics
8th Grade Math Standard 2.2
like terms
distributive property
inequality
3. Assessment is located at the bottom of the
lesson plan. Critical questions asked
throughout the lesson can be used for
assessment.
4. There is an assessment within the
lesson. You can either take a grade or observe
which students are answering the assessment
problems correctly.
5. Assessment is built into the lesson plan.
6. Use a worksheet as assessment.
7. Use any problem as a "Ticket Out the
Door."
Suggested Activities/Strategies:
For all activities listed below, the links are
numbered to correlate with each activity.
1. Use the Lesson Plan Cups and Chips. In this
lesson, students use manipulatives to visually
represent the steps they take to obtain a
solution to an algebraic equation. They
develop an understanding of the connections
between the solution involving manipulatives
and the symbolic solution.
2. Use the Linear Equation Lesson Plan. In
this lesson students will learn to construct
tables, graphs, and equations to express linear
relationships. Students translate information
about linear relations given in a table, a graph,
or an equation to one of the other forms.
3. Use the Investigation Linear Equations
Lesson Plan. This lesson incorporates
graphing calculator technology into the math
classroom. Students use the graphing
calculator to model the slope-intercept form of
linear equations and to investigate the effects
of slope and y-intercept on the line.
8. A rubric is built into the lesson.
Resources/Technology:
Kutasoftware offers multiple worksheets for
extra practice.
Math worksheets go is another worksheet site
that offers multiple practice worksheets.
ixl.com is an interactive site with opportunities
for students to solve problems. If they answer
a problem incorrectly, an explanation of what
to do to correct the answer is given.
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
PARCC and Smarter Balance.
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Mathematics
8th Grade Math Standard 2.2
4. Use the Linear Equations with One Variable
Lesson. This lesson unit is intended to help
you assess how well students are able to solve
linear equations in one variable with rational
number coefficients, collect like terms, expand
expressions using the distributive property,
and categorize linear equations in one variable
as having one, none, or infinitely many
solutions. It also aims to encourage discussion
on some common misconceptions about
algebra.
5. Play the Linear Card Game. Game cards
help pair up students to solve linear equations
for the value of a variable.
6. Conduct Drill and Practice with worksheets.
7. Use the Lesson with Distributive Property.
This has examples of problems with notes.
There are two links to videos that can be used
as resources.
8. Use the Talk and Text Lesson Plan. The
task is embedded in a three week unit on
systems of linear equations. The unit provides
students with the opportunity to deepen their
understanding of the representation and
connections of real world situations in various
forms: equations, tables, and graphs.
Furthermore, this unit allows students to
determine if and when two or more equations
in context have a solution algebraically and
graphically.
Math Arizona has explanations and overviews
for how the mathematics strands progress
from one year to the next.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
Achieve the Core is from Student
Achievement Partners, a nonprofit
organization that assembles educators and
researchers to design actions based in
evidence that will substantially improve
student achievement.
Balanced Assessments is a site with free
performance tasks to use in your classroom.
Slope of a Graph Worksheet
Test and Worksheet Generator
Graphing Linear Inequalities Worksheet
Digital Lesson on Linear Equations
Site with Multiple Lessons with Variable
Equations
Site with Multiple Lesson Plans
Site with Definitions and Examples of
Distributive Property
Link to System of Equation Lesson &
Interactive Game
Tutorial on Graphing Linear Functions
1. Cups and Chips Lesson Plan
2. Linear Equation Lesson Plan
2. Video on Graphing Linear Equations
3. Investigating Linear Equations
4. Linear Lesson with One Variable
5. Linear Card Game
6. Worksheet Site
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Mathematics
8th Grade Math Standard 2.2
7. Lesson Using Distributive Property
7. Video of Linear Equations Using
Distributive Property
7. Video #2 Linear Equations Using
Distributive Property
8. Talk and Text Lesson Plan
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Mathematics
8th Grade Math Standard 2.3
8.Math.2.3 Graphs, tables, and equations can be used to distinguish between linear and
nonlinear functions
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Define, evaluate, and compare functions.
