Hello! This is Kelly from Little Green, writing to you once again from Sydney, Australia. Well, four hours south of Sydney, to be precise! It is summer in Australia and we are on our long summer school holiday break. I am writing this post from the beautiful beach-side suburb of Kioloa, on the south coast of New South Wales, where I am holidaying with my family. The sun is shining, and the sounds of waves crashing and cicadas chirping are almost deafening! To my left, tree-covered hills and ridges fill the landscape beyond the few rows of houses in this tiny town. To my right is the ocean, with the sun rising splendidly over the blue water. There is nowhere I would rather be right now!
But we’re not here to get jealous about my beautiful, warm, sunny location; we’re here for mathematical inspiration! And today I want to use one of my favourite math manipulatives as the starting point for that inspiration: the Hundred Chart. This versatile tool has been instrumental in the development of mathematical understanding in countless students. In fact, I would hazard a guess that pretty much every teacher reading this post used one when he or she was a student and has used one at least once with their own students.
Why has this particular tool stayed with us for so long when so many other great tools have come and gone? In my opinion, it is because it is both versatile and simple. Sure, you can buy a super-expensive, whizz-bang, high-tech Hundred Chart, but equally effective is a dodgy black-and-white blurry photocopy of a Hundred Chart, or even a hand-drawn Hundred-Chart on the back of a fast food store napkin! It is often the simple things that stand the test of time and become our constant companions in the classroom.
So, I’m dedicating this post to the Hundred Chart. May it continue to be our mathematical friend for many years to come.
Here are a few ways I use a Hundred Chart:
Using a Hundred Chart as a counting aid in the early years will help familiarise students with its use and provide them with an effective aid to help them ‘follow along’ with counting. I would introduce this tool with five-year-olds as soon as they have a firm grasp on the idea that numerals represent numbers and are beginning to count to numbers larger than ten. If you are working with numbers up to twenty or thirty, shield the lower numbers on the chart (with a piece of paper, for example) to allow your students to focus on the numbers they are working with.
Skip Counting Aid
Skip counting is a terrific precursor to multiplication. A Hundred Chart can be used as an aid to the skip counter. Begin by modelling this skill to students then have them ‘have a go’ on their own. Simply point to the numbers as you count and be sure to ‘notice’ out loud any obvious patterns (e.g. when counting by twos, you skip one number each time).
Looking for Patterns in the Times Tables
For me, Mathematics is all about locating patterns, looking for logic and making order. If our students can see the patterns in the times tables, they will have a much richer understanding of them than if they simply commit them to memory. Of course, knowing your tables off by heart is important too, but we want our students to be able to do more than rattle off a few numbers! A great way to see the patterns is to colour in the multiples of a particular set on a Hundred Chart.
To extend this further, have them choose a different colour to colour in the multiples of a different set on the same Hundred Chart. In this way, they can see where the sets overlap and can draw conclusions based on this visual evidence.
Showing One More, One Less, Ten More and Ten Less
With a simple modification, a Hundred Chart can be used to help students easily see one more, one less, ten more and ten less than any number. Using cardstock or sturdy paper, create a shield with a cut-out in a cross shape that will reveal the desired numbers (see picture below). Students can move this shield around the chart to discover one more, one less, ten more and ten less of any number (except numbers on the edge of the chart – some explicit teaching is required to help students find the answers for the numbers on the edge).
Once your students are familiar with the use of the Hundred Chart, it can be used to help students calculate the answers to addition and subtraction problems to 100. For example, the problem 83-54 might look a little daunting to a student, but it can be easily solved using a Hundred Chart. Begin by putting your finger on the 83 square. To subtract fifty, move your finger up five spaces to the 33 square. To subtract four, move your finger to the left (then up to the end of the row above) four spaces to the 29 square. Easy! Allowing students to use the Hundred Chart in this way will build a strong foundation for mental strategies, such as the ‘jump’, ‘split’ and ‘compensation’ strategies (search for these terms in a Math glossary if you are unfamiliar with them).
Demonstrating Working Out
Demonstrating Working Out
When students are able to use mental strategies to solve addition and subtraction problems, a Hundred Chart can be used to allow them to demonstrate their working to you or to the rest of the class. It is always fascinating to see the different ways other people solve the same problem. Using the above example of 83-54, some students may use a completely different strategy. They may, for example, make the 83 into 80 by subtracting 3, subtract 50, subtract 4, and then add on the 3 they took away at the beginning. Or, they might start by subtracting the tens (80-50), add on 3, and then subtract 4. Using a Hundred Chart to assist in demonstrating thinking will help the abstract thought of an individual become visual for others.
This is certainly not an exhaustive list of ways to use a Hundred Chart – there are certainly many other terrific uses for this versatile tool. How do you use a Hundred Chart in your classroom? Feel free to share any brilliant ideas you have come up with in the comment section below.
And one quick plug: a huge giveaway is about to happen on the Little Green blog! Make sure you keep an eye out for it - you won't want to miss it!
Right, back to the beach for me! See you next month!