You will learn
- Arrange objects in equal rows.
- Find the number in each row.
- Find the number of rows.
- Write the division sentence.
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
- An array is rows and columns.
- Share the total into equal rows.
- Find how many rows or how many in a row.
- Write the division sentence.
Words to know
Objects in rows and columns.
Across.
Down.
Share or group equally.
1. Discover: planting trees
A farmer has 45 trees and plants them in 9 equal rows. How many trees are in each row?
2. Understand: division using arrays
An array shows division clearly. 24 counters in 4 equal rows gives 6 in each row: 24 ÷ 4 = 6.
If the rows hold 6 each, we get 4 rows: 24 ÷ 6 = 4.
20 ÷ 4 = 5; 30 ÷ 5 = 6; 28 ÷ 7 = 4; 32 ÷ 8 = 4; 45 ÷ 9 = 5.
Idea 1: In each row
20 counters in 4 rows: 20 ÷ 4 = 5 in each row.
Idea 2: How many rows
18 counters in rows of 6: 18 ÷ 6 = 3 rows.
Idea 3: Columns
32 in 8 columns: 32 ÷ 8 = 4 in each column.
Why arrays? They show division as a picture.
3. Worked examples
Example 1 (I show you): Rows
20 counters in 4 rows. How many in each?
- 20 ÷ 4.
Answer: 5
Example 2 (We do it together): Number of rows
18 in rows of 6. How many rows?
- 18 ÷ 6.
Answer: 3
Example 3 (You try): Columns
32 in 8 columns. How many in each?
Show the steps and answer
- 32 ÷ 8.
Answer: 4
Did you know?
The same array shows two multiplications and two divisions.
Why this matters
Arrays link multiplication and division.
4. Explore: build the array
You need 24 counters.
- Arrange 24 counters in 4 equal rows.
- Count each row.
- Re-arrange in rows of 6.
- Count the rows.
Think about it: what did you notice?
24 ÷ 4 = 6; 24 ÷ 6 = 4.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- There are ___ in ___ rows.
- Each row has ___.
- The division is ___ ÷ ___ = ___.
- The array shows ___ × ___ = ___.
Guided practice
Question 1. 20 counters in 4 rows. How many in each row?
5.
Question 2. 18 in rows of 6. How many rows?
3.
Question 3. 45 trees in 9 rows?
5 each.
Independent practice
Level 1: Start
- 20 in 4 rows
- 18 in rows of 6
- 30 chairs in 5 rows
- 28 in rows of 7
- 32 in 8 columns
Level 2: Grow
- 15 in 3 rows
- 16 in rows of 4
- 27 in 9 columns
Level 3: Stretch
- 42 in 6 rows
- 56 in rows of 8
- Ana arranges 20 in 4 rows and says each row has 80. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A hall has 30 chairs in 5 equal rows. How many chairs in a row?
Show a sample answer
6 chairs.
Another one. Arrange 24 desks in equal rows in two ways. Write the division sentences.
Show a sample answer
4 rows of 6: 24 ÷ 4 = 6; 6 rows of 4: 24 ÷ 6 = 4
7. Common mistakes
Fix: Rows go across.
Fix: We share the total, so we divide.
Fix: Rows go across. Columns go down.
8. Lesson summary and revision card
- I can arrange objects in equal rows.
- I can find the number in each row.
- I can find the number of rows.
- I can write the division sentence.
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
- Arrays show division.
- Rows and columns.
- Total ÷ rows.
11. Next lesson
Next lesson: Division with remainders. 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.
- 20 counters in 4 rows. How many in each row? [2 marks]
- 18 in rows of 6. How many rows? [2 marks]
- 30 chairs in 5 rows. How many in each row? [2 marks]
- Write the multiplication for 4 rows of 7. [1 mark]
- Ben says 32 in 8 columns gives 40 in each. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 20 ÷ 4 [1] = 5 [1]
- 18 ÷ 6 [1] = 3 [1]
- 30 ÷ 5 [1] = 6 [1]
- 4 × 7 = 28 [1]
- No [1]. He added [1]. 32 ÷ 8 = 4 [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
- 20 in 4 rows
- 18 in rows of 6
- 30 in 5 rows
- 28 in rows of 7
- 32 in 8 columns
- 20 counters in 4 rows gives ___ in each row.
- 18 in rows of 6 make ___ rows.
- 30 chairs in 5 rows gives ___ per row.
- 28 in rows of 7 make ___ rows.
- 32 in 8 columns gives ___ in each column.
Homework
Arrange 24 stones in different equal rows. Write the division sentences.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 20 in 4 rows | 5 | 2 |
| 18 in rows of 6 | 3 | 2 |
| 30 in 5 rows | 6 | 2 |
| 28 in rows of 7 | 4 | 2 |
| 32 in 8 columns | 4 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5; 2 3; 3 6; 4 4; 5 4.
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 5; 7 3; 8 6; 9 4; 10 4.
Independent practice answers. Level 1: 1 5; 2 3 rows; 3 6 per row; 4 4 rows; 5 4 per column. Level 2: 1 5 per row; 2 4 rows; 3 3 per column. Level 3: 1 7 per row; 2 7 rows; 3 She multiplied. 20 ÷ 4 = 5 because 4 × 5 = 20..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Arrange objects in equal rows | 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 Find the number in each row | 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 Find the number of rows | 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 Write the division sentence | 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: Counting columns when asked for rows. Rows go across.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Build the array with counters in rings.
- 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 uses arrays to understand division. You do not need to be good at mathematics to help.
- Arrange sweets or counters in rows.
- Ask: how many rows? how many in each?
- Draw arrays together.
- 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: arrange objects in equal rows; find the number in each row; find the number of rows; write the division sentence.
Prerequisite knowledge. Lessons 1 to 4.
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 24 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.
Key questions. How many in all? How many rows? How many in each row?
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 columns when asked for rows. Rows go across.
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. Build the array with counters in rings. 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.A.2 and 3.OA.B.6; Cambridge Primary Mathematics Stage 3 (division with arrays). These sources informed the lesson.