The Dairy Farm
Class 5 · Mathematics
5 ideas in Class 5 Mathematics, explained in plain words, with games and quizzes to practise.
Swapping the Order in Multiplication
Part of: Order and patterns in multiplication
3 rows of 5 buttons and 5 rows of 3 buttons look different, but both hold 15 buttons. Turning the rows into columns swaps the two numbers and keeps the total the same. So 3 × 5 and 5 × 3 always match, and this is true for any two numbers.
Why it matters. Knowing that order does not matter halves the number of facts a child must remember. Without it, children treat 6 × 13 and 13 × 6 as two separate hard problems.
Try it in two minutes
- Lay out 4 rows of 6 coins or buttons. Ask your child to count the total.
- Turn the page around so there are 6 rows of 4. Ask: has the total changed?
- Ask your child to say the multiplication for each view and compare the two answers.
Try at home. Ask your child to pick any two numbers under 15 and show with objects that both orders give the same total.
Multiplying by 10s, 100s and 1000s
Part of: Multiplying by tens, hundreds and thousands
To find 40 × 30, think of 4 tens times 3 tens. First do 4 × 3, which is 12. Then count the zeros hiding in the two numbers (one and one, so two zeros) and write them after 12 to get 1200. The digits shift to the left and zeros fill the empty places.
Why it matters. Rounded numbers such as 20, 300 and 5000 appear in money, distance and quantity problems. Counting zeros wrongly is the most common slip, so a clear pattern saves many mistakes.
Try it in two minutes
- Write 3 × 4 on paper and ask for the answer.
- Write 30 × 4, then 30 × 40, then 300 × 40 below it. Ask your child what happens to the answer each time.
- Ask: how many zeros did we start with and how many are in the answer?
Try at home. Ask your child to make up three problems like 60 × 200 and use the zeros pattern to answer them.
Doubling and Halving
Part of: Easy ways to multiply
If you halve one number and double the other, the product stays the same. For example 16 × 5 becomes 8 × 10, which is 80. Think of 16 rows of 5 chairs; joining pairs of rows gives 8 rows of 10 chairs, the same chairs in a neater shape.
Why it matters. It turns tricky problems into friendly ones, especially with 5, 25 and 50. Children who see this build mental maths confidence.
Try it in two minutes
- Ask your child for 14 × 5. Let them try in their own way first.
- Show: halve 14 to get 7, double 5 to get 10, then 7 × 10 is 70.
- Try 12 × 25 together and ask which numbers were easier to work with.
Try at home. Ask your child to find three multiplications at home or in a shop bill where doubling and halving makes the sum easier.
Using the Nearest Multiple
Part of: Easy ways to multiply
To find 6 × 19, use 20 instead. 6 × 20 is 120, but we used one group too many, so take away one 6 to get 114. If the number is just above a round number, like 21, we add the extra group instead of subtracting.
Why it matters. Numbers like 19, 21, 29, 49 and 99 are very common in prices and counting. This trick makes them quick to handle in the head.
Try it in two minutes
- Ask for 5 × 19. Then show 5 × 20 is 100 and one 5 has to go, giving 95.
- Try 8 × 31 with your child: 8 × 30 is 240 and then add one more 8.
- Ask: do we add or subtract when the number is a little below the round one?
Try at home. Ask your child to find 9 × 49 or 7 × 51 using the nearest round number and explain every step.
Breaking Numbers into Parts to Multiply
Part of: Multiplying bigger numbers
To find 23 × 4, split 23 into 20 and 3. Then 20 × 4 is 80 and 3 × 4 is 12, and 80 + 12 is 92. The same idea works when both numbers are split, with the tens parts and ones parts each multiplied and then all added.
Why it matters. This method follows place value, so children see why the answer is right. It prepares them for the usual written method for larger numbers.
Try it in two minutes
- Ask your child to split 32 into 30 and 2.
- Multiply each part by 5: 30 × 5 is 150 and 2 × 5 is 10.
- Add the two answers together and ask your child to check with a different split.
Try at home. Pose a real problem, such as 18 rows with 15 chairs, and ask your child to solve it by breaking the numbers in parts.
What your child will practise
- Breaking Numbers into Parts to Multiply: Number Quest (Collect the Answer)
- Doubling and Halving: Space Quick Fire (Quick Fire)
- Multiplying by 10s, 100s and 1000s: Space Quest (Flip and Match)
- Swapping the Order in Multiplication: Desert Puzzle (Clue Puzzle)
- Using the Nearest Multiple: Ocean Quest (Flip and Match)
- Quiz: Breaking Numbers into Parts to Multiply (8 questions)
- Quiz: Doubling and Halving (8 questions)
- Quiz: Multiplying by 10s, 100s and 1000s (8 questions)
- Quiz: Swapping the Order in Multiplication (8 questions)