Mastering Math Facts

Mastering math facts is a process. There are ways to practice math facts that support the best way to teach children mathematics.

It is because they have not been taught strategies they can use for learning their basic facts.

They have continued to practice math facts and take timed tests instead of developing their conceptual understanding of the foundations of math.

They lack number sense and strategies to manipulate numbers.

We need our students to be mastering math facts. There is solid research for this:

The research shows students need a conceptual understanding of math fact operations and algorithms:

Math Timed Tests and Drills

"Do not subject any student to fact drills unless the student has developed an efficient strategy for the fats included in the drill...Drill prior to development of efficient methods is simply a waste of precious instructional time," (Van DeWalle, John A. Elementary and Middle School Math).

Students must have regular, daily practice with their facts.

1. This is not mastering math facts. This is daily practice of skills and strategies students are developing.

2. These tests are not graded. They are practice only. The goal is leading to fluency. The students first work on getting all of the problems correct within a certain time, then they work on increasing their speed.

3. I make sure each student has an efficient strategy for learning math facts (finger counting is not efficient) before allowing them to do a timed "test."

My students view these daily practices more like math fact games.

The problem with rote work comes when it is used exclusively for teaching math facts. Research shows that overemphasizing memorization and frequently administering timed tests is actually counter-productive, (National Research Council, 2001).

So...drills and rote work have a purpose, but it is not to teach children mathematics. Never keep a child from moving on with meaningful math experiences simply because they are struggling with their basic facts.

Strategies for Memorizing Math Facts

First concentrate on strategies and concepts.

Over time, most students will develop their own efficient techniques that will lead to automaticity, which is mastering math facts.

We'll start with specific strategies for math addition facts, then you can click over to the next page for more strategies for mastering math facts in subtraction, multiplication and division.

Math Addition Facts

Use the doubles as a starting point for math addition facts. For example, 4 + 4 and 6 + 6 are easier for a child to remember. Then teach them how to use these doubles as a strategy for solving other combinations, such as 4 + 5 and 7 + 6.

You must be explicit with showing your thinking. Say, "This is what I did in my head while solving this problem. I know that 6 + 6 = 12, so I first used my doubles," (write or draw this on the board). "Then I added one more to the sum since 7 is one more than 6," (again, show this on the board). "That gives me a sum of 13. 7 + 6 = 13."

2. Counting on

"Counting on" is efficient only when the number being added on is less than 5. If we use it beyond addends of 5, children start to use their fingers, which is reinforcing an inefficient strategy. Always begin from the larger of the two numbers.

3. Ten Frame

These are some of the easiest facts to memorize. When learning math addition facts that make a ten, use a Ten Frame for create a visual image.

This is highly important for students who have difficulty with using their gestalt imagery for manipulating numbers. These students lack a concrete image of what numbers look like while they are being added.

The Ten Frame below shows a visual image of 7 + 3 = 10.

Let's use the example of 6 + 2. Using number cubes, make a set of 6 and another set of 2. Join them together (the two sets become one), and count the joined set.

Be sure to point at each cube as you and the student counts.

5. Make a Ten or Using a Ten

Students use the knowledge built from a Ten Frame to find the sums of larger numbers. Using this strategy, we can teach students to use the derived fact of "what makes a ten" to solve the equation.

For example, to find 8 + 3, teach the student to decompose 3 into 2 + 1. Use that to show them that 8 + 2 = 10. 10 + 1 = 11, so 8 + 3 = 11.

A more advanced way could be: 14 + 9 = 9 + 1 + 10 + 3 = 10 + 10 + 3 = 23.

While this may seem to take a long time, with practice it becomes a very efficient method for calculating the sums of larger numbers and mastering math facts.

Remember that different strategies are used by different students. There is no strategy that is perfect for every child. Students need to choose the strategy that works best for them.

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