Trigonometric equations and the CAS calculator

There are lots of ways of solving trigonometric equations on the Classpad but I have avoided using Trisolve as it takes away the thinking aspect of trigonometric equations. Instead I focussed on setting up equations in eActivities with the intent to complement them with the Geometry section later.

eActivities are a great place to store frequently used equations. In this instance, I wanted to keep all of the trigonometric and circle equations in one place ie sine, cosine & tan ratios, sine rule, cosine rule, sector, segment equations, circumference, area.

To do this I opened an eActivity from the main menu.

Then I started a new eActivity by going File -> New. Then I saved it by going File->Save. I called it Trig Formulae.

So then I inserted a Numsolve strip to hold my equation.

Once the strip was added I used the soft keyboard to name it the Sine ratio. Then I pressed solve to put the equation in.

Using the mth tab in the soft keyboard and then selecting the Trig option at the base of the soft keyboard I entered 'sin('. Directly below the mth tab, the theta button can be found and then closed the bracket. Don't type the word 's' 'i' 'n' using the soft keyboard as it won't work - it will treat it as s x i x n.

Then using the 2D tab, I created a fraction and using the var option entered o ÷ h. I hit exe, then closed the equation using the x at the top left hand corner of the window.

I then tried it out using the example opp=7, hyp=14, theta = ? I left theta blank, made sure the angle was selected (with the dot next to it coloured in) and pressed solve in the toolbar. Viola, theta = 30°. If you get some weird answers check that the calculator is set in degrees mode. If the answer is still weird, reset the calculator and it seems to work.

Update (25/3/09): After using this with the class for a few days (especially with radians) I noticed a few strange results where the calculator would return unexpected answers (eg for the above example -330°). To fix this, set the Lower bound to 0 and the upper bound to 180 (for degrees) or pi/3.14159 (for radians) and the results will appear as expected.

I then set about putting in the cosine ratio.

It's a great tool for things like the cosine rule where students find it hard to transpose equations and forget negative signs or for circle, segment and sector equations that are commonly forgotten.

Here is a link to other CAS calculator posts.

Favourite places to eat in Perth

A bit off topic today, but as I live north of the river there are a number of places that I love to eat. There is no real order to them as we like them all depending on what we feel like.

T5 Expresso, Joondalup: Sub $10 breakfast, great coffee, nice people, not too busy. Cosy little place to start the day found in every city around the world, other than Perth. Until now!

Bistro 38: Joondalup Country club. Great buffet during summer and if you can catch one of their special nights with entertainment it's a great time for two. Even their naff Christmas in July was great (where two years of ballroom dancing lessons came second to a drunken wife doing the pointy dance (I'll point at you.. pose.. I'll point at them.. pose...). I think we've sent at least two letters to Bistro 38 complimenting them on their excellent service.

Sensations 43, Ocean Reef: A little restaurant serving pizza, pasta and other cafe dishes. We can go there before 6.00pm with bubs and not have to worry too much about annoying other patrons or go during the day and have a coffee. The owners are lovely once you get to know them, friendly and inviting.

Shennai Tandoori, Ocean Reef: A local restaurant that has great Indian/Pakistani food tailored to the anglified palette. I think we have gone 200 times and ordered the same meal - Papadums, Chicken Tikka, Lamb Korma, Chicken Korma, 2 Naan, 1 large Pilaf Rice - which is enough for dinner and breakfast. Ask for booth 7.

The Grapevine Restaurant, Heathridge: A hearty Italian meal, a little dearer than we usually spend but we always expect to be stuffed by the end of it. Service is great (we're not partial to being in the alfresco area as it tends to be a little hot and loud) and they even drove us home one night when we couldn't get a taxi.

Conti's Restaurant, Wangara: This is a lovely quaint restaurant, we've had many a great anniversary dinner there. Don't be put off by the location. The steak and peppercorns (the carpetbag or 'Madagascar' from memory) is great, as is anything else on the menu. The 'Coles tray' for the vegetables seems strange, but keeps the vegetables nice and warm. I love how the lights dim every so often for no real reason. It's easy to get absolutely stonkered as you spend a leisurely evening.

Friends Restaurant, Perth: This is one of our favourite restaurants, with Clive and Lesley being two of the nicest people in the world. This, to my mind, is what we compare any other restaurant around the world (in fact the only other restaurants we have enjoyed to their level is Francois' mussels in white wine sauce on Melbourne's Toorak Rd and The Loose Box in the Mundaring (insert any dish on the menu here).) Mortgage your house, order some expensive wine and/or Champagne and enjoy.

