Teachers and parents often want their children to know their addition and subtraction facts so well that they can regurgitate them instantly. In an attempt to accomplish this rote learning feat, children are subjected to flashcards and timed tests. However, research shows that a different part of the brain is involved in rote memory compared to mathematical thinking.
In fact, the only person who likes flashcards is the person who doesn’t need them. For those needing the practice, a missed flashcard reminds them of what they don’t know. An unintended unfortunate outcome of flash cards and timed tests is math anxiety.
Rote memorization has its place in learning, but mastering addition and subtraction facts is not one of them.
So, how should we help students learn their math facts? By teaching them strategies.
Strategies to Learn Addition Math Facts
Addition is more than just memorizing a numeric symbol plus another numeric symbol equals a different numeric symbol. One way to think of addition is finding a whole amount when two or more parts are known and understood. Students who understand place value find it easier to learn the sum of two numbers. Basic addition math facts, 1 + 1 through 9 + 9, are best learned through visualizable strategies and frequent practice and use.
Group by Fives
Before learning the addition strategies below, the student must first be able to recognize quantities, specifically the ability to group in fives, like the fingers on their hands. When introducing an addition strategy, the student must be encouraged to use concrete objects grouped in fives. Over time, the student can mentally visualize eliminating the need for concrete objects. For example, if you were asked to add 4 + 3, imagine a group of 4 objects and then imagine another group of 3 objects. Then imagine taking one object from the group of three objects and giving it to the group of 4 objects. So, now you have one group of 5 and another group of 2, which you know as 7.
Let’s look at another example. If asked to add 7 and 3, you can first think of 7 as 5 and 2. The 2 combined with the 3 makes another 5. And you know that 5 + 5 is 10. In written form, this equation looks like this:
7 + 3 = (5 + 2) + 3 = 5 + (2 + 3) = 5 + 5 = 10
While this equation appears complicated, this process is quick and efficient when working with objects. Students do not need to write out the process in equation form.
Two Fives Strategy
A strategy to use for slightly larger sums is the Two Fives Strategy. Here’s how this strategy works with problems such as 7 + 6. First, consider 7 as a group of 5 and 2 and 6 as a group of 5 and 1. The Two Fives Strategy (hence the strategy name) is 10 and 2 plus 1 is 3. This gives us a sum of 10 + 3 or 13. Children can use their hands while using this strategy. When they think of 7, they show two fingers on their left hand. When they think of 6, they show one finger on their right hand. They combine the two fives and add their raised fingers, giving the answer as 10 + 3 or 13.
Make a Ten Strategy
Another great strategy to teach is Make a Ten Strategy. With this strategy, students take a sufficient amount from the smaller number to make the number into a 10. Let’s look at 8 + 8 as an example. We can take 2 from one of the 8s and give it to the other 8 to make 10. This gives us 10 + 6, which is 16.
Should we teach the Doubles Strategy? One textbook author suggests that students find the doubles easier to learn. However, I believe that children learn the doubles math facts faster simply because teachers and parents have the students practice them more frequently.
It is important to remember that a child is considered to know a math fact if they can answer it in 2 to 3 seconds, not necessarily instantaneous. The teacher and parent should give the student enough time to process the math fact and the appropriate strategy to solve it.
Strategies to Learn Subtraction Math Facts
Subtraction can also be thought of as modified addition: finding one of the parts when given the whole and another part. For example, when looking at this math fact, 3 + ___ = 7, we can see that 7 is the whole and 3 is a part. What is the other part? Four. We can also write this equation as 7 – 3 = ___. When stating this equation, avoid saying, 7 take away 3. This is incorrect grammar. In addition, students can often learn subtraction math facts when they think of it as addition. Instead, when stating subtraction math facts, use the term minus, such as 7 minus 3.
Three subtraction strategies will help students master math facts: Going Up Strategy, Taking Part from Ten Strategy, and Taking All from Ten Strategy. To prepare students for these strategies, make sure they understand that 15 is 10 and 5. Let’s explore these strategies by working through the math fact of 15 – 8.
Going Up Strategy
When using this strategy for 15 – 8, we first start with the 8. Then consider that 2 can be added to 8 to get to 10, and 5 more is needed to get to 15. So, 2 + 5 is 7; therefore, 15 – 8 is 7.
Taking Part from Ten Strategy
For the math fact 15 – 8, we will start by partitioning 8 into easy to subtract quantities, such as 5 and 3. So, 15 – 5 is 10. Then subtract the remaining 3 from the 10, leaving 7 as the difference.
Taking All from Ten Strategy
Again, we will use the same math fact of 15 – 8 to explore the Taking All from Ten Strategy. For this strategy, we will subtract the entire 8 from the 10 first and discover we are left with 2. Then we add the 2 to the remaining 5 from the 15, giving us a final difference of 7. The Taking All from Ten Strategy was used in the Middle Ages. Using this strategy, they did not need to memorize subtraction math facts that had a minuend between 11 and 18.
Jo Boaler, a Stanford mathematics professor and author (2015), makes a strong case for having good mental strategies when learning addition and subtraction math facts when she states the following:
I have never committed math facts to memory, although I can quickly produce any math fact, as I have number sense and I have learned good ways to think about number combinations. My lack of memorization has never held me back at any time or place in my life, even though I am a mathematics professor.