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What is Ascending Order?
Ascending Order
Find out what ascending order means with this Teaching Wiki. Includes descending order, examples, and
resources for learning about arranging numbers.
What does ascending order mean?
In maths, ascending order means the process of arranging numbers from smallest to largest from left to
right.
It can also mean arranging letters or words in alphabetical order from A to Z.
Ascending means “going up”, so ascending order means that the numbers are going up. 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 from there, just as the number of steps climbs. When they are
arranging numbers in ascending order, they can think about which order the numbers would go in if
they were on a staircase.
A number line is a great visual aid to help children understand what ascending order means.
Different coloured number lines.
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 counters with the numbers
on them so that 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 number, so you can write it first.
The number with the most digits is the largest number, 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.
Numbers iced on cookies.
Negative numbers
It might seem a little confusing at first glance, but arranging negative numbers in ascending order isn’t
that different from arranging positive numbers.
The higher the number after the negative sign, the smaller the value of the number. For example, -73 is
smaller than -5.
This means that if you were to arrange them in ascending order, those two numbers would read like this:
-73, -5.
Fractions
Ordering fractions into ascending order is easy. For fractions with the same denominator, the fraction
with the smallest numerator goes first. When fractions have the same numerator, the ones with the
largest denominator is the smallest.
When fractions have the same numerator, the fraction with the highest denominator is the smallest.
This is 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.
Multicoloured fraction wall.
To order fractions with different numerators and denominators, you have to convert them so that they
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 parts are 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 that you have these whole numbers: 87, 3, 47, 150, 1743, 574.
To order those numbers, you first need to look for the shortest number. This will be the smallest. In this
case, the smallest number is 3.
Then, you need to look for the longest number, which is also the biggest number. In this case, that is
1743.
Then, you need to find the next smallest number. You can see that it is either 47 or 87, because those
numbers are the shortest from the ones remaining in the list. 47 is smaller than 87, so our list begins to
look 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. This means that we can slot them into the list in the right
place.
The final list in ascending order is: 3, 47, 87, 150, 574, 1743.
Ascending order in primary school
Children will need to learn how to order numbers in primary school.
Girl surrounded by floating numbers.
In KS1, they will learn how to order two-digit numbers. In KS2, they will need to know how to order
decimals.
What does descending order mean?
Descending order means the opposite of ascending order. It means the process of arranging numbers so
that they are going 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 conceptualise descending order.
The process for arranging numbers in descending order is the same as arranging 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.
Sequencing numbers resources for teaching and learning
We have lots of resources to help teachers and parents explain to children what ascending order means.
Check out some of our favourites to get started.
Ordering Numbers 0-10 and 0-20 PowerPoint – Ideal for EYFS learners. This engaging PowerPoint will
help little ones understand how to order numbers up to 20.
Year 3 Diving into Mastery: Order Fractions Teaching Pack – This comprehensive pack is ideal for
teaching Year 3 pupils about arranging fractions in ascending order. It includes a PowerPoint and
mastery worksheets to help children learn and apply their knowledge.
Year 4 Diving into Mastery: Order Decimals Teaching Pack – You can use this fabulous pack to help
children develop fluency and reasoning skills as applied to ordering numbers. It is a great introduction to
a process that might seem a little confusing at first.
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What is Ascending Order?
Ordering Decimal Numbers Activity
Ordering Decimal Numbers Activity
Ordering Decimals Up to 3 Places Worksheet
Ordering Decimals Up to 3 Places Worksheet
Ascending Order Worksheet
Ascending Order Worksheet
Ordering Coins and Notes Worksheet
Ordering Coins and Notes Worksheet
Ascending and Descending Display Poster
Ascending and Descending Display Poster
Pop the Balloons – Ordering Numbers to 10 PowerPoint Game
Pop the Balloons – Ordering Numbers to 10 PowerPoint Game
Pop the Balloons – Ordering Numbers to 20 PowerPoint Game
Pop the Balloons – Ordering Numbers to 20 PowerPoint Game
Year 3 Diving into Mastery: Order Fractions Teaching Pack
Year 3 Diving into Mastery: Order Fractions Teaching Pack
Order Fractions: Differentiated Maths Activity Sheet
Order Fractions: Differentiated Maths Activity Sheet
Ordering Integers KS3 Walkthrough Worksheet
Ordering Integers KS3 Walkthrough Worksheet
Jumbled Up Number Ordering Differentiated Worksheet
Jumbled Up Number Ordering Differentiated Worksheet
Under the Sea Themed Cut and Stick Number Ordering Activity 1-20
Under the Sea Themed Cut and Stick Number Ordering Activity 1-20
Ordering Decimals KS3 Walkthrough Worksheet
Ordering Decimals KS3 Walkthrough Worksheet
Ordering Negative Numbers KS3 Walkthrough Worksheet
Ordering Negative Numbers KS3 Walkthrough Worksheet
Fractions Lesson 6: Ordering Fractions, Decimals and Percentages
Fractions Lesson 6: Ordering Fractions, Decimals and Percentages
Pop the Balloons – Ordering Numbers to 30 PowerPoint Game
Pop the Balloons – Ordering Numbers to 30 PowerPoint Game
Year 3 Comparing Pounds and Pence Differentiated Maths Activity Sheets
Year 3 Comparing Pounds and Pence Differentiated Maths Activity Sheets
Ordering Decimals - Puzzle Grids
Ordering Decimals - Puzzle Grids
Ordering Numbers Activity Sheet
Ordering Numbers Activity Sheet
PlanIt Maths Year 3 Measurement Lesson Pack 20: Convert between Pounds and Pence
PlanIt Maths Year 3 Measurement Lesson Pack 20: Convert between Pounds and Pence
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