Are you a 3rd grade teacher looking for fun and effective ways to introduce the properties of addition to your students? If you’re new to teaching third grade, you may have never taught these types of strategies before. You may be wondering what exactly these properties of addition are yourself. In this blog post, I’m breaking down some fun ways to teach the associative property of addition and the commutative property of addition. Read on for effective strategies and activities for introducing the properties of addition that your students will love!
What are the Properties of Addition?
Properties of addition are a set of rules or strategies that your students can use when adding 2 or more numbers. These properties of addition strategies make it much easier for students to solve problems and determine calculations. This is especially true when they begin solving more in-depth and complex problems.
There are 4 basic properties of addition: Commutative Property, Associative Property, Distributive Property, and Identity Property. In 3rd grade, students focus on learning strategies for the associative property of addition and the commutative property of addition.
What is the Commutative Property of Addition?
The commutative property of addition is when you take an addition problem and you can change up the order of the addends, but the sum remains the same. No matter what order the addends are in, you always reach the same result.
Your students most likely have an understanding of this concept, even if they don’t recognize the mathematical vocabulary term commutative property of addition. In 2nd grade, they may call these “turn-around facts.”
Commutative Property of Addition Example
When teaching math properties in 3rd grade, it’s super important to give students concrete examples to model the property in focus. When introducing the commutative property of addition, you could use this example:
You go to the grocery store and buy a soda and a bag of chips. At the counter, you hand the cashier the soda and the bag of chips. Does it matter which item they scan first? No! Regardless of the order that the cashier scans the items, the amount will always remain the same.
When using this example, you can have your students turn and talk to a neighbor to discuss their answers. This is a great way to encourage mathematical discussions and vocabulary in your classroom.
What is the Associative Property of Addition?
The associative property of addition is used when adding 3 or more multi-digit numbers. Parentheses are used with this property, which will probably be the first time that your students are exposed to using them in math.
With this property, 2 addends are grouped inside of the parentheses to be added first. It doesn’t matter which 2 numbers students group in the parentheses. Once that sum is reached, students add that number to the 3rd addend. No matter which way you group the addends, the sum will always stay the same.
Associative Property of Addition Example
To introduce the associative property of addition in 3rd grade, you can use an example such as 31 + 11 + 5 = 47. Model for students how no matter what the order of the addends are and no matter which 2 addends are placed inside of the parentheses, the sum will remain the same.
You can model this using these equations:
(31+11) + 5 = 47 and 31 + (11+5) = 47
Since this is the first time students have been exposed to using parentheses in math, when introducing this math property in 3rd grade, it’s important to remember that when they see parentheses in the problem, those are the numbers they need to solve first.
Therefore, if the parentheses are around the first 2 addends, those are the numbers that they will want to solve first. If they are around the last 2 addends, those are the numbers that they will solve first. It’s extremely important to share with students that it doesn’t matter the order, but whatever the parentheses are around, those are the numbers that are being solved first.
Students can practice different examples using an interactive math journal activity.
Properties of Addition Anchor Chart
When it comes to introducing new strategies and concepts, such as the properties of addition, I always recommend starting out by introducing one property at a time by creating a whole-class anchor chart. On the anchor chart, only fill out the space for the property you are introducing that day. Filling out the entire anchor chart and introducing all properties at once can be very overwhelming to students.
The commutative property is the first property of addition that I introduce. On day 1, you can talk about the property and discuss what the commutative property is while completing that portion of the properties of addition anchor chart. You might practice that skill for a few days before introducing the associative property of addition and adding it to the whole-group anchor chart.
Having a whole-group anchor chart is a powerful visual aid for students, especially as they’re being introduced to this concept for the first time.
In order to get students actively learning and working with these properties of addition, I like to have them create a matching mini-version of the properties of addition anchor chart in their interactive math journal. This allows them to be actively working and exploring this concept while we are creating the whole-group anchor chart together.
This helps them take ownership in their learning and also serves as a great reference for them to look back on throughout the year. If they ever need an example on how to do something, they can simply flip back using their math journal concept organization tabs and look in their math journal.
Properties of Addition Activities
When introducing and practicing the commutative and associative properties of addition, there are a few effective activities and games I like to use to practice these strategies with students.
Switch and Add
For the first activity, call 4 students up to the front of the room. 2 students hold a number sign or just a plain sheet of paper with a number written on it. The other 2 students hold pieces of paper that have the + sign and the = sign.
The students have to put each sign in order to complete the problem. After getting in order, the students switch addends and add again. For example, if the problem is 33 + 17 = 50, the students model that no matter which order the addends are, either 33 + 17 or 17 + 33, the sum stays the same.
By seeing the students with the number signs physically switch places without changing the sum, students get a better visual understanding of the commutative property of addition.
You can have the students at their seats solve the problem on a whiteboard and show the turn-around fact to represent the commutative property. They can even direct the students with the posters to switch places to model the turn-around fact.
You can do a similar activity to model the associative property by having 3 number posters, 2 + sign posters, an = sign poster, and by adding 2 parentheses posters. This option requires 8 students to model that no matter how you group the numbers or which addends the parentheses go around, that the sum will stay the same. You can use number cards and place value mats to determine the numbers and to allow the students at their seat to solve and model the problem along with the volunteer students.
Roll It, Add It, Flip It
Another properties of addition activity I like to use to practice this strategy uses dice. It’s called, Roll It, Add It, Flip It. Give your students a set of 3 dice. If you don’t have enough for each student to have 3, give them 1 dice and they can roll it 3 times to create a 3-digit number.
They roll the dice to create an addition problem and solve for the sum. Then, they have to show the commutative property by flip flopping the addends and solve to see if their sums are the same.
You can use the same activity to model the associative property of addition by having students roll the dice enough times to create 3 addends. Then, they can write in parentheses and model different ways to group the addends inside of the parentheses to always reach the same sum.
Drop and Add
Drop and Add is another really fun game that you can practice properties of addition with. You can find this activity as well as the others inside of my 3rd Grade 3-Digit Addition and Subtraction Strategies Guided Math unit.
To play, students have a piece of paper with a number grid on it. They drop a pom pom ball onto the number grid 3 times. Whatever number it lands on each time, they record to create a 3-digit number. Then, they repeat to create another 3-digit number. These 2 numbers become their addends and they solve for the sum.
Students then show the commutative property of addition by flip-flopping the addends and solving for the sum again. If they get the same sum with both equations, then their answer is correct. This is also a great method to teach students for double-checking their work.
Students can use this properties of addition game to practice the associative property by dropping the pom poms enough times to make 3 addends. They can write the equation and write in parentheses, modeling different ways to group the addends to find the same sum.
I hope these tips, strategies, and activities for introducing and practicing the properties of addition in 3rd grade help you feel more confident as you teach these concepts.
Check out my YouTube video to learn more about introducing these concepts and to get a sneak peek at these properties of addition activities!
Want to get your 3rd Grade Addition and Subtraction Strategies lesson plans done for you? Check out my 3rd Grade 3-Digit Addition and Subtraction Strategies Guided Math unit, complete with 20 days of lesson plans, activities, games, and more!
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