Multiplication and Division
Multiplication and Division introduces the two ideas behind these operations before children memorise times tables: multiplication as counting equal groups (or repeated addition), and division as sharing an amount equally or grouping it into equal sets.
Before you start
Make sure you're comfortable with these topics first:
Method
- Start concrete: use real, identical objects such as counters or cubes, arranged into equal groups the child can physically count and re-count.
- For division, share a real pile of objects one at a time into hoops, plates or hands, dealing them out like playing cards, to build the idea of EQUAL sharing.
- Move to pictorial: draw the groups as a simple array, rows and columns of dots or circles, so the child can see rows times columns without needing real objects.
- Introduce the x and the / symbols only once the array picture is secure, e.g. 3 rows of 4 becomes 3 x 4 = 12, and sharing 12 into 3 equal groups becomes 12 / 3 = 4.
- Link the two operations explicitly: division is multiplication in reverse, so 4 x 3 = 12 and 12 / 3 = 4 describe the very same array, just read in a different direction.
- Watch for the classic misconception that multiplication should be solved like addition, so a child works out 3 x 4 by adding 3 + 4 = 7 instead of finding 3 equal groups of 4.
- Watch for the sharing misconception: when dividing, children often deal objects out unevenly, giving the first group extra, rather than sharing one at a time round and round, then miscount the result as fair shares.
Worked example
There are 4 plates, and 20 strawberries are shared equally between them. How many strawberries go on each plate?
- Draw 4 plates in a row, the pictorial stage of the problem.
- Share the strawberries out one at a time, plate by plate, going round and round until all 20 are used up.
- After sharing, count how many strawberries ended up on one plate.
- Each plate gets 5 strawberries, because 4 equal groups of 5 make 20 (4 x 5 = 20).
- Write this as a division number sentence: 20 / 4 = 5.
Practice questions
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Q1Draw 3 equal groups with 5 counters in each group. How many counters are there in total?Show answer
Answer: 15 counters (3 groups of 5 is 3 x 5 = 15)
Q2An array has 2 rows of 6 dots. Write the multiplication that matches the array, and work out the total.Show answer
Answer: 2 x 6 = 12 dots
Q3Femi has 18 grapes and shares them equally between 3 bowls. How many grapes go in each bowl?Show answer
Answer: 6 grapes (18 shared between 3 is 18 / 3 = 6)
Q4There are 12 eggs. They are put into boxes that each hold 6 eggs. How many boxes are needed?Show answer
Answer: 2 boxes (12 / 6 = 2)
Q5Circle the calculation that means '4 equal groups of 7': A) 4 + 7 B) 4 x 7 C) 4 - 7Show answer
Answer: B) 4 x 7
Q6Write the multiplication and the answer shown by an array of 5 rows with 2 counters in each row.Show answer
Answer: 5 x 2 = 10
Q716 party favours are shared equally among 4 children at a party. How many party favours does each child get?Show answer
Answer: 4 party favours each (16 / 4 = 4)
Exam-style questions
Written in the style of a KS1 Maths exam paper, with a full mark scheme.
Nine cupcakes are arranged into an array with 3 equal rows. How many cupcakes are in each row? Describe the array, and write the division sentence.
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Tobias says that 4 x 5 gives the same answer as 4 + 5, because both calculations use the numbers 4 and 5. Work out both calculations and explain whether Tobias is correct.
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A baker puts 24 muffins onto trays, with 4 muffins on each tray. Marcus says he will need 8 trays. Is Marcus correct? Show the correct working.
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Free printable worksheet
Want more practice on paper? Download the multiplication and division worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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