1. How can change best be represented
mathematically?
2. Define a function as a rule that assigns to
each input exactly one output.
2. Why are patterns and relationships
represented in multiple ways?
3. Show that the graph of a function is the set
of ordered pairs consisting of an input and the
3. What properties of a function make it a
corresponding output.
linear function?
4. Compare properties of two functions each
4. What are functions?
represented in a different way (algebraically,
graphically, numerically in tables, or by verbal
5. What are ways to compare properties of two descriptions.)
functions differently?
5. Interpret the equation y = mx + b as defining
6. What does the graphing of a function show? a linear function, whose graph is a straight line.
7. What are examples of functions that are not
linear?
6. Give examples of functions that are not
linear.
8. How can having credit or having debt
impact people's financial goals?
7. Use functions to model relationships
between quantities.
9. How can you find the slope of a line with
only two points?
8. Construct a function to model a linear
relationship between two quantities.
9. 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.
10. 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.
11. Describe qualitatively the functional
relationship between two quantities by
analyzing a graph.
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Mathematics
8th Grade Math Standard 2.3
12. Sketch a graph that exhibits the qualitative
features of a function that has been described
verbally.
Academic Vocabulary:
functions
relationships
linear function
quantities
rate of change
initial value
qualitative features
credit
debt
ordered pair
non-linear function
finances
financial goals
input
output
independent variable
dependent variable
coordinates
constant
Suggested Activities/Strategies:
For all activities listed below, the links are
numbered to correlate with each activity.
1. Use the y=mx + b Matching Cards Activity.
This activity matches equations and graphs.
2. Drill and Practice with worksheets. Students
can be put into pairs where they can work on a
problem and check with their partner to ensure
they both have correct answer. If they don't,
both students should examine each other's
problems to decide who made a mistake and
where.
13. Analyze how credit and debt impact
personal financial goals.
Assessment:
All assessments are found in the suggested
activities links, correlating with their
numbers, unless listed below.
1. To assess, determine if cards are matched
correctly.
2. Assessment is the graded worksheets.
3. You may wish to bring the class back
together for a discussion of the findings. Once
the students have been allowed to share what
they found, summarize the results of the
lesson.
4. Because this lesson can be done in teams,
have all students share results.
5. Assessment is found at the bottom of the
lesson.
6. Assessment is found at the end of the
activity. (Answer questions 1-10.)
Resources/Technology:
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
PARCC and Smarter Balance.
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Mathematics
8th Grade Math Standard 2.3
3. Use the Lesson on Introduction to Functions
designed to introduce students to the idea of
functions and their representations as rules and
data tables, including the mathematical notions
of independent and dependent variables.
4. Use the Graphs and Functions Lesson Plan
designed to introduce students to graphing
functions. These activities can be done
individually or in teams of as many as four
students. Allow for two to three hours of class
time for the entire lesson if all portions are
done in class.
5. Use the Rise, Run Triangle Lesson. This
lesson offers students a method for finding the
slope of a line from its graph. The skills in this
lesson can be applied as a tool to real-world
examples of rate of change and slope.
6. Use the Math is Fun Interest Activity. This
gives an introduction to the concepts of
personal finance and interest. It explains how
much is paid for the use of money (as a percent
or an amount).
7. Go to Smart Exchange if you have a
SmartBoard or Airliner and choose from
multiple lessons.
8. Go to the Share My Lesson website and
choose from multiple 21st Century Lesson
Plans.
Math Arizona has explanations and overviews
for how the mathematics strands progress from
one year to the next.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
Achieve the Core is from Student
Achievement Partners, a nonprofit organization
that assembles educators and researchers to
design actions based in evidence that will
substantially improve student achievement.
Balanced Assessments is a site with free
performance tasks to use in your classroom.
