What is number sense?

Number sense is the fundamental skill that all mathematical learning rests upon. In short, number sense means understanding how the basic rules of numbers work.

Unless you’re a teacher, it’s not unusual if you haven’t heard of number sense. We often talk about children struggling with maths, but we often prescribe practice worksheets to solve the issue instead of questioning whether our children have strong number sense.

So how does maths work? Here are the basic principles that all mathematical concepts rely on:

1. Numerals are symbolic

Before you have mathematical equations, you have numbers. 1, 2, 3, 4 and so on. Numerals like these are actually symbols that represent quantities.

For example, the numeral ‘5’ symbolises the word ‘five’ which represents five of something, such five blocks. This is what we mean by cardinal numbers, or numbers that represent a quantity.

2. Order is important

We often follow discussions of cardinal numbers with talking about ordinal numbers. Ordinal numbers refer to the order that numbers or items are arranged in. For example, in a race, athletes are awarded 1st, 2nd, and 3rd place.

3. More than, less than

Number order also symbolises a hierarchical value, where one number is greater than another, such as $100 is worth more than $50. However, it’s important to know that the numerals themselves don’t represent a value since they are representational. For example, 1st place is better than 2nd place, even though 2 is more than 1.

4. Patterns

Without the key rules above, it is impossible to understand relationships between numbers, or number patterns.


  • Even numbers are those that can be divided by 2 without any remainders: 2, 4, 6, 8, 10, 12…
  • Odd numbers are those that, when divided by 2, leave a remainder: 1, 3, 5, 7, 9, 11…
  • The Fibonacci pattern is a sequence of numbers where each term is the total of the two previous numbers in the pattern: 0, 1, 1, 2, 3, 5, 8, 13… This pattern is seen in the spirals of a sea shell, the arrangement of petals on sunflowers, in the swirls in your fingerprints, and elsewhere in nature. The golden ratio, explaining why some examples of nature, artwork and architecture are visually appealing, is based upon the Fibonacci pattern.

5. Mental computing

Understanding basic number patterns is essential for helping us to mentally calculate or estimate the answer to a math problem quickly, without using a calculator.

Mental maths isn’t about memorisation, because learning times tables by rote doesn’t necessarily mean that we know how to use times tables to solve problems. Instead, practicing mental calculation increases the speed at which the brain recalls knowledge and solves mathematical problems.

6. Estimation

Estimation is an important part of mental computing because it enables us to get a rough answer which helps us to verify the exact answer using a calculator.
For example, if I go to a café and order a cappuccino for $4.50 and a wrap for $11.25, I can estimate my bill to be $17.00 so I know how much cash to present to the cashier without having to empty the entire contents of my wallet on the counter. If the cashier asks for more than $17.00, I’ll know there’s something wrong with the bill and can ask them to check my order.

Rounding up and rounding down is crucial to estimation and is a skill that requires number sense to understand which numbers round up and which round down. In my example, I rounded my coffee to $5.00 and my meal to $12.00 in order to estimate the minimum whole dollars I needed to hand over. Likewise, if I gave a $20.00 note, my estimation that my bill was just under $17.00 tells me that I need at least $3.00 change. If I get less than $3.00, I need to ask the cashier to verify my order.

7. Time

Estimation and rounding are also essential skills of number sense required to understand how to read analog and digital clocks and how to plan my time. Let’s say we’ve agreed to meet for dinner at 7:00pm. It will take me 15 minutes to travel to the restaurant, and an hour to get ready beforehand. This means I need to start getting ready by 5:45pm at the latest. Without good number sense, I would struggle to make it to dinner on time.

How can a tutor help?

Number sense develops over time, and a bit of confusion is totally normal when grappling with new concepts. However, if the struggle is ongoing, it is better to ask for help sooner than later. Left unaddressed, prolonged struggles with maths can lead to or worsen maths anxiety which makes learning and asking for help much harder.

Similarly, if your child struggles with number sense, it is possible that they might have Dyscalculia, a learning disability that makes it difficult to understand and process numeric information. Symptoms of Dyscalculia can appear as early as pre-school but usually become clearer as children get older, which is why it is rarely diagnosed until children reach school.

As we’ve seen, number sense is vital for functioning well in every day life. People with Dyscalculia struggle with all the mathematical parts of daily living: measurements, time, managing their finances, directions and more. As a result, many people with dyscalculia suffer from maths anxiety.

Whether your child experiences dyscalculia or maths anxiety, or struggles to comprehend their maths homework, engaging a tutor can make the world of difference to their maths success at school and later in life.

Nepean Tutoring boosts a team of creative tutors who are experienced with working out the best ways to help your child make sense of numbers. Tutoring gives your child immediate feedback on their learning, helping them to practice mathematical skills effectively. Even better, our tutors make learning enjoyable, and we know that when your child enjoys learning, their confidence improves too.
We have tutors working throughout the summer holidays to give your child a head-start for next year, and if that doesn’t work for you, it’s not too early to lock in a tutor for Term 1 2022 so you don’t miss out.

If your child struggles with number sense, give Nepean Tutoring a call today.


Reference: Thank you to Kerry Joseph for sharing her experiences living with Dyscalculia.