When I was teaching elementary math in Southern California one of my favorite teaching aids was the hundreds chart.  I would burn up my photocopying budget reproducing hundreds charts so my students could color patterns showing the multiples of 2, 3, 5 or 7.  It really comes as no surprise to me that Hands-On Math Hundreds Chart is one of my favorite apps.  No longer is necessary to provides students with paper hundreds charts.  Using the app students just pick a color and a marker and then away they go marking patterns on the chart.

The interface is intuitive.  The markers function like objects and can picked up and moved.  To complete remove an object simply drag it off the chart.

A Teaching Tool

So what can you do with a hundreds chart?  Which concepts can you teach?  One of the first activities to do with young students is skip counting.  Pick a color and a type of marker.  To count by 3’s, for example, begin by tapping the cell labelled ‘3’ and then continue to 6, 9, 12, 15, etc.  Eventually a pattern begins to emerge.  Perhaps some of your students will discover that the pattern for 3 creates diagonal lines.  Encourage students to use math vocabulary in describing their hundreds chart explorations.

But more can be done with a hundreds chart.  Marking patterns to show multiples of a given number is a great way to practice and learn multiplication tables and it is easy for teachers to check students work with just a glance at the iPad screen.  But there must be more that can be done with a hundreds chart.

Least Common Multiple

The reason the Hands-On Math Hundreds Chart app has 8 colors and 6 shapes is so that overlapping patterns can be created on the chart.  When kids start overlapping patterns things get really interesting, mathematically speaking.  Understanding Least Common Multiple, in my mind, is an essential skill for success in mathematics.  Using Least Common Multiple (LCM) students can reduce fractions to simplest terms.  LCM is the smallest positive integer that is evenly divisible by two other numbers, a and b.

Let’s define a as 3 and b as 5 (which also happen to be two prime numbers, but more on that later).  Here’s what the chart will look like after a pattern for 3 has been marked with a red square.

Now let’s overlay the pattern for 5 with a blue circle.  Things are starting to get interesting…

At this point a teacher would want to ask the students to find all the numbers that got both marks, the red square and the blue circle.  I would recommend that the students mark these numbers with a yellow highlight (transparent yellow square).

Wow! Look at that the yellow highlighted numbers also make a pattern.  This numbers are the common multiples of 3 and 5.  Now study the chart and find the smallest number in this set.  15 is the LCM of 3 and 5.

Find the LCM of other numbers.  Just tap the eraser to completely erase the chart. Oh, and remember, if you only want to remove one marker just slide it off the chart.

A Classic Lesson

The first 4 prime numbers are 2, 3, 5, and 7.  In mathematics, the sieve of Eratosthenes is a pattern that reveals the prime numbers.  To investigate the pattern on the Hands-On Math Hundreds Chart, begin by marking the pattern for the number 2 and then we will mark 3, 5, and 7.  The procedure involves skipping the first number in the series and then marking out all the multiples.  So, skip 2 and then more out 4, 6, 8, 10, etc.  The chart should look something like this:

Use a different color for each number.  Now mark out the pattern for 3, but remember to not mark 3 since it is also prime.  Continue by marking the patterns for 5 and 7.  If a number is already marked just skip it.  Since the next prime is 11 and 11² is 121 so not on the chart and we don’t need it for this experiment.

When the marking procedures are finished, the chart should look like this:

The numbers that did not get marked are prime numbers.  All the marked numbers are composite numbers.

Get Creative!

There are lots of ways to make math fun using Hands-On Math Hundreds Chart.  Make up your own problem sets so that when the problems are answered correctly a picture is created.  For more information about this app click here.