Written by contributing writer Roan of Joyful Always.
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Addition, subtraction, multiplication, and division facts must be memorized by every child. While there are various computer programs and games available for these math drills, in my experience I have found that old-fashioned paper flashcards have proven most successful in my homeschool.
I have also found that the flashcards that I make myself, work better than the store bought kind. I like to teach my children their math facts in families, so this is how I create personalized math flashcards.
Supplies Needed:
- 5″ x 8″ blank index cards
- markers
- rubberbands
Procedure:
- On the front of each index card, right a math fact. (1 + 1 =). Using the same color marker, create a set of index cards with all of the 1 + facts. (Like 1 + 2 =, 1 + 3=, 1 + 4=, etc.) So you will have a set of index cards with the 1 + facts.
- On the back of each index card, write in pencil the answer to the math fact that is on the other side of the card. I write this answer in one of the upper corners of the card.
- Also on the back of each card, write a different set of math facts using a different color marker. (2 +0=, 2 +1=, 2 + 2=, etc.). On the reverse side of the card write in pencil the answer to this fact in one of the upper corners.
- Bundle this set of flashcards—the 1 + cards and the 2 + cards with a rubber band.
- Repeat this procedure until you have a set of cards for each family that you want to drill.
I make similar flashcards for subtraction facts, but each card set is all the numbers minus a certain number. For example 10 – 1, 9 – 1, 8 – 1, 7 – 1, etc. Remember to use a different color marker for each set. This helps sort the cards if you or your child accidentally drops them.
The reason that I write in pencil the answer to each fact on the reverse side of the card is so younger children can drill the flashcards with each other. The child doing the drilling can see the answer while the child being drilled can see the math fact on the other side.
After the child has mastered a family of flashcards (like the 3 +), we move to the next family (4 +). When all facts of a particular kind are mastered (addition, subtraction, multiplication, or division), I will shuffle all of the families together and continue to drill the mixed up sets on a daily basis until the child has memorized all of the facts. Since the cards are color-coded, they are easily separated into their respective families and are ready for the next child to learn.
I make two sets of flashcards for each family for multiplication and division. One set is made just like the addition and subtraction ones, and then the second set has the answers included in the math fact. The front of the card would have 4 x 5 = 20. The next card would have 4 x 6 = 24. I write these sets with answers in the same color as I write the set that does not have the answer on the front. When my child is learning each new family, like the 2′s or the 3′s or whichever ones, I have them flip through the cards one by one, reading the fact aloud. ”Two times two equals four. Two times nine equals 18.” After they have orally reviewed the set, then I drill them with the same fact family without the answers.
Eventually, we move to daily drills without practicing with the answers included cards first. And then after each family is mastered, we move to shuffling all fact families together and drilling the entire set. One note: when I drill an entire set, I do not drill all of the cards in one day. We will just drill about 20-30 or them, and then I insert a small slip of paper on top before I put the rubber band around the set. I always know to just start with the card that is underneath that slip of paper.
All of this may sound rather complicated, but once you make your flashcards, you will have them forever! I am currently drilling addition facts with my first grader using flashcards that I made for my now 12th grader!
The main thing to remember is that with patience and consistent practice, your child will master his basic math facts.
Roan is the homeschooling mother of five children, and she has been drilling various math facts for 12 years! You can read about her homeschool, her homemaking, her family, and her marathon training at her personal blog, Joyful Always.
I totally thought your first statement was a lead in to debunk a myth. I’m shocked (and terrified) that it isn’t.
Although I agree that it’s helpful for kids learning math to not have to stumble on the “math facts” – I vehemently disagree that every child must memorize all math facts!
If your children respond well to the drills – enjoying making the flashcards and doing the drills – then great. Many kids do. And if a parent finds that their children do well with this – then they should try their hand at your suggestions.
But a lot of kids freak when drilled on math facts. And pressuring them to continue degrades their natural curiosity about math. And eventually destroys it.
Kids in that boat are the ones that struggle with their high school levels of math – and end up making the homeschooling parent miserable.
So if your children are fact-based kids, then yes – have them drill with flashcards. If not, let them grow and discover the math facts as they need them. Allow them to learn the value in having them committed to memory. And when they’re ready to, they’ll put them in memory – their own way.
There is definitely merit to memorizing facts. So much of math past early elementary hinges on know those facts cold. Teaching, encouraging, and reinforcing those facts at a young age paves a way for success in math in the upper grades. Good luck doing well in algebra, solving equations if you need manipulative to figure 3×7.
I would distinguish between “Memorizing” math facts and “committing them to memory”. Yes, they must be committed to memory. But memorization, to me, means learning the “fact, that is being able to say e.g. 6 X 7 = 42, without having the meaning of what one is saying even enter one’s brain. The understanding of the fact must be there as part of the learning. I dislike flash cards because they divorce the numbers from the meaning.
“Drill and Kill” takes all the joy out of learning math. Math is about a lot more than arithmetic and math “facts”. Would you expect your child to love and learn music if they spent most of their time practising scales on the piano?
To me, it is *much* more important what the child will be able and willing to do at 18, than what (s)he can (grudgingly?) do at age 8.
I urge all parents of children learning math to read Patricia Clark Kenschaft’s book “Math Power: How to help your Children Love Math Even if You Don’t”.
Alice Horrocks
I like teaching “fact families” with flashcards too. I make triangle shaped cards. On the bottom two corners I write a fact like 5 + 2, putting one number in each corner. Then the sum is put on the top corner. When we review the cards we cover the top corner with our finger. Or, sometimes we even cover one of the bottom corners for 5 + ? equals 7.
Then, when it’s time to review subtraction we cover one of the bottom corners so that you see 7-5 or 7-2. The child quickly realizes that these three numbers always go together.
You can do the same thing with multiplication/division cards. It’s worked VERY well for my kids.
Wow! I love this idea. :) Thank you!
How do you determine they have passed off that fact? If they can say it automatically, with out hesitating to figure it out?
That is exactly how I determine if they know the facts. When they can quickly give the answers to one “family” of facts, we then begin drilling the next family. After two or three families are mastered, I mix those cards together and do periodic drills using those cards as well as the cards we are currently working on.
A million times – THANK YOU. I’ve been trying and trying to figure out a way to get my seven year old to memorize addition and subtraction, to no avail. This concept is so basic, yet I know it’s going to be so effective for her. Really wish I’d thought to do this sooner! I’m looking forward to getting started.
Again, thank you.