Unit 1: Number Systems, Irrational Numbers and
Scientific Notation
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Generic Course
1st Marking Period
5 weeks
Published
Unit Overview
Work with exponents, rational numbers, irrational numbers, perform operations with numbers in scientifc notation
Benchmark assessment 1 will be given after chapter 2 in Glencoe Course 2 book.
Transfer
Students will be able to independently use their learning to appropriately apply skills in real‐life situations ...
Know there are irrational numbers.
Be able to find decimal expansion of all rational numbers
Approximate irrational numbers on a number line
Apply properties of exponents
Write and understand scientific notation
Perform operations with numbers in scientifc notation
Meaning
Understandings
Students will understand that numbers are rational and irrational and can be written in different ways.
Essential Questions
At the end of this unit, students should be able to answer
•
How can mathematical ideas be represented?
•
Why is it helpful to write numbers in different ways?
Application of Knowledge and Skill
Students will know...
Students will know...
•
Decimals that “terminate” actually repeat the digit zero. (2.5 = 2.5000000000 ) (8.NS.1)
•
Numbers that repeat in their decimal form are called rational. (8.NS.1)
•
Numbers that do not repeat in their decimal form are called irrational. (8.NS.1)
•
The number is irrational. (8.EE.2)
•
The square root of the area of a square represents the side length of the square. (8.EE.2)
•
Exponent operation properties. (8.EE.1)
•
Apply exponent rules to perform operations with numbers in scientific notation.
Students will be skilled at...
Students will be skilled at...
•
Distinguish between rational and irrational numbers. (8.NS.1)
•
Convert a decimal expansion which repeats eventually into a rational number. (8.NS.1)
•
Find rational approximations of irrational numbers. (8.NS.2)
•
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them
approximately on a number line, and estimate the value of expressions.(8.NS.2)
•
Evaluate square roots of small perfect squares and cube roots of small perfect cubes. (8.EE.2)
•
Use square root and cube root symbols to solve and represent solutions of equations. (8.EE.2)
•
Apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1)
•
Estimate very large or very small quantities using a single digit times a power of ten. (8.EE.3)
•
Express how much larger one number expressed as a single digit times a power of ten is than another in the
context of the situation. (8.EE.3)
•
Express numbers in scientific notation. (8.EE.4)
•
Perform operations with numbers expressed in scientific notation and a mix of scientific notation and decimal
notation. (8.EE.4)
•
Choose appropriate units of measurements for a given number in scientific notation. (8.EE.4)
•
Interpret scientific notation that has been generated by technology. (8.EE.4)
Academic Vocabulary
From Marzano Proficent Scale:
Approximation, compare, convert, decimal, estimate, expansion, expression, irrational number, nonrepeating,
nonterminating, number line, rational, rational number, size, value
Compare, cube root, decimal, digit, equation, equivalent, evaluate, exponent, expression, integer, large, measurement,
number, numerical, operation, perfect cube, perfect square, power of 10, quantity, reasoning, scientific notation, small,
solution, square root, symbol
Additional words:
Radical, Square root, Cube root, Equation, Variable, Property, Unknown, Solution, Integer, Inverse operations
Learning Goal 1
Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational
approximations to estimate roots and to compare real numbers
Objective 1--(Level 1 Recall)
SWBAT:
Write fractions as decimals and decimals as fractions.
Note Clarifications from PARCC EOY:
i) Tasks do not have a context.
ii) 50% of tasks require students to write a fraction a/b as a repeating decimal by showing, filling in, or otherwise
producing the steps of a long division a ÷ b.
iii) 50% of tasks require students to write a given repeating decimal as a fraction.
iv) Tasks should involve no more than two repeating decimals i.e. 2.16666..., 0.23232323.
MA.8.CCSS.Math.Content.8.NS.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP6
MA.K‐12.CCSS.Math.Practice.MP7
MA.K‐12.CCSS.Math.Practice.MP8
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Objective 2--(Level 3 Strategic Thinking)
SWBAT:
Write and evaluate expressions involving powers and exponents
Clarification from PARCC EOY:
i)Tasks do not have a context.
MA.8.CCSS.Math.Content.8.EE.A.1
MA.8.CCSS.Math.Content.8.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP8
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Use square root and cube root symbols to represent solutions to equations of the form x = 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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and express regularity in repeated reasoning.
Learning Goal 2
Work with radicals and integer exponents
Objective 3--(Level 3 Strategic Thinking)
SWBAT:
Apply the properties of integer exponents to simplify and write equivalent numerical expressions. Simplify a real
number expressions by mutiplying and dividing monomials
Clarifications for PARCC EOY:
i) Tasks do not have a context.
ii) Tasks center on the properties and equivalence, not on simplification. For example, a task might ask a student to
classify expressions according to whether or not they are equivalent to a given expression.
iii) 50% of expressions should involve one property
iv) 30% of expressions should involve two properties
v) 20% of expressions should involve three properties
vi) Tasks should involve a single common base
MA.8.CCSS.Math.Content.8.EE.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 4--(Level 1 Recall)
SWBAT:
Use the Laws of Exponents to find powers of monomials
Clarifications from PARCC EOY:
None provided
MA.8.CCSS.Math.Content.8.EE.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 5--(Level 2 Skill/Concept)
SWBAT:
Simplify expressions involving negative exponents.
MA.8.CCSS.Math.Content.8.EE.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 6 -- (Level 3 Strategic Thinking)
In real‐world problem solving situations choose units of appropriate size for measurement of very small and very large
quantities.
Performance Clarifications for EOY:
i) Task have “thin context”.
ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks. iii) Tasks may
require students to recognize 3.7E‐2 (or 3.7e‐2) from technology as 3.7 x 10‐2
MA.8.CCSS.Math.Content.8.EE.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very
small quantities, and to express how many times as much one is than the other.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7 -- (Level 1 -Recall)
Use scientific notation to write large and small numbers.
MA.8.CCSS.Math.Content.8.EE.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 8 -- (Level 2- Skill/Concept)
Compute with numbers written in scientific notation.
Interpret scientific notation when using technology
MA.8.CCSS.Math.Content.8.EE.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 9 -- (Level 2 - Skill/Concepts)
Find square roots and cube roots.
MA.8.CCSS.Math.Content.8.NS.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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 (e.g., pi ).
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 10 A -- (Level 2 --Skill/Concept)
Estimate square roots of non‐perfect squares.
MA.8.CCSS.Math.Content.8.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
Use square root and cube root symbols to represent solutions to equations of the form x = 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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 10 B -- (Level 2 - Skill/Concept)
Estimate square and cube roots.
MA.8.CCSS.Math.Content.8.NS.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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 (e.g., pi ).
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 11 -- (Level 2 - Skill/Concept)
Compare mathematical expressions
MA.8.CCSS.Math.Content.8.NS.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
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 (e.g., pi ).
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Summative Assessment
Chapter Test/Unit Test
Unit Project
Performance based assessment
21st Century Life and Careers
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.A.1
WORK.5‐8.9.1.8.A.2
WORK.5‐8.9.1.8.A.4
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.B.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.C.1
WORK.5‐8.9.1.8.C.2
WORK.5‐8.9.1.8.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.D.1
WORK.5‐8.9.1.8.D.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.2.8.1
WORK.5‐8.9.2.8.A.1
The ability to recognize a problem and apply critical thinking and problem‐solving skills to solve the problem is
a lifelong skill that develops over time.
Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and
problem‐solving skills.
Implement problem‐solving strategies to solve a problem in school or the community.
Design and implement a project management plan using one or more problem‐solving strategies.
Gathering and evaluating knowledge and information from a variety of sources, including global perspectives,
fosters creativity and innovative thinking.
Use multiple points of view to create alternative solutions.
Collaboration and teamwork enable individuals or groups to achieve common goals with greater efficiency.
Determine an individual's responsibility for personal actions and contributions to group activities.
Demonstrate the use of compromise, consensus, and community building strategies for carrying out different
tasks, assignments, and projects.
Leadership abilities develop over time through participation in groups and/or teams that are engaged in
challenging or competitive activities.
Effective communication skills convey intended meaning to others and assist in preventing misunderstandings.
Employ appropriate conflict resolution strategies.
Demonstrate the ability to understand inferences.
Digital media are 21st‐century tools used for local and global communication.
The nature of the 21st‐century workplace has shifted, demanding greater individual accountability,
productivity, and collaboration.
Educational achievement, career choice, and entrepreneurial skills all play a role in achieving a desired
lifestyle.
Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income.
WORK.5‐8.9.2.8.3
WORK.5‐8.9.2.8.B.1
Income affects spending decisions and lifestyle.
Construct a simple personal savings and spending plan based on various sources of income.
Formative Assessment and Performance Opportunities
MAP Assessments
Tests
Quizzes
Informal Assessments
Graded Classwork
Surveys
WhiteBoard Activities
Exit tickets
Group activities
Projects
Teacher Observations
Student Interviews
Differentiation / Enrichment
•Factoring
•Lesson Extentions
•Manipulatives
•Modifications as per IEP/504
•Perfect squares and cubes
•Review and Practice
•Rules of operations with integers
•Simplifying radicals
•Small Group Instruction
•Understanding of Distributive Property
Unit Resources
http://connected.mcgraw‐hill.com/
Additional files located in folder that may need to be edited for CCSS
Video for Powers of 10: http://www.youtube.com/watch?v=0fKBhvDjuy0
http://www.illustrativemathematics.org/
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http://learnzillion.com/
https://www.khanacademy.org/
http://insidemathematics.org/index.php/8th‐grade
http://illuminations.nctm.org/LessonsList.aspx?grade=3&standard=all
Unit 2: Expressions & Equations
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Generic Course
2nd Marking Period
16 weeks
Published
Unit Overview
Write and solve two‐step equations with variables on both sides.
Solve systems of equations algebraically and by graphing.
Benchmark Assessment #2 will be given after chapter 4.
Transfer
Students will be able to independently use their learning to ...
•
Solve and graph linear relationships and identify a relationship as linear using a table or equation.
•
Graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the ‐
value that will generate the given ‐value for both equations. Students recognize that graphed lines with one
point of intersection (different slopes) will have one solution, parallel lines (same slope, different ‐intercepts)
have no solutions, and lines that are the same (same slope, same ‐intercept) will have infinitely many
solutions.
Meaning
Understandings
Students will understand that
•
Unit rates can be explained in graphical representation, algebraic equations, and in geometry through similar
triangles.
•
The solution to a system of two linear equations in two variables is an ordered pair that satisfies both
equations.
•
Some systems of equations have no solutions (parallel lines) and others have infinite solutions (be the same
line).
Essential Questions
Students will keep considering...
•
How can you communicate mathematical ideas effectively?
•
What is equivalence?
•
Why is one variable dependent upon the other in relationships?
•
What makes a solution strategy both efficient and effective?
•
How is it determined if multiple solutions to an equation are valid?
•
How does the context of the problem affect the reasonableness of a solution?
•
Why can two equations be added together to get another true equation?
Application of Knowledge and Skill
Students will know...
Students will know...
•
Understand the characteristics of linear equations in graphs, tables and equations.
•
Unit rate of a proportion relates to the slope of a linear line.
Students will be skilled at...
Students will be skilled at...
•
Determine whether a relationship is linear.
•
Compare graphs, tables, and equations of proportional relationships.
•
Graph proportional relationships and interpret the unit rate as the slope.
•
Estimate solutions by graphing equations.
•
Solve systems by graphing, substitution, or elimination (combination).
•
Determine if a system has one solution, no solutions, or many solutions.
•
Interpret the solution to a system of equations in context.
Academic Vocabulary
Multiplicative Inverse, properties, two‐step equation, null set, identity, linear relationship, constant rate of change,
slope, rise, run, direct rate of change, constant of variation, constant of proportionality, y‐intercept, slope‐intercept
form, x‐intercept, standard form, point‐slope form, system of Linear Equations, Simultaneous equations, Linear
equations, Rate of change, Parallel, Substitution, Eliminiation, Intersecting lines, Origin, Axis, compare, coordinate
plane, equation, graph interpret, intersect, line, origin, point proportional relationship, similar, slope, table, triangle,
unit rate, vertical, Coefficient, distributive property, equation, example, infinite, integer, like, linear, rational number,
solution, term, Analyze, decrease, function, functional relationship, graph, increase, initial, linear, model, nonlinear,
qualitative, quantity, relationship, sketch, value.
Learning Goal 1
Linear equations in one variable can have one solution, infinitely many solutions, or no solutions.
Write and solve two‐step equations and solve equations with variables on both sides.
Objective 2.1--(Level Two: Skill/Concept)
SWBAT:
1. Solve equations with rational coefficients.
Note Clarifications from PARCC EOY:
i) Pool should contain task with and without contexts.
ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks.
MA.8.CCSS.Math.Content.8.EE.C.7
MA.8.CCSS.Math.Content.8.EE.C.7a
MA.8.CCSS.Math.Content.8.EE.C.7b
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
MA.K‐12.CCSS.Math.Practice.MP7
Solve linear equations in one variable.
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.
Objective 2.2a --(Level Two: Skill/Concept) INQUIRY LAB
SWBAT:
1. Use a bar graph to write and solve two‐step equations.
Note Clarifications from PARCC EOY:
i) Pool should contain task with and without contexts.
ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks
MA.8.CCSS.Math.Content.8.EE.C.7
MA.8.CCSS.Math.Content.8.EE.C.7a
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Solve linear equations in one variable.
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).
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 2.2b -- (Level Two: Skill/Concept)
SWBAT:
1. Solve two‐step equations.
Note Clarifications from PARCC EOY:
i) Pool should contain task with and without contexts.
ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks
MA.8.CCSS.Math.Content.8.EE.C.7
MA.8.CCSS.Math.Content.8.EE.C.7a
MA.8.CCSS.Math.Content.8.EE.C.7b
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Solve linear equations in one variable.
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 2.3--(Level Two: Skill/Concept)
SWBAT:
2. Write two‐step equations that represent situations.
Clarification from PARCC EOY:
i) Tasks do not have a context.
ii) Given a non‐vertical line in the coordinate plane, tasks might for example require students to choose two pairs of
points and record the rise, run, and slope relative to each pair and verity that they are the same.
iii) The testing interface can provide students with a calculation aid of the specified kind for these tasks.
