Mathematical Practices and Problem Solving
The Mathematical Practices domain is tested through the other strands: FAST Math includes multi-step problems that require you to choose a strategy, represent the situation, justify an answer, and check whether the result is reasonable. Florida’s Mathematical Thinking and Reasoning standards emphasize active problem solving, multiple representations, precision, communication, pattern recognition, reasonableness, and real-world application.
What the practices look like in items
- Represent a problem with an equation, table, diagram, or number line before computing.
- Identify the quantities and the units, then decide which operation each step requires.
- Explain why an answer is reasonable using estimation or an inverse operation.
- Generalize a pattern and test the rule on a second case.
- State an answer with the correct unit and answer the exact question asked.
Planning a multi-step problem
- Restate the question in your own words.
- List the given information and the units.
- Choose a model: an equation for an unknown, a diagram for area or volume, or a table for a pattern.
- Solve one step at a time, keeping exact values.
- Check with estimation and ask whether the size and unit make sense.
Worked example
A rectangular tank is 5 feet long, 4 feet wide, and 3 feet high. It is filled two-thirds of the way with water. How many cubic feet of water are in the tank?
- Find the full volume: 5 × 4 × 3 = 60 cubic feet.
- Find two-thirds of 60: 60 ÷ 3 = 20, and 20 × 2 = 40 cubic feet.
- Check another way: two-thirds of the 3-foot height is 2 feet, and 5 × 4 × 2 = 40 cubic feet. The answer, 40 cubic feet, matches both models and has the correct cubic unit.
Traps that cost marks
- Stopping after the first step and reporting the full volume instead of the filled volume.
- Answering with a number but no unit, or with the wrong unit.
- Losing track of what the question asks while computing an intermediate value.
- Accepting an answer that is numerically possible but unreasonable in context.
- Failing to show or describe the representation when an item asks for an explanation.