You will learn
- Plan the steps.
- Choose operations.
- Record each step.
- Check reasonableness.
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
- Read and plan the steps.
- Choose the operation for each step.
- Record each step clearly.
- Check the answer makes sense.
Words to know
More than one step.
Decide the steps.
Add, subtract, multiply, divide.
Makes sense.
1. Discover: school stores
A school buys 24 boxes with 36 pencils each and gives out 450. How many pencils remain?
2. Understand: multistep problems
- 24 × 36 = 864; 864 − 450 = 414 pencils.
- 250 pupils, buses seat 45: 250 ÷ 45 = 5 r25, so 6 buses are needed.
- 12 notebooks at 175 each: 2,100. Pay 2,500: change 400.
Idea 1: Two steps
12 packs of 175: 12 × 175 = 2,100. Change from 2,500: 2,500 − 2,100 = 400.
Idea 2: Remainders
250 people, 45 per bus: 250 ÷ 45 = 5 r25, so we need 6 buses.
Idea 3: Combine
8 boxes of 125 minus 300: 1,000 − 300 = 700. 45 × 6 + 30 = 270 + 30 = 300.
Why record steps? They show your thinking and help you check.
3. Worked examples
Example 1 (I show you): Two steps
12 × 175 then 2,500 minus the result
- Multiply first.
Answer: 400 change
Example 2 (We do it together): Buses
250 people, 45 per bus
- 5 r25 means one more bus.
Answer: 6 buses
Example 3 (You try): Combine
8 boxes of 125 minus 300
Show the steps and answer
- 8 × 125 = 1,000.
Answer: 700
Did you know?
The remainder in a real problem often means one more is needed.
Why this matters
Real problems almost always need more than one step.
4. Explore: plan
You need paper.
- Find the total.
- Subtract what was given out.
- Check by adding back.
- Write the answer.
Think about it: what did you notice?
414.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- First I find ___.
- Then I ___.
- The answer is ___.
- It makes sense because ___.
Guided practice
Question 1. 24 × 36?
864.
Question 2. 864 − 450?
414.
Question 3. Buses for 250 pupils at 45?
6.
Independent practice
Level 1: Start
- 12 × 175
- 2,500 − 2,100
- 250 ÷ 45 with remainder
- 8 boxes of 125 minus 300
- 45 × 6 + 30
Level 2: Grow
- 6 packs of 12 pens and 8 more pens. How many pens?
- A 100 m rope is cut into 12 m pieces. How many whole pieces?
- 4 × 35 − 20
Level 3: Stretch
- Three friends each buy a 240 ticket and a 60 snack. Total?
- Ana pays 3 × 450 from 2,000. How much is left?
- Ben says 5 groups of 18 plus 12 is 5 × 30 = 150. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
12 notebooks cost 175 each. You pay 2,500. Change?
Show a sample answer
400.
Another one. A shop sells 36 books at 15 each and 20 pens at 8 each. How much money is taken?
Show a sample answer
36 × 15 + 20 × 8 = 540 + 160 = 700
7. Common mistakes
Fix: Round up for buses.
Fix: Re-read the question to see what is asked.
Fix: Decide what the remainder means.
8. Lesson summary and revision card
- I can plan the steps.
- I can choose the operations.
- I can record each step.
- I can check reasonableness.
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
- Plan.
- Label each step.
- Check.
11. Next lesson
Next lesson: Equivalent fractions. 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.
- 12 packs of 175 sheets are bought. How many sheets? [2 marks]
- A bill is 2,100 and 2,500 is paid. Find the change. [2 marks]
- 250 people travel in buses of 45. How many buses? [3 marks]
- There are 8 boxes of 125; 300 are sold. How many are left? [3 marks]
- Ali says 45 × 6 + 30 = 75 × 6 = 450. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 12 × 175 [1]; 2,100 [1]
- 2,500 − 2,100 [1]; 400 [1]
- 250 ÷ 45 = 5 r25 [1]; one more bus is needed [1]; 6 [1]
- 8 × 125 = 1,000 [1]; 1,000 − 300 [1]; 700 [1]
- No [1]. Multiply first: 270 [1]. 270 + 30 = 300 [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 12 × 175
- 2,500 − 2,100
- Buses for 250 at 45
- 8 × 125 − 300
- 45 × 6 + 30
- 24 boxes of 36 pencils:
- 864 − 450 =
- Buses for 250 at 45 each:
- 12 × 175 =
- Change from 2,500 for 2,100:
Homework
Create a multistep problem about a shop and solve it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 12 × 175 | 2,100 | 2 |
| 2,500 − 2,100 | 400 | 2 |
| Buses for 250 at 45 | 6 | 2 |
| 8 × 125 − 300 | 700 | 2 |
| 45 × 6 + 30 | 300 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2,100; 2 400; 3 6; 4 700; 5 300.
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): 6 864; 7 414; 8 6; 9 2,100; 10 400.
Independent practice answers. Level 1: 1 2,100; 2 400; 3 6 buses; 4 700; 5 300. Level 2: 1 80; 2 8 pieces (4 m left); 3 120. Level 3: 1 900; 2 650; 3 Only 18 is multiplied: 5 × 18 + 12 = 102..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Plan the 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 Choose 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 Record 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 |
| O4 Check reasonableness | 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: Ignoring the remainder. Round up for buses.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Solve 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 that need more than one step. You do not need to be good at mathematics to help.
- Use shopping to practise two-step problems.
- Ask: what do we find first?
- Ask what a remainder means.
- 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 the steps; choose operations; record each step; check reasonableness.
Prerequisite knowledge. Lessons 1 to 5.
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 the first step? Does my answer make sense?
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. Ignoring the remainder. Round up for buses.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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. Solve 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): Grade 5 » Operations & Algebraic Thinking; Grade 5 » Number & Operations in Base Ten. 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 5.NBT.B.6; Cambridge Primary Mathematics Stage 5 (problem solving). These sources informed the lesson.