MA.8.CCSS.Math.Content.8.EE.C.7
MA.8.CCSS.Math.Content.8.EE.C.7a
MA.8.CCSS.Math.Content.8.EE.C.7b
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Solve linear equations in one variable.
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 2.4a (Level Two: Skills/Concept) INQUIRY LAB
SWBAT: Solve equations with variables on each side using algebra tiles.
MA.8.CCSS.Math.Content.8.EE.C.7
MA.8.CCSS.Math.Content.8.EE.C.7a
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP5
Solve linear equations in one variable.
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).
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Objective 2.4b -- (Level Two: Skills/Concept)
SWBAT:
1. Solve equations with variables on each side.
Note Clarifications from PARCC EOY:
i) Pool should contain task with and without contexts.
ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks
MA.8.CCSS.Math.Content.8.EE.C.7
MA.8.CCSS.Math.Content.8.EE.C.7a
MA.8.CCSS.Math.Content.8.EE.C.7b
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Solve linear equations in one variable.
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Learning Goal 2
Understand the connections between proportional relationships, lines, and linear equations.
Objective 3.1--(Level One: Recall)
SWBAT:
Identify proportional and nonproportional linear relationships by finding a constant rate of change.
Clarifications for PARCC EOY:
i) Tasks do not have a context
MA.8.CCSS.Math.Content.8.EE.B
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
Understand the connections between proportional relationships, lines, and linear equations.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 3.2a --(Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Use a graphing calculator to fnd rate of change.
MA.8.CCSS.Math.Content.8.EE.B.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
proportional relationships represented in different ways.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 3.2b -- (Level Two: Skill/Concept)
SWBAT: Use tables and graphs to find the slope of a line.
MA.8.CCSS.Math.Content.8.EE.B.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
proportional relationships represented in different ways.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 3.3 -- (Level Two: Skill/Concept)
SWBAT: Use direct variation to solve problems.
MA.8.CCSS.Math.Content.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
proportional relationships represented in different ways.
MA.8.CCSS.Math.Content.8.EE.B.6
MA.8.CCSS.Math.Content.8.F.A.2
MA.8.CCSS.Math.Content.8.F.B.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions).
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 3.4--(Level Two: Skill/Concept)
SWBAT:
Graph linear equations using the slope and y‐intercept.
Clarifications from PARCC EOY:
i) Pool should contain tasks with and without contexts.
MA.8.CCSS.Math.Content.8.EE.B.6
MA.8.CCSS.Math.Content.8.F.A.3
MA.8.CCSS.Math.Content.8.F.B.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
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.
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 3.5a -- (Level Three: Strategic Thinking) INQUIRY LAB
SWBAT: Graph and analyze slope triangles
MA.8.CCSS.Math.Content.8.EE.B.6
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP5
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Objective 3.5b -- (Level Two: Skills/Concepts)
SWBAT: Graph an equation using x‐ and y‐ intercepts.
MA.8.CCSS.Math.Content.8.EE.C.8c
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Solve real‐world and mathematical problems leading to two linear equations in two variables.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 3.6 -- (Level Three: Strategic Thinking)
SWBAT: Solve problems by using the guess, check, and revise strategy.
MA.8.CCSS.Math.Content.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 3.7a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: use graphing technology to find one solution for a set of two equations.
MA.8.CCSS.Math.Content.8.EE.C.8
MA.8.CCSS.Math.Content.8.EE.C.8a
MA.8.CCSS.Math.Content.8.EE.C.8b
MA.8.CCSS.Math.Content.8.EE.C.8c
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP5
MA.K‐12.CCSS.Math.Practice.MP7
Analyze and solve pairs of simultaneous linear equations.
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.
Solve real‐world and mathematical problems leading to two linear equations in two variables.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Look for and make use of structure.
Objective 3.7b -- (Level Three: Strategic Thinking)
SWBAT: solve systems of linear equations by graphing.
MA.8.CCSS.Math.Content.8.EE.C.8
MA.8.CCSS.Math.Content.8.EE.C.8a
MA.8.CCSS.Math.Content.8.EE.C.8b
MA.8.CCSS.Math.Content.8.EE.C.8c
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Analyze and solve pairs of simultaneous linear equations.
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.
Solve real‐world and mathematical problems leading to two linear equations in two variables.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 3.8 -- (Level Two: Skills/Concepts)
SWBAT: Solve systems of equations algebraically.
MA.8.CCSS.Math.Content.8.EE.C.8
MA.8.CCSS.Math.Content.8.EE.C.8a
MA.8.CCSS.Math.Content.8.EE.C.8b
MA.8.CCSS.Math.Content.8.EE.C.8c
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Analyze and solve pairs of simultaneous linear equations.
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.
Solve real‐world and mathematical problems leading to two linear equations in two variables.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 3.9 -- (Level Three: Strategic Thinking)
SWBAT: Solve real world mathematical problems using systems of linear equations.
MA.8.CCSS.Math.Content.8.EE.C.8
MA.8.CCSS.Math.Content.8.EE.C.8a
MA.8.CCSS.Math.Content.8.EE.C.8b
MA.8.CCSS.Math.Content.8.EE.C.8c
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP5
Summative Assessment
Analyze and solve pairs of simultaneous linear equations.
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.
Solve real‐world and mathematical problems leading to two linear equations in two variables.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Unit Test
Unit Project
Performance based assessment
21st Century Life and Careers
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.A.1
WORK.5‐8.9.1.8.A.2
WORK.5‐8.9.1.8.A.4
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.B.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.C.1
WORK.5‐8.9.1.8.C.2
WORK.5‐8.9.1.8.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.D.1
WORK.5‐8.9.1.8.D.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.2.8.1
WORK.5‐8.9.2.8.A.1
WORK.5‐8.9.2.8.3
WORK.5‐8.9.2.8.B.1
The ability to recognize a problem and apply critical thinking and problem‐solving skills to solve the problem is
a lifelong skill that develops over time.
Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and
problem‐solving skills.
Implement problem‐solving strategies to solve a problem in school or the community.
Design and implement a project management plan using one or more problem‐solving strategies.
Gathering and evaluating knowledge and information from a variety of sources, including global perspectives,
fosters creativity and innovative thinking.
Use multiple points of view to create alternative solutions.
Collaboration and teamwork enable individuals or groups to achieve common goals with greater efficiency.
Determine an individual's responsibility for personal actions and contributions to group activities.
Demonstrate the use of compromise, consensus, and community building strategies for carrying out different
tasks, assignments, and projects.
Leadership abilities develop over time through participation in groups and/or teams that are engaged in
challenging or competitive activities.
Effective communication skills convey intended meaning to others and assist in preventing misunderstandings.
Employ appropriate conflict resolution strategies.
Demonstrate the ability to understand inferences.
Digital media are 21st‐century tools used for local and global communication.
The nature of the 21st‐century workplace has shifted, demanding greater individual accountability,
productivity, and collaboration.
Educational achievement, career choice, and entrepreneurial skills all play a role in achieving a desired
lifestyle.
Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income.
Income affects spending decisions and lifestyle.
Construct a simple personal savings and spending plan based on various sources of income.
