Multi-step Word Problems and Choosing the Operation

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Plan the Steps in Your Copy
5 Class Challenge
6 Write It Down
7 What Did We Notice?
8 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a real shopping moment: you buy 4 sandwiches at €3 each, then you split the bill evenly between 2 people. Before we work anything out, hands up: which calculation would you do first, and which one comes second?

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

We will work through three money problems together, each built in stages on the board. Watch for the signal words that tell us which operation each step needs, and make a rough estimate before every answer is revealed. Predict each result before you see it.

Three money problems

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Key point

The zeros and the cent columns catch people out, so let's say every step aloud before we check it, and make a rough estimate first each time.

Today we'll work through three problems together, planning the steps out loud before we calculate. First, eight pencils cost sixty cent each, and the total is shared between four friends. Next, five stickers cost €1.40 each, so how much change from €10? Last comes our trip problem: a €120 bus plus €6 entry for each of thirty pupils, so what does the trip cost each pupil?

Plan the steps for each shopping and trip problem, name the operation for each step, then work it out.

8 pencils cost 60c each. The total is shared equally between 4 friends. How much does each friend pay?
5 stickers cost €1.40 each. How much change do you get from €10?
A class trip has a €120 bus plus €6 entry for each of 30 pupils. What is the cost per pupil?

Ways to start:

Read the problem twice and underline the question at the end.
Sketch a bar to show what each step produces before you calculate: one bar for the total, then split or take away for step two.
Ask: which calculation do I need first, and what does its answer let me do next?

Stretch:

Estimate the answer roughly before you calculate — does your exact answer land near it?

Answers & strategies (teacher)

8 pencils cost 60c each. The total is shared equally between 4 friends. How much does each friend pay? — €1.20 (8 × 60c = €4.80, then €4.80 ÷ 4 = €1.20)
5 stickers cost €1.40 each. How much change do you get from €10? — €3.00 (5 × €1.40 = €7.00, then €10 − €7.00 = €3.00)
A class trip has a €120 bus plus €6 entry for each of 30 pupils. What is the cost per pupil? — €10.00 (30 × €6 = €180, + €120 = €300, then €300 ÷ 30 = €10.00)

+15 XP

4 - Plan the Steps in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy (or on your plan-then-solve sheet), for each problem write the steps as a short plan (Step 1: …, Step 2: …) with the operation named, sketch a bar to show what each step produces, then show the working and box the final answer.

+10 XP

5 - Class Challenge ~8 mins

Key point

Each clue is its own mini-problem, and its answer feeds the next clue. We work through them in this order: Clue 1 is a single operation, Clue 2 needs two steps, and Clue 3 needs three steps to reveal the final amount. The mystery answer only appears when every clue is solved in order.

Clue 1: The school shop sells copybooks at €1.50 each. What do 4 copybooks cost?
Clue 2: Add a €2.20 ruler to your Clue 1 total, then pay with a €10 note. What change do you get?
Clue 3: Now buy 4 notebooks at €1.10 each. Using the change from Clue 2, how much was already spent from the €10, and what is the grand total with the notebooks?

Solve each clue in order — each answer unlocks the next — to reveal the final amount spent at the school shop.

Clue 1: The school shop sells copybooks at €1.50 each. How much do 4 copybooks cost?
Clue 2: Add a €2.20 ruler to the €6.00 from Clue 1, then pay with a €10 note. How much change is there?
Clue 3: Now buy 4 notebooks at €1.10 each. Using the €1.80 change from Clue 2, how much was already spent from the €10, and what is the grand total with the notebooks?

Ways to start:

Solve Clue 1 on its own, then carry its answer straight into Clue 2.
For each clue, name the operation for every step before you work it.

Stretch:

Estimate the grand total roughly before you add — does it land near your exact answer?
Extension: a 4.5 m ribbon roll is cut into 0.9 m lengths. How many lengths is that? Estimate first, then check by dividing.

Answers & strategies (teacher)

Clue 1: The school shop sells copybooks at €1.50 each. How much do 4 copybooks cost? — €6.00 (4 × €1.50)
Clue 2: Add a €2.20 ruler to the €6.00 from Clue 1, then pay with a €10 note. How much change is there? — €1.80 (€6.00 + €2.20 = €8.20, then €10 − €8.20 = €1.80)
Clue 3: Now buy 4 notebooks at €1.10 each. Using the €1.80 change from Clue 2, how much was already spent from the €10, and what is the grand total with the notebooks? — €12.60 (4 × €1.10 = €4.40, €10 − €1.80 = €8.20, then €8.20 + €4.40 = €12.60)

+15 XP

Pupil practice

Module 2 · Operations and Computational Fluency Number

Lesson 27 · Multi-step Word Problems and Choosing the Operation

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