You will learn
- Plan multiple steps.
- Use order of operations.
- Keep track of working.
- Check each step.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Break the problem into steps.
- Follow the order of operations.
- Show your working.
- Check each step.
Words to know
More than one step.
Rules for the sequence.
Written steps.
Between start and end.
1. Discover: pencil shop
A shop has 12 packs of 8 pencils. It sells 3/4 of them. How many are left?
2. Understand: multistep
- Total: 12 × 8 = 96.
- Sold: 3/4 of 96 = 72.
- Left: 96 − 72 = 24.
- Order of operations: 5 + 3 × 4 = 17, not 32.
Idea 1: Steps
12 packs of 8 pencils: 12 × 8 = 96. 3/4 sold: 96 ÷ 4 × 3 = 72. Left: 96 − 72 = 24.
Idea 2: Order
5 + 3 × 4 = 5 + 12 = 17. (5 + 3) × 4 = 8 × 4 = 32.
Idea 3: Working
Write each step so you can find errors.
Why brackets? They change which part is done first.
3. Worked examples
Example 1 (I show you): Total
12 packs of 8
- 12 × 8.
Answer: 96
Example 2 (We do it together): Order
5 + 3 × 4
- Multiply first.
Answer: 17
Example 3 (You try): Brackets
(5 + 3) × 4
Show the steps and answer
- Brackets first.
Answer: 32
Did you know?
Brackets, then multiply and divide, then add and subtract.
Why this matters
Multistep calculations solve real problems accurately.
4. Explore: steps
You need paper.
- Find the total.
- Find the part.
- Subtract.
- Check.
Think about it: what did you notice?
24.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- Step 1: ___ = ___.
- Step 2: ___ = ___.
- By the order of operations, I do ___ first.
- The answer is ___.
Guided practice
Question 1. 12 × 8?
96.
Question 2. 3/4 of 96?
72.
Question 3. Left?
24.
Independent practice
Level 1: Start
- Total pencils
- Number sold
- Number left
- 5 + 3 × 4
- (5 + 3) × 4
Level 2: Grow
- 6 + 4 × 3
- (6 + 4) × 3
- 20 − 12 ÷ 4
Level 3: Stretch
- (20 − 12) ÷ 4
- 3 × (2 + 8) − 4 × 2
- Ben says (5 + 3) × 4 = 17. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
12 packs of 8; 3/4 sold. How many left?
Show a sample answer
24.
Another one. A shop has 9 packs of 6 pens. It sells 2/3 of them. How many are left?
Show a sample answer
18
7. Common mistakes
Fix: Multiply first.
Fix: Follow the order of operations.
Fix: Show every step.
8. Lesson summary and revision card
- I can plan multiple steps.
- I can use the order of operations.
- I can keep track of working.
- I can check each step.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Write every step.
- Follow the order.
- Check each step.
11. Next lesson
Next lesson: Mathematical modelling. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- A shop has 12 packs of 8 pencils. How many pencils in all? [2 marks]
- It sells 3/4 of them. How many are sold? [2 marks]
- How many pencils are left? [2 marks]
- Work out 5 + 3 × 4. [2 marks]
- Ali says (5 + 3) × 4 = 17. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 12 × 8 [1]; 96 [1]
- 96 ÷ 4 = 24, then × 3 [1]; 72 [1]
- 96 − 72 [1]; 24 [1]
- Multiply first: 3 × 4 = 12 [1]; 5 + 12 = 17 [1]
- No [1]. Brackets first: 5 + 3 = 8 [1]. 8 × 4 = 32 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 12 × 8
- 3/4 of 96
- Left
- 5 + 3 × 4
- (5 + 3) × 4
- 12 × 8
- 3/4 of 96
- 96 − 72
- 5 + 3 × 4
- (5 + 3) × 4
Homework
Make a three-step problem for a friend.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 12 × 8 | 96 | 2 |
| 3/4 of 96 | 72 | 2 |
| Left | 24 | 2 |
| 5 + 3 × 4 | 17 | 2 |
| (5 + 3) × 4 | 32 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 96; 2 72; 3 24; 4 17; 5 32.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 96; 7 72; 8 24; 9 17; 10 32.
Independent practice answers. Level 1: 1 96; 2 72; 3 24; 4 17; 5 32. Level 2: 1 18; 2 30; 3 17. Level 3: 1 2; 2 22; 3 Brackets first: 8 × 4 = 32..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Plan multiple steps | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Use order of operations | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Keep track of working | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Check each step | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Adding before multiplying. Multiply first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Two-step problems.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child solves problems with several steps. You do not need to be good at mathematics to help.
- Plan a shopping total in steps.
- Ask: what do I do first?
- Write each step down.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: plan multiple steps; use order of operations; keep track of working; check each step.
Prerequisite knowledge. Lesson 2.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What is step one? Does the order matter?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Adding before multiplying. Multiply first.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Two-step problems. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Standards for Mathematical Practice. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.OA.A.1 and 6.EE.A.1; Cambridge Primary Mathematics Stage 6 (order of operations). These sources informed the lesson.