## Reasoning in Geometry

07/28/2010

We are currently learning Angles, Triangles and Quadrilaterals. More to the point, we are learning about using what we know (facts) to convey our thinking (reasoning) through reading, writing and speaking (language).

Most of the facts and language used for reasoning have been learned in year 7. This year, the focus is on putting it all together.

For example, students already know of the 90, 180 and 360 degree angles. They know these are called right, straight, and revolution angles respectively. They know the symbols for these as well. This allows them to reason that adjacent angles are complementary or supplementary or at a point.

Here's a list of the language we use:
• angles at a point
• vertically opposite angles
• corresponding angles, || lines
• alternate angles, || lines
• co-interior angles, || lines
• angle sum of a triangle
• exterior angle of a triangle
• equal sides of an isosceles (or equilateral) triangle
• equal angles of an isosceles (or equilateral) triangle
• angle sum of a quadrilateral

## Parent-Teacher evenings

07/28/2010

Thank you to all parents and students who attended the Parent Teacher evenings. It is good to look back as a way forward. That is, it is good to see what went well and where things can improve.

It's always good to have a good conversation on learning.

## Inequalities

06/09/2010

At first, students could not think of any examples of inequalities in real life. With an example of  children as age < 13, however, they were soon off to name several. We even had a few fun digressions as we explored some "stories" behind the examples. Here are some of them:
1. speed > 40 at school zones is speeding - somebody told a story of her granddad being booked for driving too slow (concept of minimum is important, too)
2. senior age > 50, it brought a discussion that this is too young
3. marrying age >= 16, too young again
4. 13 <= teen <= 19
5. wins > 4 to qualify to next debating round - and a nod to one of the members of the debating team!

It soon became clear that inequalities are just as present in real life as equations are.A quick revision of step graphs showed the students that they have also seen the graphing of inequalities before.

Students were again reminded of the guiding principles regarding working with equations with the addition of:
• with inequalities, multiplying or dividing by a negative number means reversing the sign

I believe the constant focus on the big picture with regards to equations is starting to pay off as the students are working more confidently.

## Working with Equations

05/31/2010

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.

## Investigating Mary Ward's Open Circle

05/12/2010

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.

## Learning Online

05/09/2010

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.

## Learning Strategies - by the students

04/18/2010

1 Comment

At the end of Term 1, we had a brainstorming activity to list some strategies on how to improve our maths. Working in groups, students listed strategies pertaining to Homework, Assessment preparation and Class Behaviour. Here's what the students came up with:

Homework
• Practice, practice, practice
• Revise topics on notes or textbook
• Self-correct - learn from mistakes
• Seek help - class buddy, parent, teacher, Munch (Maths at Lunch)
Assessment Preparation

• Space out time for study
• Work on weaknesses, e.g. re-do exercises you found hard
• Seek help  (see above)
• Do the Practice tests
• Revise topics on notes or textbook

In-class Behaviour
• Put hand up to ask if you don't understand
• No unnecessary talking
• Take notes

## Maths in Music

03/24/2010

We are currently investigating maths in music.

The task over 2 lessons is to look at patterns (rules) in lyrics and music and present these patterns via a digital poster. This activity helps reinforce previous knowledge on Percentages and Algebra, applied to a very real context.

The class is using Taylor Swift's song, The Best Days. They are all working with their buddies.

Finding patterns in lyrics

Students look at visual patterns using Wordle or WordItOut to find the most common words (Mode). They count the occurences of words in the lyrics and write out algebraic rules in expression form and also in words, e.g.

(k / w) * 100% as the percentage of the word 'know' in the lyrics

In fact, this is how Word Clouds (like Wordle and WordItOut) work, i.e. by correlating the frequency of occurrence and the font size on the resulting graphic.

Finding patterns in music

Year 8s are currently learning how to play the guitar. Part of this task is to look at the song's chords and create a Frequency Distribution Table and Chart in Excel spreadsheets. This reinforces a previous topic on Percentage Composition as well as a review of some Data concepts.

Students look at a visual representation of music in Audacity to see peaks and troughs in the volume as well as when repeated segments occur.

Students can then play with the Tempo and its effects in beats per minute and duration of a 15-second music segment. Audacity shows the percentages of change visually as well as in numbers.

Music students can opt to look at patterns using music sheets for the same song. It is hoped that students see that knowledge of fractions (and percentages) are very much in use here.

Maths is in Music

Students are engaged and are using a variety of ICT tools to help them see the maths in music. They get to see how information can be presented in a variety of ways.

Posters will be showcased on this web so keep visiting.

## Current Topic - Algebra

03/14/2010

We've just finished Percentages and have started Algebra.

We are refining our algebraic techniques which we've started learning in year 7. These include the four operations (add, subtract, multiply, divide) as well as basic Index Laws and expansion of expressions, possibly even factorising...maybe.

Some very basic things to remember are:
• pronumerals (the letters) represent numerical values - numbers in disguise; also known as variables (opposite of constant), because the values they represent can change
• numbers before letters (coefficient then pronumeral) when writing terms, e.g. 2y
• numbers before letters when multiplying and dividing pronumerals, e.g. 3b x 4c = 3 x 4 and b x c = 12bc
• no need to write 1, e.g. write b, instead of 1b
• invisible operation means to multiply, e.g. 8m or 9(n+ 1) both mean multiply
• like terms (matching pronumerals) apply to addition and subtraction, e.g. 4a + 5a, and 6mn - 2mn
• x and x-squared are not like terms
• b + b is not the same as b x b, b + b = 2b but b x b = b^2; ^ means raised to the power of
• rule means formula or equation or number sentence, i.e. expect to see the = sign, e.g. A = bh, t = 2m + 1. Rules can have variables and/or constants.
• algebraic expressions do not have the = sign, e.g. 3a + 5
• in Algebra, use what you learned about operating with whole numbers, directed numbers, fractions, decimals and percentages as well as order of operations

It's hard to believe that we've actually covered all of the above already.

## Author

I am the 8MATE2010 teacher as well as an ICT integrator. I use technology to facilitate learning with a social bent and realistic context, where possible.

Mrs Mawby