Cocos Restaurant, South Perth: I must admit it's been ages since we've been, but I have very fond memories of the Tempura Whiting and having coffee overlooking the foreshore. A bit of a place for Perth's movers and shakers (Probably why I haven't been for ages!).

Kings Park Tea Rooms: OMG.. the service is ordinary, but with a glass of wine and a light meal during spring, for a lunch catchup few places are its equal.

There you go.. with the exception of home dinners and family invites which ALWAYS take precedence (coming from a family and extended family of awesome cooks and chefs) this is where we like to go!

Bon Appetit!

Time.

Time doesn't seem to be my friend at the moment. I wake up, feed Mackenzie when I can, go to school, tutor my year 11's, take my classes, wait on the phone for 15 mins, complain to payroll that they forgot to pay me last week (I have to wait another fortnight for it to arrive as it was a stuff up), teach my classes, come home and crash on the couch for 3 hours and here I am. Baby exploding with poop.

I have so much stuff to write..

e-activities in the CAS calculator are a great place to hide all the trigonometry formulas (sine rule and the like) using "Strips" and Numsolve - Updated 22/3 click here to see how.

The verify function in the main pane (bottom cell of the right icon in the toolbar 'f(x)') is a great way of testing what part of an equation has been incorrectly simplified, expanded or factorised.

My polar coordinates and vectors is rusty so I've had to sit and do the exercises in the book..

Tests to write, assignments to mark, programmes to amend..

Need to go back to sleep!

Phones, Cameras and Facebook.

Not so long ago, the fight club issue was raised with kids after school organising fights and filming them. The infamy caused through posting these film grabs on u-tube and the damage to local schools needs to be acknowledged. It took these incidents to change the current policy (or perhaps enforce an existing one?) on mobile phone use in schools.

When mobile phones were first allowed on campus my initial thoughts were that this was a bad idea. It has proven true with sms bullying, filming of teachers and posting them on the Internet, sms'ing during class, loss and theft of phones and the like. Teachers spend a portion of each day confiscating phones and returning them, facing a barrage of abuse and pleading from students.

Information technology and personal technologies have other negative influences. The insular antisocial behaviour such as being constantly on an IPod cannot be measured. In many cases it is a way of managing a lone student (allowing them the dignity of choosing to be on their own) rather than facing the real issue of an isolate in the playground and assisting with social integration. The lone student is often subject to the worst kinds of bullying in the form of exclusion and schools must respond to this kind of treatment or face the extreme measures taken by lonely students in other areas of the world.

Facebook is another tool that causes concern. I started my own Facebook page and have had 'friend' requests from students. I declined these obviously, as a teacher is not a friend. A friend has to face issues that a teacher does not and vice-versa. To transcend this relationship is fraught with danger. Yet I had to think - am I being old fashioned? Has friendship been redefined by Facebook and become some sort of watered down acquaintance? Could it be a way of hearing about their successes and failures post school? Being conservative by nature, my original position stands.. as a male teacher, I don't think you can be too careful - watered down friendship or not.. it crosses the line.

The Internet itself in general is the great time-waster. Setting firm guidelines is required to keep students on task and maintaining standards of behaviour requires strong penalties. Yet the greatest penalty (denial of Internet) is often removed as an option as multiple classes require students to use the Internet and the same student performs the same misdemeanors in each class as they know the penalties are light.

Technology is a wonderful thing but to use it effectively is a skill. I am not sure education institutions have spent the time to master this skill and I would like to see some real evidence of where and when it is used to improve results of students.

Mackenzie Surprise

Anyone that knows me well, knows that I have a predilection to a Big Mac. Some wag at Kendra's work seems to know this and has started referring to my wee dear as Little Mac.

Anyhow, she seems to have a new game that I am told is common to all babies. It's 1.30 in the morning and we're doing the late feed. She commonly needs her nappy changed at this time, and it's normally the gross one smeared all through her nappy.. That's ok.. you get accustomed to it..

So you unfasten her clothes, take off the nappy, wipe off the poop, clean her up, put on the nappy cream reach for the nappy and...

whammo..

you're swimming in a tide of Mackenzie pee.. a wonderful 20 sec gush.. all over the change mat, all through her clothes.. in her hair.. and to top it all she just rolled the back of her head into that toxic nappy.

oh well.. off with the rest of her clothes.. I needed that fifth shower today anyway..

:-)

Change management and the half cohort

When I heard the 'local solutions for local issues' chant last year, a siren went off in my head saying here comes another case of pushing responsibility down the line. The half cohort has been mismanaged thus far and schools now have to find 'innovative solutions' to maintain student levels and thus staffing levels.

