CMS Curriculum Guides 2011-2012
8th Grade Math
Unit Title: The Shapes of Algebra
Suggested Time: 25 days (75 to 90 minute Blocks)
Enduring understanding (Big Idea): Write and use equations of circles; Determine if lines are parallel or perpendicular by looking at patterns in their
graphs, coordinates, and equations; Find coordinates of points that divide line segments in various ratios; Find solutions to inequalities represented by
graphs or equations; Write inequalities that fit given conditions; Solve systems of linear equations by graphing, by substituting, and by combining
equations; Graph linear inequalities; Describe the points that lie in regions determined by linear; Use systems of linear equations to solve problems;
Choose strategically the most efficient solution method for a given system of linear equation.
Essential Questions:What patterns relate the coordinates of points on lines and curves? What patterns relate the points whose coordinates satisfy linear
equations? Does the problem involve an equation or an inequality? Does the problem call for writing and/or solving a system of equations? If so, what
method would be useful for solving the system? Are there systematic methods that can be used to solve any systems of linear equations?
Unit Plans
Common Core Standards Alignment
Connection to 2003 Standards
Investigation 1
Analyze and solve linear equations and pairs of simultaneous linear
equations.
8.EE.8.b- Solve systems of two linear equations in two variables algebraically,
and estimate solutions by graphing the equations. Solve simple cases by
inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because
3x +2y cannot simultaneously be 5 and 6.
Goal 3.02
Analyze and solve linear equations and pairs of simultaneous linear
equations.
8.EE.8 -Analyze and solve pairs of simultaneous linear equations
Goal 5.02; 5.03
Equations for Circles and Polygons
Problems 1.1,1.2
This was a Geometry I goal
Math Reflections
Investigation 2
Linear Equations and
Inequalities
Problems 2.1, 2.2, 2.3
Math Reflections
8.EE.8a- 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
8.EE.8b- Solve systems of two linear equations in two variables algebraically,
and estimate solutions by graphing the equations. Solve simple cases by
inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because
3x +2y cannot simultaneously be 5 and 6.
CMS Curriculum Guides 2011-2012
8th Grade Math
8.EE.8c- Solve real-world and mathematical problems leading to two linear
equations in two-variables. For example, given coordinates for two pairs of
points, determine whether the line through the first pair of points intersects the
line through the second pair.
Investigate patterns of association in bivariate data.
8.SP.3- Use the equation of a linear model to solve problems in the context of
bivariate measurement data, interpreting the slope and intercept. For example, in
a linear model for a biology experiment, interpret a slope of 1.5 cm/hr. as
meaning that an additional hour of sunlight each day is associated with an
additional 1.5 cm in mature plant height.
Investigation 3
Equations with Two or More
Variables
Problems 3.1, 3.2, 3.3
Math Reflections
Analyze and solve linear equations and pairs of simultaneous linear
equations:
8.EE.8- Analyze and solve pairs of simultaneous linear equations
8.EE.8a - 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.
8.EE.8b- Solve systems of two linear equations in two variables algebraically,
and estimate solutions by graphing the equations. Solve simple cases by
inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because
3x +2y cannot simultaneously be 5 and 6.
8.EE.8c- Solve real-world and mathematical problems leading to two linear
equations in two-variables. For example, given coordinates for two pairs of
points, determine whether the line through the first pair of points intersects the
line through the second pair.
Define, evaluate, and compare functions.
8.F.3- Interpret the equation y = mx +b as defining a linear function, whose
graph is a straight line; give examples of functions that are not linear. For
example, the function A = s² giving the area of a square as a function of its side
length is not linear because its graph contains the points (1,1), (2,4), and (3,9),
which are not on a straight line.
Goal 5.01a; 5.01b; 5.01c; 5.01d;
5.02; 5.03
CMS Curriculum Guides 2011-2012
8th Grade Math
Investigate patterns of association in bivariate data.
8.SP.3- Use the equation of a linear model to solve problems in the context of
bivariate measurement data, interpreting the slope and intercept. For example, in
a linear model for a biology experiment, interpret a slope of 1.5 cm/hr. as
meaning that an additional hour of sunlight each day is associated with an
additional 1.5 cm in mature plant height.
Investigation 4
Solving Systems of Linear
Equations Symbolically
Problems 4.1, 4.2, 4.3, 4.4
Analyze and solve linear equations and pairs of simultaneous linear
equations:
8.EE.8 -Analyze and solve pairs of simultaneous linear equations
Goal 5.01a; 5.01b; 5.01c; 5.01d;
5.02; 5.03
8.EE.8a- 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
Math Reflections
8.EE.8b - Solve systems of two linear equations in two variables algebraically,
and estimate solutions by graphing the equations. Solve simple cases by
inspection.
8.EE.8c - Solve real-world and mathematical problems leading to two linear
equations in two-variables.
Define, evaluate, and compare functions.
8.F.3- Interpret the equation y = mx +b as defining a linear function, whose
graph is a straight line; give examples of functions that are not linear. For
example, the function A = s² giving the area of a square as a function of its side
length is not linear because its graph contains the points (1,1), (2,4), and (3,9),
which are not on a straight line.
Investigation 5 (MOVED to
Algebr for Common Core)
Linear Inequalities
Prepares for A-REI-12
Goal 5.01a; 5.01b; 5.01c; 5.01d;
5.02; 5.03
CMS Curriculum Guides 2011-2012
8th Grade Math
5.1, 5.2, 5.3
Math Reflections
Prior Knowledge: Thinking about shapes. Working with coordinates. Finding midpoints of line segments. Formulating, reading, and interpreting
symbolic rules. Working with the triangle inequality. Solving problems in geometric and algebraic contexts. Solving linear equations.
Mathematical Practices Standards for Common Core
1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and critique the
reasoning of others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for and make use of
structure 8-Look for and express regularity in repeated reasoning
Resources
Lab-Sheet
Additional Practice/Skills Worksheets
CMS Curriculum Guides 2011-2012
8th Grade Math
CMP2 Website –online & technology resources
Formal Assessment
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Check-Ups
Partner Quiz
Unit Test
Assessment Options
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Notebook check
Multiple-Choice
Question Bank
ExamView CD-ROM
Parent Guide-Unit Letters
Spanish Assessment Resources
PHSchool.com
TeacherExpress CD-ROM
LessonLab Online Courses
Unit Technology Tips