8th Grade Mathematics Quarter 2 Curriculum Map
2013-2014
2nd Nine Weeks – Oct to Nov
Suggested Number of Days: 10 -14
Unit: Introduction to Functions
Unit Summary (Learning Target/Goal):
Define and evaluate functions, and use functions to model relationships between quantities; analyze linear graphs to express
qualitative relationships between two quantities; understand and interpret linear functions, and give examples of non-linear functions.
CCSS for Mathematical Content:
Key Vocabulary:
Expressions and Equations---Understand the connections between proportional
relationships, lines and linear equations.
8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Compare two different proportional relationships represented in different ways. For example,
compare a distance-time graph to a distance-time equation to determine which of two moving
objects has greater speed.
Functions---Define, evaluate, and compare functions.
8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph
of a function is the set of ordered pairs consisting of an input and the corresponding output.
continuous data
discrete data
function
function rule
linear
linear function
nonlinear
nonlinear function
parabola
proportional relationship
quadratic function
Example: Which function generalizes the pattern in the table?
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.
Functions---Use functions to model relationships between quantities.
8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a
graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph
that exhibits the qualitative features of a function that has been described verbally.
Example: Function
Grade 8 Quarter 2 1
8th Grade Mathematics Quarter 2 Curriculum Map
2013-2014
Example: Not a Function
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct arguments and critique the reasoning of others
4. Model with mathematics
6. Attend to precision
7. Look for and make use of structure
Grade 8 Quarter 2 2
8th Grade Mathematics Quarter 2 Curriculum Map
Explanation/Examples:
-Interpret a graph
- Sketch a graph
- Evaluate functions
- Input-Output tables and graphs
- Proportional relationships in tables
- Linear functions in tables
- Graph discrete data
- Graph continuous data
- Non-linear functions from graphs, tables and equations
- Non-linear functions from descriptions
Resources:
Prentice Hall Mathematics
Common Core Course 3
Chapter 3
Prentice Hall Mathematics
Common Core Course 3 Online resources
2013-2014
Assessment:
- Classwork/Homework
- Lesson quizzes
- Unit test
- District Common Formative
Assessment
SAS Curriculum Pathway
Shordor.com
Mathwarehouse.com/algebra
Reflection/Notes:
2nd Nine Weeks – Nov
Suggested Instructional Days: 12-16
Unit: Graphing Functions
Unit Summary (Learning Target/Goal):
Graph proportional relationships and interpret the unit rate as the slope of the graph. Write and graph functions to model linear
relationships and compare two functions represented in different ways.
CCSS for Mathematical Content:
Key Vocabulary:
Expressions and Equations—Work with radicals and integer exponents.
•
8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare
two different proportional relationships represented in different ways. For example, compare a
distance-time graph to a distance-time equation to determine which of two moving objects has greater
speed.
linear function
rate of change
slope
slope-intercept form
slope of a line
y-intercept
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points
on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin
Grade 8 Quarter 2 3
8th Grade Mathematics Quarter 2 Curriculum Map
2013-2014
and the equation y = mx + b for a line intercepting the vertical axis at b.
Example:
Functions—Define, evaluate, and compare functions.
8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a
function is the set of ordered pairs consisting of an input and the corresponding output.
Example: Which function generalizes the pattern in the table?
8.F.2. Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a linear function
represented by a table of values and a linear function represented by an algebraic expression,
determine which function has the greater rate of change.
8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line;
2
give examples of functions that are not linear. For example, the function A = s giving the area of a
square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and
(3,9), which are not on a straight line.
Functions—Use functions to model relationships between quantities.
Grade 8 Quarter 2 4
8th Grade Mathematics Quarter 2 Curriculum Map
8.F.4 Construct a function to model a linear relationship between two
Determine the rate of change and initial value of the function from a
of a relationship or from two (x, y) values, including reading these from
from a graph. Interpret the rate of change and initial value of a linear
terms of the situation it models, and in terms of its graph or a table of
2013-2014
quantities.
description
a table or
function in
values.
Example: Find the rate of change and the initial value of the function.
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
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
Explanation/Examples:
- Finding the slope of a line
- Slopes of horizontal and vertical lines
- Finding slope from a table
- Finding slope and y-intercept
- Graphing functions of the form y=mx
- Writing a function rule from words
- Writing a rule from a table
- Writing an equation from a graph
- Comparing rates of change of linear functions
- Comparing initial values of linear functions
Comparing nonlinear functions
Comparing proportional functions
Resources:
Assessment:
Prentice Hall Mathematics
Common Core Course 3
- Classwork/Homework
- Lesson quizzes
- Unit test
- District Common Formative
Assessment
Prentice Hall Mathematics
Common Core Course 3
shodor.org- Resources for
computational science
Math Warehouse- Algebra
Grade 8 Quarter 2 5
8th Grade Mathematics Quarter 2 Curriculum Map
2013-2014
Reflection/Notes:
Unit 5: Systems of Linear Equations
2nd Nine Weeks – December
Suggested Instructional days: 8 -12
INTERIM ASSESSMENT 2: DECEMBER 9-13
Unit Summary (Learning Target/Goal):
Analyze and solve systems of linear equations algebraically, and estimate solutions by graphing the equations; model and solve realworld problems using two linear equations.
CCSS for Mathematical Content:
Key Vocabulary:
Expressions and Equations---Analyze and solve linear equations and pairs of simultaneous linear
equations.
elimination method
solution of a system
substitution method
system of equations
8.EE.8. Analyze and solve pairs of simultaneous linear equations.
8.EE.8.a. 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.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.
8.EE.8.c. 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.
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
7. Look for and make use of structure
Grade 8 Quarter 2 6
8th Grade Mathematics Quarter 2 Curriculum Map
Explanation/Examples:
-Solve a system by graphing
- Use substitution
- Solve for a variable and using substitution
- Solve a system by adding, subtracting, multiplying
2013-2014
Resources:
Assessment:
Prentice Hall Mathematics
Common Core Course 3
- Classwork/Homework
- Lesson quizzes
- Unit test
- District Common Formative
Assessment
Reflection/Notes:
Grade 8 Quarter 2 7