Your First Lesson on Maths Word Problems: What to Cover and How (Alberta, Canada)

The first lesson on word problems decides how the rest of the unit goes. Get it wrong and you spend six weeks with a class that reads a question, hunts for two numbers and picks an operation by mood. Get it right and students reach the Division 3 and 4 outcomes asking what the situation is before asking what the math is. Here is a plan for that opening period, with timings.

The thing not to do first

Do not open with keyword lists. "Altogether means add, left means subtract" is the fastest way to teach a class to stop reading. It survives easy questions and collapses on every Provincial Achievement Test item written by someone who anticipated it. Establish instead that a word problem describes a situation and the math models it. Everything you build over six weeks depends on students holding that distinction.

A four-phase period with timings

1. Phase one, ten minutes: problems with no numbers. Five situations with the quantities removed. "A phone plan charges a fixed monthly fee plus an amount per gigabyte. Jordan is deciding between two plans." Students say what is happening and what would change the answer. No calculation is possible, which is the point.
2. Phase two, fifteen minutes: numbers added, one at a time. Return to two of the situations and reveal the numbers. Students write the relationship before they compute anything. You are looking for a sentence or an expression, not an answer, and you say so.
3. Phase three, twenty minutes: the same situation asked three ways. Keep the context fixed and change what is unknown. Find the cost given the data. Find the data given the cost. Find where two plans cost the same. One relationship generates three questions, which is the insight the unit is built on.
4. Phase four, ten minutes: a problem that cannot be solved. Hand out one question with missing information. Students must say what is missing and why it matters. Some will solve it anyway by inventing a number, and that is the most useful thing that will happen in the lesson.

Phases two and three need a bank of situations with a consistent structure, so the pattern is visible rather than accidental. Linear contexts are cleanest because students can hold the relationship in one line, and Algebra – Linear Functions and Systems of Equations | Foundations & Problem Solving Workbook | GRADE 7–10 supplies graded versions of the same context, so students who finish early take the comparison question while others build the first expression.

What to say when they ask for the method

Somebody will ask whether there is a set of steps. There is, but give it as questions rather than a procedure. What is the situation. What is changing and what stays the same. What am I asked to find. What would a wrong answer look like. Leave those on the board for the unit. The last matters most: a student who says the answer should be between forty and sixty dollars before calculating catches their own errors on a Diploma Exam.

The exit check, and what each answer tells you

Five minutes, one question, no calculator. Give a short situation and ask for two things: the relationship, and an estimate to the nearest ten. Not the exact answer, because you are diagnosing modeling rather than arithmetic.

Sort into three piles. A correct relationship with a sensible estimate means they are ready for harder contexts. A correct relationship with a wild estimate means the algebra is ahead of the number sense, and short daily practice fixes that faster than a reteach; Algebra – Daily Warm-up Exercises | Bell Ringers & Quick Practice | GRADE 5–9 is built for that five-minute opening slot and keeps estimation in the room every day without costing you a lesson. No relationship at all, just two numbers and an operation, means the keyword habit is installed and you go back to no-number problems.

Where the next four lessons go

Lesson two takes the same situations into two-step relationships. Lesson three separates modeling errors from calculation errors by keeping the model easy and the arithmetic heavy. Lesson four brings in contexts where a quadratic is the honest model, and by then students write the relationship before touching a number; Algebra – Quadratic Equations and Complex Solutions | Advanced Problem Solving Workbook | GRADE 8–11 carries that step with worked solutions students can check themselves against. By lesson five you should be able to put an unfamiliar situation on the board and watch the class start writing a relationship without being told to, which is the whole return on spending your first period on situations rather than keywords.

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