Addition and Subtraction Strategies

When working on the addition facts stress the commutative property in which 6 + 2 = 2 + 6.  Be sure to point out that although the order of the addends is different, the sum is the same.  This way, your child will know twice as many facts!  Begin working on the addition facts, naming the related subtraction facts as you practice each fact strategy.  Focus on the subtraction facts themselves once your child feels confident with adding.  His or her familiarity with the fact families will make learning the subtraction facts much easier.

+0:  Show that when zero is added to a number it doesn't change the total.

+1, +2, and +3:  Practice counting on (or counting back, for subtraction) by 1, 2, and 3.  For example, to know 6 + 2, your child can say 6, 7, 8.  It is easier to begin with the larger addend when counting on.  For example, when adding 3 + 8, begin with 8 and count on to 11.

Doubles:  The doubles facts come very easily for children.  They are 0 + 0, 1 + 1, 2 + 2, ...  Help your child see that the sums are always even numbers, or counting by twos.  The doubles facts serve as benchmarks for the doubles + 1 facts and hidden doubles, so knowing them well can help your child learn a significant number of facts.

Doubles + 1:  These facts are those where there is a difference of one in the addends, such as 4 + 5, 7 + 6, and 8 + 9.  Your child can use doubles to figure out that if 4 + 4 = 8, then 4 + 5 must be one more, or 9.  Have your child model this idea with materials or drawings as many times as needed until you are sure it makes sense to him or her.  When practicing these facts, it may be helpful to ask your child to name the double so that you are sure he or she is making the connection between the doubles and the doubles + 1 facts.

Hidden Doubles:  Think of 6 + 4 as 5 + 5.  Again model this idea so that your child can see that with these facts they can make each addend the same by taking from one and giving to the other.  This is a more challenging strategy for many students to grasp.  If it seems to cause more confusion than help, move on to another strategy and revisit this one later.

Finding a Hidden Ten:  If your child knows the ways to make ten (1 + 9, 2 + 8, 3 + 7, and 5 + 5), it can help when learning larger sums.  For example, 8 + 5 can be thought of as (8 + 2) + 3.  The 5 has been broken apart so that a ten can be made.  The it is easier to think of 10 + 3.

+ 9:  Adding 9 to a number can be thought of as adding 10 and subtracting 1.  For example, 6 + 9 is 15 because 6 + 10 is 16, minus 1 equals 15.

Keep in mind that these are suggested strategies.  Some may work better than others, and your child may discover yet a different strategy that works well for him or her.  At first, your child will need time to think through each fact strategy, but with practice it will take less and less time. 
In some cases, facts may be approached using a combination of strategies.  For example, 7 + 5 can be thought of as a hidden double or hidden ten.  Ask your child how he or she is thinking about each fact so you know which strategies seem to make the most sense.  Always encourage your child to use the strategies that work best for him or her.

It may be helpful to keep track of the facts explored by your child on a 10-by-10 grid such as the one found on this page.  As you and your child practice a set of facts, write them in a different color on the grid.  You may also want to make flash cards that are color coded by strategy as well.  For example, the doubles facts can be written green on the grid and also on green index cards.  This way, if your child would like to focus on one strategy or group of facts, they can be easily identified.  You can download a blank grid so you can fill it in as your child learns new facts.

Source:  Montgomery County Public Schools. 1996.  Mathematics at home:  A guide for parents, grades K-2.  Rockville, MD:  Author.