Division Using Different Strategies

To end my unit on division, I had students work through different word problems. They were quite good at understanding the problem but the challenge was that they had to use a variety of the strategies we learnt in class to solve the word problems. Here is some of their work:

 

In this example, this student showed how to solve division problems using sharing, inverse operations, and repeated addition.

Teaching Division using Inverse

I often find division the hardest of the operations to teach simply because I think I struggle myself to simplify it for students. This time around I really tried to break it down and provide students with as many strategies as possible to help them understand the concept.

Our strategies included: vocabulary, sharing, repeated addition and repeated subtraction and we have now moved on to inverse operations.

Repeated addition and subtraction provided a great segway into inverse operations as students were able to make the connection between multiplication and division on their own. It is great when students can make these connections as you see the lightbulb switch in their head.

My students also love making posters in maths, so we rarely do worksheets and take a simple activity and turn it into a 5 star project. So here, I present to you, our inverse posters:

Division Strategies

My post "Sharing in Division" is about an activity that I use often at the beginning of my unit on division to teach the strategy of "sharing". 

The next two strategies I teach in division are "repeated subtraction" and "repeated addition". My maths class loves hands-on activities so I am constantly thinking of different ways to teach lessons which will keep my students engaged. This strategy could have been taught simply by using a worksheet, but instead, I had students solve their division equations on a sentence strip using a number line.

This lesson was taught over two days, one for repeated addition and one for repeated subtraction. The simple fact of having students complete their number lines on a sentence strip, rather than on a piece of paper in their notebook caused students to stay engaged and focused (and also very excited) throughout this maths lesson. Another thing that is wonderful about my maths students is their excitement when they see their work displayed, hence students put in extra effort when they are completing a task that will be displayed.

For repeated subtraction, students were given a division equation and had to solve it using a number line. They began by drawing the line and started by placing the dividend on the right side. They then jumped backward by the amount of the divisor until they got to zero (hence, repeated subtraction). The number of jumps they made was the answer (quotient) to their division equation.

For repeated addition, students completed a number line again, however, this time they started on the left side of the number line at zero. They then proceeded to make jumps in the amount of the divisor until they reached the dividend amount. Again, the number of jumps they made was the answer (quotient) to their division equation.

 After teaching repeated addition, students made the realisation that "division is like multiplication" which was amazing as it segwayed perfectly into teaching the inverse operations strategy.

Division Simplified

Here is a poster that I make with the children when we start our unit on division. 

It is crucial that students use the correct mathematical vocabulary but sometimes you need to break it down for the students to help them remember what the vocabulary means.

Keeping this poster up and showing 3 different ways to remember the formal algorithm. It is also very helpful for EAL (English as an Additional Language) students in a mainstream class to help them remember the correct mathematical vocabulary and to remember what the vocabulary means.

Sharing in Division

The classic banana sharing activity! I have used this to teach division multiple times. When teaching any of the number operations (addition, subtraction, multiplication, division), I try to make sure that I am teaching the students many different strategies that they can use to solve equations. 

For basic division, the main strategies I teach are: sharing, inverse operations, and chunking/splitting. I always start with sharing as it is the simplest and most basic way to explain division. This activity is a concrete approach to teaching the sharing strategy.

Each student is given a worded division problem and pictures of bananas as their counters. They need to solve the problem by sharing their bananas between the amount of people in their problem to show how many bananas each person receives. 

In this example, the problem is the following:  

"There are 20 bananas in a bunch. Two people will share them. How many bananas will each person receive?"

This student cut out the twenty bananas from their bunch and split them between the two people to solve the problem. Although this seems like a very simple task, it is a great introduction into division and is an easy way for you, as a teacher, to identify whether the students in your class understand the concept of division through sharing.