The process of teaching math facts is relatively simple and straightforward. It involves gradually moving children from the concrete (manipulating actual objects) to the abstract (solving math problems on paper). There are six basic steps which can be used to teach any mathematical operation (addition, subtraction, multiplication, or division). These steps help children scaffold their knowledge (build on the information they already know), and increase their confidence and enthusiasm as they experience success at each point along the way. The first five steps ensure that children understand the meaning of math facts and have a variety of problem-solving strategies they're comfortable with. In the final step, children will become proficient at math fact memorization through regular, ongoing practice.

Use simple manipulatives or household objects to enable children to see why basic math facts are true. Show two blocks in one pile and three blocks in another. Push the two piles together, and ask the child how many there are altogether. Practice this with a few different amounts to build confidence, then introduce the terminology. For example, you might say, "You took a pile of 4 blocks, and added a pile of 2 blocks. Now we have one big pile of these 4 blocks plus these 2 blocks. We have 6 blocks! You just figured out that 4+2=6!"

When children are comfortable with using concrete objects to find the answer to basic problems, begin writing down the facts they solve. "You had 8 cubes and you took away 3 cubes, leaving only 5. You solved 8 take away 3 equals 5. Here's how to write that: 8, then this line, which is a symbol for taking away, then 3, then these two lines which are called an equal sign. At the end we write 5." Continue solving problems with concrete objects and have children practice writing down the equation (number sentence).

Instead of presenting the math fact verbally and writing it down after children have solved, you can now begin presenting the problem in a written format first. Write a math fact on a piece of paper or whiteboard, and have children solve using concrete objects. Have the child complete the number sentence by writing the answer. Practice this step until children can reliably find the correct answer using concrete objects.

Tell children you have some other strategies (ways) to solve math facts that are even faster than using manipulatives. Introduce one strategy per lesson so that children do not become confused. Strategy examples include: counting on one's fingers (a perfectly acceptable method for beginners); drawing pictures of objects, making tally marks; using a number table (such as an addition chart or multiplication table); using a calculator; and memorizing. Emphasize that there is no one right method for solving a math problem, and encourage children to use the strategies that are most helpful for them.

Over time, most children will notice that memorization is the fastest strategy for solving math facts, although you may need to point this out explicitly for some children ("You didn't even have to draw a picture for 2x3! Imagine how quickly you could solve problems if you had more multiplication facts memorized!"). With this realization and some encouragement, children will become eager to master the skill. Flash card games are an extremely effective method for helping children memorize math facts, and with groups of children, can be practiced in pairs. Set a timer for three minutes, and see how many cards children can correctly answer in that time, sorting the cards into a 'correct' pile and 'incorrect' pile. When the timer goes off, count the number of correct cards and note progress (perhaps through a chart or graph). Review the incorrect cards again, adding them to the 'correct' pile once the child provide the right answer.

Provide daily math fact practice through a variety of activities so that children do not lose interest. Timed math drills with worksheets are very popular with most children, as kids enjoy seeing how many math facts they can solve in a set amount of time. Computer games can also be helpful. Provide a choice of activities so that children will be motivated, and insist that some math fact practice be completed everyday for 2-10 minutes. When children have learned multiple operations, they may alternate days of practice (addition on Mondays, subtraction on Tuesdays and so on).

#### Tip

When teaching subtraction, instruct children to use the word 'minus' in place of the phrase 'take away' as soon as they are able to understand how the operation works. This will prevent them from being confused when solving word problems in which they are not 'taking away', but must 'find the difference' or determine 'how many more'.

#### Warning

Learning math facts is difficult when children have not mastered rote counting (naming numbers in order), one-to-one correspondence (recognizing that each object correlates with one number), and number recognition (understanding that a written numeral '4' refers to four objects). Be sure that children are proficient in these skills before teaching any operations.