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Using an efficient column method for multiplication

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visibility 80update 5 months agobookmarkshare

🎯 In this topic you will

  • Estimate the result of multiplying a whole number up to 1000 by a one-digit number.
  • Accurately multiply a whole number by a one-digit number.
 

🧠 Key Words

  • estimate
  • product
Show Definitions
  • estimate: To find an approximate answer that is close to the exact value, often by rounding numbers to make calculations easier.
  • product: The answer you get when two or more numbers are multiplied together.
 

Why Multiplication Matters ✏️

W e all learn how to multiply numbers in school, and many people use multiplication in their jobs.

 

A Real-Life Example ✈️

I magine you are in charge of putting fuel into a plane.

 

Working Out the Fuel ⛽

T o work out how much fuel is needed, you need to multiply the amount of fuel burned every hour by the journey time.

 

Why Accuracy Is Important 🎯

I f you get the calculation wrong, the plane will not be able to reach its destination.

 
📘 Worked example

Calculate $346 \times 9$.

Estimate: $350 \times 10 = 3500$

Step 1. Work from right to left.
$6 \times 9 = 54$ (write $4$ in the ones column and carry $5$ tens).

Step 2.
$40 \times 9 = 360$. Add $50$ to give $410$ (write $1$ in the tens column and carry $4$ hundreds).

Step 3.
$300 \times 9 = 2700$. Add $400$ to give $3100$ (write $1$ in the hundreds column and $3$ in the thousands column).

Check your answer is close to your estimate.

Answer:

$346 \times 9 = 3114$

Multiplication is done from right to left. First multiply the ones, then the tens, and finally the hundreds, carrying extra values to the next column each time.

Estimating first helps check that the final answer is sensible.

 

❓ EXERCISES

$1.$ There are $12$ months in a year. How many months are there in $8$ years?

👀 Show answer
There are $12 \times 8 = 96$ months in $8$ years.

$2.$ Write the answers that are odd numbers.

a. $27 \times 5$

b. $13 \times 8$

c. $58 \times 4$

d. $33 \times 9$

👀 Show answer
$27 \times 5 = 135$ (odd) and $33 \times 9 = 297$ (odd). The odd answers are from parts $a$ and $d$.

$3.$ One screw has a mass of $6$ grams. What is the total mass of $408$ screws?

👀 Show answer
$408 \times 6 = 2448$. The total mass is $2448$ grams.

$4.$ Multiply $288$ by $8$.

👀 Show answer
$288 \times 8 = 2304$.

$5.$ Find the product of $428$ and $9$.

👀 Show answer
$428 \times 9 = 3852$.

$6.$ Here is a number machine. Copy and complete the table.

👀 Show answer
Each input is multiplied by $5$, giving outputs $615$, $1725$, and $2835$.

$7.$ Copy the following and write the same digit in each box to make the calculation correct.

👀 Show answer
The missing digit is $4$. The calculation is $346 \times 4 = 1384$.

$8.$ A $6$-day ski lift pass for an adult costs $\$209$. There are $8$ adults in the ski group. What is the total cost of the ski lift passes?

👀 Show answer
$209 \times 8 = 1672$. The total cost is $\$1672$.

$9.$ Tara says, “A $3$-digit number multiplied by a $1$-digit number will always give a $4$-digit number”. Is she correct? Explain your answer.

👀 Show answer
She is not correct. For example, $100 \times 2 = 200$, which is a $3$-digit number, not a $4$-digit number.
 

🧠 Think like a Mathematician

Task: Use the first triangle to find the rule, then use the rule to complete the other two triangles.
You will show you are generalising when you find the rule.

Given triangles:

Triangle 1 (example):
Top: 363
Bottom-left: 121
Bottom-right: 3
Triangle 2 (complete the top):
Top: ?
Bottom-left: 482
Bottom-right: 9
Triangle 3 (complete the top):
Top: ?
Bottom-left: 415
Bottom-right: 7

Method:

  1. Look at Triangle 1 and decide what operation connects the two bottom numbers to the top number.
  2. Test your idea by checking it matches all three numbers in Triangle 1 (not just two of them).
  3. Write the rule in words and then in algebra (this is the “generalising” part).
  4. Use your rule to calculate the missing top numbers for Triangles 2 and 3.
  5. Quick-check: Does your answer make sense (e.g., if you multiply by a bigger number, the top should be bigger)?

Follow-up Questions:

1. What is the rule in words?
2. Write the rule using algebra. Let the bottom-left number be $a$ and the bottom-right number be $b$.
3. Use the rule to find the missing top number in Triangle 2.
4. Use the rule to find the missing top number in Triangle 3.
👀 show answer
1: The top number is the bottom-left number multiplied by the bottom-right number.
2:$\text{Top} = a \times b$
3: Triangle 2 top: $482 \times 9 = 4338$
So the missing top number is 4338.
4: Triangle 3 top: $415 \times 7 = 2905$
So the missing top number is 2905.
 

📘 What we've learned

  • We learned how to multiply a whole number by a 1-digit number accurately using known multiplication facts.
  • We practiced estimating answers when multiplying whole numbers up to $1000$ by a 1-digit number to check if results are reasonable.
  • We used estimation strategies such as rounding to nearby friendly numbers before calculating.
  • We developed confidence in checking multiplication answers by comparing the exact value with an estimated result.

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