# Number sense

Number sense is a broad term that refers to a general understanding of numbers that we develop either intuitively, or through practice. It is something we build as a basis that enables us to approach and understand more complicated mathematics.

Number sense has many forms, from understanding the size of numbers (magnitude) and how they relate to each other, to recognizing number patterns, how numbers are affected by various operations, and more. Below are some of the key concepts of number sense that we should try to develop and hone throughout our lives.

## Everyday applications of number sense

Number sense is something that we will use to some degree throughout our lives, whether it be through mathematical studies, our jobs, or simply everyday activities.

### Estimation

The ability to make estimations, whether for scientific use or everyday use, is an important skill to develop. Being able to quickly and accurately estimate numbers in your head is an example of having good number sense.

One way to improve this aspect of number sense is to practice basic arithmetic. For example, the more comfortable we are with our multiplication table, percentages, and decimals, the more likely that we will be able to recognize, or form compatible numbers to facilitate our estimations. Below is an example of an everyday situation in which number sense is helpful.

Example

Travis, walks into a cash only store and picks up 2 candy bars for \$0.99 each, an apple for \$1.69, a bag of chips for \$1.39, and a sandwich for \$4.88. Estimate how much Travis will have to pay for all of it together if there is a 8.25% sales tax.

While it's not necessarily difficult to calculate the exact value Travis needs to pay, if all Travis needs to do is figure out if he has enough cash on him to pay for all the items, we only need a rough estimate of the total cost. Because we want to know that Travis has enough money, we also want to overestimate, rather than underestimate, the cost of the items.

• \$0.99 is close to \$1, so 2 candy bars is ~\$2
• \$1.69 is close to 1.7 and 1.39 is close to 1.4. We may recognize that 1.4 + 1.7 is slightly more than 3, since 1.5 + 1.5 = 3. We can therefore overestimate the bag of chips and the apple as ~\$4
• We round up the cost of the the sandwich \$5.00
• We estimate the sales tax as 10% since it is much easier to calculate than 8.25%
• 2 + 4 + 5 = \$11

10% of \$11 is the same as multiplying 11 by 1/10, or dividing by 10, so 10% of \$11 is \$1.10. We can overestimate this again, as \$2, since whole numbers are easier to add. Thus, if Travis knows that he has more than \$13 (2 + 4 + 5 + 2) in cash, he knows that he can afford all of the items.

### Measurement

Another aspect of number sense is understanding units of measurement. This includes knowing what units of measurement to use to achieve the desired degree of precision. For example, if we are trying to measure the length of your phone screen, we may use centimeters, inches, or some other similar unit of measurement. We wouldn't use meters, miles, kilometers, or some other significantly larger unit of measurement because they are much larger units of measurement.

For example, if your phone screen were 6 inches long, it is approximately 0.0000947 miles long. If you were to tell someone that something you owned was 0.0000947 miles long, they would likely have little to no concept of how large the item is, but if you told them it was 6 inches long, they would be much more likely to understand what you are talking about. Inches would therefore be an appropriate choice (there are others) of units. On the other hand, if you told someone you ran 1 mile, even if they don't know exactly how far that is, they would have a decent idea of how far you ran. Telling them you ran 63,360 inches would not be an appropriate choice of units.

### Did you know?

Developing number sense is a lifelong process and is never completely learned. While some people may inherently have a better sense of numbers than another, it is something that can be learned and improved with practice!

One example of this is temperature. Degrees Fahrenheit is a unit of measurement of temperature that is commonly used in the United States. If you told someone in the US that it is 75°F outside, they would have a general idea of what that felt like. If instead you told them it was 23.9°C outside, they may have less of an idea, at least to begin with. If you never use, or convert Fahrenheit to Celsius (or vice versa), you may never gain a sense of what 23.9°C (or 75°F) feels like. However, if every time you check the weather to see what the temperature is, you chose to convert the temperature, over time you would gain a sense of how Fahrenheit and Celsius are related without having to directly convert them. This is true for many other aspects of number sense; practice and exposure over time will improve your number sense.