Multiplication
🧩 Let’s Start with a Problem
A class is making small thank-you cards for a school event.
Each card needs the same number of stickers. The students want to know how many stickers they need altogether before they start decorating.
They could count every sticker one by one, but that might take a long time. There may be a smarter way to count equal groups.
🔍 Think About It
If there are $4$ cards and each card has $6$ stickers, how could you find the total without counting every sticker separately?
💡 Why This Matters
Multiplication helps us count equal groups quickly and clearly.
We use it when we arrange objects, buy packs of items, share supplies, plan seats, or check if an answer seems reasonable.
⚡ Quick Warm-Up
Activity $1$: Look for equal groups.
Imagine $3$ plates with $5$ biscuits on each plate. What is the same about each plate?
Think about it: Equal groups make multiplication useful.
Activity $2$: Choose a smart way to count.
A teacher has $8$ boxes. Each box has $4$ pencils. Would you count by ones, skip-count, or use multiplication?
Think about it: A quick method should still give a sensible total.
Activity $3$: Make an estimate first.
A shop sells erasers in packs of $9$. Maya buys $6$ packs. Before calculating exactly, do you think the total is closer to $50$ or $100$?
Think about it: Estimating helps you check whether your final answer makes sense.
➡️ Ready to Learn
Now let’s learn how multiplication helps us count equal groups and check our answers efficiently.
🎯 In this topic you will
- Use the associative law to regroup factors in multiplication and make calculations easier.
- Estimate products when multiplying a whole number (up to 1000) by a 1-digit number.
- Multiply a whole number by a 1-digit number accurately.
🧠 Key Words
- associative law
- carry
Show Definitions
- associative law: A multiplication rule that says you can change how numbers are grouped (using brackets) without changing the final product.
- carry: In written addition or multiplication, the step where you move an extra value (like a ten) to the next place value because a digit total is $10$ or more.
🍫 Splitting a Chocolate Bar
Do you enjoy eating chocolate? This bar could be split into $24$ pieces or into $6$ lots of $4$ or $4$ lots of $6$.
🧮 Multiplying and Estimating
In this unit, you will multiply larger numbers by $1$-digit numbers. You should always estimate the size of the answer first to check your answer is about right.
❓ EXERCISES
1. Magda calculates $14 \times 5$ using factors. She spills ink on her work. What number is under the ink blots?
👀 Show answer
Since $14 = 7 \times 2$, the missing number is $2$.
So $14 \times 5 = 7 \times 2 \times 5 = 7 \times 10 = 70$, and both ink blots cover $2$.
2. Amir and Ben work out $4 \times 15$.
Which method do you like best? Explain why.
Discuss your answer with your partner.
Think of other ways to work out $4 \times 15$.
👀 Show answer
Both methods are correct and give $60$.
Amir's method: $4 \times 15 = 4 \times 5 \times 3 = 20 \times 3 = 60$.
Ben's method: $4 \times 15 = 2 \times 2 \times 15 = 2 \times 30 = 60$.
Example preference: Ben's method can feel efficient because doubling $15$ to get $30$ is quick, then doubling again gives $60$.
3. Work out the following. Estimate your answer first.
a. $47 \times 5$
b. $29 \times 4$
c. $89 \times 3$
d. $74 \times 6$
Compare the methods you used with your partner.
Identify the advantages and disadvantages of each method.
👀 Show answer
a. Estimate: $50 \times 5 = 250$. Exact: $47 \times 5 = 235$.
b. Estimate: $30 \times 4 = 120$. Exact: $29 \times 4 = 116$.
c. Estimate: $90 \times 3 = 270$. Exact: $89 \times 3 = 267$.
d. Estimate: $70 \times 6 = 420$ (or $75 \times 6 = 450$). Exact: $74 \times 6 = 444$.
4. Sultan uses the grid method to work out his calculations, but he spills ink on his work.
Copy and complete the calculations.
a. $47 \times 3 =$
b. $93 \times 4 =$
c. $51 \times 5 =$
d. $87 \times 4 =$
👀 Show answer
a. $47 \times 3 = (40 \times 3) + (7 \times 3) = 120 + 21 = 141$. Missing number: $120$.
b. $93 \times 4 = (90 \times 4) + (3 \times 4) = 360 + 12 = 372$. Missing numbers: $90$ and $360$.
c. $51 \times 5 = (50 \times 5) + (1 \times 5) = 250 + 5 = 255$. Missing number: $250$.
d. $87 \times 4 = (80 \times 4) + (7 \times 4) = 320 + 28 = 348$. Missing numbers: $7$ and $320$.
5. Find the product of $56$ and $5$.
👀 Show answer
$56 \times 5 = 280$.
6. Pencils are sold in packs of $5$. Each pack costs $95$ cents. Fatima buys $4$ packs of pencils. How much does she spend?
👀 Show answer
$4 \times 95 = 380$, so she spends $380$ cents (that is $3.80$).
7. Use the digits $2$, $3$ and $5$ once to make the multiplication with the greatest product.
Work out the answer.
Compare your answer with your partner.
The person with the larger answer should explain their method.
👀 Show answer
To make the product as large as possible, use the largest digit as the multiplier and make the largest possible two-digit number with the other two digits.
$32 \times 5 = 160$.
8. Work out the following. Estimate your answer first.
a. $174 \times 4$
b. $129 \times 7$
c. $189 \times 3$
d. $119 \times 8$
Compare the methods you used with your partner.
Identify the advantages and disadvantages of each method.
👀 Show answer
a. Estimate: $170 \times 4 = 680$ (or $175 \times 4 = 700$). Exact: $174 \times 4 = 696$.
b. Estimate: $130 \times 7 = 910$. Exact: $129 \times 7 = 903$.
c. Estimate: $190 \times 3 = 570$. Exact: $189 \times 3 = 567$.
d. Estimate: $120 \times 8 = 960$. Exact: $119 \times 8 = 952$.
🧠 Think like a Mathematician
A 3-digit number is multiplied by 3. There are five different missing digits in the calculation: 1, 2, 6, 7, 8.
Calculation (with blanks):
Clues:
- The sum of the digits of the 3-digit number is 24.
- The digits in the 3-digit number are consecutive numbers, but they are not written in order.
- The answer is between 2000 and 3000.
Follow-up Questions:
👀 show answer
First, the digits are consecutive and sum to 24. So they must be 7, 8, 9 because $7+8+9=24$.
The middle digit shown is 9, so the number is either 897 or 798 (not in order, so 789 is not allowed).
Now multiply by 3 and use the “missing digits are 1, 2, 6, 7, 8” condition:
- 798 × 3 = 2394 (missing digits would include 3 and 4, so it does not match).
- 897 × 3 = 2691 (missing digits are exactly 1, 2, 6, 7, 8, so it matches).
Therefore, the completed calculation is: 897 × 3 = 2691 (and 2691 is between 2000 and 3000).