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CCSS.MATH.CONTENT.2.OA.A.1

Basics on the topicOrder 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 or, the commutative order property of addition.

What is the commutative order property of addition? You may have heard grown ups say that cars commute, well did you know that numbers do too? Commute is another way to say travel. Cars travel from one place to another, and numbers can too!

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 ten frames for example.
3 Once you have solved the first equation, create another
by moving, or, rearranging the addends.
4 Solve again using ten frames.

Even though the addends commuted, the sum remains the same!

Let’s practice the order in addition with the commutative property of addition in the example below.

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, 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 ten frames.
• Once you have solved the first equation, create another by moving, or, rearranging the addends.
• Then, solve again using ten 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? The commutative property of addition means that the order in which you add does not change the sum! Let’s take a look at an example of the commutative property of addition 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!

Today we learned about the order in adding. That's when you decide which numbers to add first. We also learned 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 changing order of addition property and commutative property of addition exercises and worksheets.

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

Hints

How many pencils and how many erasers were put into each bag? These are your addends.

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 ten 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.

The commutative property tells us that we can add the two addends in any order and we still get the same answer. For example, 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 colored squares is equal to 16 + 8.

Solution
• There were two options that correctly displayed this problem.
• Since there were 16 balloons and 8 pieces of candy, we could do: 16 + 8 = 24 OR 8 + 16 = 24.
• How many treats are in each party bag?

Hints

Count how many heart stickers there are and how many 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.