A 60-minute tutoring plan

An example maths lesson: the student can solve simple equations but struggles with brackets. By the end, they solve a new equation and check the answer without prompts.

1. 0–5
   min

   Recall without notes

   Give 2x + 3 = 11. Instead of asking what you covered last time, watch whether the student can choose an operation and apply it to both sides.

   “Solve it and check by substitution. How do you know your answer fits?”

   If subtracting 3 is the obstacle, work on a simple equation first. Brackets can wait.

2. 5–15
   min

   One diagnostic task

   Give 2(x + 3) = 14 and ask for the reason behind the first step. Writing 2x + 3 = 14 identifies a point to work on; a wrong final answer alone does not.

   “What does the two outside the brackets mean? Show what it multiplies.”

   If they solve it independently, move to a harder variation. Skip an explanation they no longer need.

3. 15–45
   min

   An example with less and less help

   Show 3(x + 2) = 21. Write 3x + 6 = 21 and explain that step. In 4(x + 1) = 28, leave expanding the brackets to the student. Then give 5(x + 1) = 30 from the start.

   “What is the first line without brackets? Explain it before you calculate.”

   Stop explaining once they can choose the next step. If the mistake returns, compare two lines and set another short attempt.

4. 45–55
   min

   Check with a new problem

   Hide the earlier solutions. Give 2(x − 3) = 10. The student solves it and substitutes the answer. Then show the incorrect 2x − 3 = 10 and ask what differs.

   “Which number should change, and why? Does your x work in the original equation?”

   Record what they did independently and what still needed a question. The answer alone is not enough.

5. 55–60
   min

   Close the lesson

   Return to the goal. The student records one thing they can do and one to revisit. Set two short problems for later: one similar, one with a change of sign.

   “How will you check next time that you expanded the brackets correctly?”

   Begin the next lesson with one of these problems, without looking at the solution.

This is an example schedule, not a scientifically optimal allocation of minutes. Allow more time for diagnosis in a first session.

Before the lesson

• One goal the student can demonstrate independently.
• A short recall task from the previous lesson, without notes.
• A diagnostic task and an idea of the error it may reveal.
• A worked example and a different problem for independent practice.
• Time left for a check, a closing note and two tasks for later.

Lucyboard · lucyboard.com/en/tutoring-tips