Mathematics Grade Level Considerations for High School

1. Mathematics Grade Level Considerations for High School

2. Considerations for High School • 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. Words vs. Numerals • Use numerals for numbers that are used to solve a problem • Use numerals for numbers that appear in equations 19 + x = 35 Sarah sold 9 adult tickets for a total of $45. What was the price of each adult ticket?

6. 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., 11 A.M., 12:30 P.M.) • Ordered pairs and coordinates (e.g., (3,4))

7. 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)

8. Contexts • Appropriate contexts: • Sports familiar played during physical education (basketball, soccer) • School activities (class trips, library, music, children’s games) • Buying movie tickets, fruit, or drinks • Inappropriate contexts: • Skiing • Backyard swimming pools • Paying a mortgage or using retirement funds

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

10. High School Standards • Not grade-level specific • Know and be able to do to be college and career ready upon graduation from high school

11. High School Conceptual Categories • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability

12. Number and Quantity • Kindergarten through Middle School: • Extend understanding of numbers • High School: • Extend understanding of quantity • Model wider variety of units

13. Algebra • Middle School • Algebraic expressions, equations, and inequalities • High School: • Solve equations and manipulate formulas of increasing complexity

14. Functions • Earlier Grades • Define, evaluate and compare functions • Use functions to model relationships • High School: • Function notation • Concepts of domain and range • Model real-world situations • Linear and quadratic functions

15. Modeling • Modeling: Choosing and using appropriate mathematics and statisticsto: • Analyze empirical situations • Understand situations • Improve decisions

16. Geometry • High School: • Euclidean Geometry • Increasingly precise definitions • Developing formal proofs • Congruence, similarity, and symmetry • Geometry of right triangles and circles

17. Statistics and Probability • Study of how to use data to make decisions and predictions • High School: • Gather, display, and examine data to inform decisions • Randomization

18. High School Common Core State Standards • Define additional mathematics required for advance courses such as Calculus and Statistics

19. Appendix A • Organize standards into model pathways to college and career readiness

20. Claim 1 Concepts and Procedures: Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. Selected Response Constructed Response Technology-Enhanced Extended Response and Performance Tasks

21. Number and QuantityAssessment Targets Extend the properties of exponents to rational exponents Use properties of rational and irrational numbers Reason quantitatively and use units to solve problems

22. AlgebraAssessment Targets Interpret the structure of expressions Write expressions in equivalent forms to solve problems Perform arithmetic operations on polynomials Create equations that describe numbers or relationships Understand solving equations as a process of reasoning and explain reasoning Solve equations and inequalities in one variable Represent and solve equations and inequalities graphically

23. FunctionsAssessment Targets Understand the concept of a function and use function notation Interpret functions that arise in applicationsin terms of a context Analyze functions using different representations Build a function that models a relationship between two quantities

24. GeometryAssessment Targets Prove geometric theorems

25. Statistics and ProbabilityAssessment Targets Summarize, represent, and interpret data on a single count or measurement variable

26. 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

27. 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

28. 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

29. 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

30. High School MathematicsGrade Level Considerations Vocabulary, style, context, and item difficulty Common Core State Standards structured as conceptual categories instead of domains Claims from the Smarter Balanced Mathematics Content Specifications