Knowledge management is a key aspect in any organisation. If we let an ill thought out decision and implementation (like the half cohort) damage our long term ability to provide a service, this is a very poor management decision. Yet this is what we are faced with. When smaller numbers come in next year, schools face losing FTE. With a loss of FTE comes a loss in capability to deliver and retain content and a loss of knowledge of how to manage our students.

Innovative solutions typically means something experimental cobbled together with a low chance of success, with little forethought. This is because true innovative solutions requires a lot of work prior to implementation - after all, if it was easy everyone would be doing it already and it would not be innovative.

Once we have identified possible solutions we than have to consider how that change will occur. Managing change requires patience, skill and understanding on part of the participants. Change is a technical problem - not a people problem as too often people see it.

Steps in change management are:
a) determining the need for change
b) determining the obstacles to change
c) implementing change
d) evaluating change
(Human Resource Management, R.J. Stone, 2002)

In this case a driver for change is that we need to reduce FTE in 2010 and preserve school capability post the half cohort with fewer staff to share the load. Potentially the reverse issue happens in 2011 as the students held back in 2010 will appear in 2011. Using that knowledge (on face value) change may not be required as although retaining staff is more expensive than letting staff go, schools face the issue in 2011 of trying to restaff. A second driver for change is to re-instate job security. Whilst this issue is over the head of staff, good staff are more likely to consider opportunities elsewhere in case the job axe reaches them.

We then reach the second test, 'how to implement change'. Schools are now looking at where the 'fat' can be trimmed. Timetabling in this aspect is one of the biggest concerns. If a teacher leaves/retires/is let go organically another teacher of similar ability is rarely available on staff that fits the timetable to teach the topic (and if they do, they leave another similar hole elsewhere on the timetable). As restaffing is not an option, the solution here is usually a teacher teaching out of area or an 'innovative solution' to be used such as using leftover capability of various teachers to share a class, multi-age grouping (MAG - eg. grouping yr8/9 classes together) or integrated classrooms (eg. combined English/S&E classes).

The third test is the biggest concern where innovative solutions are bandied about. There is no doubt in my mind that given time and money, any solution can be made to work. My concern is that neither time nor money are available for such. For example, integrated classrooms may take up to five years to get right with dedicated staff committed to the project - one out of the box cannot work as student content and contextual entry points are different at each school. Furthermore staff that can create and plan these engaging projects are few and far between. Leftover capacity is nearly always a poor option. MAG streamed classes require a lot of skill to teach and have issues attached related to differences in work ethic and have the tendency to be taught to the middle (or bottom). MAG unstreamed classes exacerbate developmental, context ual and content issues thus requiring even more from the teacher than streamed classes. If we consider that the main issue resolves itself after 5 years we need to again ask whether these solutions warrant the change requirements for implementation.

The fourth test is the big one. If we are truly contemplating change we need to evaluate current performace before change has occurred, such that we can check later that the change has been positive. It is this step that shows good management from poor management. Pre-defined outcomes need to be set if we are to avoid 'crisis management' and move to structured 'change management'. NAPLAN is not the answer (though it can be one measurable) as it only measures what can be assessed in a snapshot test. It does not take into account staffing issues, affective requirements and behavioural response. More so it does not predict or respond to the potential success or damage to students in upper school (as is seen in some poorly managed middle school programmes). To realise the perils of over reliance on NAPLAN take a look at year 8 NAPLAN results and map them to senior school students. Ask yourself what happened to the block of students that did well in year 8 but were lost by year 10.

Furthermore if we instigate change 'from the hip' it makes it much more difficult to learn from our mistakes. If we know what we have done poorly, we can then do it differently in the future. This need to reflect is the key to success and to my mind, when this occurs, it is true 'change'. Something we need to consider more when defining future success.

Story of Mackenzie's birth

Wednesday Feb 18.
Baby late for appointment.. Doctor says will induce on Tuesday.

Monday Feb 23
5:59am Baby decides it wants to choose its own birthday and it's time to take a walk on the outside. Contractions 10 mins apart.
10:00am Doctor calls and suggests it might be a good time to come in. Kendra decides that she needs to clean house, do makeup and drop the rabbit off.. Contractions 8mins apart. Russell's heart rate at stroke levels.
10:08am Russell able to teleport wife to hospital 23km away. Contractions 4 mins apart.
11:00am Contractions 2 mins apart. Topped up oxytocin to speed up contractions. 0.5mm dilation. Doctor puts in epidural.
1pm Baby changes mind and decides it's too nice a day to be outside (this is where we should have realised baby was a girl). Sets up camp and goes nowhere. 1cm dilation.
5pm Doctor decides its time to come out. Wheeled into theatre. Doctor realises epidural put in wrong place - it's doing nada other than making one leg numb. Tries something else. This seems to work better.
6pm Doctor cuts hole in abdomen and reaches for baby. Doctor calls baby a scallywag. Wedged under Kendra's 6pack and won't come out.
6.05pm Kendra complains she's feeling cold. That's because her bp has dropped to 50. Madly having 3 bags of saline pumped into her.
6.45pm Kendra's 6pack becomes a 4pack - Baby pulled out with gouged eyeballs, growling, wedged no longer. Doctor holds up gruesome blood encrusted baby. Husband of year says - "gees that's an ugly baby"...
7.00pm Baby cleaned up. Husband says "gees now she's all pretty" and gets a nice cuddle. Kendra's lippy is still on and she looks suitably glam during both labour and major surgery - what a marketing opportunity for Revlon!
8.00pm Kendra back in room and says she is feeling sore - told that she can have a Panadol for the night. Pain score 4-5