Algebra I Resources
Intro to Functions YouTube Video
Graphing Rational Functions Tutorial
Slope and Rate of Change Tutorial
Online Math Calculators and Solvers
Points of Intersections Calculators
Cool Math.com
Worksheet Creator
Slope Rate of Change
1. Cards for Activity
1. Cards 2
2. Worksheet Site
2. Worksheet Link for Intro to Functions
2. Graphing Linear Equations Worksheet
Option
2. Linear Equation Worksheet
3. Lesson Plan for Introduction to Functions
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Mathematics
8th Grade Math Standard 2.3
4. Graphs and Functions Lesson Plan
5. Rise, Run Triangle Lesson
6. Math is Fun Interest Activity
7. Smart Exchange
8. Share My Lesson
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 3.1
8.Math.3.1 Visual displays and summary statistics of two-variable data condense the
information in data sets into useable knowledge
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Construct and interpret scatter plots for
1. How is it known that two variables are
bivariate measurement data to investigate
related to each other?
patterns of association between two quantities.
2. How is it known that an apparent trend is
just a coincidence?
3. How can correct data lead to incorrect
conclusions?
4. How do you know when a credible
prediction can be made?
5. How can you construct and interpret scatter
plots to investigate patterns between two
quantities?
6. How can you use the equation of a linear
model to solve problems in the context of
bivariate measurement?
7. How does the equation of a linear model
help to interpret the slope and intercept?
2. Describe patterns such as clustering,
outliers, positive or negative association, linear
association, and nonlinear association.
3. 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.
4. Use the equation of a linear model to solve
problems in the context of bivariate
measurement data, interpreting the slope and
intercept.
5. Explain patterns of association seen in
bivariate categorical data by displaying
frequencies and relative frequencies in a twoway table.
6. Construct and interpret a two-way table
summarizing data on two categorical variables
8. How do two-way tables help explain
patterns of association that are seen in bivariate collected from the same subjects.
categorical data?
7. Use relative frequencies calculated for rows
or columns to describe possible association
9. How can the use of relative frequencies
between the two variables.
describe possible association between two
variables?
10. Without graphing how can you tell if two
lines are parallel?
Academic Vocabulary:
scatter plots
bivariate measurement
clustering
outliers
positive association
Assessment:
All assessments are found in the suggested
activities links, correlating with their
numbers, unless listed below.
1. For assessment, click on Now You Try It at
the bottom of page one and assess what
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 3.1
negative association
linear association
nonlinear association
slope
intercept
two-way table
relative frequencies
variables
line of fit
trend line
correlation
positive correlation
negative correlation
no correlation
students do.
2. Choose any worksheet that you want to use
as an assessment.
3. Have students develop a systematic plan for
collecting and entering data into the Scatterplot
Manipulative Activity. An expanded
explanation found at teacher link at the top of
the page.
4. Several Activities have assessments built
into them.
5, 6, 7, & 8. Assessments are built into the
lessons. Select the assessment you wish to use.
Suggested Activities/Strategies:
9. This lesson has a homework link. You can
use that as an assessment or grade any of the
students' scatterplots or tables.
Resources/Technology:
For all activities listed below, the links are
numbered to correlate with each activity.
Examples and worksheets dealing with slope
and lines can be found at algebra tutor.
1. Teach Slope using the Parallel and
Perpendicular Lines Activity from Purple
Math.
Examples of scatter plots
2. Conduct Drill and Practice with
worksheets. See links in resources.
Examples of parallel lines
3. Use the link for Math is Fun- Scatter Plot
Tutorial. Examples are given for how to build
a graph (scatter plot) using a t-chart and
interpret results using line of best fit and slope.
Links are available for more activities and
graphs using data at the bottom of the page
labeled Data Index. Assessment can be found
at the end of the activity. (Answer questions 110.)
4. If you have a SmartBoard or Airliner, there
are several lessons at Smart Exchange that can
Examples of relative frequency
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 3.1
be used for these standards. It is free to join.
PARCC and Smarter Balance.
5. There are several lessons located at the free
site Share My Lesson. Most are 21st Century
Lessons.
Math Arizona has explanations and overviews
for how the mathematics strands progress from
one year to the next.
