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Grade 11 - Claim 1 - Target L

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Mathematics

Target L

Interpret functions that arise in applications in terms of a context

Sample Item

Grade 11

Test

Claim 1

Concepts and Procedures

Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Grade

Grade 11

Content Domain

Functions

Standards

IF-4IF-5IF-6
Major

Standards

  • IF-4

    For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description...

  • IF-5

    Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble...

  • IF-6

    Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student interprets key features of a graph or a table representing a function modeling a relationship between two quantities.

  • 2

    The student sketches graphs showing key features given a verbal description of a relationship between two quantities that can be modeled with a function.

  • 3

    The student relates the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

  • 4

    The student calculates and interprets the average rate of change of a function presented symbolically or as a table and estimates the rate of change of a function from a graph.

Item Guidelines

Depth of Knowledge

  • M-DOK1

    Recall includes the recall of information such as fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be...

  • M-DOK2

    Skill/Concept includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a...

Allowable Item Types

  • Matching Tables
  • Hot Spot
  • Graphing
  • Multiple Choice, single correct response
  • Multi-Select, multiple correct response
  • Equation/Numeric

Allowable Stimulus Materials

written description of key features of a function, graphs of functions in the coordinate plane, tables containing domain and range values of functions, functions presented symbolically

Key/Construct Relevant Vocabulary

x-intercept, y-intercept, interval, increasing interval, decreasing interval, relative maximum, relative minimum, symmetry, axis of symmetry, end behavior of a graph, limit, periodicity, average rate of change

Allowable Tools

Calculator

Target-Specific Attributes

Key features include x- and y-intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Functions are in two variables.

Accessibility

Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items. Language Key Considerations: Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the...

Development Notes

Tasks for this target will require students to sketch graphs based on given key features and to interpret key features of graphs, with emphasis on interpreting the average rate of change over a specified...

Task Models

Task Model 1a

  • Item Types

    Matching Tables

  • Depth of Knowledge

    M-DOK1

  • Standards

    IF-4

Target Evidence Statement

  • The student interprets key features of a graph or a table representing a function modeling a relationship between two quantities.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to identify true statements regarding key features of a given graph of a function that models a relationship between two quantities. The statements will be in the context...

Stimulus

The student is given a graph representing a function that models the relationship between two quantities in a real-world situation familiar to 15- to 17-year-olds, e.g., temperature change over time, or population change over...

Example 1

Example Stem: This graph shows the population of mice in a study, modeled as a function of time. The study begins on day 0 and ends on day 200.

The title of the graph is Mouse Population Over Time. The horizontal axis, t, is labeled Time (in days) and ranges from 0 to 200. The vertical axis, p, is labeled Population and ranges from 0 to 200. The plotted line begins at 0, a little less than 140; curves up between 20 and 40, 160; curves down between 80 and 100, 140; curves up to 160, a little more than 180; and ends at 200, 120.

Determine whether each statement is true according to the graph. Select True or False for each statement.

Statement True False
The mouse population was decreasing between day 40 and day 80.
The least number of mice during the study was 130.
The mouse population was at its greatest around day 160.
There are two intervals of time where the mouse population is decreasing.

Rubric: (1 point) The student correctly selects true or false for each of the interpretations of key features of the graph (e.g. T, F, T, T).