Break a problem into smaller jobs and explain how they connect.

DO NOW AND PRIOR LEARNING · 5 MINUTES

Ask: “What needs to happen to get ready for school?”

Students list possible jobs. Compare responses and identify broad parts, such as getting dressed, preparing food and packing a bag.

Explain that a familiar task can contain several smaller problems.

EXPLAIN AND MODEL · I DO · 10 MINUTES

Model breaking “get ready for school” into smaller jobs. Select “pack my bag” and break it down further:

1. Check the timetable.

2. Identify what is needed.

3. Collect the items.

4. Pack them.

Think aloud about each part’s result. Draw a dependency arrow to show that checking the timetable informs which books to collect.

Contrast “books”, an item, with “choose the books needed today”, a subproblem.

Key idea: Decomposition identifies the parts. Sequencing puts actions into an order.

GUIDED PRACTICE AND CHECK · WE DO · 10 MINUTES

Task 1: Breaking a problem into parts

Decompose brushing teeth together into three parts: preparation, cleaning and finishing.

Ask students to suggest smaller steps within each part. Identify what must happen first and what each part produces.

Check everyone’s understanding:

“Is toothpaste a subproblem?”

Expected response: No. “Prepare the toothbrush” is a job with a result.

Together, improve a vague instruction such as “clean your teeth”.

COLLABORATIVE PRACTICE · 15 MINUTES

Task 2: Sort and explain

In pairs, choose a familiar task, such as tying shoelaces, packing sports equipment or organising a desk.

1. Make a task map with at least three meaningful subproblems.

2. Label each part’s result.

3. Draw an arrow showing one dependency.

4. Write precise instructions for one selected part.

5. Swap with another pair. Follow or trace their instructions and identify an assumption or missing step.

6. Revise your instructions using the feedback.

Discuss: Why can an apparently simple task require many detailed steps?

COUNTING ALGORITHM AND FLOWCHART · 15 MINUTES

Task 3: Make a task map 

Introduce the problem: “Say the numbers 1 to 5 in order.”

First, write a sequential algorithm:

Start → Say 1 → Say 2 → Say 3 → Say 4 → Say 5 → Stop

Then introduce a loop that reuses instructions:

1. Start.

2. Set number to 0.

3. Ask: “Is number greater than 4?”

4. If Yes, stop.

5. If No, add 1 to number, say number, then return to the question.

Translate the algorithm into a flowchart using:

• Ovals for Start and Stop.

• Rectangles for setting or changing the number.

• Parallelograms for saying the number.

• A diamond for the decision, with arrows labelled Yes and No.

Students trace both charts and record the numbers said. Check that both say 1, 2, 3, 4, 5, without saying 0 or 6.

Key idea: Decomposition helps identify the jobs: initialise, check, update and output. A flowchart shows how the algorithm connects those jobs.

INDEPENDENT EVIDENCE AND PLENARY · 5 MINUTES

Students independently:

1. Name two subproblems from their chosen task.

2. Give the result of one.

3. Explain one dependency.

4. Complete: “Decomposition helps because…”

Collect the task map and counting trace.

Next lesson: Apply these ideas to instructions for making a sandwich.

Lesson 2 · Applying decomposition — Make a sandwich

Break a task into smaller jobs, write precise instructions, and improve them through testing.

DO NOW AND PRIOR LEARNING · 5 MINUTES

Ask students to answer without looking at their notes:

1. What does decomposition mean?

2. What are three smaller jobs involved in making a sandwich?

3. Which jobs must happen in a particular order? Why?

Compare responses. Check that students identify jobs, such as preparing the bread, rather than simply listing ingredients.

EXPLAIN AND MODEL · I DO · 10 MINUTES

Show the ingredients and equipment, or paper sandwich props.

In pairs, students write a short, numbered set of instructions for making a sandwich. Ask them to include one clear action per step.

Choose one example and follow it exactly as written, within the agreed food-handling and equipment routines. Students watch for missing details or unexpected results.

Think aloud about the smaller jobs:

1. Prepare the bread.

2. Add the filling.

3. Assemble the sandwich.

Identify each job’s output and explain how another job uses it.

Key idea: Decomposition identifies smaller jobs. An algorithm gives precise instructions for carrying them out.

GUIDED PRACTICE AND CHECK · WE DO · 10 MINUTES

Ask: “Which instruction caused a problem, and why?”

Together, identify a missing, unclear or incorrectly ordered step.

1. Rewrite the instruction.

2. Ask students to predict what will happen.

3. Test the revised instruction.

4. Check whether the change worked.

Students review and improve their own instructions before another demonstration.

Key idea: Debugging means finding and fixing errors. Retesting checks whether the fix worked.

COLLABORATIVE PRACTICE · 18 MINUTES

Pairs join another pair. Use paper props or approved ingredients, following the teacher’s food-handling and equipment instructions.