Tuesday Feb 24
8.15am Husband goes to work after paying $115 to lie on the floor.
9.00am Kendra complains pain worse than contractions. Nurse rereads chart and realises that it should have been Pethedine not Panadol. Pain score 8 without Pethedine. Pain score now "Happy smiley face" with Pethedine. Birth forms explained and completed under the influence. Baby name now AppleMoonbeamFlowerChild.
3pm Russ renames child Mackenzie Trudy.


Wednesday Feb 25
Learning about baby language.
Going pink - hungry
Going pink - hot
Going pink - needs nappy changed
Going pink - needs cuddle
Going pink - wind
Looking forward to romantic dinner provided by hospital on Friday. Husband still paying $115 per night to sleep on floor, grumpy and giving out high number of detentions at school. Kicked in head by nurse in morning. Mackenzie eats, poops and sleeps. Is suitably adorable. (update 28/3: Hospital acknowledges fee is exorbitant and agrees to waive it.. yay!)

Thursday Feb 26
9am Moved to nice room with bed for two. Mackenzie eats, poops and sleeps. Still adorable.

Friday Feb 27
5pm Romantic dinner set up. Comprises plastic flowers, plastic tray and red tablecloth. Can't stop laughing. Russell realises that he has been doing it wrong all these years. Promises to buy plastic flowers in future and some plastic trays. Mackenzie eats, poops and sleeps. Even more adorable.

Saturday Feb 28
5pm Go home. Mackenzie decides she has slept enough and goes pink at irregular 2 hr intervals. This adorable thing doesn't seem to wear off. Parents realise that they are clueless but are enjoying the ride.

Sunday Mar 8
It's great to be home.. We're having a special time and Mackenzie has been wonderful spending much time hiccuping and creating frothy milkshake pants. She's so cute albeit we are a little biased. Russ denies being wrapped around Mackenzie's little finger, he just does whatever she wants, whenever she wants. He has taken a couple of weeks off to care for Kendra during her recovery, and then Mackenzie's wonderful doting grandparents will stay with Kendra until the school holidays. We're learning all her little messages and enjoying her windy smiles.

Life is good.

Putting urgency back into the curriculum.

The developmental curriculum has slowed the pace of the curriculum to the desired pace of students. As far as I can tell, the desired pace of a good many students is a slow crawl (perhaps even falling backwards). I lay the blame for this at the idiotic levels based assessment programme that has finally been turfed.

The idea of standardised grades across the state is plain stupid as it prevents some students ever having success in their reports. It is no wonder that motivation for these students that face constant failure is low (despite achieving during term and learning at an appropriate rate). The obvious solution is to use NAPLAN to gauge state-wide performance and normalise class grades.

The need now is to forget the pace students desire (in too many cases it is slower than what they can actually do) and create a pace that is optimum for learning. Despite hearing comments otherwise, they are not the same thing. To say that a child (with no experience of what they can do) should set the pace of their learning is wrong. An programme/syllabus of work that has been tested and improved through years of experience is bound to have a higher proportion of success than a one off experimental curriculum by inexperienced teachers solely based on the current cohort. Teachers need a syllabus well paced and sequenced to assist students complete the programme required for school leaving and thus assist in identifying when remedial or extension action is required to assist students (preferably with a streaming mechanism to reduce performance pressure) - this would be a far better result than drifting kids bobbing at the same level for years at a time.

The programme drives the class, and the urgency created by a required pace of work provides the anxiety required for proper learning. The pendulum swings and again teachers can focus on teaching to a programme rather than facilitating what students see themselves able to do. After all, students in the workforce need to manage their work to meet deadlines, where better to learn than through assessment in school.

Hooray!

