Algebraic Reasoning and Expressions
The Algebraic Reasoning and Expressions domain tests multi-step word problems with the four operations, interpretation of remainders, true and false equations, writing equations with an unknown, and numerical patterns and input-output tables. The emphasis is on representing a situation correctly and explaining why a result makes sense.
Equations and unknowns
- An equation is true only when both sides have the same value. Check each side separately before deciding.
- Use a letter or symbol for an unknown quantity, then write an equation that matches the situation. For example, if 4 equal boxes hold 32 markers, 4 × b = 32.
- A multi-step problem may need two operations. Decide what must be found first, then use that result in the next step.
Remainders in context
- A remainder is what is left after dividing. The context decides whether to drop it, round the quotient up, or report it separately.
- If every item must be transported or packed, extra items usually require one more container, so round the quotient up.
- If whole groups are being formed and extras cannot make a group, use the quotient without the remainder.
Patterns and tables
- An input-output table follows one rule for every row. Test the rule on more than one row before extending the table.
- A rule may use two operations, such as multiply by 3, then add 2. Apply the operations in the stated order.
- Numerical patterns can increase or decrease by a constant amount, or follow a multiplicative rule.
Worked example
A field trip has 125 students. Each van holds 8 students. How many vans are needed? Divide: 125 ÷ 8 = 15 remainder 5. Fifteen vans carry 120 students, but 5 students still need transport. Because every student must go, one more van is needed: 16 vans.
Traps that cost marks
- Reporting only the quotient and ignoring the remainder when the context requires another group or container.
- Rounding up when the question asks how many full groups can be made.
- Checking only one side of an equation or assuming an equation is true because the numbers look familiar.
- Applying a two-step table rule in the wrong order.
- Writing an equation for the wrong unknown, such as using the total when the question asks for the number in each group.