Making Connections in Mathematics
From the very first week of school, the fourth graders in my building have been practicing their multiplication facts. They learned them in third grade, of course, but they needed review at the start. Once they began to remember the facts, I began focusing on their fluency. We do a weekly 20-question multiplication quiz on the computer that is timed. (I gave them five minutes the first time, then three, and then have held it steady at one minute for quite some time now.) The quiz is graded quite easily and I am able to record to scores and monitor growth. Additionally, they are tested on all 100 of the facts about every 4-6 weeks on a six-minute test done in the classroom. These scores are also recorded and tracked. To continue to increase fluency, we will play games like Around the World with twelve-sided dice. The results have been outstanding! I am so very pleased to see how many students have mastered their multiplication facts!
When we first started working on division a couple of months ago, the students quickly saw the connection between multiplication and division as inverse operations of each other. But we have continued to practice the multiplication facts. Today, though, was one of the first times that several suddenly caught the importance of these facts in other areas of math.
We are working on a variety of topics related to fractions during our Mix-Up Math groups and I have been teaching my two groups how to identify factors so that they can simplify fractions. While listing the factors of numbers such as 12, 18, 24, 36, 49, and 100, they figured it out: the factors of 12 are 1, 2, 3, 4, 6, and 12. They know these because they know their basic facts: 1×12=12, 2×6=12, 3×4=12, 4×3=12, 6×2=12, and 12×1=12. Likewise, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 because 1×24=24, 2×12=24, 3×8=24, 4×6=24, 6×4=24, 8×3=24, 12×2=24, and 24×1=24. Then they realised that 12/24 can be simplified to 6/12, which can be simplified to 3/6, which can be simplified even further to 1/2. By using the basic facts, they can identify common factors and find equivalent fractions.
It was a very simple connection, but one of great importance: if they know their basic multiplication facts, they can find equivalent fractions, simplify fractions, write fractions in simplest form, compare fractions, and order fractions! They will also be able to use equivalency to find common denominators in order to add and subtract fractions! As we started touching on the different skills they will be working on, the connections were being made and my students finally understood why we put so much emphasis on mastering the multiplication facts! There really is a method to the madness and a reason for the things we do!