Does all this mean that I am against OBE? Not really. I have always liked the idea of outcomes as a guide for a programme of work. It is like the backbone of a programme showing what needs to be taught. It's also all I've been taught via tertiary study. Tied to scope and sequence documents and Progress maps, OBE concepts are a good thing - give me anything that helps me understand the underlying concepts and ideas behind the curriculum. OBE is not a panacea - clearly it has shown to be poor for grading assessment, poor in promoting homogeneous classes, weak when promoted with collaborative learning and negative when tied to a developmental programme with weak students.

Wind..

Poor baby Mackenzie couldn't sleep the other night. We now know there is another pink she can turn.. WINDY! Now I have some incling of what Colic is.

She's sleeping great again.. And if she's having trouble nodding off I sit and play nursery rhymes to her on my guitar (as long as the song doesn't have an F or B flat I'm ok) and she nods off. Magic!

Might go catch a few minutes kip between feeds.

ZZZZZzzzzzzzz...........

24 hrs without sleep. Head feeling a bit wonky.

So this is why you would discourage young mums from coming to school.. And kids staying up all night playing WoW.. grrr...

Slowly learning baby talk.. Going pink.. needs feeding.. or going pink.. too many blankets on.. or going pink.. needs nappy changed.. or going pink.. feeling grizzly..

zzzznnnkkk. (sound of head hitting desk)

Baby Mackenzie & Paternity Leave

Our wonderful baby girl Mackenzie was born on Monday.. After sleeping on the floor in the hospital for three days, I'm glad to be home. Working this week was hard, with little sleep and wanting to spend time with Mackenzie but I know being able to help when the baby goes home is more important after watching other mothers struggle without the assistance of the hospital midwives. My students were understanding and my colleagues supportive so that was good!

I suppose the downside is that I'm not as prepared to help with our baby as I would have been if I had been at the hospital all week. Dr says I need to take two weeks to help with Mum's recovery. I may need to have two weeks recovery from the fluff Mackenzie just did!

Organising leave has been a bit of an experience. The new EBA has clause 34.1 that allows partners to have five days paid leave. Payroll (after initially saying it was like carer's leave and I directed them back to the EBA to check) acknowledged that this was not a sick leave allocation and it was an additional leave allowance.

This raised a second issue that there is no code in HRMIS for relief to be allocated against when I am on Partner leave. AFAIK HRMIS has not been updated for the new EBA leave requirements. Multiple calls to district office has left this unresolved.

All this checking and outlining requirements to relief teachers chewed up my DOTT making it difficult to create enough time to adequately prepare relief lessons and get back to the baby quickly after school to give my wife some respite. I didn't anticipate needing to take off more than a few days. I'm am going to owe some chocolate to our great relief teachers.

Interim reports are due next week, so I need to do them at home between sleeps. Since my HoD is taking my level 3 classes (these classes I know will be ok - albeit they may be more judgemental of my teaching style), I can mark my tests today, collect my Modelling assignments on Thursday, look in on my 10's some time next week and all should be right when I get back.

There's nothing worse than going back after an extended leave and there being a heap of mess, unsettled students and lagging programmes to fix. Hopefully I've done enough.

The big news of the week is no more levelling for assessment. Yay for the minister!

Now to focus on the family for a little while. She's soo cute!

The big day...

The big day has arrived and we're getting ready to go to the hospital. Fingers crossed all goes well. We have no idea what we're supposed to do today except wait for contractions to be 10 mins apart... They're about 12 now. Very nervous.

but... Yay!

3D trig, bearings and angle of elevation have proven themselves a stumbling block again. Once a diagram was constructed from a worded problem, students were able to complete problems. Walking students through constructing answers seems to have raised their confidence. Next year I will suggest adding a full lesson to just constructing (not solving) 3D, bearing and angle of elevation problems.

Oblivion has me hooked again. That stupid game is a weekend wrecker.

A generational approach vs the "me" generations

Baby boomers and generation y have a lot in common. Both have come in boom times and both are self centred. It is no wonder why they have such difficulty relating to their parents and their social responsibility.

I look forward to the slow shift where we look to setting up future generations and not just where we have enough loan capacity available to get our next plasma TV and leaving debt to future generations.

How can you expect to have loving relationships when your personal philosophy centres around the pleasure principle? The decline in birth rate and the fact that couples are deferring having children gives me hope as it indicates that current relationships are starting to understand the responsibility required for a happy family, and seek to raise children in an environment free of the financial and emotional strains seen in their divorced parents. I for one am one of those - paranoid about debt levels and very cautious before embarking on child raising.

For me it was a case of taking a holistic approach to our future, considering all aspects and trying to balance them - career, marriage, security, need for purpose, even spiritual requirements. Teaching was great as it was something I enjoy doing, is relatively stable, has a greater purpose and allows me time with my family +1 - to provide them with support. It did take ten years of work in other industries to be able to afford to enter teaching.. but it was time well spent as I can use this experience to help my students. Hopefully as my child grows up, our well established relationship (now in its 13th year) and my new educational knowledge will help raise a well adjusted and capable child. In time, all that I have will be theirs and hopefully they will continue and mark their mark on the world (I can hear you laughing - but I can try!).

You can't plan for everything, but to not plan is to never fully appreciate success or to learn effectively from failure. Only a few days to go before the baby arrives... Yay!

Evidence Based Education

Evidence based education is the new buzzword in education. It shares an acronym similar to OBE but is remarkably different in its approach to teaching. We need to be careful in engaging in more edubabble.

At face value it sounds much like common sense. From what I have read it can be summed up as following: "Systemic change in education should only occur with valid, statistically supported evidence." Today, where information is so easily shared there is no excuse for implementing blanket change without scientifically verified support (note that I don't say pseudo-scientific).

You can imagine some resistance from teachers as this sounds that it might take any chance of introducing new ideas/methods into the classroom. To my mind it is hard to argue against a process that ensures that the majority of what teachers do is tried and tested (if it fails, it is easier to detect why) and new ideas are limited to a small portion of the curriculum/pedagogy.

The prescribed evidence based methods would be imbued at teacher training programmes. This ensures that the majority of teachers perform at least at a minimum standard by being educated in tried and true methods. Higher risk alternative strategies or optimisation strategies would only be used as an adjunct to the tried methods.

As a parent you would not want your child subject to scientifically unsound/unproven educational methods. But.. with proof comes a necessity for time to find proof and judge what level of proof is required. This is not conducive to the immediate political needs for success in education. The issue it brings to mind is, "can the need for evidence march at the pace required for results?" ..and will the need for results and commercial lobbying compromise any findings made to the point of irrelevancy. I suggest this irrelevancy and bastardisation of results is exactly what will happen.

Change of this type would take at least 15 years to develop content, rotate in new teachers, start new students on their 12 year journey and develop change management processes to effectively monitor progress. Can you imagine a minister standing up and saying we will start the process now and if a subsequent government doesn't mess with it, we will have a good educational results in 2024? The long term nature of education is a good reason to divorce it from political imperatives and place it into a vehicle responsible to government via regulated requirements. I imagine this was first intended with the Curriculum council or SEA.

OBE was an opportunity for teaching to become a true profession again with each teacher becoming a curriculum expert for a given range of students. For those trained in the concept and with the necessary horsepower and support to use it, OBE is a wonderful curriculum development tool. Unfortunately the poor implementation of OBE, the tangling of cooperative learning with OBE and issues with assessment/levelling made it an unmitigated disaster in WA.
Despite this it still would be a mistake to throw the baby out with the bathwater.

EBE is the pendulum swinging and brings a new range of opportunities with the pressure of performance on teachers falling back to professional curriculum writers and systemic decision makers. It too needs to be taken with care until any evidence of success justifies the hype.

Driving school curriculum

The connection between middle school (yr 8-9) and senior school (yr 10-12) in the absence of a prescribed syllabus is cause for concern. When a teacher is limited by timetabling to only teach middle school classes they can lack the perspective gained by teaching senior school classes.

Similarly teachers only teaching in senior school that never teach lower school classes can lack an understanding of the difficulties in teaching younger students.

Where there are middle schooling practices, we have to be ever so careful to ensure that the "developmental" curriculum in middle school is dovetailed into the prescribed and effectively "streamed" curriculum of senior school... or else we end up with cream puffs with little resilience and disparate understanding/skills.. that when faced with pressure of performance they sadly crumble.

To not have cooperation between the middle and senior school is a real recipe for disaster. By not pushing hard enough in middle school, students find it difficult to adjust to the rigor of senior school. By pushing too hard, students become disengaged and arrive at senior school unable to enter effectively into more demanding subjects.

I believe that the only way forward is with strong leadership and it has to come from the staff that have taught and have an understanding of the needs of all five years. As staff with courses of study experience only exist in the senior school, under normal circumstances, this is where you would normally find that person. Typically they are well respected and driven individuals, although recently they may be feeling disempowered and ill used.

Once that person is identified they need to be empowered with the ability to make change such that the transition of students through middle to senior school promotes the highest outcomes from students. Being part of performance management and hiring processes for learning area staff may be a good idea.

Secondly they need to identify areas of intervention that will improve results across all five years at school, in assessment practices, student motivation, ICT implementation, curriculum development, statistical analysis of results and pedagogy ideas.

Thirdly they need to be a conduit to other learning areas to measure the amount of transference of information, examining opportunities for application of mathematical concepts effectively.

Lastly these leaders need to be recognised for their achievements and clear measurables need to be defined to show them any progress that is made. This needs to be a positive process with focus on success and examining failures for better ways to achieve desired outcomes.

With the dogs breakfast that currently exists with the lack of a current syllabus and the imminent failure of the development of a national curriculum, the opportunity exists to enhance state schools through effective identification of issues and the subsequent change management. State schools that face this challenge head on will avoid the catastrophe that is approaching post the disaster of the OBE implementation.

Baby Week

We're all prepped and ready for the arrival of our first new family member..

nursery finished... tick
house tidy... tick
bag packed ... tick
classes prepped for next week... tick

baby?? late of course.. just like it's mother.

My wife had a dream that she was having a Labrador. We checked on the ultrasound and it definitely is a baby.

I'll take a day off when it's due and then another four days when they come home. It's all very exciting and we're both looking forward to meeting our new family member. I've been telling my students that we'll name the baby Eunice or Eugene to make sure they grow up a maths dork, study hard, don't get boyfriends/girlfriends until they are at least 40 and make lots of money.

I'm finding the 3A MAT Trig test difficult to construct as my first attempt was too easy. I'll have to beef it up again later.

:-)

Escalating issues with students.

Some teachers are really good at identifying a potential behaviour issue with a student and bopping it on the head. Occassionally a student just gets a bee in their bonnet and won't let it go. What starts as a shoosh directed at a student when I start my lesson, ends with the student on in-school suspension for multiple misdemeaners during the lesson and ongoing issues for months thereafter.

There's a knack for diffusing students and when I'm concentrating usually I can pick the student and prevent them from doing stupid things. My favourite list of things to prevent these events is as follows:

Sleep well: If I'm tired I'm bound to miss the signs of a student ready to blow and probably respond with less patience than I normally would.
Maintain firm class rules: Respect, responsibility, doing your best.
Look for storm clouds: Student body language on entering the room can give an indication to their mood.
Use of humour: Sometimes a simple laugh can turn a student around.
Check their understanding of the topic: If a student feels hopeless they may compensate with poor behaviour to hide the issue.
Low key responses: Have a range of responses that don't draw attention to the student (eg. hand signals, proximity, diversion, interacting with nearby students, sending on an errand.)
Backup responses: Moving students, talking to them out of class, preventing students sitting near disruptive influences, extra homework, class detention.

If all these fail (and the student continues to disrupt the class) or a critical incident occurs (abuse of teacher/student, uncontrollable anger, damage to school equipment, visibly upset/crying) then upline referral is required - probably resulting in suspension. This of course causes further issues (my estimate) is that it takes 4 days to catch up for every day missed in senior school. The quality of the upline support will dictate how easy it is to re-introduce the student to class and resolve the issue.

When suspension occurs I see this as my failure - albeit sometimes I wish I knew some of the 'confidential' information within the school so that I could modify my responses to errant behaviour accordingly.

Rewarding effort of teachers

Today I received a certificate from the Principal in recognition of the summer school run for our 3A maths students and a letter of appreciation from the school. It acknowledged the engagement of students in the summer school programme and recognised the planning required for such an undertaking. Our other two mathematics teachers in the senior school received similar commendations. This is really positive performance management (albeit in normal business it would be accompanied with pay rises or condition benefits). One really negative thing about teaching is that career progression requires entry into management roles and lateral "teaching students" advancement is not really catered to (level 3CT is the one exception and IMHO I haven't met a worthy recipient).

It is nice to put another letter/certificate in my Portfolio!

Now for planning next year's summer school with involvement from schools and students in adjacent areas. It would be great to be able to get some publicity/media attention and for participating students to be able to choose lecture/tutorials based on student needs and interests.

On another front, in the senior school we have a rolling class strategy in year 10 math, where each of the three senior school math teachers take turns following a top year ten class through to year 12. The middle school maths programme (developed last year by the senior school) has made a difference already, with the current year 10 coordinator already noticing that our top students have made solid gains in algebra compared to last year. Our middle school teacher has done well by these kids implementing the programme - a real achievement for the school.

The year 11 3A course is moving along swimmingly thus far. Yay!

Absolute value and the 3A MAT course

Ok. Absolute value - easy enough, to take the absolute value of a number, make it positive if it wasn't already. easy peasy...

... until you start to look at IyI=IxI and ask students to graph it..

... then ask them to find the intersection of Ix-3I=I2x+4I algebraically
... then ask them to find Ix-3I<=I2x+4I

Students really bogged down when they reached inequalities. The approach I used was similar to that by Sadler in his 3A book for MAS. The problem was that I really wasn't sure they understood what they were doing.. they could follow the algorithm but understanding was eluding them.