6. The CensusAtSchool website has several
lessons on Bivariate Measurement
Data. Explore the site and choose.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
7. The Learn Zillion website also has several
lessons and resources to use for these
standards.
Achieve the Core is from Student
Achievement Partners, a nonprofit organization
that assembles educators and researchers to
design actions based in evidence that will
substantially improve student achievement.
8. Use the 8th Grade Common Core Statistic
Lesson. Students extend their understanding of
cluster and outlier from univariate data to
bivariate data. They summarize bivariate
Balanced Assessments is a site with free
categorical data using two-way tables of counts performance tasks to use in your classroom.
and/or proportions and examine these for
patterns of association.
9. Use this Scatter Plot/Bivariate Measurement
Lesson. In the session, students will study
statistical problems by collecting and
analyzing data on two variables.
Line Plotter Interactive Site
Examples of Bivariate Measurement Data
YouTube Video on Scatter Plots
1. Slope Activity
2. Graphing Slope Intercept Worksheet
2. Scatter Plots and Line of Best Fit
Worksheet
2. Positive/Negative Correlation Worksheet
3. Scatter Plot Interactive Lesson
3. Scatter Plot Tutorial
4. Smart Exchange
5. Share My Lesson
6. Example Lessons on Bivariate
Measurement Data
6. Census at School
7. Learn Zillion
8. Common Core 8th Grade Lesson on
Statistics
9. Scatter Plot/Bivariate Measurement Lesson
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 4.1
8.Math.4.1 Transformations of objects can be used to define the concepts of congruence and
similarity
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Verify experimentally the properties of
1. What advantage, if any, is there to using the rotations, reflections, and translations.
Cartesian coordinate system to analyze the
properties of shapes?
2. Describe the effect of dilations, translations,
rotations, and reflections on two-dimensional
2. How can you physically verify that two lines figures using coordinates.
are really parallel?
3. Demonstrate that a two-dimensional figure
3. What are the properties of rotations,
is congruent to another if the second can be
reflections, and translations?
obtained from the first by a sequence of
rotations, reflections, and translations.
4. What is the effect of dilations, translations,
rotations, and reflections on two-dimensional
4. Given two congruent figures, describe a
figures using coordinates?
sequence of transformations that exhibits the
congruence between them.
5. How do you know if one two-dimensional
figure is congruent to another?
5. Demonstrate that a two-dimensional figure
is similar to another if the second can be
obtained from the first by a sequence of
6. Describe a sequence of transformation with
rotations, reflections, translations, and
two congruent figures.
dilations.
7. How do you know if one two-dimensional
6. Given two similar two-dimensional figures,
figure is similar to another when the second is
describe a sequence of transformations that
obtained from the first by a sequence of
exhibits the similarity between them.
rotations, reflections, translations, and
dilations?
7. 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.
Academic Vocabulary:
Assessment:
All assessments are found in the suggested
activities links, correlating with their
rotations
numbers, unless listed below.
reflections
translations
1. Game score is the assessment.
dilations
coordinates
2. Use a worksheet or combination of
congruent
worksheets to assess.
transformations
similar
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 4.1
parallel lines
angle sum
exterior angle
coordinate plane
interior angle
transversal
3 & 4. Assessments are built into each activity.
5. Assessment is built into the activity. Allow
students to explain the concepts of translation,
reflection, and rotation. The students should
share about the places where the activity was
difficult. Ensure that all students understand
the three concepts before moving on to another
lesson.
6. No Assessment. This activity is used as an
introduction to Translations, Rotations,
Reflections.
7. The game is interactive, so the student score
is the assessment.
8. Assessments are built into the lessons.
Suggested Activities/Strategies:
For all activities listed below, the links are
numbered to correlate with each activity.
9. This lesson has both traditional and
authentic assessment ideas at the bottom of the
lesson plan.
Resources/Technology:
Definitions and examples of flips
Examples of angles and shapes
1. Play the Pool Geometry Game.
2. Conduct Drill and Practice with
worksheets. See links in resources.
