Wednesday, October 31, 2012

Memorizing Addition and Subtraction Facts

I've talked with some of you who have had a similar problem- getting your child to memorize addition/subtraction math facts. This is a really crucial skill, because as they start doing more advanced math concepts (beginning with multiplication) they will need to quickly recall addition facts to solve the problem they are doing in the most efficient way possible.  When they start working on fractions and finding common factors, chances are if they haven't learned addition/subtraction facts they haven't memorized multiplication facts either- thus creating a big mess of a domino effect.

First- ASSESS the problem areas
Before you start trying different strategies, see what they already KNOW and what they DON'T. Most kids know addition/subtraction facts 0-2 or 3 and then 10's. It's what's in between that gets fuzzy. Once you know what they need to work on, start at the bottom and work your way up. 
Note: Be sure your child can demonstrate the meaning of addition and subtraction before working on memorizing facts. Memorization is meaningless if they don't know what the fact means.  

Second- how NOT to drill math facts

Some people think "drill is kill", and many people think it's necessary.

And of those that use it, not everyone knows HOW to actually drill math facts effectively.

You know, this is NOT the most effective way: Shuffle the flash cards and start asking randomly.

Why? Because you are not utilizing techniques that help our brain remember quicker.

For example, it is easier to remember when the mind can tie the fact into something already known.

This is the idea behind silly rhymes such as "five, six, seven, eight - fifty-six is seven times eight."

Besides those, we want to show our children the PATTERNS in math.

So this is how I start drilling math facts (whether addition or multiplication):

I make a list on paper, IN ORDER. For example, lately we've been doing this with my daughter:

8 + 2
8 + 3
8 + 4
8 + 5
8 + 6
8 + 7
8 + 8
8 + 9

We went through the answers and notice how each one is ONE MORE than the next! That's a pattern!

Then I would point to a fact and say the problem so she'd both see and hear it (using two senses). You can additionally MOVE her finger on the chart with yours - so she's using three senses. This should help the auditory, visual, and kinesthetic learners all.

When I'd point to a fact further down the list, automatically she'd know it's more than a fact that is up on the list. It's a visual pattern.

First, I drilled just a few of them, namely 8 + 3, 8 + 5, and 8 + 8 until she remembered those.

After that, I would go first to 8 + 8 which she knew, and immediately after that to 8 + 9, and she was able to deduce it from knowing 8 + 8.

I would gradually add new facts in a similar manner - using the known facts as "stepping stones" so that the new fact was one more or less than a well-known fact.

And so we go "round and round" on this chart.

= > The chart creates an organized context for the addition facts.

Obviously, the child is also associating the position of the fact on the chart with the answer, and so after this is well remembered, it will still take another effort to remember the facts when they're in isolated context, such as in a game, or in a math book, or on flash cards.

*Note from Mrs. Houlin* I've found using flashcards to be effective IF: you choose 3-5 cards to work on with one common addend, like 5+6, 5+7, 5+8, and work on those until those are memorized before moving on to a new group of flashcards. 

As mentioned above, patterns can be very useful when learning/memorizing facts.

Third- Using Number Tricks 

This section introduces addition and subtraction facts with a number of easy-to-use tricks that can be used together with the practice activities, to help memorize basic facts. These tricks are listed below in pairs:

How To Use These Resources To Help Learn Math Facts

Follow these steps to help your child memorize basic addition and subtraction facts using the tricks from Susan Greenwald's Two Plus Two Is Not Five workbook.
  1. First, test to see which facts your child knows. Then record them. Create a chart (you can use this addition chart to help) and mark any facts that are already known.
  2. Teach each trick to your child and use counters (e.g. buttons) to model the trick making sure your child understands the concept behind the trick.
  3. Practice at least three times a week. Each trick begins with it's introduction. Work through these with your child and then allow them to try the practice activities.
  4. Encourage your child to use the trick's name. This will help with recalling the trick and the related facts.
  5. Notice how each trick is followed by practice activities that cover the trick as well as activities from previously learned tricks; All facts are reviewed as new ones are learned.
  6. Work at whatever speed suits your child.
  7. Use the Math Fact cards on a daily basis to review facts.

Fourth- Make memorizing them a game!

Play "War".
Math War is a card game that can make learning math facts a lot of fun for kids. You can buy math war cards for addition, subtraction, multiplication and division. Basically you deal the deck of cards to each player. In each round the player with the highest answer wins. You can also come up with your own variations on the game. Math War is easy enough that you could do it with a kindergartner and perhaps a preschooler.

