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!!

Formative assessment - How different governement systems function

Criteria:
* Knowledge about the different forms of goverments
* AK strand: Governance and civil society
* Related concepts: Governance and civil society
* Self-management skills: Making informed choices

TASK: Analyse the problem given and think how this could be solved by at least three forms of governments (Anarchy, Monarchy, Oligarchy, Democracy, Parliamentary, Communist, Federal, Dictatarian or Autocratic). You need not come up with the exact solution - just the possible procedure would be enough.

Problem: The citizens are complaining about paying too much taxes to the government. They want the taxes to be reduced.

Your response should be in the form of a comment to this post.

Weekend Homework

UOI: Home survey

Task: Talk to your parents about how your house/family is governed. Some questions you may discuss:

* What systems are in place?
* How do these systems affect your life?
* What will happen if one of the systems stops working?
* What are the responsibilities of each individual?
* What are the rights of each individual?
* How are problems solved?
* Who takes the major decisions? Why?

You can also make a pictorial representation of the same.

English: Using reading strategy: Create

Task: Make an advertisement for the book you are reading. The poster must:

* Be visually appealing with bright colours and less text
* Make the viewers want to read the book
* Have interesting captions (use simile (as __ as a ____) and alliterations (words starting from same sound) if possible)

Reading for understanding

                                              

It isn't like I'm an expert in reading, but I would like to share how I go about it in the classroom.

It goes unsaid that the best way to enhance language skills in any child is through extensive reading and by accomplishing follow-up tasks. At a school where most of the students need assistance in English, reading becomes an essential part of our daily routines.

Based on their reading and comprehension levels, each student in my class has been given a book to read. Everyday, they are given to time to read one or two chapters. Based on the chapters, the students do a variety of tasks. Each day, we focus on a different reading strategy (Predict, Skim and Scan, Visualise, connect, Create, Wonder, Evaluate, Infer and Summarise). Students choose a task related to the reading strategy chosen on that day. For example, today, we focused on 'Create'. Few chose to create posters, others created comic scripts. Some students also created role plays. Some students worked in groups and others worked individually. 

We keep modifying the way we cater to reading in the classroom. This keeps the students engaged and exited. Earlier, the students were given 'reading bingo' sheets from which they chose tasks. At the moment, we are following 'strategy of the day'. Soon, we will begin with structured novel study. We also regularly do guided reading using the Oxford Reading Tree books.

Circle activity

We did a very interesting activiliy in math yesterday. The students were asked to cut out a circle from coloured A4 sheets. They learnt the different pars of the circle by 'playing' with this circle cut-out. For example, the edge of the shape is the cicumference. The line created when they folded the circle into two equal halfs is called a diameter. The line created when the circle is folded into a quarter is the radius. The cross-section of these two lines in the center. The smaller part of the circumference is the arc. The line created when they randomly folded the circle is the chord. The chord divides the circle into sectors.

After getting thorough with this vocabulary, the students created more 2D shapes with the circle: a cone (by folding it twice so that the circumference touches the center); a triangle (doing the same thrice); a trapezium (folding one end of the triangle); a hexagon (folding all three ends of the triangle) and a rhombus (Folding two ends of a triangle). They also created a tetrahedron (triangular based pyramid) by holding together the three corners of the triangle.

Apart from being informative, the engagement was highly engaging for the students, especially the girls. Some of the boys did mention that they didn't like sitting in the same place for a long time... :) Most of the students felt they were doing origami!!

Free time in the classroom

I'm sure my Principal will be alarmed by reading the title! Jokes apart, giving some (structured) free time to the students in the classroom is a very effective way to channelise their energies in the right direction.

We all have routines at home, but, aren't there times when we need a break from our schedules to either catch-up on something or just to suffice our yearning for 'change'. At times, we priorotize things that need more attention from us at that particular point of time. When we say that a classroom is like a second home for a child, then doesn't the same rationale apply to them as well?? Change can a be a source of motivation for all of us.

Our current unit is on buildings and structures and the students have been engrossed in making many models using different materials, especially legos. Lately I have been giving them some time during classes to make whatever they want with the legos and the 2D and 3D shapes. Doing this has enhanced the creativity of the students and has made them feel like architects and engineers.

When the students spend time with model making, I sit with students who need more assistance in basic skills like reading and arithmetic. It has been working well for me as well as the students - A Win Win situation!