3. If you have a SmartBoard or Airliner, you
can find multiple lessons free at Smart
Exchange.
4. Share My Lesson is a website that has
several free lessons for these standards. Most
are 21st Century Lessons. Login and search
for topics.
5. Use the Interactive Lesson as an
introduction to translations, reflections, and
rotations.
Site for web-based student activities Mister
Teacher
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 4.1
6. Use this YouTube Video on Motion
Geometry from Discovery
Education. TeacherTube also has videos.
7. Play the interactive Congruent Figures
Concentration Game.
8. Learn Zillion has several lessons on
understanding angle sums, exterior angles,
angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for
similarity of triangles.
9. This Lesson matches the informal argument
standard from Youngstown City School
System. In this unit, students will be
introduced to parallel lines, transversals, and
the angles created when they cross. From here,
students expand their knowledge by using
similar triangles and their properties to create
parallel lines and apply the concepts of this
unit while they construct a geometry city.
1. Pool Geometry Game Link
2. Translation Worksheet
2. Math Drills Worksheets
2. Congruent Triangle Worksheets
2. Triangle Worksheets (More Difficult)
2. Angle Sum Worksheet
2. Printable Graph Paper Link
3. Smart Exchange
4. Share My Lesson
5. Interactive Lesson
6. YouTube Video
6. TeacherTube
7. Congruent Figures Concentration Game
8. Learn Zillion
9. Lesson on Informal Arguments
PARCC and Smarter Balance.
Math Arizona has explanations and overviews
for how the mathematics strands progress from
one year to the next.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
Achieve the Core is from Student
Achievement Partners, a nonprofit organization
that assembles educators and researchers to
design actions based in evidence that will
substantially improve student achievement.
Balanced Assessments is a site with free
performance tasks to use in your classroom.
Link to Site with Games for Geometry
Mister Teacher
Super Teacher Worksheets
Math is Fun
YouTube Congruent Triangles Video
TeacherTube Video Congruent Figures
Congruent Figures Interactive Game
Definitions of Dilations
Video on Dilations
Site with Multiple Lessons for Informal
Arguments
Tangled Web Game
Properties of Transformations
Math.Com
Math Chimp 8th Grade Math Games
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 4.2
8.Math.4.2 Direct and indirect measurement can be used to describe and make comparisons
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Explain a proof of the Pythagorean Theorem
1. Why does the Pythagorean Theorem only
and its converse.
apply to right triangles?
2. Apply the Pythagorean Theorem to
determine unknown side lengths in right
2. How can the Pythagorean Theorem be used
triangles in real-world and mathematical
for indirect measurement?
problems in two and three dimensions.
3. How are the distance formula and the
3. Apply the Pythagorean Theorem to find the
Pythagorean theorem the same? Different?
distance between two points in a coordinate
system.
4. How are the volume formulas for cones,
cylinders, prisms, and pyramids interrelated?
4. State the formulas for the volumes of cones,
cylinders, and spheres and use them to solve
5. How is the volume of an irregular figure
real-world and mathematical problems.
measured?
6. How can cubic units be used to measure
volume for curved surfaces?
7. How can you find the distance between two
points in a coordinate system using the
Pythagorean Theorem?
Academic Vocabulary:
Pythagorean Theorem
coordinate system
volume
cone
cylinder
sphere
converse
right triangles
indirect measurement
distance formula
Assessment:
All assessments are found in the suggested
activities links, correlating with their
numbers, unless listed below.
1. You can use any of the activities in the
independent practice located toward the bottom
of the lesson plan for an assessment.
2. For assessing the Measure Up Activity,
scroll to the bottom of the lesson and click the
assessment icon.
3. Print and use different worksheets to
assess for correctness. Teacher can use
individual sheets or create a packet. See links
below.
4, 5, 6, & 7. Assessment is located under its
own tab within each lesson.