Formative Assessment and Performance Opportunities
MAP Assessments
Tests
Quizzes
Informal Assessments
Graded Classwork
Surveys
WhiteBoard Activities
Exit tickets
Group activities
Projects
Teacher Observations
Student Interviews
Differentiation / Enrichment
•Calculators
•Centers
•Clickers
•Computer
•Document Cameras
•Graphing Calculators
.
.
.
.
.
.
•Lesson Extentions
•Manipulatives
•Modifications as per IEP/504
•Review and Practice
•Small Group Instruction
•Smartboards
Unit Resources
Glencoe Math: Built to the Common Core
Chapter 2 Equations in One Variable
Chapter 3 Equations in Two Variables
www.connected.mcgraw‐hill.com
This site contains large PDFs with tasks for units 3 & 4
http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm
http://www.illustrativemathematics.org/
http://learnzillion.com/
https://www.khanacademy.org/
http://insidemathematics.org/index.php/8th‐grade
http://illuminations.nctm.org/LessonsList.aspx?grade=3&standard=all
.
.
.
.
.
.
Unit 3: Functions
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Generic Course
3rd Marking Period
5 weeks
Published
Unit Overview
Invesitgate and understand linear functions.
Understand what makes a function.
Determine if a function is linear or non‐linear.
Students should have exposure to other types of functions so that they understand there are other types besides
two categories of "linear" and "non‐linear". Experiment with data to create and understand scatter plots.
Benchmark 2 will be given after chapter 4.
Transfer
Students will be able to independently use their learning to ...
Students will understand that functions describe relationships and will be able to compare and construct a function.
The equation y=mx+b will be interpreted as a straight line, where m and b are constants. Students learn to recognize
linearity in a table when constant differences between input values produce constant differences between output
values, and they can use the constant rate of change and initial value appropriately in a verbal description of a context.
Students will establish a routine of exploring functional relationships algebraically, graphically, and numerically in
tables and verbal descriptions. When using functions to model a linear relationship between quantities, students learn
to determine the rate of change of the function which is the slope of a graph.
Students will apply experience with coordinate planes and linear functions in the study of association between two
variables related to a question of interest. The shape is a description of the cloud of points on a plane, the center is the
line of best fit, and the spread is how far data points are from the line.
Meaning
Understandings
Students will understand that
•
A function is a specific topic of relationship in which each input has a unique output which can be represented
in a table.
•
A function can be represented graphically using ordered pairs that consist of the input and the output of the
function in the form (input, output).
•
A function can be represented with an algebraic rule.
•
The equation is a straight line and that slope and y‐intercept are critical to solving real problems involving
linear relationships.
•
Changes in varying quantities are often related by patterns which can be used to predict outcomes and solve
problems.
•
Linear functions may be used to represent and generalize real situations.
•
Written descriptions, tables, graphs, and equations are useful in representing and investigating relationships
between varying quantities.
•
Different representations (written descriptions, tables, graphs, and equations) of the relationships between
varying quantities may have different strengths and weaknesses.
•
Linear functions may be used to represent and generalize real situations.
•
Slope and ‐intercept are keys to solving real problems involving linear relationship models of data.
•
Some data may be misleading based on representation.
Essential Questions
Students will keep considering...
•
How can you find and use patterns to model real‐world situations?
•
How can we model relationships between quantities?
Application of Knowledge and Skill
Students will know...
Students will know...
The charactersitics of a linear function in an equation, table, and a graph.
How the changes in a variable affect the function on an equation, table and a graph.
Students will be skilled at...
Students will be skilled at...
•
Verify that a relationship is a function or not. (8.F.1)
•
Reason from a context, graph, or table after knowing which quantity is the input and which is the output.
(8.F.1)
•
Represent and compare functions numerically, graphically, verbally and algebraically. (8.F.2)
•
Interpret equations in form as a linear function. (8.F.3)
•
Determine whether a function is linear or non‐linear. (8.F.3)
•
Identify and contextualize the rate of change and the initial value from tables, graphs, equations, or verbal
descriptions. (8.F.4)
•
Construct a model for a linear function. (8.F.4)
•
Describe the qualities of a function using a graph (e.g., where the function is increasing or decreasing). (8.F.5)
•
Sketch a graph when given a verbal description of a situation. (8.F.5)
•
Use similar triangles to explain why the slope is the same between any two distinct points on a non‐vertical
line in the coordinate plane. (8.EE.6)
•
Derive the equation for a line through the origin. (8.EE.6)
•
Construct and interpret scatter plots and two‐way tables for patterns such as positive or negative association,
linearity or curvature, and outliers. (8.SP.1)
•
Generate an approximate line of best fit. (8.SP.2)
•
Use the equation of a linear model to solve problems in the context of bivariate measurement data. (8.SP.3)
•
Interpret the slope and ‐intercept of the line of best fit in context. (8.SP.3)
•
Show that patterns of association can also be seen in bivariate categorical data by displaying frequencies and
relative frequencies in a two‐way table. (8.SP.4)
•
Construct and interpret a two‐way table summarizing data on two categorical variables collected from the
same subjects. (8.SP.4)
Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
(8.SP.4)
Academic Vocabulary
Function, Graph of a function, Domain, Range, Input/output, Ordered pairs/coordinate plane, Slope, Rate of change,
Unit rate, Linear/non‐linear functions
Bivariate data, Clustering, Outlier, Positive/negative association, continuous data, dependent variable, independent
variable, relation, range, linear equation, discrete data, quadratic function, qualitative graphs,function table
Learning Goal 1
Define, evaluate, compare functions
Objective 1--(Level 1 Recall)
SWBAT:
Translate tables and graphs into linear equations.
MA.8.CCSS.Math.Content.8.F.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 2--(Level 2 Skill/Concept)
SWBAT:
Represent relations using tables and graphs.
MA.8.CCSS.Math.Content.8.F.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 3--(Level 2 Skill/concept)
SWBAT:
Determine whether a relation is a function.
Find function values and complete function.
MA.8.CCSS.Math.Content.8.F.A.1
MA.8.CCSS.Math.Content.8.F.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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).
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 4--(Level 2 Skill/Concept)
SWBAT:
Represent linear functions using tables and graphs.
MA.8.CCSS.Math.Content.8.F.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 5--(Level 3 Strategic Thinking)
SWBAT:
Solve problems by making a table.
Compare properties of functions represented in different ways.
MA.8.CCSS.Math.Content.8.F.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions).
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 6 -- (Level 3 Strategic Thinking)
Find and interpret the rate of change and initial value of a function.
MA.8.CCSS.Math.Content.8.F.B.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
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7 -- (Level 3 Strategic Thinking)
Determine whether a function is linear of non‐linear.
MA.8.CCSS.Math.Content.8.F.B.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 8--(Level 2 - Skill/Concept)
Graph quadratic functions.
MA.8.CCSS.Math.Content.8.F.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 9 -- (Level 2-Skill/Concept)
Use a graphing calculator to graph families of non‐linear functions.
Sketch and describe qualitative graphs.
MA.8.CCSS.Math.Content.8.F.B.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Summative Assessment
Chapter Tests
Unit Test
Unit Project
Performance based assessment
21st Century Life and Careers
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.A.1
WORK.5‐8.9.1.8.A.2
The ability to recognize a problem and apply critical thinking and problem‐solving skills to solve the problem is
a lifelong skill that develops over time.
Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and
problem‐solving skills.
Implement problem‐solving strategies to solve a problem in school or the community.
WORK.5‐8.9.1.8.A.4
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.B.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.C.1
WORK.5‐8.9.1.8.C.2
WORK.5‐8.9.1.8.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.D.1
WORK.5‐8.9.1.8.D.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.2.8.1
WORK.5‐8.9.2.8.A.1
WORK.5‐8.9.2.8.3
WORK.5‐8.9.2.8.B.1
Design and implement a project management plan using one or more problem‐solving strategies.
Gathering and evaluating knowledge and information from a variety of sources, including global perspectives,
fosters creativity and innovative thinking.
Use multiple points of view to create alternative solutions.
Collaboration and teamwork enable individuals or groups to achieve common goals with greater efficiency.
Determine an individual's responsibility for personal actions and contributions to group activities.
Demonstrate the use of compromise, consensus, and community building strategies for carrying out different
tasks, assignments, and projects.
Leadership abilities develop over time through participation in groups and/or teams that are engaged in
challenging or competitive activities.
Effective communication skills convey intended meaning to others and assist in preventing misunderstandings.
Employ appropriate conflict resolution strategies.
Demonstrate the ability to understand inferences.
Digital media are 21st‐century tools used for local and global communication.
The nature of the 21st‐century workplace has shifted, demanding greater individual accountability,
productivity, and collaboration.
Educational achievement, career choice, and entrepreneurial skills all play a role in achieving a desired
lifestyle.
Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income.
Income affects spending decisions and lifestyle.
Construct a simple personal savings and spending plan based on various sources of income.
Formative Assessment and Performance Opportunities
MAP Assessments
Tests
Quizzes
Informal Assessments
Graded Classwork
Surveys
WhiteBoard Activities
Exit tickets
Group activities
Projects
Teacher Observations
Student Interviews
Differentiation / Enrichment
•Calculators
•Centers
•Clickers
•Computer
•Document Cameras
•Graphing Calculators
•Lesson Extentions
•Manipulatives
•Modifications as per IEP/504
•Review and Practice
•Small Group Instruction
•Smartboards
•www.connected.mcgraw‐hill.com
Unit Resources
Additional files located in folder that may need to be edited for CCSS
www.connected.mcgraw‐hill.com
http://www.illustrativemathematics.org/
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http://learnzillion.com/
https://www.khanacademy.org/
http://insidemathematics.org/index.php/8th‐grade
http://illuminations.nctm.org/LessonsList.aspx?grade=3&standard=all
Site has links and lesson for making graphs for various stories to compare time and distance or time and height
http://blog.mrmeyer.com/?p=213
This site has large PDF files with various tasks for functions for units 3 & 4 including sample answers and rubrics for
other students
http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm
Scatter plot:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L673
http://illuminations.nctm.org/LessonDetail.aspx?id=L646
http://illuminations.nctm.org/LessonDetail.aspx?id=L298
http://www.pbs.org/teachers/connect/resources/4442/preview/
http://www.pbs.org/teachers/connect/resources/4384/preview/
http://www.education.ucsb.edu/ucsbpt3/afield/teacher_projects/jimsfinal/Jimstudent.htm
Unit 4: Geometry
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Generic Course
3rd Marking Period
17 weeks
Published
Unit Overview
Understand how to apply and solve the Pythagorean Theorem. Understand congruence and similarity using physical
models, transparencies, or geometry software. Solve real‐world and mathematical problems involving volume of
cylinders, cones, and spheres.
Benchmark 3 will be given after chapter 6.
Transfer
Students will be able to independently use their learning to ...
•
Apply the Pythagorean theorem to real‐world context.
•
Solve Pythagorean theorem problem for missing sides of a right triangle (2‐D and 3‐D problems) and distances
on the coordinate plane.
•
Explain and prove the Pythagorean Theorem its converse.
•
Describe the effect of translations, reflections, rotations, and dilations on geometric figures.
•
Describe transformations that produce congruent and similar figures.
•
Find the volume and surface area of cones, cylinders, and spheres.
•
Apply Volume and Surface area to real‐world context.
•
Find a missing dimension given the volume of rounded object.
•
Give volume in terms of pi.
•
Evaluate square roots of small perfect squares and cube roots of small perfect cubes
•
Use square root and cube root symbols to solve and represent solutions of equations.
Meaning
Understandings
Students will understand that
•
Right triangles have a special relationship among the side lengths which can be represented by a model and a
formula.
•
The Pythagorean Theorem can be used to find the missing side lengths in a coordinate plane and real‐world
situations.
•
The Pythagorean Theorem and its converse can be proven.
•
Rounded object volume can be calculated with specific formulas.
•
Pi is necessary when calculating volume of rounded objects.
•
Every number has a decimal expansion.
•
The value of any real number can be represented in relation to other real numbers such as with decimals
converted to fractions, scientific notation and numbers written with exponents ( ).
Essential Questions
Students will keep considering...
•
How can you use different measurements to solve real‐life problems?
•
How can algebraic concepts be applied to geometry?
•
How can we best show or describe the change in position of a figure?
•
How can you determine congruence and similarity?
•
Why are formulas important in math and science?
•
Why does the Pythagorean Theorem apply only to right triangles?
•
How does the knowledge of how to use right triangles and the Pythagorean Theorem enable the design and
construction of such structures as a properly pitched roof, handicap ramps to meet code, structurally stable
bridges, and roads?
•
How can the Pythagorean Theorem be used for indirect measurement?
•
How do indirect measurement strategies allow for the measurement of items in the real world such as
playground structures, flagpoles, and buildings?
•
How do we determine the volume of rounded objects?
•
Why are quantities represented in multiple ways?
•
How is the universal nature of properties applied to real numbers?
Application of Knowledge and Skill
Students will know...
Students will know...
•
The Pythagorean Theorem
•
When to appy the Pythagorean Theorem
•
The volume formulas for cylinders, cones and spheres.
•
The number is irrational.
•
The square root of the area of a square represents the side length of the square.
Students will be skilled at...
Students will be skilled at...
•
Explain a proof of the Pythagorean Theorem and its converse.
•
Use the Pythagorean Theorem to solve for a missing side of a right triangle given the other 2 sides in both 2‐D
and 3‐D problems.
•
Apply the Pythagorean Theorem to solve problems in real‐world contexts.
•
Apply the Pythagorean Theorem to find the distance between two points in the coordinate system.
•
Find the volume of rounded objects in real‐world contexts.
•
Give volume in terms of and using or
•
Find a missing dimension given the volume of rounded object.
•
Evaluate square roots of small perfect squares and cube roots of small perfect cubes
•
Use square root and cube root symbols to solve and represent solutions of equations.
