We hear all the time now about how math is not fun. I firmly believe that math is fun, and the way to show it to students of today is to expose them to the problem solving side of mathematics.This series of blog posts lays out several ways to illustrate the fun side of math, with some concrete illustrated exercises.
There is a second very important objective behind these posts. We are at a new turning point in our usage of computers – they are now coming into our homes, cars, everywhere and automating much of the repetitive portions of our lives. This means that the jobs of tomorrow are going to demand more and more serious problem solving skills.
In this post, we talk about helping kids discover beautiful patterns in math.
Help kids discover beautiful patterns in math
One of the things that makes math really fun and engaging is the discovery of amazing patterns, some of which are not always immediately obvious. It’s what creates beauty in mathematics. And it is possible to create exercises that allows or helps kids to discover these patterns. The learning created through self-discovery will stay in their mind for a long long time. Below are some examples of such exercises. We’ll start with a medium difficulty example, and then illustrate some simpler activites that are possible for younger kids.
- Question to ask students : What is the sum of the first 2 odd numbers, first 3 odd numbers, first 4 odd numbers, first 5 odd numbers and so on.
1+3 = 4
1+3+5 = 9
1+3 +5 +7 = 16
1+ 3+ 5 + 7 +9 = 25
1+3 + 5+ 7+ 9 + 11 = 36
Do we see a pattern here ? What pattern do we see ?
Answer : The sums are squares of 2,3,4,5,6 .. and so on. Isn’t that amazing !
Follow-up question : Can you illustrate why that happens ? Below is a diagram that shows it beautifully, in a proof without words
2. Here’s another example. This is a really fun way to practice multiplication, and observe patterns, and learn about prime numbers.
Step 1 : Let’s start by creating a hundred board – this is the numbers 1-100, is rows of 10.
Step 2 : Then let’s color in all multiples of 2, let’s say with the color yellow. Do you see a fun pattern on the board? Answer : All the multiples form alternate straight lines down the board.
Step 3: Now let’s color all the multiples of 3 on the board – with the color blue. The color blue forms a fun pattern on the board.
Question : What about all the cells that are the color green ? Can you tell what they are multiples of ?
Answer : They are multiples of 6
Question : Why do you think that is the case ? You didn’t deliberately set out to color the multiple of 6 green. It just happened.
Answer : Because 2X3 makes 6. And the color yellow and blue is on the squares with numbers that multiples of 2, and multiples of 3, and yellow and blue combine to make green. They may of course observe other patterns e.g. every alternate multiple of 3 is a multiple of 6, when you look down the columns, every 3rd number is a multiple of 3, just like in the rows. Discovering some of these patterns by yourself is very much why this is a fun and engaging exercise.
It is possible to continue to color the multiples of different numbers upto 10 this way, and make many different observations.
Step 4 : E.g let’s color the multiples of 4 orange ?
Question : Observe, do you color any white squares ? No ! Why ?
Answer : Because all the multiples of 4 are also multiples of 2, and hence they are already colored when we did the multiples of 2.
It is a similar observation with multiples of 8.
Similarly, you can observe patterns with 2 and 5 both colored.
Step 5 : Let’ s finish coloring all the multiples of 1-10.
Question : Are all of the squares from 1-100 colored ? No ! What can you tell about the numbers that are still white ?
Answer : They are prime numbers. They are divisible only by themselves and 1.
We hope you and children you teach enjoy these exercises. If you get a chance to try any of these exercises out, or like the approach or would like to see more ideas, do drop me a line via the contact page.
About the Author : The author is the founder of Minds On Play LLC, which creates educational logic puzzles games for kids and adults to develop critical thinking and problem solving skills.