Content Order in Adding
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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 twenty-two 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? Twenty-two 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 thirty-seven plus fifteen we get fifty-two, and if we add fifteen plus thirty-seven we also get fifty-two!

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.

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

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Order in Adding.
• What equation does this show?

Hints

There 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?

Solution

There 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.

Hints

What 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?

Solution

The image shows the pair that shows 5 + 8 = 13 and 8 + 5 = 13.

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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.

Hints

The 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.

Solution

There 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?

Hints

There 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?

Hints

Count 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.

Hints

Look 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.

Solution

The image shows the pairs matched correctly.