Academic Vocabulary
Converse, coordinate system, dimension, distance, length, point, proof, Pythagorean theorem, side, unknown, Cone,
cylinder, formula, mathematical, real world, sphere, volume, Exponent, Radical, Irrational number, Rational number,
Square root, Cube root, Perfect cube, Perfect square, Cylinder, Cone, Sphere, Volume, Pi, In terms of pi, Radius, Height,
Slant height, Legs of a triangle, Hypotenuse, Right triangle, Pythagorean triple, Distance formula, perpendicular lines,
parallel lines, transversal, interior angles, exterior angles, alternate interior angles, alternate exterior angles,
corresponding angles, inductive reasoning, deductive reasoning, paragraph proof, informal proof, two ‐ column proof,
formal proof, theorem, transformation, pre‐image, image, translation, congruent, reflection, line of reflection,
rotation, center of rotation, corresponding parts, similar, similar polygons, scale factor, indirect measurement,
composite solids, hemisphere, lateral area, total surface area, similar solids
Learning Goal 1
•
Describe a sequence of transformations that exhibits the similarity between two similar two‐dimensional
figures (8.G.A.4)
•
Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using
coordinates (8.G.A.3)
Objective 5.1a --(Level Two: Skill/Concept) INQUIRY LAB
SWBAT:
1. Examine angle relationships formed when parallel lines are cut by a transversal. 8.G.5
MA.8.CCSS.Math.Content.8.G.A.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP5
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Objective 5.1b -- (Level Two: Skill/Concept)
SWBAT: Identify relationships of angles formed by two parallel lines cut by a transversal.
MA.8.CCSS.Math.Content.8.G.A.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 5.2 -- (Level Three: Strategic Thinking)
SWBAT: Write geometric proofs.
MA.8.CCSS.Math.Content.8.G.B.6
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Explain a proof of the Pythagorean Theorem and its converse.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 5.3a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Explore the relationship among the angles of a triangle.
MA.8.CCSS.Math.Content.8.G.A.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 5.3b -- (Level Two: Skill/Concept)
SWBAT: Find the missing angles measures in triangles.
MA.8.CCSS.Math.Content.8.G.A.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 5.4 -- (Level Two: Skill/Concept)
SWBAT: Find the sum of the angle measures of a polygon and the measure of one interior angle of a regular polygon.
MA.8.CCSS.Math.Content.8.G.A.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 5.5 -- (Level Two: Skill/Concept)
SWBAT: Use the Pythagorean Theorem.
MA.8.CCSS.Math.Content.8.EE.A.2
MA.8.CCSS.Math.Content.8.G.B.7
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
Use square root and cube root symbols to represent solutions to equations of the form x = 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.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real‐world and
mathematical problems in two and three dimensions.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 5.6a -- (Level Three: Strategic Thinking) INQUIRY LAB
SWBAT: Prove the Pythagorean Theorem and its converse.
MA.8.CCSS.Math.Content.8.G.B.6
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP7
Explain a proof of the Pythagorean Theorem and its converse.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Look for and make use of structure.
Learning Goal 2
Use the Pythagorean Theorem to find side lengths of right triangles and distances on the coordinate plane.
Understand and apply the Pythagorean Theorem
Objective 5.6b -- (Level Two: Skill/Concept)
SWBAT: Solve problems using the Pythagorean Theorem
MA.8.CCSS.Math.Content.8.EE.A.2
MA.8.CCSS.Math.Content.8.G.B.7
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Use square root and cube root symbols to represent solutions to equations of the form x = 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.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real‐world and
mathematical problems in two and three dimensions.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 5.7 -- (Level Two: Skill/Concept)
SWBAT: Find the distance between two points on the coordinate plane.
MA.8.CCSS.Math.Content.8.EE.A.2
MA.8.CCSS.Math.Content.8.G.B.8
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
Use square root and cube root symbols to represent solutions to equations of the form x = 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.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 6.1a -- (Level Two: Skill/Concept)
SWBAT: Identify and apply flips, slides, and turns.
MA.8.CCSS.Math.Content.8.G.A.1
MA.8.CCSS.Math.Content.8.G.A.1a
MA.8.CCSS.Math.Content.8.G.A.1b
MA.8.CCSS.Math.Content.8.G.A.1c
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP8
Verify experimentally the properties of rotations, reflections, and translations:
Lines are taken to lines, and line segments to line segments of the same length.
Angles are taken to angles of the same measure.
Parallel lines are taken to parallel lines.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and express regularity in repeated reasoning.
Objective 6.1b -- (Level Two -- Skill/Concept)
SWBAT: Graph translations on the coordinate plane.
MA.8.CCSS.Math.Content.8.G.A.1
MA.8.CCSS.Math.Content.8.G.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP8
Verify experimentally the properties of rotations, reflections, and translations:
Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using
coordinates.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and express regularity in repeated reasoning.
Objective 6.2 -- (Level Two: Skill/Concept)
SWBAT: Graph reflections on the coordinate plane.
MA.8.CCSS.Math.Content.8.G.A.1
MA.8.CCSS.Math.Content.8.G.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Verify experimentally the properties of rotations, reflections, and translations:
Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using
coordinates.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 6.3a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Identify rotational symmetry.
MA.8.CCSS.Math.Content.8.G.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Verify experimentally the properties of rotations, reflections, and translations:
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 6.3b -- (Level Two: Skill/Concept)
SWBAT: Graph rotations on the coordinate plane.
MA.8.CCSS.Math.Content.8.G.A.1
MA.8.CCSS.Math.Content.8.G.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Verify experimentally the properties of rotations, reflections, and translations:
Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using
coordinates.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 6.4a (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Identify dilations
MA.8.CCSS.Math.Content.8.G.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using
coordinates.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 6.4b -- (Level Two: Skill/Concept)
SWBAT: Use scale factors to graph dilations.
MA.8.CCSS.Math.Content.8.G.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using
coordinates.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7.1a -- (Level Two: Skill/Concept)
SWBAT: Draw compositions of translations, reflections, and rotations.
MA.8.CCSS.Math.Content.8.G.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 7.1b -- (Level Two: Skill/Concept)
SWBAT: Use a series of transformations to create congruent figures.
MA.8.CCSS.Math.Content.8.G.A.1
MA.8.CCSS.Math.Content.8.G.A.1a
MA.8.CCSS.Math.Content.8.G.A.1b
MA.8.CCSS.Math.Content.8.G.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Verify experimentally the properties of rotations, reflections, and translations:
Lines are taken to lines, and line segments to line segments of the same length.
Angles are taken to angles of the same measure.
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7.2a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Determine which three pairs of corresponding parts can be used to show that two triangles are congruent.
MA.8.CCSS.Math.Content.8.G.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 7.2b -- (Level Two: Skill/Concept)
SWBAT: Write congruence statements for congruent figures.
MA.8.CCSS.Math.Content.8.G.A.2
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7.3a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Investigate properties of similar triangles.
MA.8.CCSS.Math.Content.8.G.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 7.3b -- (Level Two: Skill/Concept)
SWBAT: Use transformations to create similar figures.
MA.8.CCSS.Math.Content.8.G.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 7.4 -- (Level Two: Skill/Concept)
SWBAT: Identify similar polygons and finding missing measures of similar polygons.
MA.8.CCSS.Math.Content.8.G.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7.5 -- (Level Two: Skill/Concept)
SWBAT: Solve problems involving similar triangles.
MA.8.CCSS.Math.Content.8.G.A.5
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 7.6 -- (Level Two -- Skill/Concept)
SWBAT: Relate the slope of a line to similar triangles.
