The class is working with equations and have to remember these 5 points or guidelines:
  1. There is an = sign (expressions don't)
  2. LHS = RHS (balancing strategy)
  3. to solve for x, isolate it (make it the subject)
  4. use inverse or opposite operations to help isolate x
  5. during, check using points above; after, check by substitution
These points are revised in every lesson. The idea is that if they stick to these points, they can solve any type of equation: 1-step, 2-step, x on both sides, equations with fractions and directed numbers and grouping symbols.


Students have had a chance to practice using computers - see Interactives page as well as on paper. This is critical to increase proficiency in solving equations. 

 
 
The idea of Mary Ward's open circle is often mentioned at school. It is commonly understood as 'welcoming'.

Since we have just had a major test and about to start a new topic, I thought it would be good to round up the Circle topic, so-to-speak, in the context of Mary Ward's open cirlce.

The class had a very interesting discussion about what a circle is by exploring the following questions:

1. Why did Mary ward use the idea of an 'open circle'?
2. Can a circle be open?
3. How big is an 'open circle' (assume semi-circle though an arc formed by a 270 degree angle is probably more apt) to accommodate 5, 8 or 10 people if each person used up 50 cm (standard-ish measurement for table settings, for example).

The class had to use the terms and formulas they learned in the past couple of weeks. In particular, they agreed that the points around the circle are equi-distant to the centre and that this distance is the radius (all points around any circle share the same radius). This means everyone in the 'open circle' are on equal footing - not like an 'open square' where people in the corners can be excluded. We all agreed that a circle cannot be open because a full cirlce, by definition, must be 360 degrees - any less and you've got an arc, not a circle. Nevertheless, we stuck to 'open circle' as it does sound better than 'arc', in the Mary Ward context.

Question 3 has an underlying question - how to describe 'big- ness'; a great time to review Circumference, Radius and Diameter - and the relationship of these three parts. Doing the maths was deemed tricky because most forgot that the circumference formula they were familiar with (pi x diameter) is for a full cirlce and that we needed to halve that for this question (being a semi-circle). That is, we needed to look at it as a partial circle (sector) and adjust accordingly; we had covered perimeter and area of sectors. So, in fact, Q3 could also have considered area, as a measure of big-ness.

There was a question 4 we didn't get to because we ran out of time - "How many could there be before the open circle defeats its purpose of accommodating open and inclusive conversation?" This would have illustrated an i application of maths, i.e. prediction.

This was a very contextual application of mathematical learning and no real absolute answers, except for Q3. Q1 and Q2 answers were at best conjectures although grounded in mathematical concepts - which may not have been the basis of the metaphor in the first place. This was a great opportunity to deepen understanding of our Loreto tradition as well as of properties of circles in an unconventional and, generally, fun way.
 
 
The class has had a couple of lessons using MathsOnline - a fantastic and free online resource. 

I have assigned tasks - on Circle. Students watch the video - as many times as they have to - and then answer the worksheets.

Most students love that they are able to work at their own pace. The site is also good for revising previous topics.