The Power of Five ... Helping Young Learners With Marh Fluency

We are always looking for ways to improve our students' math fluency. The constant lament that children cannot do times tables is a familiar one. The force feeding of number operations is both tiring and very time consuming. On the other hand students do need a degree of facility with numbers and if we as teachers can get there with a little slight of hand so be it. The following is not designed to be a panacea for all of our computational issues but merely a tool to get students thinking about numbers.

There are a number of  "short cuts" that we can use that I have found children enjoy and handle with a certain amount of ease. One, I call, for lack of a better label, is the Power of 5. Very simply  put, I ask a class of grade 5 or 6 students, what is the answer to 5 x 18. Usually the wheels start grinding and upon asking what is the process taking place inside their brains. I hear a variety of responses, such as, "I'm multiplying 5 x 10 and 5 x 8 and adding the two answers together".  Many will tell you they are doing the traditional algorithm. This and other strategies are fine of course. However ask them what is half of 18. The answer 9 is quickly given. Place a zero after the 9 (0). Try 5 x 14, 5 x 16. Smiles ...  as the solutions are found easily. This is the starting point. Odd numbers can be mastered with a bit of practice but a lesson in developing a facility with them is the second step in this strategy.

Move to more challenging questions 5 x 68 and 5 x 124. Now we do an interesting thing, I ask my students to read the number as they read a sentence from left to right. Now ask yourself what is half of each digit ... 6 > 3, 8 > 4, the answer 340.   It is a real joy to see children who struggle with numbers tell you how easy it was to find half of 64 looking at the number this way. Now with 124, reading left to right. If the first digit is one join it with the second digit (12) and find  half  > 6, half 4 > 2, the answer is 620. Try a very large number 2 684 428. Students get a kick out of doing this without a calculator. The answer is  13 422 140. Now as a bonus you have then reading a very large number. And you will see the light come on for some of the students who find number operations a challenge. With today's access to worksheets programs it is easy to reinforce this concept.

Teachers and  parents need to be aware that doing this gets students thinking about numbers in a non-traditional manner and that is always good!

The best results I have found with this is the use of short, maybe 15 minute teaching blocks 2 to 3 times a week to get students doing these automatically. Step 1 the multiplication of even numbers is mastered quickly, step 2 working with odd numbers will be addresses  in the next article/blog. Be prepared to answer why we add zeros.

Initially this may seem to be a very simple or basic concept  but having explored it in some depth we can take this a long way. Think, are not multiplication and division opposite operations? How does this apply to what we are doing?  Also we can challenge students to see 25 or 75 can be connected to what we are doing, working with decimals is obviously a big part of what we are doing.