OREGON MATH STANDARDS (2021): [8.AFN]
Overview
The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.
Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.
2021 Oregon Math Guidance: 8.AFN.A.1
Cluster: 8.AFN.A - Define, evaluate, and compare functions.
STANDARD: 8.AFN.A.1
Standards Statement (2021):
Understand in authentic contexts, that the graph of a function is the set of ordered pairs consisting of an input and a corresponding output.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
7.RP.A.2 | 8.AFN.A.2, 8.AFN.A.3, 8.AFN.B.5, HS.AFN.A.1 | HS.GM.A.1 | 8.F.A.1 8.AFN.A Crosswalk |
Standards Guidance:
Clarification
- Understanding that a function is a rule that assigns exactly one output to each input.
Boundaries
- Use of function notation is not required in Grade 8.
Teaching Strategies
- Students should be able to use algebraic reasoning when formulating an explanation or justification regarding whether or not a relationship is a function or not a function.
Communication
- Describe the graph of a function as the set of ordered pairs consisting of an input and the corresponding output. Formal language, such as domain and range, and function notation may be postponed until high school. (Please reference pages 4 and 5 in the Progression document).
Examples
- If a function gives the number of hours it takes a person to assemble n engines in a factory, then the set of positive integers would be an appropriate domain for the function.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 8.AFN.A.2
Cluster: 8.AFN.A - Define, evaluate, and compare functions.
STANDARD: 8.AFN.A.2
Standards Statement (2021):
Compare the properties of two functions represented algebraically, graphically, numerically in tables, or verbally by description.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
7.AEE.B.4, 7.RP.A.2, 8.AFN.A.1, 8.AEE.B.5, 8.AEE.B.6 | 8.AFN.B.5, HS.AFN.B.4 | N/A | 8.F.A.2 8.AFN.A Crosswalk |
Standards Guidance:
Teaching Strategies
- Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.
Examples
- Given a linear function represented by a table of values and a linear function represented by an algebraic equation, determine which function has the greater rate of change.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 8.AFN.A.3
Cluster: 8.AFN.A - Define, evaluate, and compare functions.
STANDARD: 8.AFN.A.3
Standards Statement (2021):
Understand and identify linear functions, whose graph is a straight line, and identify examples of functions that are not linear.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
8.AFN.A.1, 8.AFN.A.2, 8.AEE.B.6 | 8.AFN.B.4, 8.AFN.B.5, HS.AFN.D.10 | N/A | 8.F.A.3 8.AFN.A Crosswalk |
Standards Guidance:
Clarifications
- Students should be given opportunities to explore how an equation in the form y = mx + b is a translation of the equation y = mx.
- In Grade 7, students had multiple opportunities to build a conceptual understanding of slope as they made connections to unit rate and analyzed the constant of proportionality for proportional relationships.
- Students should be given opportunities to explore and generalize that two lines with the same slope but different intercepts, are also translations of each other.
- Students should be encouraged to attend to precision when discussing and defining b (i.e., b is not the intercept; rather, b is the y-coordinate of the y- intercept). Students must understand that the x- coordinate of the y-intercept is always 0.
Teaching Strategies
- Students should be given the opportunity to explore and discover the effects on a graph as the value of the slope and y-intercept changes using technology.
- Students should be able to model contextual situations using graphs and interpret graphs based the contextual situations.
- Students should analyze a graph by determining whether the function is increasing or decreasing, linear or non-linear.
- Students should have the opportunity to explore a variety of graphs including time/distance graphs and time/velocity graphs.
Progressions
- Students learn to recognize linearity in a table: when constant differences between input values produce constant differences between output values. The proof that y = mx + b is also the equation of a line, and hence that the graph of a linear function is a line, is an important piece of reasoning connecting algebra with geometry in Grade 8. (Please reference page 5 in the Progression document).
Examples
- For example, A) determine if an equation represents a linear function and give examples of both linear and non-linear functions and B) show that the function A = s^2 is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 8.AFN.B.4
Cluster: 8.AFN.B - Use functions to model relationships between quantities.
STANDARD: 8.AFN.B.4
Standards Statement (2021):
Construct a function to model a linear relationship in authentic contexts between two quantities.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
7.RP.A.2, 8.AFN.A.3 | 8.AFN.B.5, HS.AFN.A.3, HS.AFN.D.8, HS.AFN.B.4, HS.AEE.B.4, HS.AFN.D.10 | 8.DR.D.4, HS.DR.D.11 | 8.F.B.4 8.AFN.B Crosswalk |
Standards Guidance:
Clarification
- 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.
Teaching Strategies
- This learning objective also includes verbal descriptions and scenarios of equations, tables, and graphs.
Progressions
- Graphs are ubiquitous in the study of functions, but it is important to distinguish a function from its graph. For example, a linear function does not have a slope but the graph of a non-vertical line has a slope.
- The slope of a vertical line is undefined and the slope of a horizontal line is 0. Either of these cases might be considered “no slope.” Thus, the phrase “no slope” should be avoided because it is ambiguous and “non-existent slope” and “slope of 0” should be distinguished from each other. (Please reference page 6 in the Progression document).
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 8.AFN.B.5
Cluster: 8.AFN.B - Use functions to model relationships between quantities.
STANDARD: 8.AFN.B.5
Standards Statement (2021):
Describe qualitatively the functional relationship between two quantities in authentic contexts by analyzing a graph.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
8.AFN.A.1, 8.AFN.A.2, 8.AFN.A.3, 8.AFN.B.4 | HS.AFN.D.10, HS.AFN.C.6 | N/A | 8.F.B.5 8.AFN.B Crosswalk |
Standards Guidance:
Clarification
- Identify 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.
Teaching Strategies
- Students should use algebraic reasoning to show and explain that the graph of an equation represents the set of all its solutions.
- Students continue to build upon their understanding of proportional relationships, using the idea that one variable is conditioned on another.
- Students should relate graphical representations to contextual situations.
- Students should use tables to relate solution sets to graphical representations on the coordinate plane.
Examples
- Illustrative Mathematics:
- Student Achievement Partners: