Like so many other children, I am a visual learner, and when it comes to math I need manipulatives.
Unfortunately, most kids are not asked how they learn best, but if a more visual, hands on method had been introduced I feel my struggle with basic division, which eventually led to mass confusion in long division, would have been eased… or even better, non-existent.
Knowing the why and the logistics behind the method can make or break someone’s understanding of a concept.
Maybe that’s the inner scientist in human nature.
It was when I took my Montessori training years ago, that I understood the value behind knowing the why, and the necessity of seeing division by using manipulatives.
And now teaching division – basic and long – is so… much… fun.
This tutorial shows you an example of how you can teach the first concepts of division by dividing up lily pads between the frogs. Not only will the kids love to create fairness amongst the frog community, but they’ll also learn the underlying logic behind the mathematical principle of division. This is a more concrete version than the tutorial I show with horses and apples, so please be sure to take a look at both.
I also strongly urge anyone to practice this with an older child – middle and high school – that may be having difficulty understanding the concept.
Sometimes you just have to go back to basics.
Objective: to learn the basics of division.
Deeper Objective: to sensorially learn the basic concepts of division by using manipulatives and points-of-interests such as frogs and lily pads.
1. nine small frogs
2. beads or gems equaling to 81 resembling lily pads/flowers (you can also consider using black beads and introduce them as flies) *I actually picked went through a box of over a thousand varieties of beads to find 81 lilypad-like leaves. I’m sure you can find something similar in a bulk bead container.
3. division slips (Montessori Printshop are what I use, since they do not go greater than a divisor of 9 and there are no remainders).
4. clear glass gems with the division and equal symbols (I wrote my symbols with a permanent marker on the back. You can also just use paper to write the symbols)
5. large-grid graph paper (if the child is to write the problem and answer – Livable Learning has some great free ones in 1cm to 2 in)
Explain to the child the vocabulary words: dividend, divisor, and quotient.
Dividend: the number in a division problem that is to be divided up.
Divisor: the number in a division problem that is to receive the dividends.
Quotient: the answer to a division problem (how many items each divisor received)
I often like to explain to the child a little about division first, putting emphasis on the word divisor with an ancient royal English accent as though these divisors feel as if they should be receiving some sort of wealth. I also like to explain to kids with brothers and/or sisters that in order for all of them to remain calm, that each child (or divisor) needs to receive the same amount of what is being divided (candy? seashells? Pokemon cards?)… or there’d be an argument.
Gather all of your materials and place them on your rug.
Place each material into organized spaces on the rug to avoid distraction. Leave plenty of space in the middle for the frogs to collect their lily pads. The division and equal symbols should be in the center. I use the lid of the lily pad container as the spot for the dividends (lily pads/items to be divided) so they stay in one place. Leave a few inches of space between the division symbol and the equal symbol for the divisors (frogs).
Blindly pull a division slip out of the box and place it above the division symbols.
Read the problem to the child by pointing to each number and symbol. Show the child the dividend (in this case, 12) and say, We are going to put down 12 lily pads as dividends.
Count out loud to 12 lily pads and put them in the dividend lid. The child can count with you. You can also have them do it themselves by asking, Can you put 12 lily pads into the lid?
Do the same with the frogs by showing the child the divisor on the division slip (in this case 2), and intentionally place two frogs in the space between the division symbol and the equal symbol. Now say, Now we can divide the 12 lily pads up between the two frogs!
Make a point of taking one lily pad at a time, set it underneath the first frog and say, One for you. Then place another one underneath the next frog and say, One for you! Then repeat the process with the first frog, then the second frog.
Continue this process until all of the lily pads are evenly distributed between the two frogs.
Move the lid, division symbol, and equal sign to the side so that only the frogs, lily pads, and division slip remain. Go over the problem again, saying 12 divided by 2 equals… how many lily pads does each frog have? The child should say 6. Repeat the problem again, encouraging the child to say it with you… 12 divided by 2 equals 6!
If you are using graph paper to write the problem and answer, place the division slip above the graph paper and either have the child write the problem down, or write it yourself to show them how to write the problem. This step can also be done in the very beginning.
Have the child count out again how many lily pads each frog has, explain again that this is the quotient, or the answer to the division problem, then show them where to write the answer on the graph paper. Give a high five and a big congratulations on her first division problem!!
Here is the process in pictures with another division problem: 21 divided by 3. Enjoy, and HAVE FUN WITH IT!
Another high five!!
Be sure to take a look at Teach Basic Division – Using Horses and Apples