### General Information

**Subject Area:**Mathematics

**Grade:**8

**Domain-Subdomain:**Functions

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Define, evaluate, and compare functions. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

### Test Item Specifications

**Assessment Limits :**

Function notation must not be used. Nonlinear functions may be included for identifying a function.**Calculator :**Neutral

**Context :**Allowable

### Sample Test Items (3)

**Test Item #:**Sample Item 1**Question:**A graph is shown.

How do you determine if this is a function or not?

**Difficulty:**N/A**Type:**OR: Open Response

**Test Item #:**Sample Item 2**Question:**A graph of a function is shown

Create a table to show the relationship of the values of x to the values of y.

**Difficulty:**N/A**Type:**TI: Table Item

**Test Item #:**Sample Item 3**Question:**Create a table of values to show a relation that is

**not**a function.**Difficulty:**N/A**Type:**TI: Table Item

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Tasks

## Student Center Activity

## Tutorials

## Virtual Manipulatives

## STEM Lessons - Model Eliciting Activity

Students are asked to determine a procedure for ranking healthcare plans based on their priorities. After they have determined a procedure, they are asked to revise it based on a new set of data.

## MFAS Formative Assessments

Students are asked to determine if each of three equations represents a function.

Students are asked to determine whether or not each of two graphs represent functions.

Students are asked to determine whether or not tables of ordered pairs represent functions.

## Original Student Tutorials Mathematics - Grades 6-8

Learn how to determine if a relationship is a function in this interactive tutorial that shows you inputs, outputs, equations, graphs and verbal descriptions.

## Student Resources

## Original Student Tutorial

Learn how to determine if a relationship is a function in this interactive tutorial that shows you inputs, outputs, equations, graphs and verbal descriptions.

Type: Original Student Tutorial

## Problem-Solving Tasks

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.

Type: Problem-Solving Task

This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function, which is violated in the table of values of the two populations. Noteworthy is that since the data is a collection of input-output pairs, no verbal description of the function is given, so part of the task is processing what the "rule form" of the proposed functions would look like.

Type: Problem-Solving Task

This task can be played as a game where students have to guess the rule and the instructor gives more and more input output pairs. Giving only three input output pairs might not be enough to clarify the rule. Instructors might consider varying the inputs in, for example, the second table, to provide non-integer entries. A nice variation on the game is to have students who think they found the rule supply input output pairs, and the teachers confirms or denies that they are right. Verbalizing the rule requires precision of language. This task can be used to introduce the idea of a function as a rule that assigns a unique output to every input.

Type: Problem-Solving Task

In this task, the rule of the function is more conceptual. We assign to a year (an input) the total amount of garbage produced in that year (the corresponding output). Even if we didn't know the exact amount for a year, it is clear that there will not be two different amounts of garbage produced in the same year. Thus, this makes sense as a "rule" even though there is no algorithmic way to determine the output for a given input except looking it up in the table.

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

This video explains why a vertical line does not represent a function.

Type: Tutorial

This video demonstrates how to check if a verbal description represents a function.

Type: Tutorial

This video shows how to check whether a given set of points can represent a function. For the set to represent a function, each domain element must have one corresponding range element at most.

Type: Tutorial

In this tutorial, you will practice using an equation in slope-intercept form to find coordinates, then graph the coordinates to predict an answer to the problem.

Type: Tutorial

## Virtual Manipulatives

This animation helps students to understand the function concept through the machine metaphor. The domain elements are dragged into the machine, which then goes through some process and outputs the range element corresponding to the input. The user is asked to complete the outputs for the remaining inputs.

Type: Virtual Manipulative

In this activity, students enter inputs into a function machine. Then, by examining the outputs, they must determine what function the machine is performing. This activity allows students to explore functions and what inputs are most useful for determining the function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.

Type: Problem-Solving Task

This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function, which is violated in the table of values of the two populations. Noteworthy is that since the data is a collection of input-output pairs, no verbal description of the function is given, so part of the task is processing what the "rule form" of the proposed functions would look like.

Type: Problem-Solving Task

This task can be played as a game where students have to guess the rule and the instructor gives more and more input output pairs. Giving only three input output pairs might not be enough to clarify the rule. Instructors might consider varying the inputs in, for example, the second table, to provide non-integer entries. A nice variation on the game is to have students who think they found the rule supply input output pairs, and the teachers confirms or denies that they are right. Verbalizing the rule requires precision of language. This task can be used to introduce the idea of a function as a rule that assigns a unique output to every input.

Type: Problem-Solving Task

In this task, the rule of the function is more conceptual. We assign to a year (an input) the total amount of garbage produced in that year (the corresponding output). Even if we didn't know the exact amount for a year, it is clear that there will not be two different amounts of garbage produced in the same year. Thus, this makes sense as a "rule" even though there is no algorithmic way to determine the output for a given input except looking it up in the table.

Type: Problem-Solving Task

## Virtual Manipulative

This animation helps students to understand the function concept through the machine metaphor. The domain elements are dragged into the machine, which then goes through some process and outputs the range element corresponding to the input. The user is asked to complete the outputs for the remaining inputs.

Type: Virtual Manipulative