This site has 5 iPhone/iPad apps recommended for practicing math facts:  

You can try using number rhymes or songs (found here These are really "iffy"- they work great for some kids, and not at all for others. Give it a try, it wouldn't hurt!

Last- Recommended Order

1. First, start with the doubles: 1+1, 2+2, etc, all the way up through 12+12. Make sure she knows these inside out, upside down and backwards. Take your time and get it right - almost everything else is based on these patterns.

2. Learn Counting by 2’s. Memorize this inside out and backwards.

3. After that, go to the 12 addition facts that are "one more than" the doubles: 1+2, 2+3, 3+4, etc, all the way up to 12+13. The answer is always one more than the doubles, which we definitely know. Example: 7+8: Since 7+7 = 14, then one more is 15.
4. Next, move on to the "doubles plus 2". 1+3, 2+4, 3+5, up to 11+13. There are 2 ways to look at this: First, the double plus 2 more (some kids like this).
Second, notice that if you change the "piles" and borrow one from the larger pile and put it into the smaller, you have doubles - of the counting number that is "missing" between the two you are adding. We call this group the Missing Doubles.
Example: 6+8: If you borrow one from 8, that leaves 7. Put the one you borrowed in the 6 pile and you have 7 again. So 6+8 is the same as 7+7 and that we know also. Notice that 7 is the counting number between 6 and 8.

5. Adding 1 is a joke, adding 2 is easy, also.
6. Adding ten: practice with the single digit numbers: 10+1 through 10+9. You write down the number (not the 10, the other one) and stick a 1 in front of it.

7. Adding 9: Same as 10, but it is one less. I like to subtract one before I put the one in front of it. 9+5 One less than 5 is 4; with a 1 in front of it is 14. I've also seen this taught this way: Think of 10+5 instead of 9+5, then take away 1. 10+5=15 take away one is 14.
Make sure she can count by 2's and understands the pattern blocks, through 100. Now, can she count by 2's, starting with 1? (the odd numbers). If not, this is really important. She needs the beginning pattern (1, 3, 5, 7, 9) and understanding of the whole block through 101.

8. Last one here: Add 4:
9. Since 4 is 2+2, and counting by 2's is so easy (see above), just "count by 2's, twice". This is why the odd numbers are so important:
Example: 37+4: Counting by 2's, is 39 / 41. No carrying, quick and easy, anybody can "count up 2" in their heads.

This is usually all the patterns a student needs to get started. They start finding their own patterns after that, and remembering their facts because they are so relaxed - you can always figure them out quickly and efficiently if you forget. 

 Good luck! :-)


Behind the Classroom Doors said...

Love, Love, Love, your article. Teaching math facts is very difficult. The root of the problem is a lack of understanding number sense. When a child has a strong foundation of how numbers work basic facts come easy. Can you tell I am passionate about this? Another site I like is: Does anyone else have a favorite?

Cam @Ms. Understood said...

Thank you for this. My oldest very easily just "got" math and the patterns, and he never had to work very hard to memorize all his math facts and recall them with perfection. But my youngest…oh boy. He doesn't seem to retain anything; even if he seems to "get" it one day, he won't remember it the next. We're working on addition facts up through the 10 family, and while he has an easy time with the +1s and the doubles, everything else is a struggle. No matter how may flash cards, practice sheets, addition games, or apps on iPod and computer he uses, he STILL has to stop and count up. No matter how many times he sees a combination, he doesn't retain it. He's 6.

Rayna Jones said...

I am having a hard time because my son uses his fingers and feels badly about it. I am going to incorporate these ideas starting now.

Another helpful hint: adding to ten. Make flasshcards with individual numbers that add to 10 .... 2 and 8 for example. Color each pair that adds to 10 a different color, 2 and 8 may be blue, 7 and 3 may be green. Play any game you can think of, and before you know it, these "fact families" become second nature.

Thanks for the great advice.

Marshie said...

I always wondered why I am such a visual learner, I still sometimes use my hands and im an adult! I've now figured out the missing pieces! Embarrassing but I guess I fell through the system. This will help the areas I'm weak in and make me feel like math is something other people do. Thanks !

Anonymous said...

My son was using his fingers but he is now using a website to help but I will begin using flash cards. We also play game called BOOM, in this game I have written on popsicle sticks the math facts without the answers. Each player has to pull a stick, if they know the answer they can keep the stick if not put the stick back. And if you get a stick with BOOM the player has to give back sticks. We play them game for 5 minutes. It's kind of like UNO.

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