(Last Updated On: August 23, 2022)
Hello, my name is Ken Ray. I have a master’s degree in elementary education. I have taught every primary grade from pre-kindergarten jumpstart to 2nd grade. When teaching addition, I notice that the students in my class who know these 5 strategies do mental math quickly and efficiently. I am writing this post to help give you what I believe is the best base for a successful math foundation through these 5 strategies of addition.
🏗️ The Foundation for Addition
Your child must be able to count in order to do addition. If your child sees 3 pieces of candy and 4 pieces of candy in 2 groups, they must be able to then count 1,2,3,4,5,6,7 – 7 pieces of candy. Counting is the first step for students. Once they can count to 10 consistently, you can start introducing strategies for mental math.
Notes Before Starting
There are a couple of important notes to mention before starting. First, you must go slow before you go fast. This applies to every strategy. If there is a time element to the problem, a child will revert back to what they know best. Right now, they will be counting on their fingers. We want to avoid this. Kids can count very quickly and though this leads to the answer the fastest when you are doing 3+8, it quickly becomes inefficient when double-digit addition and multiplication are introduced. Stress that you do not care about speed in the beginning, you care about the strategy. Always check for understanding of the concept, not just the answer. Focus on “how did you get the answer?”, not just on if the answer was correct.
Children will go with what they know the best. They may get the answer quicker using near doubles than make a 10. That is fine in the real world. Use what you know the best to get the answer, but when teaching the strategy, go slow and make sure they are solving the equation using make a 10 by having them explain the steps back to you so that they fully understand the strategy and are not just using what they already know to solve the problem. They will eventually get faster at it, and it may eventually overtake other strategies of addition as the preferred method!
🖐️ The Big 5 Strategies to Improve Mental Math
- Count on up to 3
- Adding 0
- Near Doubles
- 10 Frame Facts and Make a 10
Strategies for Addition 1. Counting On Up to 3
This strategy is a little cheating. Instead of memorizing 5+1=6 and 6+3=9 we are going to focus on grabbing the bigger number and counting 1, 2 or 3 numbers higher. This is efficient in the beginning and kids will naturally start to memorize these facts in time. There is no need to drill and kill these facts. That will lead to boredom. Just teach them one strategy.
The strategy is simple, if you see an addition problem with a 1, 2 or 3 in the problem, grab the bigger number in your head and hold up the other number on your hand, be it a 1, 2 or 3 and count on using the number in your head. For instance, if the problem is 4+2, the kid should make a grabbing motion with his/her hand and put the 4 in their head, then hold the 2 fingers up. Ask them, “what is the number in your brain?” When they answer 4, you say, “Count on.” They should then say, “5” as they put down 1 finger and “6” as they put down the last finger. You will have to demonstrate this several times before they understand it. You should then do it with them several times before they go solo.
How is the Counting On Strategy Different than Counting, Shouldn’t We be Getting Away from Counting?
This strategy is more procedural than conceptual and will be soon discarded as the kids will memorize their plus 1 and plus 2 facts, however, I like it because it gives them a strategy to alleviate a lot of unnecessary boredom of memorizing plus 1 and plus 2 facts. As they learn more complex strategies, the “count on” strategy will be left behind. That being said, it is a great beginner strategy to develop “number sense.” It will start slowly.
In the beginning, kids will just try to count. Let’s take the earlier example, 4+2=__. Kids will want to hold up 4 fingers and 2 fingers and count them all at first. Then kids will want to only hold up 2 fingers, but then count 1,2,3,4 then 5 with one finger and 6 with the other. It is not until the kids can just grab 4 in their head and know that 5 comes after 4 that they have mastered the “count on” strategy.
Eventually, kids will develop more efficient ways to count, this is an effective placeholder before the plus 1 / plus 2 facts are memorized or make a ten fact is learned.
Strategies for Addition 2. Adding 0
This may seem simple, but whenever kids see a plus sign, they want to make the number bigger. This fact will be easy for most kids to grasp after they see concrete examples on both sides of the plus sign and in part-part-whole models.
Word problems are usually the best for kids to realize the “adding 0” strategy. One example could be you have 5 pieces of candy, and your parents give you 0 more pieces of candy. How many pieces of candy do you have now? This will be an easy problem to act out if your child does not get it right away.
Once they understand it, you can go through the “(1-9)+0= / 0+(1-9)= / 0+0=” facts relatively quickly.
Strategies for Addition 3. Doubles Facts
There are 10 doubles facts. These are relatively easy to memorize and have lots of fun activities that go with them. One of my favorites is the Doubles Rap. These facts go straight through the 0-9 grid and lead to understanding near doubles. This also sets up an understanding of multiplication.
