Problem Solving and Algorithm Development (Weeks 1-2)

Lesson objectives

By the end of the week, learners should be able to:

1. Define a problem and state how to solve it step by step.
2. Distinguish a problem from a solution by separating steps into an algorithm.
3. Name three types of algorithm: sequential, selection and iteration.
4. State why an algorithm must be precise about inputs and outputs.
5. Trace a simple sequential algorithm on paper.

Key vocabulary

• Problem: a task requiring a clear path toward an answer.
• Algorithm: a finite sequence of precise instructions solving one problem.
• Sequential algorithm: a list of steps carried out in order.
• Selection algorithm: an algorithm containing if-then-else branches.
• Iteration algorithm: an algorithm repeating steps under a condition.
• Input: data entering an algorithm.
• Output: data leaving an algorithm as the result.
• Finite: an algorithm that stops after a fixed number of steps.

Common misconceptions

• "An algorithm is a finished answer." An algorithm is the procedure; the answer comes after running it.
• "Algorithms always use loops." Sequential algorithms solve problems without repetition.
• "An algorithm can change what it does halfway through." Algorithms are complete before execution begins.

Teacher activities

1. Starter: present the problem "calculate the average of five numbers" and ask how to start solving it.
2. Define algorithm and model writing the problem steps sequentially on the board.
3. Introduce selection and iteration by modifying the same problem with branches and loops.
4. Emphasise precision in input, output and control structures.
5. Trace the resulting three versions step by step on paper.
6. Close with the exit question about why precision matters.

Student activities

1. Read the starter problem and write the first step of an algorithm in their own words.
2. Write a full sequential algorithm for calculating an average.
3. Add a selection branch and an iteration loop to the same algorithm.
4. Trace each version step by step and compare them.
5. State why an algorithm must be precise about inputs and outputs.
6. Answer the exit question in one sentence about algorithm precision.

Practical / learning evidence

Three worked algorithms on paper, one sequential, one with selection and one with iteration, each showing the result clearly. Hand in all three for marking.

Resources and preparation

Blank algorithm worksheets, sample number lists and numbered step cards. Offline route: paper worksheets, no device needed. Display any worked examples carefully and never let learners modify them before tracing.

Assessment for learning

Inspect each algorithm for correct steps and termination. Mark the traces for matching the stated inputs and outputs. Flag any learner who leaves an algorithm unfinished mid-way.

Inclusion and homework

Provide the sequential template prefilled for learners who need scaffolding and allow oral completion of the selection and iteration additions. Extend confident learners with four problems and a problem-versus-solution distinction homework.