enVision Mathematics Topic 3
8th Grade; November (3 weeks); 2nd Quarter
Embedded Files
Topic Title(s):
Use Functions to Model Relationships
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
2. Algebra and Functions
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
8.F.A. Functions: Define, evaluate, and compare functions.
Define a function as a rule that assigns to each input exactly one output. Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required for Grade 8.) (CCSS: 8.F.A.1)
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. (CCSS: 8.F.A.2)
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. (CCSS: 8.F.A.3)
8.F.B. Functions: Use functions to model relationships between quantities.
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. (CCSS: 8.F.B.4)
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. (CCSS: 8.F.B.5)
Make connections between the information gathered through tables, equations, graphs, and verbal descriptions of functions. (Entrepreneurial Skills: Inquiry/Analysis)
Define variables as quantities and interpret ordered pairs from a functional relationship with respect to those variables. (MP2)
With and without technology, analyze and describe functions that are not linear with the use of equations, graphs, and tables. (MP5)
See a function as a rule that assigns each input to exactly one output; this structure does not “turn inputs into outputs”; rather, it describes the relationship between items in two sets. (MP7)
Recognize patterns of linear growth in different representations of linear functions. (MP8)
Describe in writing the qualitative features of linear or nonlinear functions. (Entrepreneurial Skills: Literacy/Writing)
Model real-world situations with linear functions. (MP4)
Explore properties of linear functions and how those properties appear in the structure of linear equations in slope-intercept form. (MP7)
Use strategies to calculate the rate of change in a linear function (slope) and use properties of linear functions to create equations. (MP8)
Inquiry Questions
Why is it important to know if a mathematical relationship is a function?
How can you determine if a function is linear or nonlinear?
What is the minimum information needed to write a linear function for a relationship between two quantities?
What are some quantitative and qualitative features of graphs of functions?
Coherence Connections
This expectation represents major work of the grade.
In Grade 7, students analyze proportional relationships and use them to solve real-world and mathematical problems.
In Grade 8, this expectation connects with understanding the connections between proportional relationships, lines, and linear equations and with using functions to model relationships between quantities.
In Grade 8, this expectation connects with defining, evaluating, and comparing functions and with investigating patterns of association in bivariate data.
In high school, students use function notation, analyze functions using different representations, build new functions from existing functions, and extend from linear functions to quadratic, exponential, and other more advanced functions.
Academic Vocabulary & Language Expectations:
Relation, function, constant rate of change, initial value, linear function, nonlinear function, interval
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 3
Let's Investigate! Tasks
Let's Investigate! Sort It Out (TE) (relates to Lesson 3-2)
Let's Investigate! Graph Me a Story (TE) (relates to Lesson 3-5)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Building Linear Equations, Identify Properties of Functions from Descriptions, Write the Equation of a Function, Linear Functions in Tables and Graphs, Translate Among Representations of Functions, Compare Slope and Initial Value of Functions, Linear and Nonlinear Functions
Coherence Map/Concept Progressions: 8.F.A.1, 8.F.A.3, 8.F.B.4
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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