Concrete examples lead to instant recall. Examples of concrete doubles most kids get are:
- 4 legs on each side of a spider – 8
- 5 fingers on each hand – 10
- 6 eggs in each sleeve- 12
- 8 crayons in each sleeve – 16
- 9 wheels on each side of an 18-wheeler
The last concept about doubles I want to leave you with is a more complex one that you could come back to later on after near doubles. It is when the addends are 2 apart, like 5+7 or 4+6. If you can see that 6+8 are two apart from each other, you can quickly make it into a 7+7 doubles fact. Take one from the 8 and give it to the 6.
Strategies for Addition 4. Near Doubles
This concept is getting a little more complex. Now that your child has developed a number sense with count on and knows their doubles facts, they are ready for “near doubles.” I hear this strategy is also referred to as doubles plus 1. When a kid sees an addition problem where one addend is the one more or less than the other addend, they can use the near double strategy.
Take the smaller of the two addends and make a doubles fact and add 1. Let’s take 8+7=__. Your child must know that 8 is one more than 7 and that 7 is the smaller of the 2 numbers. They will then take the 7 because it is smaller and add 7+7. He/She will get 14 from the doubles fact and then can count on one more. (7+7+1=) (14+1=15), so (8+7=15).
If you want to get more complicated with this, you can introduce Doubles minus 1. This is where you take the bigger of the numbers and make a double and then subtract 1. I find this to further complicate the idea, but if you want to go a little deeper conceptually, you can introduce subtraction to the mix. The same example, 8+7= (8+8-1) (16-1=15), so (8+7=15).
Strategies for Addition 5. Ten Frame Facts and Make a 10
Learning all the ways to make 10 sets you up to manipulate many addition equations into simpler forms. First, you must memorize all the ways to make 10. When teaching make a 10, use various techniques and activities like using the Make 10 Rainbow and Ten Frames. Kids should easily recognize the 11 addition problems that make a 10: 0+10, 1+9, 2+8… 9+1, 10+0.
That was the first part; the second part is a little more complicated to learn. This next skill is usually learned around 1st grade. Your child has to know a few concepts to be successful with this strategy.
- First, your child must have some number sense. 8 is closer to 10 than 6.
- Secondly, your child must be able to think of 15 or 19 as a 10 and some ones (5 or 9 in these cases)
- Lastly, this requires a little more brain space for the mental math
Steps to Make a 10
The first detail you want your child to look at in the addition sentence is whether there is a number close to 10. This works great with 9’s or 8’s, less with 7’s and 6’s. The next detail you want them to notice is there enough to make a 10. If not, you should be able to count on or just know your plus 1,2, 3 facts at this point.
If there is enough to make a 10, you will take the bigger number and make a 10 by taking part of the other number. Ex. (7+9=__) the biggest number in this equation is 9, so we take that number and make a 10. Because we know our 10 frame facts, we automatically know 9+1=10 so we know we need to take 1 from the 7. This is where the extra brain power is needed and a little simple subtraction. 7-1=6. Eventually, we will be able to do this all in our heads, but when learning the process, you want to write it all down.
I find that using a number bond for the smaller number really helps kids see how to break it up on paper. After they see it on paper, they transition into doing it mentally.
Are these the only addition strategies? Nope, not even close. Your kid may make up their own addition strategy that no one has ever even thought of. These are just 5 solid strategies that once mastered can be used to solve over 80% of any addition problem efficiently, quickly and mentally. Why did I only do addition and not subtraction? Because if you know your fact families, you can change any subtraction problem into an addition problem. Addition is much easier for early elementary and my brain.
- near double (7+7=14) (14+1=15) (7+7+1=15)
There are a lot of addition games and worksheets out there; I could dedicate a whole post to that. If you are looking for some you could go to Pinterest or just search Google, but I would recommend joining TPT. TeachersPayTeachers is a site you can join for free and download free material, there are resources you can pay for, but you can find what you need for free most of the time. Search for your topic (doubles, near doubles, make a 10, etc.) and select the price (free) and it will pull up all of the material it has. Trust me, you won’t regret the one-minute sign-up!
Will these strategies for addition work with double-digit addition?
Most definitely! These strategies will work with multi-digit number addition. The only extra information you will need to learn is place value and carrying tens.
78 + 37 = __
Ones place: 8 + 7 = __ is a near double that’s (15)
Tens Place: 7 + 3 =__ Ten fact (10)
10 tens + 15 ones = 100 + 15 = 115
These strategies for addition are designed for multi-digit addition and mental math! In 1st grade learn the strategies with single digit numbers, but they are really useful when you get to 3rd grade and you are encountering 3-digit addition.