1. Group your sandwich instructions into smaller jobs.

2. Name the output of each job.

3. Swap instructions with the other pair.

4. Take turns reading the instructions, making the sandwich and observing.

5. Follow the instructions as written. Pause if a step is unclear and record the problem.

6. Improve the instruction and test it again.

Record your findings:

Original instruction → Problem observed → Improved instruction → Retest result

Discuss: Which jobs depend on an output from an earlier job?

INDEPENDENT EVIDENCE · 12 MINUTES

Students work independently.

1. Draw a task map showing three or four smaller jobs involved in making the sandwich.

2. Label each job’s output.

3. Draw arrows showing dependencies between jobs.

4. Choose one job and write precise instructions for it.

5. Explain what would happen if one required output was missing.

Use the sentence starter:

“_____ depends on _____ because _____.”

Key idea: A useful task map shows both the smaller jobs and how they connect.

PLENARY · 5 MINUTES

Students complete these statements independently:

1. Decomposition helped us by…

2. One unclear instruction was…

3. We improved it by…

4. Our retest showed…

Invite two students to share their explanations. Ask the class to check whether each explanation includes evidence from a test.

Collect: Original and improved instructions, test record, individual task map and exit responses.

Lesson 3 · Algorithms and bubble sort

60 minutes

Use clear, ordered instructions to sort cards, trace each pass, and record evidence about how the algorithm works.

Year 9 curriculum knowledge K1
Computational thinking uses decomposition, abstraction, pattern recognition, algorithms, and evaluation to analyse problems for digital solutions.

Year 9 curriculum practice P1
Explain simple problems by identifying purpose, users, inputs, outputs, constraints, context, and key steps.

Knowledge focus
An algorithm uses clear, ordered steps to solve a problem. Different algorithms can produce the same sorted output. Selection sort repeatedly selects the smallest remaining item and places it at the sorted boundary.

Practice and evidence
Represent and trace a precise sorting algorithm using physical cards. Evidence: an individual selection-sort trace and a paired comparison log retained for Lesson 6.

Learning intentions

• Explain what an algorithm is.

• Follow and trace selection sort accurately.

• Identify the sorted and unsorted regions.

• Record comparisons and actual swaps consistently.

Resources
Number cards 1–6 for each pair; a boundary marker such as a ruler or strip of paper; a small “smallest so far” marker; timers; recording sheets.

DO NOW AND PRIOR LEARNING · 5 MINUTES

Students answer independently before reviewing answers:

1. How did recognising a pattern help you adapt a counting method?

2. Write three smaller jobs involved in making toast. Which must happen in a particular order?

3. Describe one error in a previous set of instructions and explain how you corrected it.

Briefly connect their answers:

Decomposition helps us identify the smaller jobs. Pattern recognition helps us notice repeated actions. Today, we will organise repeated actions into a precise algorithm and check that it works.

EXPLANATION AND MODELLING — I DO · 10 MINUTES

Introduce algorithms

An algorithm is a set of clear, ordered steps for solving a problem. Someone else should be able to follow the steps without guessing.

Recall that more than one valid order of toast-making instructions can achieve the same result, provided necessary dependencies are respected. Similarly, different sorting algorithms can produce the same ordered list.

Give pairs six shuffled cards and one minute to arrange them from smallest to largest. Ask:

• What did you do first?

• Could another pair follow your explanation exactly?

• Did everyone use the same method?

Explain that they will now follow one specific algorithm: selection sort.

Activity 4 · Selection-sort procedure

Display and model these instructions:

1. Lay out the cards in a row. Place the boundary marker before the first card. All cards are initially unsorted.

2. Mark the first card in the unsorted region as the smallest so far.

3. Compare each remaining unsorted card with the smallest so far, moving from left to right.

4. If a card is smaller, move the smallest-so-far marker to it.

5. After checking the whole unsorted region, swap the selected smallest card with the first unsorted card. If it is already there, leave it in place.

6. Move the boundary one position to the right. The card just placed is now in the sorted region.

7. Repeat until only one unsorted card remains. It is already in its final position.

Counting rules

• Count one comparison whenever you compare a new card’s value with the smallest value found so far.

• Count one swap when two cards exchange positions.

• Do not count selecting the first candidate as a comparison.

• Do not count a card staying in its own position as a swap.

Model the first pass

Use:

4, 2, 6, 1, 5, 3

Think aloud:

“The first unsorted card is 4, so that is my smallest so far. Is 2 smaller than 4? Yes: my smallest becomes 2. Is 6 smaller than 2? No. Is 1 smaller than 2? Yes: my smallest becomes 1. Is 5 smaller than 1? No. Is 3 smaller than 1? No.”

The smallest card is 1. Swap it with 4, then move the boundary:

1 | 2, 6, 4, 5, 3

Record 5 comparisons and 1 swap.

