Hi Mrs. Brooke,

My daughter is a second grader and I am wondering about how to help her with basic math facts. In her homework, I can see they are working on a variety of strategies (such as making 10) but she continues to rely on her fingers. She does count on from the larger number. I am wondering if using fingers is okay given her age? In addition, what strategies do you suggest for helping make the transition?

Katie Vice Trierweiler

Dear Katie,

This is a great question, and as you know, a very important one as knowing basic math facts will be so important as your daughter is met with more difficult math problems in school and in everyday life.

Typically the developmental continuum for solving basic math problems and improving computational fluency moves from concrete to abstract, so from using fingers, to objects, to pictures, to symbols, and then to memorization. Your daughter’s current strategies are very developmentally appropriate, especially given that she’s already counting on from the larger number. By the end of second grade, students should be fluent in their facts to 20, which requires that students are typically not relying heavily on their fingers as tools.

I am encouraged to hear that your child’s teacher is teaching a variety of strategies to teach basic math facts rather than just relying on flash cards or time tests. Although these methods might be effective for maintaining knowledge or improving computational fluency, they are not the most effective methods for a student to understanding math facts.

Second grade teacher Andrea Rulon says, “The most important thing that I stress is that for most kids, simply memorizing facts with flash cards is not going to help them really learn or understand the facts.”

Below are some strategies for teaching mastery of basic facts. These are what many second grade teachers I know, including Mrs. Rulon and the second grade team at Ben Franklin Elementary, teach students and recommend to parents in order to help with this basic fact understanding.

Here are some strategies for teaching mastery of basic facts:

Adding zero

When you add zero you add nothing. Make sure this understanding is in place.

Adding one (counting up)

Adding one means saying the larger number, then jumping up one number, or counting up one number. This happens every time you add one. It never changes. Never recount the larger number, just say it and count up one. Examples: 6+1=say 6 then 7, 44+1=say 44 then 45.

Adding two: Count up two

Adding two means saying the larger number, then jumping up or counting up twice. Examples: 9+2=say 9 then 10 then 11, 45+2=say 45 then 46 then 47

Commutative property

You also have to teach or review the commutative property. The answer will be the same regardless of the order you add the two numbers. 9+2=2+9 Order doesn’t matter.

Adding 10

Adding 10 means jumping up 10 (think of a hundreds chart). The ones digit stays the same but the 10’s digit increases by one. Examples: 5+10=15, 10+7=17

For older students you can relate this to higher numbers: Example 23+10=33, 48+10=58

Adding 9

Adding 9 makes sense if students understand adding 10. It sounds more difficult than it actually is. Remind students of the jump of 10–5+10=15. A student would say (in their head) “5+10=15.” The five and 15 are naming the same number of ones. With the nines,  a student must count down one in the ones. A student would say “5+9=14.” Work with lots of examples until the idea is understood:

5+10=15, 5+9=14, 7+10=17, 7+9=16

Adding 9’s another way

It should be pointed out to students that when adding nine, the ones digit in the sum is always one less than the number added to 9. For example 7+9=16, the 6 is one less than 7. Another example, 5+9=14.

Adding 8

This works exactly the same only a child must think 2 less. Using the examples above students would say; 5+10=15, so 5+8=13, 7+10=17 so 7+8= 15 (2 less)

Double numbers

To add double numbers there are a couple of strategies that might help students. When you add a double you are counting by that number once. For example: 4+4= think of 4, 8 counting by fours. Practice skip counting by each number in turn: 2-4, 3-6, 4-8 etc. This gets harder with the higher numbers but skip counting is an important skill for students to have.

Doubles occur everywhere in life. For example: an egg carton is 6+6, two hands are 5+5, 16 pack of crayons has 8+8, two weeks 7+7, legs on an insect (3 on each side) 3+3.

Near doubles

To use the near doubles strategy a student first has to master the doubles. Then, if the double is known, they use that and count up or down one to find the near double. Example: 4+4=8, 5+4=9 (count up one) Or: 4+4=8, so 4+3=7 (count down one)

Doubles plus two

This method works when the addends differ by two. When this occurs it is possible to subtract 1 from one addend and add one to the other addend. This results in a doubles fact that has already been memorized, 7+5 becomes 6+6.

Adding 5

Adding five has a strategy that is helpful but not completely effective as it is a bit tricky. You can decide if it is helpful or not. To add fives look for the five in both numbers to make a 10 then count on the extra digits. Examples: 5+7=(10+2)= 12, 5+8=5+5+3=13 Students who can see the five in 8 should have no difficulty. Students who can’t visualize numbers will find this hard. Most students can be taught to do this with some extra work.

Also, as a teacher and a parent I remind myself whenever a child in my class or even my own child is not catching on as quick as I hoped maybe I need to stop and think about this individual child and how that child learns best. Howard Gardner, a Harvard researcher, believes that there are eight intelligences – or ways kids learn best that include: musical, spatial, logical-mathematical, linguistic, bodily, intrapersonal, interpersonal and naturalist.

So, for instance maybe a math fact song would work if your child is musical. Does your child love the outdoors and is more of a naturalist? Go on a walk and collect sticks, use the math strategies with the rocks by the river. If she is artistic, get out the paint and have her create a number story and visually see the connection. Have her draw pictures and eventually move to symbols like tally marks, which are faster to draw and count. Is your child interpersonal and craves the social interaction with another? Play games and it doesn’t have to be anything fancy or expensive. There are many math games that teach the basic math facts, which require only a typical deck of cards or regular dice. Here are just a few I used with my second grade students:

Mental Math with Playing Cards (Number Sense)

Predetermine the “rule” of the game, such as “Add 5” or “Double it.” Prepare a deck of cards by removing all the face cards and jokers. Then have the child turn over one card at a time and apply the “rule” then give the answer.

Find Ten (STRAND: Number Sense-Addition: Finding Tens)

This is a math game similar to Concentration. In this game, children try to make a 10 by turning over combinations of cards that total 10. Variation: Use jokers or face cards as wild cards.

Other games include playing the card game War with two cards instead of one, Yahtzee, and rolling two dice adding them together. Games are always an effective tool to use to teach, maintain, reinforce, and most of all keep learning fun!

Although research has failed to identify any difference between girls and boys math skills, studies have found that girls often receive less encouragement in math than boys. They also are affected more than boys when having female role models/teachers in their lives who display anxiety about math.

The fact that you are willing as a mother to reach out and learn strategies in order to help your daughter master her basic math facts may have more of an impact than you may know. Your eagerness and positive approach on math could ultimately alleviate years of anxiety and produce a child who loves math, enabling her to enter and find success in fields of technology, science, engineering, and math in the future if she so chooses. As your child’s first and most important teacher, with your continued support and encouragement in math, your child will stop counting on her fingers and instead be counting endless opportunities.

Joy Brooke is the first and most important teacher of her 5-year-old son and 3-year-old daughter. She resides in downtown Kirkland with her husband and two children. Brooke is a National Board Certified teacher in Literacy: Reading- Language Arts/Early and Middle Childhood, holds a B.A. in Educational Studies and a M.A. in Educational Policy and Management from the University of Oregon. The opinions provided in this column do not reflect that of the LWSD or any other organization she is affiliated.