In order for your child to have success with more advanced math, it is essential that they memorize their basic facts to the level of automaticity. This can be achieved through skill and drill repetition as well as some more creative methods. It may come quickly for your child, or it may take time, but through focused practice, they will be able to increase their proficiency. There are several links at the bottom of this article with printable worksheets, tables, and online games. In addition, there is a wide selection of pre-made games, cards, posters, placemats, etc. that practice math facts available for purchase. If you prefer, these ready to go materials can be bought without having to wrap your head around too much math!
- Know what basic math facts are and when they are learned. Your child is introduced to basic math concepts such as counting and adding using representative objects in kindergarten. Through first and second grade they will have extensive practice with adding and subtracting one digit whole numbers along with learning many other skills and concepts. In third grade your child will be introduced to multiplication facts with which they will continue to develop mastery into fourth grade when they are introduced to division. The exact order and manner in which math facts and concepts are introduced varies with the curriculum your child’s school uses and math standards, which can vary from state to state, but the above is a general guide. This article is about how to practice basic, one and two digit math facts in the form of 5 + 4 = 9, 6 – 3 = 3, 7 x 4 = 28, and 12 * 4 = 3. Essentially, your child should demonstrate mastery of these types of facts by the end of fourth grade in order to be prepared for the challenges of more advanced math.
- Understand addition/subtraction fact families. Fact families are groups of three numbers that are related to one another. 4 + 3 = 7, 7 – 3 = 4, and 7 – 4 = 3 therefore the numbers 4, 3, and 7 have a relationship to one another and are considered a fact family. Point out to your child that 4 + 3 is the same as 3 + 4 (this reversal is true for addition, but not subtraction). Using this relationship in teaching math facts to your child will help them with the concepts behind the numbers as well as memorizing the facts themselves.
- Understand multiplication/division fact families. Likewise, fact families occur with multiplication and division. 6 x 7 = 42, 42 * 7 = 6, and 42 * 6 = 7. Again, 6 x 7 is the same as 7 x 6. This reversal is true for multiplication, but not division. Keep in mind that multiplication is introduced before division. It may be beneficial to practice multiplication facts before the multiplication/division fact families are introduced.
- Create or purchase fact family flash cards. You can cut out triangles from index cards or cardstock paper. Write each of the fact family numbers in each corner and the appropriate operation sign along the sides. Making these with your child will be a learning process in itself. Use an addition/subtraction or multiplication/division table as a guide in order to make a complete set. You can generate flashcards on some of the Web sites listed below. They can also be purchased where educational materials are sold.
- Your child should understand the concept behind math facts before being expected to memorize them. In other words, they should be able to visualize the concept and apply it to real life problems in order for it to really make sense to them. Using simple objects (such as Cheerios, M&M’s, pencils, or paper clips) your child should be able to represent 12 – 3 = 9 by physically moving the objects and actually seeing the problem. Likewise, if they know that 8 * 3 = 24 then the should be able to conceptualize (as in through a drawing) that if you have 3 pizzas with 8 slices each, then you will have 24 slices in total.
Build number sense concepts through practicing counting by 2’s, 5’s, and 10’s to 100 forward and backwards. This also helps your child to understand how numbers have patterns and how they are related. If your child can count: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, etc. then 5 x 7 = 35 will be grounded in a logical pattern. Referring to a 100 chart helps to make these patterns more visual. You can also have them fill in a blank number chart and you can check it for accuracy.
Check out sites below for blank and complete charts. Without these basic understandings they will have a bunch of facts in their head that are disconnected from real life. In addition, this kind of application of math facts is needed for academic success. There is an emphasis on word problems (also called story problems) in math curriculums and standardized testing.
- Knowing how and how often to practice is important. Flashcards are the staple of learning math facts. Change it up by using standard flashcards and the fact family flash cards. Make your own sets or purchase them. The standard cards usually cost a couple dollars and are available at the grocery store and discount department stores. Keep them handy. Have a set at home and a set in the car. Practice for ten minutes or so in a session. Isolate the facts that they know and don’t know. In other words, take out the cards that are easy for them or focus just on a certain set (such as 7’s multiplication facts) for a while. Start where they are and build skills. It doesn’t matter what they should know if you don’t start at a level that is just beyond what they can do now. Build up to where they should be. Don’t overdo it. It takes practice over time.
There are many games that practice math facts in fun ways. Some are available for free online (see links to sites below). CD-ROM versions are also available at office or computer stores and are less expensive than you may think. Workbooks are also excellent, as they will have the benefit of written practice. Instead of purchasing entire books, you can print your own worksheets as needed (from the links below) and keep them together in a folder or binder. Look for card or board games that apply the concepts or integrate them yourself into a favorite game. You can practice the math facts playing UNO, a popular and easy card game. When putting down a blue 3 on a blue 4, for example, the player has to say 7 if practicing addition facts or 12 if practicing multiplication facts. Fact bingo is another fun and easy way to practice. You could make your own bingo cards with the problems in random order written on the squares and the answers on the cards that you call out. You can have a separate set for addition, subtraction, multiplication, and division, or you could combine them if your child is ready for review. You can also purchase pre-made fact bingo sets. Look for real life situations to point out how you use math. The grocery store, paying bills, and using recipes are just a few places where you can highlight the use of the concepts. Be consistent, but don’t oversell it. Your child may start to tune out if you are talking about math facts 24 hours a day, 7 days a week— that’s 168 hours a week! Oh, I just did it.
- Counting on fingers shows lack of automaticity. If your child is counting on their fingers or drawing little groups of dashes and counting them in order to solve math facts, they do not have the facts memorized. If this helps your child to develop understanding of the concept in the beginning, then it is beneficial. Let them go through this stage. But eventually they need to ‘know’ the facts; they need to memorize them and give answers almost immediately.
- Speed is the name of the game. Why is it important to be able to complete a whole page of problems in two minutes? This speed reflects the rate necessary for doing more advanced math. For example, to complete a three digit by three-digit subtraction problem requires not only knowing the correct sequence of steps, but also applying knowledge of subtraction facts multiple times within one problem. Automaticity means they can rattle off the facts as readily as they can count to ten. It becomes a set of memorized information. Again, they should always be able to explain the concepts behind the facts, as word problems are a big part of math instruction.
- Track progress. The fun thing about math fact practice is that it is easy to track improvement. Your child’s teacher may be giving the timed drills as often as every week. Praise your child for their progress. If your child is catching up with their skills, get a hold of the quizzes and do them at home. Your child’s math teacher can probably give you copies, you can print them off the Internet, or purchase workbooks. Make it fun. Put stickers on quizzes showing success or a chart recording their advancement. Post them on the fridge at home.
- Look for improvement in other areas of math. As your child starts to increase proficiency with math facts, other areas of math should start to improve. Ask your child’s teacher about this and celebrate all of your child’s successes.
Helping your child learn their basic math facts at home is the best way to ensure a strong foundation from which to build their math knowledge. Slow, steady practice is the key to making progress. Be creative and make the practice as fun as possible and your child will get a positive message about their learning and develop good habits that will cross over into other academic areas.
Susan Niz, M.Ed.