When you teach a child to add you are helping him take an important step toward mastering mathematics. Addition is a bridge to many practical applications and the foundation upon which you can teach subtraction, multiplication and division with ease. It’s worth the time you have to spend to get it right. Before you dive into addition, make sure your student’s counting skills are sufficiently strong.
If your student is ready, teaching addition is much easier. Learning addition can be broken down into at least two distinct tasks, understanding what it means to add and memorizing addition facts. There are many, many techniques for teaching addition. I encourage you to use several different techniques. Generally students retain their new skills and understanding far better when you do. How you teach a child to add can affect his long term attitude toward and success in mathematics. Keeping it fun with games and short pleasant lessons is helpful. So too is building addition on the rock-solid foundation of the child’s counting skills. After all, counting is simply adding one – again and again and again!
Start with 13 objects (I like pennies), and select one. Say “One penny AND one more (select another and place them side by side), IS…” and look expectantly at the child. Pause for as long as it takes. When the child concludes that there are two pennies, say “Two pennies AND one more IS…” When the child concludes there are three pennies repeat the process. Keep going until you and the child have concluded that 12 pennies AND one more IS thirteen pennies.
Why “AND’ and “IS?” Because your kid knows what “and” means, and he knows what “is” means. In good time you can substitute “plus” for “and” and “equals” for “is.” Don’t make a big deal of it when you do. You can briefly explain that “=” means is and “+” means “and.” That suffices. At this stage of your child’s development a lengthy explanation is a waste of time. Just CONNECT what he knows with what you’re teaching, and move on. Later, when it’s time to teach him how to solve word problems, you’ll be very glad you made this connection at the very foundation of his understanding of addition. From here on out you should use and/plus and is/equals interchangeably, so that your child comfortably equates the two.
And is a very handy word, because your child already knows that “peanut butter and jelly” are exactly the same as “jelly and peanut butter.” Take time to help your child discover that “order doesn’t matter.” One and three more are the same as “three and one more.” You’re teaching the commutative property of addition. Just don’t make your kid memorize that term. That comes later! What’s more important right now is that instead of teaching just twelve addition facts, you’re teaching twenty four, and it didn’t hurt a bit.
When it’s time to move on to “plus two,” encourage your child to “count up.” Say “one and two more is…” and wait for your child’s response. Your child may instantly recognize the answer is three, because of the counting skills you taught previously, or because this is also a “plus one” fact. Eventually, usually by “Three plus two equals…”, the child stumbles a bit. Touch the coins yourself as you say “Three, four, five, three plus two equals five.” Do NOT count all the coins. Count the third coin as three, then “count up” four, five as you touch the last two coins. Do not become concerned if your child isn’t memorizing these facts yet. Memorizing the facts is a task apart from understanding what it means to add two numbers. We will get to that.
After Two, Zero
I know, I know, that’s not how you learned to count! Adding zero is a a bonus which fits here very easily. It turns out that starting with adding zero confuses most children, but once you’ve established what addition is, adding zero (nothing) is no big deal. Remember, when you finish teaching your child to add nothing to a number, teach him to add a number to nothing. 0 + 2 = 2 = 2 + 0, etc.
Memorization of Addition Facts
OK, let’s start memorizing addition facts. For starters, let’s see what your child has already memorized. Quiz your kid on the “plus zero” facts. I’m betting that if they haven’t been memorized, they will be easy enough to memorize. Check to see which of the “plus one” and “plus two” facts are memorized. Encourage your child to highlight every fact he has memorized. Celebrate the victory, and continue to celebrate every fact masted, until your child has memorized them all.
There are a lot of tools for helping children memorize addition facts. I suggest that you start with the free or nearly free tools first.
Stop the Presses! Important Tip Here!
Language and memory are strongly connected. Each time your child reads a flash card or answers your query about an addition fact, have the child state the problem before the answer. For example, if the flash card reads 4+2, the child states “Four plus two is… six!” If the child answers incorrectly, you should state the entire fact and encourage the child to repeat the fact back to you in its entirety before moving on. This will greatly increase the speed in which your child memorizes these facts and it will improve retention of the material.
OK, Back to Work!
Build some ordinary flash cards. Instead of drilling your child outright, lay about a half dozen of the flash cards out on the table at once and allow your child to pick up the cards in the order he would like to attempt them. If he gets it right, he gets to “keep” the card, at least ’til the end of the session. If not, he puts it down and tries again. As the child’s memory gets stronger, put out more cards at a time – up to a dozen.
