Big numbers and the four operations · Years 5–6
In Big numbers and the four operations (Years 5–6) you practise 8 skills: Column addition and subtraction · Long multiplication · Long and short division · Order of operations · Clever strategies · Equations and inequalities · Estimating · Word problems. Read numbers beyond a million in groups of three from the right: the units, the thousands, then the millions. So 45,302,018 is forty-five million, three hundred and two thousand and eighteen. There is no greatest whole number: you can always add 1 and get a bigger one.
In long multiplication and division you split a number by the value of its digits: multiply each part and add the results, or take away multiples of the divisor place by place. Estimate before you work it out, and at the end check that your answer is close to the estimate. There are clever ways to work things out. To work out 28 × 5, multiply by 10 and halve. In a division you can multiply or divide both numbers by the same number and the answer does not change: 4,800 ÷ 16 equals 2,400 ÷ 8. And multiplication and division undo each other, so use one to find a missing number in the other.
Tip: Before you answer a word problem, check that it gives you enough information. Sometimes a fact is missing, and then you cannot know the answer.
What you learn
Column addition and subtraction
For example: Work out: 9,556 + 2,287
Answer and solution
The answer: 11843
Write the numbers one under the other, units under units, and work column by column from the right: 9,556
+ 2,287
────────
11,843 9,556 + 2,287 = 11,843
Long multiplication
For example: Work out: 33 × 6
Answer and solution
The answer: 198
Split the first number by place value and multiply each part: 33 × 6 = 30 × 6 + 3 × 6 30 × 6 = 180 3 × 6 = 18 180 + 18 = 198
Long and short division
For example: Work out: 234 ÷ 9
Answer and solution
The answer: 26
Take multiples of 9 away from 234, largest first: 9 × 20 = 180 234 − 180 = 54 9 × 6 = 54 54 − 54 = 0 Add up all the numbers we multiplied by: 20 + 6 = 26 The quotient is 26, with no remainder. Check: 26 × 9 = 234
Order of operations
For example: Work out: 4 × 10 ÷ 5
Answer and solution
The answer: 8
Each line does one operation: 4 × 10 ÷ 5 = 40 ÷ 5 40 ÷ 5 = 8
Clever strategies
For example: Fill in the missing number: 753,788 + 145,995 = 753,783 + ☐
Answer and solution
The answer: 146000
5 was taken from the first number, so add 5 to the second: 145,995 + 5 = 146,000 753,788 + 145,995 = 753,783 + 146,000 = 899,783
Equations and inequalities
For example: Find the missing number: 1,420 = 71 × ☐
Answer and solution
The answer: 20
To find a missing factor, divide the product by the known factor: 1,420 ÷ 71 = 20 Check: 1,420 = 71 × 20
Estimating
For example: Round 2,288 to the nearest thousand.
Answer and solution
The answer: 2000
The deciding digit is 2, so round down. 2,288 rounded to the nearest thousand is 2,000.
Word problems
For example: A factory packs 6 pencils in each box. Today it packed 127 boxes. How many pencils did it pack today?
Answer and solution
The answer: 762
127 × 6 = 762
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).