**What does ascending order mean?**

In maths, ascending order means placing the smallest to largest numbers from left to the right.

It can also mean arranging letters or words alphabetically from A to Z.

Ascending means going up, so ascending order means the numbers are going up. So it is a way of ordering numbers.

Children can imagine what ascending order means by thinking about climbing a staircase. The first step is number 1, and the steps get higher just as the number of steps rises. So when arranging numbers in ascending order, they can think about which order they would go in if they were on a staircase.

A number line is a great visual aid to help children understand ascending order.

**How to arrange numbers in ascending order**

To arrange numbers in any order, we need to compare them. Then, we can order them.

When children start learning how to order numbers, it can be helpful to have countered with the numbers on them so they can move them around.

*Integers*

- Count the number of digits that there are in each number.
- The number with the least digits is the smallest, so you can write it first.
- The number with the most digits is the most significant, so it goes last.
- If numbers have the same amount of digits, start by comparing the digit on the left (in the thousands, hundreds, or tens column).
- Then, keep moving across the number from left to right to compare the digits. Keep writing them down from smallest to biggest.
- Continue until no numbers are left, and they have all been ordered.

*Negative numbers*

It might seem a little confusing at first glance, but arranging negative numbers in ascending order isn’t that different from placing positive numbers.

The higher the number after the negative sign, the smaller the value of the number. So, for example, -73 is smaller than -5.

If you arranged them in ascending order, those two numbers would read like this: -73, -5.

*Fractions*

Ordering fractions into ascending order is easy. The fraction with the smaller numerator goes first for fractions with the same denominator. When fractions have the same numerator, the ones with the largest denominator are the smallest.

When fractions have the same numerator, the fraction with the higher denominator is the smallest. The higher the denominator, the smaller the parts of the whole. For example, ⅕ is smaller than ½. You can help children to understand this concept by looking at a fractions wall.

To order fractions with different numerators and denominators, you must convert them to have the same common denominator. Then you can compare and order them.

*Decimals*

First, see if there is a whole number as part of the decimal. The number with the smallest whole number is the smallest.

If the whole number is the same, compare the decimal parts after the decimal point just as you would compare whole numbers.

**What is an example of ascending order?**

Let’s say you have these numbers: 87, 3, 47, 150, 1743, 574.

You first need to look for the shortest number to order those numbers. This will be the smallest. In this case, the smallest number is 3.

Then, you need to look for the biggest number, the longest number. In this case, that is 1743.

Then, you need to find the following smallest number. You can see that it is either 47 or 87 because those numbers are the shortest from the ones remaining on the list. 47 is smaller than 87, so our list looks like this: 3, 47, 87, X, X, 1743.

Then we have two numbers remaining. These are 150 and 574. Looking at the digit in the hundreds column shows us that 150 is smaller than 574. It means that we can slot them into the list correctly.

The final list in ascending order is 3, 47, 87, 150, 574, 1743.

**What does descending order mean?**

Descending order means the opposite of ascending order. It means arranging numbers to go from the largest to the smallest. Descending means “going down”, so descending order means that the numbers are going down.

Children can think about going down a staircase to conceptualize descending order.

The process for arranging numbers in descending order is the same as placing them in ascending order, except that the smallest number goes on the right-hand side, and the largest number goes on the left-hand side.