Mastering Math Facts

› Math Facts

How to help children with mastering math facts, and the best ways to do it! 

We all know the students who have struggled with learning their basic math facts. Why is this?

They have continued to practice and take timed tests instead of developing their conceptual understanding of the foundations of math. Often they lack number sense and don't have an arsenal of efficient strategies to manipulate numbers.

Bear the dog waiting for his biscuit and thinking about mastering his math facts
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Memorizing Math Facts

Research shows that students need a conceptual understanding of math fact operations and algorithms:

  • before drills in each operation begin
  • after the concepts and algorithms, fact instruction requires brief drills on a daily basis
  • students need to know the goal is memorizing/mastering math facts
  • students should focus on a few facts at a time
  • students need immediate feedback
  • two key aspects of facts recall are accuracy and speed
  • teachers need to praise students on progress in memorizing facts, recording individual progress

Teaching and Learning Mathematics. 2000. March.

"Mastery of facts means that students are able to give a response in 3 seconds or less without using inefficient strategies."
~Van de Walle, 2001

Number Bonds

Number bonds are way to show both the part to whole and the whole to part method of learning about how numbers relate to each other. We want our students to instinctively realize that now matter how a number is broken up, it will always remain the same.

Being able to "make a 10" is also a critical component of mentally manipulating numbers. When considering a problem like 37 + n = 45, this can be quickly solved by realizing that:

  • 37 = 30 + 7
  • I know that 7+ 3 = 10 so 37 + 3 = 40
  • 40 + 5 = 45
  • I added a 3 and a 5, so n = 8

That type of thinking an problem solving is not unusual for a 7 year old child who is proficient with math facts, and it starts with using number bonds.  It's a great precursor to addition and subtraction facts.


number bonds for memorizing math facts
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You may be thinking that is too simple to be worth spending time on. Try it. You will be surprised at how many of your students do not understand what it really means to make a 10.

A game I like to play with Number Bonds that really helps with mastering math facts is called Roll A Bond.

  • All you need is one large dice and a whiteboard (or SmartBoard) with a blank number bond drawn on it. Put the number 10 in the middle circle, and tell the students that you are going to make a number bond that equals 10.
  • Roll the dice, and whatever number comes up, it goes into the top circle. The students then have to decide what number goes in the bottom circle to complete the bond.

You will be shocked at how many cannot do this, especially if you thought they understood their math facts.

Try giving each child their own whiteboard and having them do the numberbonds with you. Plenty of them will add the two numbers together instead of conceptualizing the whole to part.

I ended up taking three hula hoops one year to add in a more kinesthetic approach. I took 10 students at a time and rolled the dice. 4 of them moved into one hula hoop and the other 6 crowded into the other. Then we got back together as a group of 10, I rolled the dice again, and we split into two pairs again. It really took 4 rounds of this moving in variations of 10 before many of them finally got it. But it sure did pay off in future lessons!

You can always differentiate by creating number bonds up to 20 or 100 - just keep them in multiples of 10, and only do this after the students have had many opportunities to become proficient within the concept of making a 10.

The same strategies are applied for multiplication and division.

Math Timed Tests and Drills

The debate over timed tests gets as heated as handwriting and phonics.

I'll come right out and say that I am in the camp of doing timed tests...as long as the children have a solid conceptual understanding and have developed efficient processes for computing facts mentally

Timed tests help the kids gain automaticity, which means they are getting them right without even thinking about the process.  It is ingrained.

So I do timed tests because I think they have value.  I believe that kids have to engage in daily practice with known facts.

However...

1. 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.

2. 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.

Once your kids are mastering math facts, it is time to develop the automaticity that is necessary for success in the upper grades.




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