Integrate essential skills and evaluate a model
Combine number representations, measures, statistics and constraints, then test whether the model answers the practical question.
What you will tackle
- Use fractions, decimals, signed numbers, absolute values and equivalent representations
- Combine proportional reasoning, rates, percentages, measures and center statistics
- Produce, interpret, evaluate and improve models
- Check constraints, units, reasonableness and assumptions across multiple stages
Keep each stage connected to the question
A multistep problem may require converting a fraction to a decimal, finding a mean, applying a percentage and rounding a count. Preserve exact values until the final decision when possible. An absolute value describes distance from zero; a negative account balance and the size of a debt are different quantities.
A model needs both mathematics and judgement
Define variables and units, state a relationship, calculate, and compare the result with constraints and actual observations. A nonnegative integer count may need a ceiling or floor according to the question. Improve a model when residual patterns, capacity limits or omitted fixed costs make its assumptions implausible. Modeling overlaps every ACT math category; it is not an extra disjoint question total.
Build your notes, then practise
Work on paper before opening an explanation. Guided tasks provide a starting point; independent tasks remove the scaffolding; application tasks ask you to justify a method or interpretation in context.
Guided practice
Guided 1
Convert 3/8 to a decimal and percentage; find |−7|. A trip covers 24 km in 3/4 hour; find its speed. Find the median of 8,3,12,5.
Show a starting hint
Use each quantity's meaning to choose the operation.
Compare with the explained answer
- 3/8 = 0.375 = 37.5%; |−7| = 7.
- Speed = 24/(3/4) = 32 km/h.
- Order 3,5,8,12; the median is (5 + 8)/2 = 6.5.
Answer / response criteria: 0.375; 37.5%; 7; 32 km/h; median 6.5.
Independent practice
Independent 1
A room needs 46 m² of flooring. Add 8% waste; each box covers 2.5 m² and costs $32. Find the boxes needed and cost, explaining the rounding.
Compare with the explained answer
- Required coverage is 46·1.08 = 49.68 m².
- 49.68/2.5 = 19.872 boxes, so round up to 20 whole boxes.
- Cost = 20·32 = 640.
Answer / response criteria: 20 boxes; $640.
Application practice
Application 1
A transport model predicts C(n) = 40 + 3n dollars for n passengers, but a vehicle holds at most 12. A group has 25 people. Explain why simply evaluating C(25) may fail, then propose a three-vehicle model and calculate it assuming the fee is per vehicle.
Compare with the explained answer
- C(25) uses one fixed fee but exceeds one vehicle's capacity.
- At least ceiling(25/12) = 3 vehicles are needed.
- With $40 per vehicle and $3 per passenger, cost is 3·40 + 3·25 = 195.
Answer / response criteria: $195 under the revised assumptions; the single-vehicle formula gave an infeasible plan.
What can you explain now?
A transport model predicts C(n) = 40 + 3n dollars for n passengers, but a vehicle holds at most 12. A group has 25 people. Explain why simply evaluating C(25) may fail, then propose a three-vehicle model and calculate it assuming the fee is per vehicle.
Compare with the explanation
$195 under the revised assumptions; the single-vehicle formula gave an infeasible plan.
Explain the reasoning before comparing. This review records your self-assessment rather than an official score or mastery decision.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Source and review status
Coverage follows the named requirements and examples in the 2026–2027 ACT test guide and subject descriptions. That guide explicitly does not list every possible topic. The broader coded College and Career Readiness Standards are also mapped to conceptual teaching and practice; this does not calibrate a learner to a score band. The separate scientific-background context list and reading-complexity rubric have their own stated limits.
Original teaching and explained self-check practice are available. Specialist review and difficulty calibration remain pending. Essays require self-check or teacher review and are not automatically marked or awarded official scores.
Official source specification / guide