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Grade 7 - Claim 1 - Target A

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Mathematics

Target A

Analyze proportional relationships and use them to solve real-world and mathematical problems

Sample Item

Grade 7

Test

Claim 1

Concepts and Procedures

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

Grade

Grade 7

Content Domain

Ratios and Proportional Relationships

Standards

RP-1RP-2RP-2aRP-2bRP-2cRP-2dRP-3
Major

Standards

  • RP-1

    Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4...

  • RP-2

    Recognize and represent proportional relationships between quantities.

  • RP-2a

    Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight...

  • RP-2b

    Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

  • RP-2c

    Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the...

  • RP-2d

    Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the...

  • RP-3

    Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Clarifications

Tasks for this target will require students to identify and represent proportional relationships in various formats (tables, graphs, equations, diagrams, verbal descriptions) and interpret specific values in context. (See 7.G Target E for possible...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student computes unit rates and finds the constant of proportionality of proportional relationships in various forms.

  • 2

    The student determines whether two quantities, shown in various forms, are in a proportional relationship.

  • 3

    The student represents proportional relationships between quantities using equations.

  • 4

    The student interprets specific values from a proportional relationship in the context of a problem situation.

  • 5

    The student computes with percentages in context.

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
  • Multi-Select, multiple correct response
  • Matching Tables

Allowable Stimulus Materials

two-way tables, graphs of both nonlinear and linear equations, equations in two variables, diagrams

Key/Construct Relevant Vocabulary

proportional relationship, ratio, unit rate, constant of proportionality, origin, percent increase, percent decrease, percent error

Allowable Tools

Calculator

Target-Specific Attributes

None

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 graphical representations of real-world situations are assessed in Claims 2 and 3.

Task Models

Task Model 1a

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK2

  • Standards

    RP-1, RP-2b

Target Evidence Statement

  • The student computes unit rates and finds the constant of proportionality of proportional relationships in various forms.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to give the constant of proportionality between two quantities in a proportional relationship. Stimulus Guidelines: Ratios in the proportional relationship should be ratios of fractions. Context should be familiar to students...

Stimulus

The student is presented with a verbal description of a real-world situation involving a proportional relationship.

Example 1

Example Stem: David uses 14\frac{1}{4} cup of apple juice for every 12 \frac{1}{2}\text{ }cup of carrot juice to make a fruit drink.

Enter the number of cups of apple juice David uses for 1 cup of carrot juice.

Rubric: (1 point) The student enters the correct number (e.g.,12 \frac{1}{2}).