My oldest son who is in seventh grade recently had trouble with a problem in his 7th-grade math book. I couldn't believe he didn't know the answer! It was a very straightforward problem with integers and all it asked was how you could solve the problem using the Commutative Property of Addition. He couldn't remember what that property was! And this is 7th grade.
Common Core Standards for Math
Way back before the Common Core, I did teach the Properties of Addition as a third-grade teacher. But even back then I wondered why and for what purpose? I did the lessons but did not worry too much if they didn't master them. But as you can see with my son, the Properties of Addition do not go away. Students will continue to add all through school, but they may be adding fractions and integers. It doesn't matter! They do need to know that the Properties of Addition are important and that they are used continuously and ARE very useful.
I made these posters and have them hanging on my math wall all year long so the students can reference them. There's also a matching bookmark.
Those of you who teach the Common Core State Standards already know that the Properties of Addition are taught in grades 1, 2 and 3. These are the specific standards which mention Properties of Operations:
Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Teaching the Properties of Addition
So how does one go about teaching these properties and for how long? Let me answer the second part first. In my district, we are required to have an English Language Arts RtI block for English Language Arts which lasts for about 40 minutes, 4 times a week. This RtI block doesn't start until a month after school has begun. So essentially, I have an extra 40 minutes to fill each day for about a month. So I use a week (or more) of this block to specifically teach the Properties of Addition as an extra math block. That use of time has been one of the most valuable uses of time I've used all year long!
When I first began teaching the properties, I created a PowerPoint that was interactive. By interactive, I mean there are slides in the PowerPoint in which the students interact with the content on the slide (and it includes lots of animation). They interact by answering questions, discussing with a partner or writing in a math journal (or any piece of paper). I use both a math journal and the printables. The printables I created to go along with the PowerPoint so that students would be even more engaged and begin practicing the Properties of Addition immediately.
You can see a preview of this PowerPoint on my YouTube channel: YouTube Video.
or watch a version here:
The PowerPoint has gone through some revisions, but the format has remained the same. Three properties (Commutative, Zero or Identity, and Associative) are all addressed as separate lessons so it is easy to pause the PowerPoint after each lesson and continue the next day. The PowerPoint also comes with Presenter's Notes in which I give teaching suggestions and explain when to advance the animation or slide. There are also three printables included. You can find the Properties of Addition PowerPoint Lesson HERE.
Practicing with the Properties of Addition
In addition to the PowerPoint, I created a hands-on center which I actually use whole class though it can be used in small group or for intervention. This center has a work mat and number tiles but you would need to add unfix cubes or some other type of manipulative. It also has task cards which give the student a problem to work out on the work mat. In whole class grouping, I read aloud the card and project on the screen. Then I walk around as the students use their unifix cubes to build an equation.
Here's a video showing one of my students building with unifix cubes. The center has task cards for all three properties, but in this video, we were working on the Commutative Property of Addition.
Once the student has created a unifix train for the equation, they use the number tiles to build the matching equation. From there, they build another unfix train but they switch the addends around (commute the addends), and again use the number tiles to build the new equation. We then discuss what they notice. Here's the same student continuing the work:
This is a great opportunity to build and expand that math vocabulary: addends, addition symbol, equal sign, commute, sum, etc. It is so important for students to learn and use that math vocabulary when discussing mathematical concepts (or else how are they every going to understand word problems!! i.e., see my son above).
The second part of this center involves a Commutative Property Match-Up. I took a video of my youngest son (who's also in third grade) to see if he could explain how use the Commutative Property of Addition. It was interesting to note his use of vocabulary (he said that 3 + 4 is the OPPOSITE of 4 + 3). But he was able to show his understanding of this property. Check out the video:
Why is the Commutative Property Useful?
The Commutative Property is a great strategy to use when adding multidigit numbers. When I taught first grade, I taught counting up as an addition and subtraction strategy. But if students know that they can switch the order of the addends and start adding with the greater number FIRST, it makes counting up easier. Also, back when I did teach first grade, I was using Math Their Way and so the students were constantly using manipulatives to build the concept of addition and they would internalize this property. They never saw 3 + 4 as just 3 + 4, but also as 4 + 3. They knew that they could switch the addends because they had done that with the manipulatives. By learning this property, in addition, it will help immensely when we start learning the Commutative Property of Multiplication!
What about the Zero Property of Identity Property?
Don't forget to teach this one! Most students know that when you add zero, the sum is the same addend or addends. Why would this be important to know? In third grade, students learn to round (3.NBT.A1). When you round numbers, you end up 2 and 3 digit numbers with zeroes in the ones and tens place. Those numbers can easily be added using mental math. We want students to be able to mentally round, add and give an estimate to check the reasonableness of an answer. If they know that zero doesn't affect a sum, then all they need to do mentally is concentrate on adding the tens or hundreds digits to get an estimate. But read on. The Zero Property is also useful when combined with the Associative Property.
Why is the Associative Property Useful?
Do your students need to learn column addition? Do they just go about adding a column of numbers in order? STOP! Teach them to use the Associative Property of Addition! With this property, I teach students to find addends that make 10. Ten is a great number because it has a zero! And when you have zeroes in an addend, you can mentally add those numbers faster which makes addition more efficient and reliable. I have a vivid memory of my high school teacher (this is back in the 70s before math instruction was more than just arithmetic), telling us to use this shortcut: when you add find pairs of numbers that add up to 10 and cross them off as you add. Can you imagine that I didn't now this until HIGH SCHOOL! If the students have a good understanding of these properties, and you demonstrate how to use them in addition, I promise you they will become better, faster and more accurate with addition.
Continuing Throughout the Year
Don't forget to continue to teach and practice these properties throughout the year. We want the students to enter 4th grade with an absolute understanding of these properties because they will be increasing their knowledge of place value into the hundreds of thousands. I have an additional center which I use once the students have a good understanding of the Properties of Addition. It has task cards and it requires them to think critically about the Properties of Addition. You can see an example below:
If you want more information about each of these resources, click HERE to see them all. Start your teaching with a FREEBIE: Properties of Addition Practice Cards.
Finally, be sure to follow me on Pinterest. Click to see my board devoted just to the Properties of Addition!
How are you teaching the Properties of Addition to your students? I'd love to hear your ideas!