MA.8.CCSS.Math.Content.8.EE.B.6
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 7.7 -- (Level Two: Skill/Concept)
SWBAT: Find the relationship between perimeters and areas of similar figures.
MA.8.CCSS.Math.Content.8.G.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Learning Goal 3
Solve real‐world and mathematical problems involving volume of cylinders, cones, and spheres.
Objective 8.1a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Determine how some 3‐D figures are related to circles.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 8.1b -- (Level Two: Skill/Concept)
SWBAT: Find the volume of cylinders.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP6
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Attend to precision.
Objective 8.2 -- (Level Two -- Skill/Concept)
SWBAT: Find the volume of cones
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 8.3 -- (Level Two: Skill/Concept)
SWBAT: Find the volume of spheres.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Objective 8.4a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Find the surface area of cylinders using models and nets.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 8.4b -- (Level Two: Skill/Concept)
SWBAT: Find the surface area of cylinders.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 8.5a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Justify the formula for the surface area of a cone by using a net.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 8.6a -- (Level Two: Skill/Concept) INQUIRY LAB
SWBAT: Determine how changes in dimensions affect area and volume.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Objective 8.5b -- (Level Two: Skill/Concept)
SWBAT: Find the surface area of cones
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP7
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Look for and make use of structure.
Objective 8.6b -- (Level Three: Strategic Thinking)
SWBAT: Solve problems involving similar solids.
MA.8.CCSS.Math.Content.8.G.C.9
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and
mathematical problems.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Summative Assessment
Unit Test
Unit Project
Performance based assessment
21st Century Life and Careers
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.A.1
WORK.5‐8.9.1.8.A.2
WORK.5‐8.9.1.8.A.4
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.B.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.C.1
WORK.5‐8.9.1.8.C.2
WORK.5‐8.9.1.8.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.D.1
WORK.5‐8.9.1.8.D.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.2.8.1
WORK.5‐8.9.2.8.A.1
The ability to recognize a problem and apply critical thinking and problem‐solving skills to solve the problem is
a lifelong skill that develops over time.
Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and
problem‐solving skills.
Implement problem‐solving strategies to solve a problem in school or the community.
Design and implement a project management plan using one or more problem‐solving strategies.
Gathering and evaluating knowledge and information from a variety of sources, including global perspectives,
fosters creativity and innovative thinking.
Use multiple points of view to create alternative solutions.
Collaboration and teamwork enable individuals or groups to achieve common goals with greater efficiency.
Determine an individual's responsibility for personal actions and contributions to group activities.
Demonstrate the use of compromise, consensus, and community building strategies for carrying out different
tasks, assignments, and projects.
Leadership abilities develop over time through participation in groups and/or teams that are engaged in
challenging or competitive activities.
Effective communication skills convey intended meaning to others and assist in preventing misunderstandings.
Employ appropriate conflict resolution strategies.
Demonstrate the ability to understand inferences.
Digital media are 21st‐century tools used for local and global communication.
The nature of the 21st‐century workplace has shifted, demanding greater individual accountability,
productivity, and collaboration.
Educational achievement, career choice, and entrepreneurial skills all play a role in achieving a desired
lifestyle.
Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income.
WORK.5‐8.9.2.8.3
WORK.5‐8.9.2.8.B.1
Income affects spending decisions and lifestyle.
Construct a simple personal savings and spending plan based on various sources of income.
Formative Assessment and Performance Opportunities
MAP Assessments
Tests
Quizzes
Informal Assessments
Graded Classwork
Surveys
WhiteBoard Activities
Exit tickets
Group activities
Projects
Teacher Observations
Student Interviews
Differentiation / Enrichment
.
•Calculators
•Centers
•Clickers
•Computer
•Document Cameras
•Graphing Calculators
•Lesson Extentions
•Manipulatives
•Modifications as per IEP/504
•Review and Practice
•Small Group Instruction
•Smartboards
.
.
.
.
.
.
.
.
.
.
.
Unit Resources
Glencoe Math: Built to the Common Core
Chapter 5: Triangles and the Pythagorean Theorem
Chapter 6: Transformations
Chapter 7: Congruence and Similarity
Chapter 8: Volume and Surface Area
www.connected.mcgraw‐hill.com Online Curriculum Program Resources
http://blog.mrmeyer.com/?p=17442
Meatball Task Volume of cylinder and spheres
Additional files located in folder that may need to be edited for CCSS
http://www.illustrativemathematics.org/
http://learnzillion.com/
https://www.khanacademy.org/
http://insidemathematics.org/index.php/8th‐grade
http://illuminations.nctm.org/LessonsList.aspx?grade=3&standard=all
Unit 5: Scatter Plots
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Generic Course
4th Marking Period
5 weeks
Published
Unit Overview
Construct and interpret scatter plots for bivariate measurement data.
Draw lines of best fit to model data that suggest a linear association.
End of Year Benchmark can be given after this unit.
Transfer
Students will be able to independently use their learning to ...
Students will understand that functions describe relationships and will be able to compare and construct a function.
The equation y=mx+b will be interpreted as a straight line, where m and b are constants. Students learn to recognize
linearity in a table when constant differences between input values produce constant differences between output
values, and they can use the constant rate of change and initial value appropriately in a verbal description of a context.
Students will establish a routine of exploring functional relationships algebraically, graphically, and numerically in
tables and verbal descriptions. When using functions to model a linear relationship between quantities, students learn
to determine the rate of change of the function which is the slope of a graph.
Students will apply experience with coordinate planes and linear functions in the study of association between two
variables related to a question of interest. Describe patterns such as clustering,outliers, positive or negative
association, linear and non‐linear association. The shape is a description of the cloud of points on a plane, the center is
the line of best fit, and the spread is how far data points are from the line.
Meaning
Understandings
Students will understand that
•
A function is a specific topic of relationship in which each input has a unique output which can be represented
in a table.
•
A function can be represented graphically using ordered pairs that consist of the input and the output of the
function in the form (input, output).
•
A function can be represented with an algebraic rule.
•
The equation is a straight line and that slope and y‐intercept are critical to solving real problems involving
linear relationships.
•
Changes in varying quantities are often related by patterns which can be used to predict outcomes and solve
problems.
•
Linear functions may be used to represent and generalize real situations.
•
For scatter plots that suggest a linear association, informally fit a straight line
•
Written descriptions, tables, graphs, and equations are useful in representing and investigating relationships
between varying quantities.
•
Different representations (written descriptions, tables, graphs, and equations) of the relationships between
varying quantities may have different strengths and weaknesses.
•
Linear functions may be used to represent and generalize real situations.
•
Slope and ‐intercept are keys to solving real problems involving linear relationship models of data.
•
Some data may be misleading based on representation.
Essential Questions
Students will keep considering...
•
How can you find and use patterns to model real‐world situations?
•
How can we model relationships between quantities?
•
Why is learning mathematics important?
•
How are patterns used when comparing two quantities?
Application of Knowledge and Skill
Students will know...
Students will know...
The charactersitics of a linear function in an equation, table, and a graph.
How the changes in a variable affect the function on an equation, table and a graph.
How to experiment and collect data to create a scatter plot.
To analyze and use a scatter plot.
