Number Fluency: from Place Value to Surds

Numbers you can trust

Almost every question in the whole subject rests on being fluent with number, so slips here cost marks everywhere. This module gathers the core skills. The order of operations tells you which part of a calculation to do first, so that everyone reaches the same answer. Place value and rounding let you write numbers to a sensible accuracy and estimate to check your work. Factors, multiples and prime numbers describe how whole numbers are built, and lead to the highest common factor and the lowest common multiple. Indices are a short way of writing repeated multiplication. Finally surds are roots such as the square root of 2 that do not simplify to a whole number, and learning to simplify them is a key Higher skill. Every calculation in this module has been checked.

Number words

Learn what each of these means before you use it.

Factors against multiples

These two are easy to mix up, so it helps to see them side by side using the number 12.

The order of operations

When a calculation mixes different operations, there is a fixed order that keeps everyone in agreement. Deal with anything inside brackets first. Next work out any indices, such as powers and roots. Then do all multiplication and division, working from left to right. Finally do all addition and subtraction, again from left to right. The common mistake is to work strictly left to right and add before multiplying. Slow down, spot which operations are present, and handle them in that order every time. Estimating the answer first, by rounding, is a good way to catch a slip before it costs you.

Match the number term to its meaning

Use the order of operations

Work out 2 plus 3 multiplied by 4. Remember to do the multiplication before the addition.

Which number is prime?

A prime number has exactly two factors, one and itself. Which one of these numbers is prime?

• 13
• 15
• 21
• 9

Order by size

Work out each value, then put them in order of size, smallest first.

• the square root of 4
• 3
• the square root of 16
• 5

Spot the multiples of four

Select the TWO numbers that are multiples of 4.

• 12
• 20
• 14
• 18

Complete the number facts

A number with exactly two factors, one and itself, is a _____ number. The square root of 9 is _____, which is a whole number. The square root of 2 cannot be simplified to a whole number, so it is a _____. The largest whole number that divides exactly into two numbers is their highest common _____.

Match the number to its value

Spot the true number facts

Tap the TWO statements that are true.

• A prime number has exactly two factors, one and itself
• The square root of 2 is a surd because it does not simplify to a whole number
• The number 9 is a prime number
• Addition is always done before multiplication

Choose the method

Read each case and choose the best response, then think about why.

• You must work out 10 plus 6 divided by 2. Using the order of operations, which answer is correct?
• You need the lowest common multiple of 4 and 6. What is the best method?
• You must simplify the square root of 12. What is the best first step?

Explain working with number

A friend rushes number questions and keeps making careless slips. Explain how to work carefully with number, from the order of operations to surds.

• Explain the correct order of operations and why it matters
• Explain the difference between a factor and a multiple
• Explain what a prime number is
• Explain what a surd is and give an example
• Finish by explaining how rounding helps you estimate and check an answer