Build some Triangular flash card on card stock or construction paper. Triangular flash cards feature the two numbers being added in the bottom two corners and the sum in the top corner. Save these! You can use them later for subtraction! Triangular flash cards are great for helping kids memorize a sum “backwards and forwards.”
The next step is to teach your child to add ten. Why? Because adding ten is easy! This is a great time to introduce some manipulatives. If you are on a tight budget you can use construction paper or items you find around the house. Your time and attention is your strongest asset when it comes to educating your child. Spending money will NOT make you a more effective teacher for your child. If you can afford an investment of about twenty dollars, then I would suggest you purchase cuisenaire rods. They’ll make your job a little easier. Cuisenaire rods deliver a lot of bang for the buck, and have the broadest applications of any math manipulative I’m aware of. Here is a cogent but entertaining explanation on how to use cuisenaire rods to teach addition.
Master the Easiest Facts First
Why master plus one, plus two, plus zero and plus ten first? Because of the commutative property of addition! If you’ve memorized that nine plus two equals eleven you also know that two plus nine equals eleven. Each row on the addition table that you master doubles as a column which eliminates one fact from each row.
Plus ten facts are easy, but you may want to see if your student is ready to represent ten pennies with a dime. If so, things get easier. Cuisenaire rods are also rather helpful at this point. Another learning tool that comes in handy is a set of base ten blocks. Base ten blocks aren’t quite as versatile as cuisenaire rods, but they do directly illustrate the base ten nature of our number system. Alternatively, you may want to construct two-dimensional manipulatives that resemble base ten blocks. (You can also do this with cuisenaire rods.)
After Ten, Nine
Show your child that since nine is just one less than ten, the answers to the “plus nine” facts are just one less than the “plus ten” facts. Demonstrate adding nine with coins, rods or blocks, emphasizing how close nine is to ten. Use your flash cards (both sets), to help your child memorize the facts.
OK, Time to Celebrate! Look How Far You’ve Come.
Your child has already memorized more than half of the addition facts. You should celebrate together. I think ice cream is in order! The rest of the facts will come pretty easily too.
Eleven and Twelve
Use your coins, rods or blocks to show your child that adding (for example) 11+ 3 is easy if you think of it as 10 + (1 + 3) = 10 + 4 = 14. Demonstrate the “twelve plus” facts in a similar manner. 12 + 3 = 10 + (2+3) = 10 +5 = 15. After your child is comfortable with this, use your flash cards to help him commit the new facts to memory. When you’ve done so you’ll be able to highlight in all the facts I’ve marked in orange in the chart below.
I’ve made this Chart because I think it helps to explain which facts I’ll be referring to here at the end.
Let’s talk about the blue diagonal line of facts – the doubles. To teach the doubles, show the child how to solve (for example) 5 + 5 by holding up five fingers and counting by twos five times, one for each finger. Thumb, “Two.” Index finger, “Four.” Middle finger, “Six.” Ring finger, “Eight.” Pinky, “Ten.” You may further illustrate this “trick” by using you coins or base ten blocks in two side by side rows of 5.
Building on Doubles
After your child has mastered the “doubles,” it’s time to take on the facts I’ve highlighted in red. Explain to your child that these facts are just doubles that have been rearranged a bit. To illustrate four plus six equals ten and six plus four equals ten (for example), line up your two rows of five coins or blocks, exactly as you did for five plus five equals ten. Take a block or coin from one row and move it to the other. “See, there are still ten coins, but now it’s four plus six or six plus four that equals ten.” Do the same thing with all the other “red” facts.
The turquoise facts are each “one more” than a double. For example, 4+3 and 3+4 are obviously “one more” than 3+3=6. Since it’s just one more, 4+3 and 3+4 must equal one more than 6, or 7. Use this to help the child see the answer to all the turquoise facts.
This leaves us with the purple facts. There are only six of them to memorize, since the commutative property of addition means that the addends can be in any order without changing the sum. Unfortunately I don’t have any cute tricks for these. Use your manipulatives, be they coins, rods or cubes. Use both types of flash cards. Encourage yourself and your child by reminding yourselves that the end is in sight! How do you plan to celebrate?
This is a major accomplishment. You have just taught your child to add – like a boss! (Seriously, you are amazing!) By learning addition and memorizing the addition table, your child has a tremendous leg up when it comes time to tackle subtraction, multiplication and addition. He also will have an easier time overall in math class. Addition truly is a foundation skill.
I’ll be writing about memorization of the remaining math facts soon. If you have any questions or ideas to add, please leave a comment below. I always respond within twelve hours, because I love hearing from you.
All the best,