Smarter Balanced Assessment (SBAC) Mathematics: Problem Solving and Modeling Syllabus

Mathematics: Problem Solving and Modeling syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics: Problem Solving and Modeling in Smarter Balanced Assessment (SBAC), not a summary of it.

1. 1

   Problem Solving

   3 topics

   • Understanding and Defining the Problem
     • Identifying the unknown and givens
     • Restating problems in own terms
   • Selecting Strategies and Tools
     • Choosing efficient methods
     • Using estimation to check feasibility
   • Executing and Monitoring Solutions
     • Carrying out multi-step plans
     • Checking for reasonableness
2. 2

   Mathematical Modeling

   3 topics

   • Representing Real-World Situations
     • Translating context into equations
     • Choosing appropriate models
   • Interpreting Results in Context
     • Relating answers to the situation
     • Identifying limitations of a model
   • Multi-Step and Performance Task Problems
     • Integrating multiple math concepts
     • Managing extended real-world scenarios
3. 3

   Communicating Reasoning

   3 topics

   • Constructing Mathematical Arguments
     • Justifying conclusions with reasoning
     • Using definitions and properties
   • Critiquing the Reasoning of Others
     • Identifying flawed logic or errors
     • Evaluating the validity of claims
   • Explaining Methods and Results
     • Clear written and symbolic explanations
     • Using precise mathematical language

Mathematics: Problem Solving and Modeling flashcards for Smarter Balanced Assessment (SBAC)

24 of 51 cards from the Mathematics: Problem Solving and Modeling deck — real questions with worked answers.

1. In mathematical problem solving, what does it mean to "understand the problem"?

   To identify what is being asked (the goal), what information/quantities are given, what conditions or constraints apply, and what the unknowns are, before attempting any solution.

2. What are the four phases of Polya's classic problem-solving process?

   1) Understand the problem, 2) Devise a plan (choose a strategy), 3) Carry out the plan (execute), 4) Look back (check and reflect on the result).

3. When defining a problem, what is the difference between 'given information' and a 'constraint'?

   Given information is the data/facts you start with; a constraint is a restriction or condition the solution must satisfy (e.g., a budget limit, a non-negative quantity).

4. What does it mean to identify the 'unknown' in a problem?

   It is determining the specific quantity or relationship you are being asked to find—what variable or result the problem wants you to solve for.

5. Why is restating a problem in your own words a useful first step?

   It confirms comprehension, clarifies the goal and conditions, exposes hidden assumptions, and helps separate relevant from irrelevant information.

6. What is 'extraneous information' in a word problem, and how should you treat it?

   Extraneous information is data given that is not needed to solve the problem; you should recognize and set it aside so it does not affect your reasoning.

7. What is the purpose of identifying the 'type' or 'category' of a problem early on?

   Classifying it (e.g., as a rate, proportion, system of equations, or geometry problem) helps you recall and select appropriate strategies, formulas, and tools.

8. What is a problem-solving 'strategy'? Give three common examples.

   A strategy is a general plan of attack. Examples: draw a diagram, look for a pattern, work backward, guess-and-check, make a table, solve a simpler related problem, write an equation.

9. What does the strategy 'work backward' involve, and when is it useful?

   Starting from the desired end result and reversing the operations to find the unknown starting value; useful when the final outcome is known but the initial conditions are not.

10. What is the 'guess-and-check' (trial-and-improvement) strategy?

    Making a reasonable estimate, testing it against the problem's conditions, then refining the guess based on whether it was too high or too low until the condition is satisfied.

11. When is 'solve a simpler problem' a good strategy?

    When a problem involves large numbers or complex structure; solving an easier analogous version reveals a pattern or method that generalizes to the original.

12. What is an 'appropriate tool' in mathematical modeling, and name three examples.

    A resource that aids solving, chosen to fit the task. Examples: calculator, ruler/protractor, spreadsheet, graphing software, number line, manipulatives, formula reference.

13. What factors guide the choice of strategy or tool for a problem?

    The nature of the quantities, the goal, available data, required precision, efficiency, and whether estimation or an exact answer is needed.

14. What is the difference between an exact answer and an estimate, and when is each appropriate?

    An exact answer is precise and required for definitive calculations; an estimate is an approximate value useful for checking reasonableness, quick decisions, or when data is imprecise.

15. In SBAC math practice, what does 'attend to precision' mean?

    Communicating clearly with accurate definitions, correct units, appropriate level of accuracy, and careful, error-free calculation and labeling.

16. What is 'executing' a solution plan?

    Carrying out the chosen strategy step by step—performing the calculations, applying formulas, and following the plan to reach a result.

17. What does it mean to 'monitor' your solution while solving?

    Continuously checking your progress, verifying each step is correct, watching for errors, and assessing whether the approach is still working toward the goal.

18. If a chosen strategy is not working during execution, what should a problem solver do?

    Recognize it is not progressing, abandon or modify it, and select an alternative strategy—persevering by trying a different approach rather than giving up.

19. What does 'make sense of problems and persevere in solving them' (SBAC/CCSS Practice 1) require?

    Understanding the problem, planning a solution pathway, monitoring progress, and adapting/persisting through obstacles until a reasonable solution is reached.

20. Why should you check the units throughout a multi-step calculation?

    Tracking units catches errors, confirms operations are valid (you cannot add unlike units), and ensures the final answer is expressed in the correct unit.

21. What is a mathematical model?

    A representation (equation, graph, diagram, table, or function) that captures the essential relationships of a real-world situation to analyze it or make predictions.

22. What is the SBAC/CCSS practice 'model with mathematics' (Practice 4)?

    Applying math to solve real-world problems by representing situations with equations, diagrams, tables, or graphs, interpreting results, and revising the model as needed.

23. List the main steps of the mathematical modeling cycle.

    1) Identify variables and assumptions, 2) formulate a model, 3) compute/analyze the model, 4) interpret the results, 5) validate against the situation, 6) report or revise.

24. What is an 'assumption' in modeling, and why state it?

    A simplifying condition taken as true to make the situation manageable (e.g., constant speed); stating it clarifies the model's limits and the validity of conclusions.

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