You will learn
- Choose multiplication for equal groups.
- Solve one-step problems.
- Solve two-step problems.
- Check the answer.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Equal groups mean multiply.
- Find the total of all groups.
- Two-step problems need two operations.
- Check the answer and the unit.
Words to know
Same number in each group.
All together.
For each.
Needs two operations.
1. Discover: a market
24 boxes each hold 15 oranges. How many oranges? If 40 are bad, how many are good?
2. Understand: word problems
Read, picture, choose the operation.
- 24 × 15 = 240 + 120 = 360 oranges.
- 360 − 40 = 320 good oranges.
- 12 rows × 35 chairs = 420 chairs.
- 8 bags × 125 g = 1,000 g, which is 1 kg.
Idea 1: Equal groups
6 bags of 45 sweets: 45 × 6 = 270 sweets.
Idea 2: Per
8 bags with 125 g each: 8 × 125 = 1,000 g.
Idea 3: Two-step
24 boxes of 15 oranges: 24 × 15 = 360. If 40 are bad: 360 − 40 = 320 good.
Why two steps? The question asks for something after the first answer.
3. Worked examples
Example 1 (I show you): Groups
6 bags of 45
- 45 × 6 = 270.
Answer: 270
Example 2 (We do it together): Per
8 bags of 125 g
- 8 × 125.
Answer: 1,000 g
Example 3 (You try): Two steps
24 boxes of 15; 40 bad. Good?
Show the steps and answer
- 360, then −40.
Answer: 320
Did you know?
The word “per” often signals multiplication.
Why this matters
Equal groups appear in shops, farms and classrooms.
4. Explore: solve
You need paper.
- Read the problem.
- Draw boxes.
- Multiply.
- Subtract the bad ones.
Think about it: what did you notice?
320.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- There are ___ groups of ___.
- The total is ___.
- Then I ___.
- The answer is ___ (unit).
Guided practice
Question 1. 24 × 15?
360.
Question 2. 360 − 40?
320.
Question 3. 12 × 35?
420.
Independent practice
Level 1: Start
- 45 × 6
- 8 × 125
- 36 × 5
- 24 × 15
- 50 × 12
Level 2: Grow
- 7 packs of 24 cans. How many cans?
- 12 boxes of 45. How many?
- 9 bags of 150 g. Total mass?
Level 3: Stretch
- 15 rows of 32 seats. Total?
- 25 crates of 12 bottles; 40 are broken. How many are fine?
- Ana multiplies 8 bags of 125 g and says the total is 1,000 kg. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A hall has 12 rows of 35 chairs. How many chairs?
Show a sample answer
420.
Another one. 18 children each get 25 sweets. How many sweets are needed?
Show a sample answer
18 × 25 = 450 sweets
7. Common mistakes
Fix: Equal groups mean multiply.
Fix: Equal groups mean multiply.
Fix: Reread the question to see what is asked.
8. Lesson summary and revision card
- I can choose multiplication for equal groups.
- I can solve one-step problems.
- I can solve two-step problems.
- 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
- Equal groups: multiply.
- Check with estimate.
- Label answers.
11. Next lesson
Next lesson: Division fact review. 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 bag has 45 sweets. How many in 6 bags? [2 marks]
- 8 bags each hold 125 g. Find the total mass. [2 marks]
- A pack has 36 pencils. Find 5 packs. [2 marks]
- 24 boxes of 15 oranges; 40 are bad. How many are good? [3 marks]
- Kofi says 50 × 12 = 60. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 40 × 6 and 5 × 6 [1]; 270 [1]
- 8 × 125 [1]; 1,000 g [1]
- 30 × 5 = 150 and 6 × 5 = 30 [1]; 180 [1]
- 24 × 15 = 360 [1]; 360 − 40 [1]; 320 [1]
- No [1]. 50 × 10 = 500 and 50 × 2 = 100 [1]; 600 [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
- 45 × 6
- 8 × 125
- 36 × 5
- 24 × 15
- 50 × 12
- 24 boxes of 15 oranges:
- 360 oranges, 40 bad. Good:
- 12 rows of 35:
- 8 bags of 125 g:
- 45 × 6 =
Homework
Write two multiplication word problems about your home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 45 × 6 | 270 | 2 |
| 8 × 125 | 1,000 | 2 |
| 36 × 5 | 180 | 2 |
| 24 × 15 | 360 | 2 |
| 50 × 12 | 600 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 270; 2 1,000; 3 180; 4 360; 5 600.
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): 6 360; 7 320; 8 420; 9 1,000 g; 10 270.
Independent practice answers. Level 1: 1 270; 2 1,000; 3 180; 4 360; 5 600. Level 2: 1 168; 2 540; 3 1,350 g. Level 3: 1 480; 2 260; 3 The unit is grams: 1,000 g..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Choose multiplication for equal groups | 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 Solve one-step problems | 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 two-step problems | 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 | 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Adding instead of multiplying. Equal groups mean multiply.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use drawings of equal groups.
- 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 multiplication word problems. You do not need to be good at mathematics to help.
- Use shopping examples with equal packs.
- Ask: how many groups? how many in each?
- Have your child say the unit.
- 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: choose multiplication for equal groups; solve one-step problems; solve two-step problems; check the answer.
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. 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. How many groups? How many in each? Is there a second step?
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 instead of multiplying. Equal groups mean multiply.
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. Use drawings of equal groups. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.OA.A.2 and 4.OA.A.3; Cambridge Primary Mathematics Stage 4 (multiplication problems). These sources informed the lesson; no official alignment is claimed.