You will learn
- Say what an array is.
- Count rows and columns.
- Write a multiplication sentence from an array.
- See that the order does not change the total.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
Objects in rows and columns.
Objects across.
Objects down.
The answer to a multiplication.
1. Discover: planting yams
A farmer plants yams in 3 rows. Each row has 4 plants. How many plants are there? What happens if she makes 4 rows of 3?
2. Understand: arrays
An array arranges objects in rows (across) and columns (down).
3 rows of 4 is 3 × 4 = 12. If we turn the array, we get 4 rows of 3: 4 × 3 = 12. The total stays the same.
An array makes it easy to count: add each row, or count in 4s: 4, 8, 12.
3. Explore: build an array
You need 12 counters.
- Make 3 rows of 4 counters.
- Write 3 × 4 = 12.
- Turn the paper to make 4 rows of 3.
- Write 4 × 3 = 12.
Think about it: what did you notice?
3 × 4 = 4 × 3 = 12.
4. Practise
Guided practice
Question 1. 2 rows of 5?
2 × 5 = 10.
Question 2. 3 rows of 4 and 4 rows of 3. Same total?
Yes, 12.
Question 3. In an array, rows go…
across.
Independent practice
- 2 rows of 5
- 3 rows of 4
- 4 rows of 3
- 5 rows of 2
- 4 × 6
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A garden has 4 rows of 6 plants. How many plants?
Show a sample answer
24 plants.
6. Common mistake
Fix: Rows go across; columns go down.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- An array has rows and columns.
- Rows go across.
- Turning an array keeps the total.
9. Next lesson
Next lesson: Skip counting. Keep going with the next idea in this course.
Printable worksheet
- 2 rows of 5
- 3 rows of 4
- 4 rows of 3
- 5 rows of 2
- 4 × 6
Homework
Make an array with buttons or stones at home. Draw it and write two multiplication sentences.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 rows of 5 | 10 | 2 |
| 3 rows of 4 | 12 | 2 |
| 4 rows of 3 | 12 | 2 |
| 5 rows of 2 | 10 | 2 |
| 4 × 6 | 24 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10; 2 12; 3 12; 4 10; 5 24.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what an array is | 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 Count rows and columns | 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 Write a multiplication sentence from an array | 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 See that the order does not change the total | 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 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Counting rows and columns as the same. Rows go across; columns go down.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters in rows of the same length.
- 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.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: say what an array is; count rows and columns; write a multiplication sentence from an array; see that the order does not change the total.
Prerequisite knowledge. Lessons 1 and 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. 35–45 minutes.
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 12 counters. 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.
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. Counting rows and columns as the same. Rows go across; columns go down.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Use counters in rows of the same length. 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.