Understanding Least Common Multiples

A few days ago we did a very engaging and productive activity in the maths. We were aiming to learn about the concept of a least common multiple. We used 100's boards for the same.

Groups of students were first given 10 to 12 100's boards each. Each board was numbered and they  were asked to cut out all the multiples of the number written on the board. For example, if the number was 4, then all the multiples of 4 were cut. There was one board in which all the numbers were coloured with a single colour.

When each board was overlapped with the coloured hundreds boards, all the numbers seen were the multiples a given number. the image above was taken when the board numbered 6 was placed on the hundreds board. All the numbers you can see are the multiples of 6. Similarly, the image below shows the multiples of 9. This helped the students to understand multiples.

Moreover, when you overlap the 100's board numbered 6 AND 9 on the coloured board, the numbers that you can see are COMMON MULTIPLES of 6 and 9: 18, 36, 54 and 72. Amongst these the least number is 18. Hence 18 is the LEAST COMMON MULTIPLE of 6 and 9.

Learning centres in the classroom

Any curriculum that one delivers, efficient classroom management is one of the most essential elements for a successful lesson. It can open doors to fruitful inquiry and differentiation.

Talking about differentiation,  there are some factors that need to be kept in mind in terms of classroom management:

1. A variety of grouping strategies

2. Clarity of instructions

3. Flexible seating arrangements

4. Display of group members

5. Set routines

6. Minimal noise level

Apart from this, if you have learners with any disabilities or difficulty in understanding the language of instruction, you need to cater to them according to their need.

Having learning centres in the classroom gives excellent scope to authentic differentiation. There are numerous ways of achieving this:

1. Subject specific learning centres: This is the most commonly practised strategy. You can set up centres based on the various subject disciplines. A maths centre, a language centre, a science centre and a social studies centre, probably. At each centre you may keep some resources relevant to the unit being taught. You may also keep instructions for the task that is to be done in that space by a certain group of students. It is recommended to label all the centres for ease of access. The advantage of such stations is that the students can visit the place anytime for further inquiry. The resources can be easily available at all the centres. On the hand, it is challenging to manage all the centres at times and risk of the classroom being cramped. Also, there is lack of flexibility of purpose.

2. Group specific learning centres: You may choose to set up discrete stations for the different groups of students. For example, you can name the stations based on flowers, say, daffodils, tulips, lilies and marigolds. You can label the stations thematically. You can also be creative by giving badges to students and instruct them like 'Today the daffodils will.... and the marigolds will.. ' and so on. When you feel the student has moved a level, you can just replace the badge. Only the required resources can be set up according to the task. The advantage is that the stations have increased usability and decreased requirement for organisation. This is more useful if you are using the centres for a specific  purpose, say reading. But if you want to use the centres for all subject disciplines continuously, this strategy might lead to confusion. The students would be more or less restricted to these groups.

3. Use of open stations: This is what I currently use and I call them 'open' because you just have empty spaces in the classroom and give them a generic name. In my class, I call them workstation 1, 2, 3 and 4. The labels are movable too. Every time I set up a task, I just say 'A, B and C go to workstation 1 and do...'. 'D and E go to workstation 2 and do...'. This way I am always grouping and regrouping the students. All the resources are kept in a separate the resource centre and it's easy to just pick and provide the ones required. There is maximum flexibility of grouping and purpose. They are also very easy to organise. I can't think of any disadvantages, to be honest!

Students can be made to work at these centres in various ways. Sometimes for inquiry, open ended or structured, especially while dealing with scientific concepts. Different groups of students can do different tasks at the centres or the groups might rotate so that all groups end up doing all the tasks. The later is more applicable for guided reading and novel study. The previous being more applicable for numeracy based tasks.

It is needless to say that apart from these centres, an organised classroom must have dedicated spaces for reading, stationery, portfolios, notebooks, marked and unmarked student work and teacher resources. By default most of us end up having a 'miscellaneous' corner as well!!