1. Mathematics Grade Level Considerations for Grades 6-8

2. Considerations for Grades 6–8 Vocabulary Style Guide Representation of numbers Contexts Item Difficulty Assessment Targets

3. Vocabulary Items must be written so students can easily understand the item or task. Use vocabulary at or below grade-level.

4. Style

5. 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 × 10 4 = 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

6. 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? Sarah sold 9 adult tickets for a total of $45. What was the price of each adult ticket? 19 + x = 35

7. 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))

8. 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)

9. 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

10. Item Difficulty Items should include a range of difficulty Anticipated difficulty for sample items

11. 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.

12. Assessment Targets Measured in Grades 6–8 Ratios and Proportional Relationships The Number System Expressions and Equations Geometry Statistics and Probability Functions

13. Ratios and Proportional Relationships Grade 6: Ratios introduced Grade 7: Extended to proportional relationships

14. The Number System Grades 6 & 7: Rational numbers Grade 8: Irrational numbers

15. 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

16. Geometry Grade 6: Area, surface area, and volume Grade 7: Drawing and constructing figures Grade 8: Congruence, similarity, and the Pythagorean Theorem

17. Statistics and Probability Grade 6: Statistic and probability introduced Grade 7: Sampling, inferences, and probability Grade 8: Associations in bivariate data

18. Functions Grade 8: Defining, evaluating, comparing, and modeling functions

19. 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

20. 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

21. Claim 4 – Modeling and Data Analysis Performance Tasks and collections of Extended Response items Real world problems Draw upon knowledge and skills articulated in the progression of standards up to the grade being assessed Relevant verbs include: – model, construct, compare, investigate, build, interpret, estimate, analyze, summarize, represent, solve, evaluate, extend, and apply

22. 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

23. Middle School Mathematics Grade Level Considerations Vocabulary, style, context, and item difficulty Claims from the Smarter Balanced Mathematics Content Specifications