You will learn
- Read a problem carefully.
- List known facts.
- State the question.
- Plan what to find.
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 the problem carefully, twice.
- List the known facts.
- Say what you need to find.
- Plan which operations to use.
Words to know
Facts given.
What to find.
Steps to follow.
+, −, × or ÷.
1. Discover: what is asked?
Ama buys 3 books at 4.50 each and pays 20. What is the question really asking?
2. Understand: understanding problems
- Known: 3 books, 4.50 each, paid 20.
- Unknown: the change.
- Step 1: cost = 3 × 4.50 = 13.50. Step 2: change = 20 − 13.50 = 6.50.
- Underline the question and circle the numbers.
Idea 1: Known
Ama buys 3 books at 4.50 each and pays with 20. Known: 3 books, 4.50 each, 20 paid. Unknown: the change.
Idea 2: Plan
Step 1: 3 × 4.50 = 13.50. Step 2: 20 − 13.50 = 6.50. That is 2 steps.
Idea 3: Start
The first action is to read twice.
Why plan? A plan prevents using the wrong numbers or operation.
3. Worked examples
Example 1 (I show you): Unknown
Ama buys 3 books at 4.50 and pays 20
- What is asked?
Answer: the change
Example 2 (We do it together): Step 1
3 × 4.50
- Cost of all books.
Answer: 13.50
Example 3 (You try): Step 2
20 − 13.50
Show the steps and answer
- Change.
Answer: 6.50
Did you know?
Many errors come from not reading the question carefully.
Why this matters
Understanding the problem comes before choosing a method.
4. Explore: read
You need paper.
- Underline the question.
- Circle the numbers.
- Choose steps.
- Check the units.
Think about it: what did you notice?
Change 6.50.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I know ___.
- I need to find ___.
- Step 1: ___. Step 2: ___.
- The answer is ___.
Guided practice
Question 1. Cost of 3 books?
13.50.
Question 2. Change from 20?
6.50.
Question 3. What is unknown?
the change.
Independent practice
Level 1: Start
- Known facts in the book problem
- Unknown in the book problem
- 3 × 4.50
- 20 − 13.50
- Number of steps
Level 2: Grow
- Kofi buys 4 pens at 2.50 each and pays 15. The unknown
- Cost of the 4 pens
- Change from 15
Level 3: Stretch
- Which question can the facts not answer: How much change? What colour are the pens?
- How many steps: cost then change
- Ben adds 3 + 4.50 + 20 = 27.50 for the book problem. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
3 books at 4.50, pay 20. Change?
Show a sample answer
6.50.
Another one. Write the known facts and the unknown: 5 notebooks cost 3.20 each and I pay with 20.
Show a sample answer
Known: 5 notebooks, 3.20 each, 20 paid; unknown: the change
7. Common mistakes
Fix: Read first.
Fix: Pick the numbers that help.
Fix: Read and plan first.
8. Lesson summary and revision card
- I can read a problem carefully.
- I can list known facts.
- I can state the question.
- I can plan what to find.
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
- Read twice.
- List known and unknown.
- Plan steps.
11. Next lesson
Next lesson: Selecting strategies. 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.
- Ama buys 3 books at 4.50 each and pays with 20. State what you need to find. [1 mark]
- Same problem. Find the cost of 3 books. [2 marks]
- Same problem. Find the change. [2 marks]
- Same problem. How many steps are needed? Explain. [2 marks]
- Ali adds 3 + 4.50 + 20 = 27.50. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- The change [1]
- 3 × 4.50 [1]; 13.50 [1]
- 20 − 13.50 [1]; 6.50 [1]
- Multiply, then subtract [1]; 2 [1]
- No [1]. The unknown is the change, not a total [1]. The plan is 3 × 4.50 = 13.50, then 20 − 13.50 = 6.50 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Cost of 3 books at 4.50
- Change from 20
- Unknown is
- Steps needed
- First action
- Known facts in the book problem
- Unknown
- 3 × 4.50
- 20 − 13.50
- Number of steps
Homework
Rewrite a word problem in your own words.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Cost of 3 books at 4.50 | 13.50 | 2 |
| Change from 20 | 6.50 | 2 |
| Unknown is | the change | 2 |
| Steps needed | 2 | 2 |
| First action | read twice | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 13.50; 2 6.50; 3 the change; 4 2; 5 read twice.
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 3 books, 4.50 each, 20 paid; 7 the change; 8 13.50; 9 6.50; 10 2.
Independent practice answers. Level 1: 1 3 books at 4.50 each and 20 paid; 2 the change; 3 13.50; 4 6.50; 5 2 steps. Level 2: 1 the change; 2 10; 3 5. Level 3: 1 What colour are the pens?; 2 2; 3 The unknown is the change: 3 × 4.50 = 13.50, then 20 − 13.50 = 6.50..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read a problem carefully | 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 List known facts | 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 State the question | 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 Plan what to find | 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: Starting to calculate before reading. Read first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: One-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 learns to understand a problem before solving it. You do not need to be good at mathematics to help.
- Read word problems aloud together.
- Ask: what do we know? what do we need?
- Underline numbers and the question.
- 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 carefully; list known facts; state the question; plan what to find.
Prerequisite knowledge. Grade 5 problem solving.
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 do I know? What do I need to find?
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. Starting to calculate before reading. Read first.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. One-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 MP1; Cambridge Primary Mathematics Stage 6 (problem solving). These sources informed the lesson.