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 4.2
Suggested Activities/Strategies:
2. Measure Up Activity
3. Volume of Rectangular Prism Worksheet
3. Volume of Cylinder Worksheet
3. Volume of Cones and Pyramids Worksheet
Triangle Quizzes
Resources/Technology:
For all activities listed below, the links are
numbered to correlate with each activity.
Resource for surface area of cone at about
math
1. This lesson introduces and explores the
Pythagorean Theorem. Three activities give
students the opportunity to observe triangles,
learn and use the Pythagorean Theorem, and
practice different ways of determining areas of
triangles.
Resource for explanation of Geometry at
shmoop.com
2. Use the Measure Up Activity. Students
extend their knowledge of proportions to
solving problems dealing with similarity. They
measure the heights and shadows of familiar
objects and use indirect measurement to find
the heights of things that are much bigger in
size, such as a flagpole, a school building, or a
tree.
3. Conduct Drill and Practice with
worksheets. See multiple examples of
worksheets below.
4. Use the Corner to Corner Lesson Plan.
Students further explore square roots using the
diagonals of rectangles. Using measurement,
students will discover a method for finding the
diagonal of any rectangle when the length and
width are known, which leads to the
Pythagorean Theorem.
Resource for distance formula at purplemath
PARCC offers instructional and assessment
support. Click on the tab "In the Classroom"
and at the model frameworks for math.
Illustrative Mathematics contains examples of
tasks designed by the makers of the CCSS-M
(Common Core State Standards of
Mathematics.)
Inside Mathematics has tasks, rubrics, and
discussion questions that correlate with
PARCC and Smarter Balance.
Math Arizona has explanations and overviews
for how the mathematics strands progress from
one year to the next.
Math Shell is Mathematics Assessment
Resource Service (MARS) from the Shell
Centre in Nottingham, England and it
contains a number of performance tasks.
Achieve the Core is from Student
Achievement Partners, a nonprofit organization
that assembles educators and researchers to
design actions based in evidence that will
substantially improve student achievement.
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
8th Grade Math Standard 4.2
Balanced Assessments is a site with free
performance tasks to use in your classroom.
5. Use the Polygon Capture Lesson. In this
lesson, students classify polygons according to
more than one property at a time. In the
context of a game, students move from a
simple description of shapes to an analysis of
how properties are related.
6. If you have a SmartBoard or Airliner, go to
Smart Exchange and there are several lessons
on Volume.
7. There are several 21st Century Lessons on
Volume at Share My Lesson. Go to the site and
choose a lesson.
8. Use the Prove-It Lesson Plan. During this
lesson, students will be introduced to the
Pythagorean Theorem: a squared + b squared
= c squared. They will construct a right
triangle on graph paper and draw squares on
each side of the triangle.
1. Pythagorean Theorem Activity
2. Measure Up Lesson Plan
3. Pythagorean Theorem Worksheet
3. Distance Formula Worksheet
3. Distance Formula Worksheet #2
3. Volume of Prisms/Cylinders Worksheet
3. Volume of Pyramids/Cones Worksheet
4. Corner to Corner Lesson Plan
5. Polygon Capture Lesson Plan
6. Smart Exchange
7. Share My Lesson
8. Prove It Lesson Plan
Pythagorean Theorem Examples
8th Grade Interactive Activities for
Pythagorean Theorem
Pythagorean Theorem Activities
Help with Math (Tutorial)
Slope Interactive Site
Measure Volume of Irregular Shape
Experiment
Site with Multiple Geometry
Lessons/Activities
How High Interactive Activity with Volume
Site with Links to Multiple Lesson Plans
Demonstration of Pythagorean Theorem
Pythagoras' Theorem
Picking Pythagoras
Site with Multiple Pythagorean Theorem
Resources
Video on Pythagorean Theorem
PBS Lesson Plan
PowerPoint on Pythagorean Theroem
Pythagorean Theorem with Jelly Beans
Site with Multiple Resources for Pythagorean
Theorem #2
Another Pythagorean Theorem PowerPoint
Hands On Math/Real Life Applications
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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