To Master Basic Math Facts: Strategize, Then Memorize
February 18, 2014 Carol R. Rinke and John F. McAdam, Marist College
Nothing may be more feared in the minds of young children and their parents than learning the basic math facts. Just hearing the times tables takes many of us back to our own childhoods, staring at a blank page and trying to remember the dreaded 9 x 8 = 72. The good news is that our own children should not have to suffer the same fear. A substantial amount of mathematics education research shows that children do not master their math facts through memorization alone. Instead, true mastery comes from being equipped with quick and effective strategies for finding the solution. By using these strategies, children will always have the mental tools needed to find the correct answer and the confidence to use them.
With a strategy-based approach to the basic math facts, children use what they already know to figure out what they don’t know. Rather than racking their brains to remember the answer to a basic math fact, they can simply find a “helping” fact and use it as a jumping- off point. For example, let’s say that your child knows the common fact 5 x 5 = 25. She can then add one more 5 to figure out that 6 x 5 = 30. Think of this as the “one more than” strategy. There are many such strategies that parents can teach their children in order to equip them with the tools they need to master all of their math facts. As a parent, remember that as long as your child can figure out an answer quickly in her head (in about 3 seconds or less), she has mastered the fact and can use it in meaningful ways as part of her daily life.
Some of the most common strategies for basic fact mastery include:
1. Skip Counting – Perhaps the simplest strategy that children can begin learning at an early age is skip counting, that is, counting by 2s, 5s, 10s, etc. Skip counting is fun to do and children begin to hear patterns in numbers. When paired with a chart (such as Figure 1), they can even begin to see those patterns. For instance, when skip counting by 10s, see if your child notices the pattern that all the numbers end in zero!
2. Make 10 – A useful way for children to think about numbers is in relationship to 10, which can serve as a mental anchor for them. For instance, when children are learning the math fact 14 – 6 = 8, they don’t need to subtract 6 all at once. Instead, they can first take away 4 from 14 to make 10 and then take away 2 more from 10 to equal 8.
3. Doubles and Near Doubles – Many children are already familiar with doubles facts. They know that 3 + 3 = 6, for instance. They can draw upon their knowledge of doubles and simply count one more to figure out near doubles such as 3 + 4 = 7 (illustrated in Figure 2).
4. Nines – Multiplying by 10 is often clear even for young children. Because nine is so close to 10, 9 facts are fairly straightforward to work out mentally. For instance, if a child knows that 10 x 7 = 70, they can take away one 7 to figure out that 9 x 7 = 63. Nines also have lots of patterns to explore together.
5. Commutative Property – This is the mathematical way to say, “you can add or multiply numbers in any order and you get the same answer.” Based on this property, if your child knows 3 + 2 = 5, then he can solve 2 + 3 = 5 (illustrated in Figure 3). Taking this approach cuts the number of addition and multiplication facts in half!
6. Use Fact Families – Children know that addition facts are connected to subtraction facts, and multiplication facts are to division facts. Therefore, it is helpful if they learn their basic facts as part of “fact families.” For instance, an addition and subtraction fact family might include 7 + 8 = 15 as well as 15 – 8 = 7. Using this approach, again, cuts the number of math facts in half.
7. Make it Real – Finally, don’t limit your practice of basic math facts to traditional flashcards. Instead, play math games and point out math relationships in real life. For instance, while your child is racing toy cars, you might show him that each car has 4 tires and ask how he could quickly figure out how many tires are on all 6 cars without counting each one. Then, ask him how he came to his solution and make math something that you talk about together every day.