Order in Adding
Basics on the topic Order in Adding
The Commutative Property of Addition – Order in Adding
In this text we will learn more about the order of numbers in addition and addition property of order. What is order in adding? And what is the commutative property of addition definition? Let’s look at the definition for order in addition:
When we talk about order in adding, we're discussing which number to add first in an addition equation. This is also known as the commutative property or the commutative property of addition.
What is the commutative property of addition? You may have heard grown ups say that they commute to work, well did you know that numbers commute too? Commute is another way to say travel. People travel from one place to another to get to work and numbers can travel too!
Order of Addition – Rules
When numbers in addition travel, or commute, in an equation, it means those numbers have moved, or were rearranged. Even when you rearrange the addends, the sum, or total, will always be the same. When rearranging, or moving addends, follow these steps:
Step #  What to do 

1  Set up the equation 
2  Solve using a strategy, like tens frames for example. 
3  Once you have solved the first equation, create another by moving, or rearranging the addends. 
4  Solve again using tens frames. 
Even though the addends commuted, the sum remains the same!
Order of Addition – Example
Let’s practise adding numbers in any order with some commutative property of addition example problems.
We want to start by adding twentytwo and twelve. How can we use order in adding to see the sum and to see if the operation is commutative? Remember, addition can be done in any order and these are the steps to use order in addition:
 Start by setting up an equation.
 Next, solve using a strategy that works for you, like tens frames.
 Once you have solved the first equation, create another by moving, or rearranging the addends.
 Then, solve again using tens frames.
 If the sum for both operations is the same, the addition operation is commutative.
What do you notice? The sum is the same! Which equation shows the commutative property of addition? Twentytwo plus twelve!
What does the commutative property of addition mean? It means that addition in any order is possible, the sum will be the same! Let’s take a look at another commutative property of addition example and compare it to what we have been learning about order in adding.
What do you notice about the commutative property of addition? You might notice that with addition it is the same as the rules in order in adding! If we add thirtyseven plus fifteen we get fiftytwo, and if we add fifteen plus thirtyseven we also get fiftytwo!
Adding In Any Order – Summary
Today we learnt about the order in adding. That's when you decide which numbers to add first. We also learnt about the commutative property and commuting numbers. Remember, when addends commute, those numbers rearrange, but the sum alwaysstays the same.
Want more practice on the order in adding? Take a look at the end of this video for commutative property of addition activities as well as adding in any order worksheets.
Transcript Order in Adding
Mr. Squeaks and Imani are getting ready for a birthday party! They want to make party bags for their guests to take home, but, they have a problem. Mr. Squeaks wants to add mini erasers first, while Imani wants to add sprinkles first. Will the order change the total number of goodies put in the bag? Let's help Mr. Squeaks and Imani solve this problem by learning about 'Order in Adding.' What IS order in adding? When we talk about order in adding we're discussing which number to add first in an addition equation. This is also known as the commutative property. You may have heard a grown up talk about commuting, this is another way to say travel. You know that cars can travel, however, did you know that numbers can travel as well? When addends travel, or commute, in an equation, it means those numbers have moved, or, rearranged. Remember, addends are the numbers that we are ADDING together. Even when you rearrange the addends, the SUM, or total, will always be the same. Let's see if order in adding will change Mr. Squeaks and Imani's party bags. Mr. Squeaks and Imani have different opinions about what to add first in their party bags. Let's have a look at the different equations and see what answers we get. When rearranging, or moving addends, always start by setting up an equation. Here our equation is ten plus eight. Next, solve using tens frames. Ten plus eight equals eighteen. Once you have solved the first equation, create another by moving, or, rearranging the addends. Here we will rearrange to create eight plus ten. Then, solve again using tens frames. Eight plus ten equals eighteen. Even though the addends commuted, or moved, the sum remains the same! Next, Mr. Squeaks wants to start by adding twentytwo flowers, but Imani wants to start with twelve seeds. How can we use order in adding to help them see their sum? First, set up an equation. Here it is, twentytwo plus twelve. Next, solve the equation using tens frames. Twentytwo plus twelve equals thirtyfour. After that, commute your addends to create a new equation. Here, we can rearrange the addends to create twelve plus twentytwo. Use tens frames to solve this equation too! Twelve plus twentytwo equals thirtyfour. Then, compare the sums, what do you notice? The sum is thirtyfour no matter which addend comes first! Finally, Mr. Squeaks wants to add thirtythree mushrooms first, BUT Imani wants to add fifteen screws. How can they use order in adding to understand their sums? First, start by creating an equation. Next, use tens frames to solve the equation. Then, commute those addends and create a new equation! You can use tens frames to solve this new equation as well. Finally, compare the sums using tens frames. What is thirtythree plus fifteen? Thirtythree plus fifteen is fortyeight, AND fifteen plus thirtythree equals fortyeight!
Before we see those party bags, let's review! Today we learnt about order in adding. That's when you decide which addend to add first. We also learnt about the commutative property and commuting numbers. Remember, when addends commute, those numbers rearrange, but the sum ALWAYS stays the same. You can use tens frames to help add, whichever way round the numbers are! Now, let's see those party bags. "Oh no!" "Imani? Imaaani! I'm stuck in a bag! Help me out!"
Order in Adding exercise

What equation does this show?
HintsThere are two correct answers.
How many pencils and how many erasers were put into each bag? These are your addends.
Can the two addends be added together in any order?
SolutionThere are 7 pencils and 8 erasers in each bag.
7 + 8 = 15 and 8 + 7 = 15. These answers are both correct.
When we have two amounts to add together, we can add them in any order.

Match the pairs that are equal equations.
HintsWhat is the total of the first pair? First find the amount of green squares, then the amount of purple squares.
Is there another tens frame that has the same total but the addends are in the opposite order?
SolutionThe image shows the pair that shows 5 + 8 = 13 and 8 + 5 = 13.

The other pairs are:
8 + 10 = 18 and 10 + 8 = 18
12 + 22 = 34 and 22 + 12 = 34
13 + 25 = 38 and 25 + 13 = 38

Complete the equations.
HintsThe first number sentence is to add the purple and green, so count how many purple squares and put this number in the first gap.
The second number sentence is to add green and purple, so count how many green squares and put this number in the first gap.
Commutative means that we can add the two parts (addends) in any order and we still reach the same answer. e.g. 4 + 6 = 10 and 6 + 4 = 10.
SolutionThere are 14 purple and 18 green squares. These can be added together in both ways and the answer is still 32.
14 + 18 = 32 and 18 + 14 = 32.

Which images answer the question?
HintsThere are two correct options.
Which tens frames have 16 and 8 shown in purple and green?
The total number of coloured squares is equal to 16 + 8.
Solution There were two options that correctly displayed this problem.
 Since there were 16 balloons and 8 sweets, we could do: 16 + 8 = 24 OR 8 + 16 = 24.

How many treats are in each party bag?
HintsCount how many heart stickers and star stickers there are. Then add these together.
Count how many stickers there are in total on the tens frames.
Solution There are 8 star stickers and 9 heart stickers.
 In total there are 17 stickers.
 8 + 9 = 17
 9 + 8 = 17

Matching equations.
HintsLook at the two addends within the equation. Can you see another equation with those same two addends?
In an addition number sentence, the total can come at the end or the beginning of the number sentence.
SolutionThe image shows the pairs matched correctly.