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Mathematics Grade Level Considerations for High School

Considerations for High School

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Vocabulary Style Guide Representation of numbers Contexts Item Difficulty Assessment Targets

Vocabulary

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

Style

Words vs. Numerals

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Use numerals for numbers that are used to solve a problem Sarah sold 9 adult tickets for a total of $45. What was the price of each adult ticket?

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Use numerals for numbers that appear in equations

19 + x = 35

Words vs. Numerals

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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))

Commas in Numbers

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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

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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

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Inappropriate contexts: – Skiing – Backyard swimming pools – Paying a mortgage or using retirement funds

Item Difficulty

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Items should include a range of difficulty Anticipated difficulty for sample items

High School Standards

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Not grade-level specific Know and be able to do to be college and career ready upon graduation from high school

High School Conceptual Categories

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Number and Quantity Algebra Functions Modeling Geometry

Statistics and Probability

Number and Quantity

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Kindergarten through Middle School: – Extend understanding of numbers

High School: – Extend understanding of quantity – Model wider variety of units

Algebra

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Middle School – Algebraic expressions, equations, and inequalities

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High School: – Solve equations and manipulate formulas of increasing complexity

Functions

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Earlier Grades – Define, evaluate and compare functions – Use functions to model relationships

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High School: – Function notation – Concepts of domain and range – Model real-world situations – Linear and quadratic functions

Modeling

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Modeling: Choosing and using appropriate mathematics and statistics to: – Analyze empirical situations – Understand situations – Improve decisions

Geometry

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

Statistics and Probability

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Study of how to use data to make decisions and predictions High School: – Gather, display, and examine data to inform decisions – Randomization

High School Common Core State Standards

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Define additional mathematics required for advance courses such as Calculus and Statistics

Appendix A

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Organize standards into model pathways to college and career readiness

Claim 1

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

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Selected Response Constructed Response Technology-Enhanced Extended Response and Performance Tasks

Number and Quantity Assessment Targets

A. Extend the properties of exponents to rational exponents B. Use properties of rational and irrational numbers C. Reason quantitatively and use units to solve problems

Algebra Assessment Targets D. Interpret the structure of expressions E. Write expressions in equivalent forms to solve problems F. Perform arithmetic operations on polynomials

G. Create equations that describe numbers or relationships H. Understand solving equations as a process of reasoning and explain reasoning I.

Solve equations and inequalities in one variable

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Represent and solve equations and inequalities graphically

Functions Assessment Targets K. Understand the concept of a function and use function notation L. Interpret functions that arise in applications in terms of a context M. Analyze functions using different representations

N. Build a function that models a relationship between two quantities

Geometry Assessment Targets

O. Prove geometric theorems

Statistics and Probability Assessment Targets

P. Summarize, represent, and interpret data on a single count or measurement variable

Claim 2 – Problem Solving

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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

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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

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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

Claims 2, 3, and 4

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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

High School Mathematics Grade Level Considerations

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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