The difference is the result of subtracting one number from another. It is how much one number differs from another - represented by how far apart they are on a number line.

Being efficient means finding a way to solve a problem quickly whilst also maintaining accuracy.

Explore mental and written strategies to solve problems

Maths

In this unit pupils will use their knowledge of the composition of 7-digit numbers to solve problems adding and subtracting numbers whilst crossing the millions boundary They will round  7-digit numbers to the nearest million and nearest hundred thousand and solve addition and subtraction problems. In the future unit pupils round to any number of decimal places and learn about significant figures.

In the prior unit pupils estimated the value and position of numbers, including negative numbers, on unmarked or partially marked number lines and calculated intervals across 0. In this unit pupils will use their knowledge of the composition of seven-digit numbers to solve problems, adding and subtracting numbers whilst crossing the millions boundary.

Rounding and solving problems with numbers up to 7 digits

Use a number line to calculate 
69,998 + ? = 100,000

Use a number line to calculate 
190,000 − 137,999 = {{ }}

By using the constant difference concept, calculate the difference: 2,000,000 − 409,371 = {{ }}

By using the constant difference concept, calculate the missing number: 1,000,000 − {{ }} = 23,147

Use the most efficient method to solve this problem. A library has 50,000 books and some are out on loan. There are 17,998 books remaining in the library. How many are out on loan?

Use the most efficient method to solve this problem. 
A lottery winner won £1,500,000 and spent 387,399. How much money did they have left? £{{ }}

Use a number line to calculate and find the missing part. 1,398 + {{ }} = 5,000

Use the formal written column subtraction algorithm to calculate 3,976,301 − 1,432,100 = {{ }}

Use the formal written column subtraction algorithm to calculate
1,309,052 − 132,421 = {{ }} 

Lucas and Aisha play a game. Lucas wins 390,512 points and Aisha wins 200,000 fewer points. How many points does Aisha win? {{ }} points

This lesson will be removed by end of Summer Term 2025.

Explore mental and written strategies to solve problems

Lesson outcome

This lesson will be removed by end of Summer Term 2025.