Students will be skilled at...
Students will be skilled at...
•
Verify that a relationship is a function or not. (8.F.1)
•
Reason from a context, graph, or table after knowing which quantity is the input and which is the output.
(8.F.1)
•
Represent and compare functions numerically, graphically, verbally and algebraically. (8.F.2)
•
Interpret equations in form as a linear function. (8.F.3)
•
Determine whether a function is linear or non‐linear. (8.F.3)
•
Identify and contextualize the rate of change and the initial value from tables, graphs, equations, or verbal
descriptions. (8.F.4)
•
Construct a model for a linear function. (8.F.4)
•
Describe the qualities of a function using a graph (e.g., where the function is increasing or decreasing). (8.F.5)
•
Sketch a graph when given a verbal description of a situation. (8.F.5)
•
Use similar triangles to explain why the slope is the same between any two distinct points on a non‐vertical
line in the coordinate plane. (8.EE.6)
•
Derive the equation for a line through the origin. (8.EE.6)
•
Construct and interpret scatter plots and two‐way tables for patterns such as positive or negative association,
linearity or curvature, and outliers. (8.SP.1)
•
Generate an approximate line of best fit. (8.SP.2)
•
Use the equation of a linear model to solve problems in the context of bivariate measurement data. (8.SP.3)
•
Interpret the slope and ‐intercept of the line of best fit in context. (8.SP.3)
•
Show that patterns of association can also be seen in bivariate categorical data by displaying frequencies and
relative frequencies in a two‐way table. (8.SP.4)
•
Construct and interpret a two‐way table summarizing data on two categorical variables collected from the
same subjects. (8.SP.4)
Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
(8.SP.4)
Academic Vocabulary
Bivariate data, distribution, five‐number summary, line of best fit, mean absolute deviation, qualitative data,
quantitative data, relative frequency, scatter plot, standard deviation, symmetric, two‐way table, univariate data
Learning Goal 1
Construct and interpret scatter plots.
Draw lines of best fit to model data that suggest a linear association.
Objective 1--(Level 1 Recall)
SWBAT:
Use a scatter plot to investigate the relationship between two sets of data.
Construct and make conjectures about scatter plots.
MA.8.CCSS.Math.Content.8.SP.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.
Objective 2--(Level 2 Skill/Concept)
SWBAT:
Use data models to make predictions.
Draw lines of best fit and use them to make predictions about data.
MA.8.CCSS.Math.Content.8.SP.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 3--(Level 2 Skill/Concept)
SWBAT:
Use technology to describe associations in scatter plots.
Construct and interpret two ‐way tables
MA.8.CCSS.Math.Content.8.SP.A.1
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP5
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Objective 4--(Level 2 Skill/Concept)
SWBAT:
Solve problems by using a graph.
Find the measures of center and variation.
MA.8.CCSS.Math.Content.8.SP.A.3
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP2
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
Use the equation of a linear model to solve problems in the context of bivariate measurement data,
interpreting the slope and intercept.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 5--(Level 2 Skill/Concept)
SWBAT:
Find and interpret the mean absolute deviation for a set of data
MA.8.CCSS.Math.Content.8.SP.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
MA.K‐12.CCSS.Math.Practice.MP7
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Look for and make use of structure.
Objective 6 -- (Level 4 Extended Thinking)
Analyze data distributions.
MA.8.CCSS.Math.Content.8.SP.A.2
MA.8.CCSS.Math.Content.8.SP.A.4
MA.K‐12.CCSS.Math.Practice.MP1
MA.K‐12.CCSS.Math.Practice.MP3
MA.K‐12.CCSS.Math.Practice.MP4
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.
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.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Summative Assessment
Chapter Tests
Unit Test
Unit Project
Performance based assessment
21st Century Life and Careers
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.A.1
WORK.5‐8.9.1.8.A.2
WORK.5‐8.9.1.8.A.4
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.B.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.C.1
WORK.5‐8.9.1.8.C.2
WORK.5‐8.9.1.8.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.D.1
WORK.5‐8.9.1.8.D.2
WORK.5‐8.9.1.8.1
WORK.5‐8.9.1.8.1
WORK.5‐8.9.2.8.1
WORK.5‐8.9.2.8.A.1
WORK.5‐8.9.2.8.3
WORK.5‐8.9.2.8.B.1
The ability to recognize a problem and apply critical thinking and problem‐solving skills to solve the problem is
a lifelong skill that develops over time.
Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and
problem‐solving skills.
Implement problem‐solving strategies to solve a problem in school or the community.
Design and implement a project management plan using one or more problem‐solving strategies.
Gathering and evaluating knowledge and information from a variety of sources, including global perspectives,
fosters creativity and innovative thinking.
Use multiple points of view to create alternative solutions.
Collaboration and teamwork enable individuals or groups to achieve common goals with greater efficiency.
Determine an individual's responsibility for personal actions and contributions to group activities.
Demonstrate the use of compromise, consensus, and community building strategies for carrying out different
tasks, assignments, and projects.
Leadership abilities develop over time through participation in groups and/or teams that are engaged in
challenging or competitive activities.
Effective communication skills convey intended meaning to others and assist in preventing misunderstandings.
Employ appropriate conflict resolution strategies.
Demonstrate the ability to understand inferences.
Digital media are 21st‐century tools used for local and global communication.
The nature of the 21st‐century workplace has shifted, demanding greater individual accountability,
productivity, and collaboration.
Educational achievement, career choice, and entrepreneurial skills all play a role in achieving a desired
lifestyle.
Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income.
Income affects spending decisions and lifestyle.
Construct a simple personal savings and spending plan based on various sources of income.
Formative Assessment and Performance Opportunities
MAP Assessments
Tests
Quizzes
Informal Assessments
Graded Classwork
Surveys
WhiteBoard Activities
Exit tickets
Group activities
Projects
Teacher Observations
Student Interviews
Differentiation / Enrichment
•Calculators
•Centers
•Clickers
•Computer
•Document Cameras
•Graphing Calculators
•Lesson Extentions
•Manipulatives
•Modifications as per IEP/504
•Review and Practice
•Small Group Instruction
•Smartboards
•www.connected.mcgraw‐hill.com
.
.
.
.
.
.
.
.
.
.
.
.
.
Unit Resources
Additional files located in folder that may need to be edited for CCSS
www.connected.mcgraw‐hill.com
http://www.illustrativemathematics.org/
http://learnzillion.com/
https://www.khanacademy.org/
http://insidemathematics.org/index.php/8th‐grade
http://illuminations.nctm.org/LessonsList.aspx?grade=3&standard=all
Site has links and lesson for making graphs for various stories to compare time and distance or time and height
http://blog.mrmeyer.com/?p=213
This site has large PDF files with various tasks for functions for units 3 & 4 including sample answers and rubrics for
other students
http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm
Scatter plot:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L673
http://illuminations.nctm.org/LessonDetail.aspx?id=L646
http://illuminations.nctm.org/LessonDetail.aspx?id=L298
http://www.pbs.org/teachers/connect/resources/4442/preview/
http://www.pbs.org/teachers/connect/resources/4384/preview/
http://www.education.ucsb.edu/ucsbpt3/afield/teacher_projects/jimsfinal/Jimstudent.htm