Emphasise:

We check the entire unsorted region before swapping. Selection sort does not repeatedly swap neighbouring cards.

CHECK FOR UNDERSTANDING · 5 MINUTES

Every student writes an answer:

Why is the smallest selected card in its final position after this pass?

Expected reasoning:

We compared it with every other card in the unsorted region. None is smaller, so it belongs in the first available position when sorting from smallest to largest.

Also ask students to identify:

• The sorted region.

• The unsorted region.

• Whether the cards in the unsorted region must already be in order.

Inspect all responses. Re-model any uncertainty about checking every remaining card before selecting the final minimum.

GUIDED PRACTICE — WE DO · 10 MINUTES

Continue from:

1 | 2, 6, 4, 5, 3

Students predict and direct the second pass.

Ask:

1. Which card starts as the smallest so far?

2. Which cards must we compare with it?

3. How many comparisons will this pass require?

4. Does a swap need to happen?

The result is:

1, 2 | 6, 4, 5, 3

Record 4 comparisons and 0 swaps. Explain that the boundary still moves when the smallest card is already correctly placed.

Explain the sorting problem

Complete this checklist together:

Feature

Our sorting problem

Purpose

Arrange numbers from smallest to largest.

User

A student following the sorting instructions.

Input

Six number cards in a given order.

Output

The same six cards in ascending order.

Constraint

Follow selection sort, checking the whole unsorted region before placing its smallest card.

Context

A physical model of how a computer can sort data.

Key steps

Select a candidate, compare remaining values, swap if needed, move the boundary, repeat.

PRACTICE — YOU DO · 25 MINUTES

Task 1 · Sort and record — 12 minutes

Pairs reset their cards to:

4, 2, 6, 1, 5, 3

Assign roles:

• Operator: follows the procedure and moves the cards and markers.

• Observer: checks the procedure and records comparisons, swaps, and the row after each pass.

Swap roles after each pass.

Start timing when the first pass begins. Stop when the cards are sorted. Prioritise following the algorithm accurately.

Complete the trace:

Pass

Selected smallest value

Row after the pass, showing the boundary

Comparisons

Actual swaps

1

2

3

4

5

Total

Task 2 · Test already sorted input — 8 minutes

Repeat the same procedure with:

1, 2, 3, 4, 5, 6

Before starting, predict:

• Will this version of selection sort still make comparisons?

• Will it make any swaps?

Record both runs:

Starting order

Total comparisons

Total swaps

Time

4, 2, 6, 1, 5, 3

1, 2, 3, 4, 5, 6

Discuss:

What stayed the same? What changed? Use your recorded evidence.

Explain that physical timing is affected by handling cards, recording, and familiarity. One faster run alone does not establish that a method is more efficient.

Task 3 · Independent trace — 5 minutes

Each student independently traces one complete pass on:

3, 5, 2, 4, 1, 6

Record:

1. Each comparison and any change to the smallest so far.

2. The selected smallest value.

3. The row after the pass, with the boundary.

4. The number of comparisons and actual swaps.

Keep individual traces and paired logs for Lesson 6.

PLENARY · 5 MINUTES

Students answer independently:

Why is the smallest selected card in its final position after this pass?

Then complete:

“One instruction that makes selection sort precise is __________.”

Collect responses and use them to identify what needs revisiting before Lesson 6.

Responsive and adaptive teaching

Provide a numbered procedure, a physical boundary marker, and a “smallest so far” marker. If students swap too early or only compare neighbouring cards, re-model one pass and ask them to explain when a swap is allowed. Follow feedback with a fresh individual attempt.

For students needing a smaller starting task, use four cards before returning to six. Extend secure students by asking them to explain why this version still makes comparisons on already sorted input, or to test repeated values such as 3, 1, 3, 2, 1, 2.

Science of learning

Retrieve prior knowledge before reviewing it. Model explicitly with a think-aloud, check every student’s understanding, and gradually remove prompts. Give specific feedback followed by a fresh attempt. Revisit decomposition, pattern recognition, and error correction during the sorting tasks.

Potential DMI connection

Retain trace records and comparison logs as evidence for evaluating the method and explaining later improvements or choices.

Teacher reference

For 4, 2, 6, 1, 5, 3, the completed passes are:

Pass

Row after the pass

Comparisons

Swaps

1

1 | 2, 6, 4, 5, 3

5

1

2

1, 2 | 6, 4, 5, 3

4

0

3

1, 2, 3 | 4, 5, 6

3

1

4

1, 2, 3, 4 | 5, 6

2

0

5

1, 2, 3, 4, 5 | 6

1

0

Total

15

2

Already sorted input requires 15 comparisons and 0 swaps using this procedure.

The independent first pass produces 1 | 5, 2, 4, 3, 6, with 5 comparisons and 1 swap.