Hawaii State Department of Education
Please email your questions to sbac@notes.k12.hi.us
Smarter Balanced High School Mathematics Assessment
Smarter Balanced has defined four claims for mathematics.
Claim 1 focuses on concepts and procedures. Students are expected to explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. The focus is on content knowledge learned at the high school level. A variety of item types are used to collect evidence for Claim 1, including selected response, constructed response, and technology enhanced items and tasks that focus on a particular skill or concept. Content for this claim may also be evaluated at a deeper level with extended response items and performance tasks. Items and tasks have a direct connection to and emphasis on the conceptual categories defined in the Common Core State Standards for Mathematics.
Assessment targets that will guide the development of items and tasks for high school:
- Number and Quantity
- Extend the properties of exponents to rational exponents
- Use properties of rational and irrational numbers
- Reason quantitatively and use units to solve problems
- Algebra
- 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
- Functions
- Understand the concept of a function and use function notation
- Interpret functions that arise in applications in terms of a context
- Analyze functions using different representations
- Build a function that models a relationship between two quantities
- Geometry
- Prove geometric theorems
- Define trigonometric ratios and solve problems involving right triangles
- Statistics and Probability
- Summarize, represent, and interpret data on a single count or measurement variable
Claims 2, 3, and 4 are aligned to the mathematical practices from the Common Core State Standards for Mathematics and are identical across grade levels. For this reason, the Assessment Targets for Claims 2, 3, and 4 are not divided into a grade-by-grade description.
Claim 2 focuses on problem solving and requires students to solve a range of complex, well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Evidence for Claim 2 is elicited through selected response, constructed response, extended response, and technology-enhanced items and tasks that focus on problem solving.
Items and tasks written to assessment targets for Claim 2 will ask students to:
- Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace;
- Select and use tools strategically;
- Interpret results in the context of the situation; and
- Identify important quantities in a practical situation and map their relationships.
Claim 3 focuses on communicating reasoning and requires students to clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Evidence for Claim 3 is elicited through constructed response, extended response, and technology-enhanced items and tasks that focus on mathematical reasoning.
Items and tasks written for this claim will ask students to explain his or her reasoning, justify a conjecture, and assess the validity of a claim. The Claim 3 targets will require students to:
- Test propositions or conjectures with specific examples;
- Construct, autonomously, chains of reasoning that justify or refute propositions or conjectures;
- State logical assumptions being used;
- Use the technique of breaking an argument into cases;
- Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in the argument—explain what it is;
- Base arguments on concrete referents such as objects, drawings, diagrams, and actions; and
- Determine conditions under which an argument does and does not apply.
Claim 4 focuses on modeling and data analysis and requires students to analyze complex, real-world scenarios and construct and use mathematical models to interpret and solve problems. Evidence for Claim 4 is elicited through performance tasks and collections of extended response items that focus on modeling and data analysis. Claim 4 tasks are real world problems that are complex and may contain insufficient or superfluous data.
Items and tasks written for this claim will ask students to investigate problems that have more than one solution pathway, summarize the results within the context of the problem, and evaluate the solution within the context of the problem.
The assessment targets associated with Claim 4 will require students to:
- Apply mathematics to solve problems arising in everyday life, society, and the workplace;
- Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem;
- State logical assumptions being used;
- Interpret results in the context of a situation;
- Analyze the adequacy of and make improvement to an existing model
or develop a mathematical model of a real phenomenon; - Identify important quantities in a practical situation and map their relationships; and
- Identify, analyze, and synthesize relevant external resources to pose
or solve problems.
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