You will learn
- Read a problem and find what is asked.
- Plan the steps.
- Solve each step and write it down.
- Check the answer makes sense.
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 find what is asked.
- Plan the steps before you calculate.
- Write down the answer to each step.
- Check that it makes sense.
Words to know
One part of a problem.
Decide what to do first.
All added together.
What remains.
1. Discover: the busy shop
A shop had 2,500 bags of rice. On Monday it sold 1,200 and on Tuesday 800. How many bags are left?
2. Understand: multistep word problems
Many problems need more than one step. Read slowly. Ask: What do I know? What do I need to find? What do I do first?
Shop: 2,500 bags. Step 1: 1,200 + 800 = 2,000 sold. Step 2: 2,500 − 2,000 = 500 left.
School: 1,245 pupils, 320 join and 150 leave. Step 1: 1,245 + 320 = 1,565. Step 2: 1,565 − 150 = 1,415.
Write each step, then check with an estimate.
Idea 1: Plan
1,245 pupils. 320 join and 150 leave. Step 1: 1,245 + 320 = 1,565. Step 2: 1,565 − 150 = 1,415.
Idea 2: Two quantities
A farmer has 3,450 kg maize and 2,875 kg rice. Step 1: 3,450 + 2,875 = 6,325. Sells 4,000. Step 2: 6,325 − 4,000 = 2,325 kg.
Idea 3: Two spendings
Ada has 5,000. She spends 1,250 and 2,340. Total spent is 3,590. Left: 5,000 − 3,590 = 1,410.
Why plan? A plan stops us from mixing up the steps.
3. Worked examples
Example 1 (I show you): Join and leave
1,245 pupils; 320 join; 150 leave. How many now?
- 1,245 + 320 = 1,565.
- 1,565 − 150.
Answer: 1,415
Example 2 (We do it together): Farm
3,450 kg maize + 2,875 kg rice; 4,000 kg sold. Left?
- 3,450 + 2,875 = 6,325.
- 6,325 − 4,000.
Answer: 2,325 kg
Example 3 (You try): Spending
Ada has 5,000 and spends 1,250 and 2,340. Left?
Show the steps and answer
- 1,250 + 2,340 = 3,590.
- 5,000 − 3,590.
Answer: 1,410
Did you know?
Most real-life problems have more than one step.
Why this matters
Multistep problems prepare us for shopping, saving and building.
4. Explore: plan and solve
You need paper and a pencil.
- Read the shop problem.
- Write step 1 and step 2.
- Solve each step.
- Check with an estimate: 2,500 − 2,000.
Think about it: what did you notice?
500 bags are left.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The problem asks for ___.
- Step 1 is ___.
- Step 2 is ___.
- My answer makes sense because ___.
Guided practice
Question 1. Bags sold: 1,200 + 800 = ?
2,000.
Question 2. Bags left: 2,500 − 2,000 = ?
500.
Question 3. How many steps?
Two.
Independent practice
Level 1: Start
- School 1,245; 320 join, 150 leave. How many?
- Farmer: 3,450 kg maize + 2,875 kg rice, sells 4,000 kg. Left?
- Ada has 5,000. She spends 1,250 and 2,340. Left?
- A bus carries 45 on trip 1 and 38 on trip 2. How many in all?
- Write a two-step problem.
Level 2: Grow
- A shop has 4,500 eggs. It sells 2,000 and 1,250. How many are left?
- A library has 3,200 books, buys 450 and lends 600. How many are in the library?
- A pen costs 350 naira and a book costs 1,200. What do 2 pens and 1 book cost?
Level 3: Stretch
- Ali has 7,000. He spends 2,345 and then 1,655. How much is left?
- A school has 1,000 pupils. 250 join and 125 leave. How many now?
- Ben solves 1,245 + 320 − 150 by adding all three and gets 1,715. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A farmer has 3,450 kg maize and 2,875 kg rice and sells 4,000 kg. How many kg are left?
Show a sample answer
2,325 kg.
Another one. Write a two-step problem using 2,000, 500 and 300 and solve it.
Show a sample answer
A box has 2,000 pens. 500 are sold and 300 are lost. 1,200 are left.
7. Common mistakes
Fix: Reread the question to see what is asked.
Fix: Ask: does the amount go up or down?
Fix: Check that you have answered the question.
8. Lesson summary and revision card
- I can find what the problem asks.
- I can plan the steps.
- I can solve each step.
- I can check my answer.
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 the steps.
- Write each step.
- Check with an estimate.
11. Next lesson
Next lesson: Multiplication as equal groups. 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.
- 1,245 pupils. 320 join and 150 leave. How many now? [3 marks]
- A farmer has 3,450 kg maize and 2,875 kg rice and sells 4,000 kg. How many kg remain? [3 marks]
- Ada has 5,000. She spends 1,250 and 2,340. How much is left? [3 marks]
- A bus carries 45 on trip 1 and 38 on trip 2. How many in all? [1 mark]
- Why should we plan the steps first? [2 marks]
Total: 12 marks.
Marking guide and model answers
- 1,245 + 320 = 1,565 [1]; 1,565 − 150 [1] = 1,415 [1]
- 3,450 + 2,875 = 6,325 [1]; 6,325 − 4,000 [1] = 2,325 [1]
- 1,250 + 2,340 = 3,590 [1]; 5,000 − 3,590 [1] = 1,410 [1]
- 83 [1]
- To know what to do first [1]; to avoid mixing up the steps [1]
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 1,245 + 320 − 150
- 3,450 + 2,875 − 4,000
- 5,000 − 1,250 − 2,340
- 2,500 − 1,200 − 800
- 45 + 38
- A shop had 2,500 bags, sold 1,200 and 800. Left?
- 1,245 pupils, 320 join, 150 leave. Now?
- 3,450 + 2,875 =
- Ada has 5,000 and spends 1,250 and 2,340. Left?
- Before solving, we should ___ the steps.
Homework
Write a two-step problem about a market and solve it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1,245 + 320 − 150 | 1,415 | 2 |
| 3,450 + 2,875 − 4,000 | 2,325 | 2 |
| 5,000 − 1,250 − 2,340 | 1,410 | 2 |
| 2,500 − 1,200 − 800 | 500 | 2 |
| 45 + 38 | 83 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1,415; 2 2,325; 3 1,410; 4 500; 5 83.
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): 6 500; 7 1,415; 8 6,325; 9 1,410; 10 plan.
Independent practice answers. Level 1: 1 1,415; 2 2,325 kg; 3 1,410; 4 83; 5 for example I have 500 and spend 120 and 80, so 300 left. Level 2: 1 1,250; 2 3,050; 3 1,900 naira. Level 3: 1 3,000; 2 1,125; 3 Pupils who leave are subtracted. The answer is 1,415..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read a problem and find what is asked | 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 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 |
| O3 Solve each step and write it down | 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 the answer makes sense | 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: Doing only the first step. Reread the question to see what is asked.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw a bar for each step.
- 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 word problems that need more than one step. You do not need to be good at mathematics to help.
- Use real prices to make multistep problems.
- Ask: what do we do first? then?
- Write each step on paper.
- 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: read a problem and find what is asked; plan the steps; solve each step and write it down; check the answer makes sense.
Prerequisite knowledge. Lessons 1 to 6.
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 and a pencil. 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 does it ask? What is step 1? What is step 2? Does it 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. Doing only the first step. Reread the question to see what is asked.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Draw a bar for each step. 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 3 » Operations & Algebraic Thinking; Grade 3 » 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 3.OA.D.8 (two-step problems); Cambridge Primary Mathematics Stage 3 (problem solving). These sources informed the lesson.