Adding and subtracting efficiently
🎯 In this topic you will
- Use the column method of calculation to add and subtract whole numbers accurately.
🧠 Key Words
- carry
- efficient
Show Definitions
- carry: To move a value to the next column in column addition when the total in a column is ten or more.
- efficient: Describes a method that solves a calculation accurately using the fewest clear and logical steps.
Building on Number Skills
I n this unit, you will add and subtract whole numbers. You will revise methods you used earlier this year and extend them to include using a column method.
Why Addition and Subtraction Matter
B eing able to add and subtract quickly is a useful skill for everyday life. You might use addition to work out how much it costs to buy lunch in a café.
Building on Number Skills
I n this unit, you will add and subtract whole numbers. You will revise methods you used earlier this year and extend them to include using a column method.
Why Addition and Subtraction Matter
B eing able to add and subtract quickly is a useful skill for everyday life. You might use addition to work out how much it costs to buy lunch in a café.
❓ EXERCISES
1. For each of these questions, estimate the size of the answer then complete the calculation.
a. Find the sum of $456$ and $789$.
b. What is the total of $763$ and $869$?
c. What is $678$ more than $456$?
👀 Show answer
a. $456 + 789 = 1245$
b. $763 + 869 = 1632$
c. $456 + 678 = 1134$
2.
a. Subtract $456$ from $789$.
b. Find the difference between $678$ and $923$.
c. $906$ minus $858$.
👀 Show answer
a. $789 - 456 = 333$
b. $923 - 678 = 245$
c. $906 - 858 = 48$
3. What is the difference between $1000$ and the smallest $3$-digit number that does not use the digit $0$?
👀 Show answer
The smallest $3$-digit number without $0$ is $111$.
$1000 - 111 = 889$
4. Write the missing number. You can use any method.
$457 + \Box = 713$
👀 Show answer
$713 - 457 = 256$
5. Spot the mistakes and then do the calculations correctly.
👀 Show answer
a. $882 - 435 = 447$
b. $531 + 278 = 809$
6. Naomi has six digit cards.
She makes two $3$-digit numbers and adds them together.
a. What is the largest total Naomi can make?
b. What is the smallest total she can make?
👀 Show answer
a. Largest: $654 + 321 = 975$
b. Smallest: $123 + 456 = 579$
🧠 Think like a Mathematician
The numbers $1$ to $9$ are arranged as they are on a calculator.
- Choose a line of three numbers, for example $753$.
- Reverse the numbers: $357$.
- Add the numbers and record the result.
- Repeat the instructions with other lines of three numbers.
What do you notice about the results?
- You will show you are specialising when you find solutions to the problem.
- You will show you are generalising when you recognise patterns in your results.
- If you explain your results, you will show you are convincing.
Show Answers
- When you add a three-digit number formed from a straight line on the calculator and its reverse, the total is always a multiple of $11$.
- This happens because the hundreds and ones digits swap places, so their difference is repeated, while the tens digit stays the same in both numbers.
- For example, $753 + 357 = 1110$, and $159 + 951 = 1110$, showing the same total.