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Grade 11 - Claim 1 - Target N

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Mathematics

Target N

Build a function that models a relationship between two quantities

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

BF-1BF-1aBF-2
Major

Standards

  • BF-1

    Write a function that describes a relationship between two quantities.

  • BF-1a

    Determine an explicit expression, a recursive process, or steps for calculation from a context.

  • BF-2

    Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Clarifications

Tasks for this target will require students to write a function (recursive or explicit, as well as translate between the two forms) to describe a relationship between two quantities.

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student writes explicit or recursive functions to describe relationships between two quantities from a context.

  • 2

    The student translates between explicit formulas and recursively defined functions.

  • 3

    The student understands a function as a model of the relationship between two quantities.

Item Guidelines

Depth of Knowledge

  • 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

  • Equation/Numeric
  • Multiple Choice, single correct response
  • Matching Tables
  • Fill-In Table

Allowable Stimulus Materials

The student is presented with a contextual situation familiar to 16–17 year olds where a function can describe a relationship between two quantities. Contextual situations will be introduced with simple subject-verb-object sentences, avoiding long...

Key/Construct Relevant Vocabulary

Function(s), quantity, quantities, explicit, recursive, arithmetic sequence, geometric sequence, input, output, ordered pairs

Allowable Tools

Calculator

Target-Specific Attributes

When translating between an explicit function and a recursive function, functions are limited to arithmetic and geometric relations.

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

The modeling described in Standard F-FB.A.2 should be measured in Claim 4.

Task Models

Task Model 1a

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK2

  • Standards

    BF-1

Target Evidence Statement

  • The student writes explicit or recursive functions to describe relationships between two quantities from a context.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to enter a function that represents a relationship between two quantities by determining an explicit function that represents a context. Stimulus Guidelines: The student is presented with a contextual...

Stimulus

The student is presented with a contextual situation.

Example 1

Example Stem 1: Maria is making a rectangular garden. The length of the garden is 2 yards greater than its width, w, in yards.

Enter the function, f(w), that describes the area, in square yards, of Maria’s garden as a function of the width, w.

Rubric: (1 point) The student correctly enters the function describing the relationship between two quantities in the given contextual situation (e.g., f(w)=w(w+2)f(w) = w(w + 2)).

Example 2

Example Stem 2: Barb traveled 300 miles during the first 5 hours of her trip. Barb then traveled at a constant speed of 50 miles per hour for the remainder of the trip.

Enter the function, f(t), that describes the average speed during the entire trip as a function of time, t, in hours, Barb traveled after her first 300 miles.

Rubric: (1 point) The student correctly enters the function describing the relationship between two quantities in the given contextual situation (e.g., f(h)=300+50h5+hf\left( h \right) = \frac{300 + 50h}{5 + h}).

Example 3

Example Stem 3: A washing machine was purchased for $256. Each year the value is 14 \frac{1}{4}\text{ } of its value the previous year.

Enter the function, f(t)f\left(t\right), that describes the value of the washing machine, in dollars, as a function of time in years, tt, after the initial purchase.

Rubric: (1 point) The student correctly enters the function describing the relationship between two quantities in the given contextual situation (e.g., f(t)=$256(0.75)tf(t) = \$256(0.75)^{t}).