Mathematics Grade Level Considerations for Grades 6-8

Considerations for Grades 6–8

• Vocabulary

• Style Guide

• Representation of numbers

• Contexts

• Item Difficulty

• Assessment Targets

Vocabulary

• Items must be written so students can easily understand the item or task.

• Use vocabulary at or below grade-level.

Style

Overview of Mathematics Style Conventions Specific to Middle School Grades

• Use graphics or tables to present information in order to reduce the amount of reading

• Use the product dot rather than the multiplication symbol except in scientific notation

2 12

a 2a

1.2 × 104 = 12,000

• In grade 8, use the terms translate, reflect, and rotate

Translate

Reflect

Rotate

2x + 4 = 16• Use variables to indicate missing values in equations

Words vs. Numerals

• Use numerals for numbers that are used to solve a problem

• Use numerals for numbers that appear in equations

Sarah sold 9 adult tickets for a total of $45.

What was the price of each adult ticket?

19 + x = 35

Words vs. Numerals

• Use words for a number that is the first word in a sentence

• Use words for numbers zero through nine

• Use numerals for:

– Numbers 10 and above

– Numbers that precede abbreviated units of measure (e.g., 10 cm, 8 sq. ft.)

– Numbers that precede or follow symbols such as the percent sign or dollar sign (e.g., 5%, $9.32)

– Dates and years (e.g., July 4)

– Time of day that appears before A.M. and P.M. (e.g., 3 A.M., 12:30 P.M.)

– Ordered pairs and coordinates (e.g., (3,4))

Commas in Numbers

• Use commas in numbers:– With five or more digits (e.g., 90,000)

– With four digits if the number appears with numbers of five or more digits (e.g., 1,000 + 5,000 + 10,000)

– Written as words (e.g., seventy-three thousand, one hundred)

• Do not use commas in:– Numbers with four digits if all numbers with which it appears

contain four or less digits (e.g., 50 + 200 + 1000)

– Compound measures (e.g., 5 feet 9 inches tall)

Contexts

• Appropriate contexts

– Popular sports

– Bicycle riding

– Making nominal purchases

– Making and reading maps and floor plans

– School related activities

• Inappropriate contexts

– Expensive or regional sports

– Purchases that are unusual for students

Item Difficulty

• Items should include a range of difficulty

• Anticipated difficulty for sample items

Claim 1

• Selected Response

• Constructed Response

• Technology-Enhanced

• Extended Response and Performance Tasks

Concepts and Procedures: Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

Assessment Targets Measured in Grades 6–8

• Ratios and Proportional Relationships

• The Number System

• Expressions and Equations

• Geometry

• Statistics and Probability

• Functions

Ratios and Proportional Relationships

• Grade 6: Ratios introduced

• Grade 7: Extended to proportional relationships

The Number System

• Grades 6 & 7: Rational numbers

• Grade 8: Irrational numbers

Expressions and Equations

• Grade 6: Introduce algebraic expressions

• Grade 7: Create expressions and equations and use to solve problems

• Grade 8: Analyze and solve more complex problems

Geometry

• Grade 6: Area, surface area, and volume

• Grade 7: Drawing and constructing figures

• Grade 8: Congruence, similarity, and the Pythagorean Theorem

Statistics and Probability

• Grade 6: Statistic and probability introduced

• Grade 7: Sampling, inferences, and probability

• Grade 8: Associations in bivariate data

Functions

• Grade 8: Defining, evaluating, comparing, and modeling functions

Claim 2 – Problem Solving

• Selected Response, Constructed Response, Extended Response, and Technology-Enhanced items that focus on problem solving

• Items and tasks require students to construct their own pathway to the solution

• Relevant verbs include: – understand, solve, apply, describe, illustrate,

interpret, and analyze

Claim 3 – Communicating Reasoning

• Constructed Response, Extended Response, and Technology-Enhanced items and tasks that focus on mathematical reasoning

• Relevant verbs include:– understand, explain, justify, prove, derive, assess,

illustrate, and analyze

Claim 4 – Modeling and Data Analysis

• Performance Tasks and collections ofExtended Response items

• Real world problems

• Draw upon knowledge and skills articulatedin the progression of standards up to the gradebeing assessed

• Relevant verbs include: – model, construct, compare, investigate, build, interpret,

estimate, analyze, summarize, represent, solve, evaluate, extend, and apply

Claims 2, 3, and 4

• Assessment Targets for Claims 2, 3, and 4 are not divided into a grade-by-grade description

• A general set of assessment targets applicable across grade levels

Middle School MathematicsGrade Level Considerations

• Vocabulary, style, context, and item difficulty

• Claims from the Smarter Balanced Mathematics Content Specifications