I started by looking at absolute numbers and explained models for solving using number lines, graphing and algebraically. Then I used a composite approach to assist students visualise what it was they were doing with problems like:

Ix-3I<=I2x+4I

I started by displaying the graph on the board using the overhead gadget for the Classpad.

I entered Graph&Tab from the menu workpane (using the menu icon at the base of the workpane).

I selected Graph&Tab and entered Ix-3I for y1 and I2x+4I for y2. For some reason the graph workpane doesn't allow you to use the 2d tab absolute value option - so use the abs() function under the cat tab in the soft keyboard. When you hit enter it will restore the absolute value notation.

Make sure both y1 and y2 are ticked (if they are not place the cursor on the line using your stylus and hit exe). Hit the graph button in the toolbar (the first icon with the top formula pane selected). The following graph should appear:

We then looked at the original inequality again and I asked what did it really mean?

Ix-3I<=I2x+4I

One way of thinking about it was, "when is the graph y=Ix-3I less than or equal to the graph of y=I2x+4I?"

We looked at the graph and found that the part marked red on the line y=Ix-3I satisfied the inequality.

Using the intersect function under analysis in the menu bar we know that the two lines intersect at -1/3 and -7 therefore the interval is x<=-7, x>=-1/3.

We had discussed that we could also do this algebraically by using the property if IxI=IyI then x=y or x=-y to find the points of intersection.

Eg.

Ix-3I<=I2x+4I

x-3 = 2x+4

-x = 7

x=-7

x-3 = -(2x+4)

x-3=-2x-4

3x=-1

x=-1/3

I then asked students to draw a number line with the intervals marked and substitute the values back into the original inequality. We numbered the three intervals. The first interval represented x<=-7, the second -7<=x<=-1/3 and the last x>=-1/3.

We then selected a value within each of the intervals and substituted them into the inequality. If they were true then this indicated values of x that satisfied the inequality.

Ix-3I<=I2x+4I

Interval 1 (x=-8)

I-8-3I<=I2(-8)+4I

I-11I<=I-12I

11<=-12 (true)

Therefore x<=-7 is a valid interval.

Interval 2 (x=-5)

I-5-3I<=I2(-5)+4I

I-8I<=I-6I

8<=-6 (false)

Therefore -7<=x<=-1/3 is not a valid interval.

Interval 3 (x=0)
I-0-3I<=I2(-0)+4I

I-3I<=I6I

3<=6 (true)

Therefore x>=-1/3 is a valid interval.

The inequality Ix-3I<=I2x+4I is valid over x<=-7, x>=-1/3

Drawing students attention from the graph and back to the algebraic representation released the tension in the room, the screwed up faces and suddenly lights went back on.

Thank goodness!

Here is a link to other CAS calculator posts.

Eureka.. one problem solved!

Teaching students to solve equations with the balancing method can be difficult as many different skills are required. Collecting like terms, fractions, multiplying pronumerals, dealing with coefficients and the like. When adding all the complexities together students can really struggle.

Surfing around yesterday I found the following link using a classpad calculator to assist students check their understanding of how to use the balancing method. It has worked fabulously well and yr10 students that typically hate algebra (and maths) are all smiles...

Here's the sequence of lessons up to this point (first week of term one)..

1. review of algebraic terminology
2. review of collecting like terms
3. review of multiplying algebraic terms
4. solving simple equations

Students were shown x + 5 =7 and asked what was a possible value for x. They responded 2 and we discussed how the observation method is often a good method for solving equations. We discussed how this was good for simple cases but with more complicated examples it became too difficult.

I then introduced the balancing method saying we could get to the same result by making x the subject of the equation by examining the LHS and thinking what operation could we do to isolate the x value.

A student suggested that we subtract 5 and I said great.

Then I said to students that the crux of the balancing method was that anything we did on the LHS of the equation has to be done to the RHS. I wrote on the board

x + 5 = 7
x + 5 -5 = 7 - 5
x = 2

and asked how did that compare with our original answer. We then did the following example:

5x + 5 = 20

A student offered the following step:
5x + 5 - 5 = 20 -5
5x = 15

Typically students get stuck at this stage as 5÷5 =1 is not an intuitive step. For once I told them that I would divide by five and showed them how it works.

5x ÷ 5 = 15 ÷ 5 (please excuse the division symbol, I actually used fractions but it is too hard in html)

x = 3

And here's the real magic.. I then took out CAS calculators borrowed from the senior school and they did a number of examples with them. For the following example:

2x - 2 = 15

Their brains started making connections and they actually were using the calculators to check that their logic was correct rather than to give them just answers.

You can see from the example that each step in the calculator mimics the steps to answer the problem on paper. It is easy to see how after each operation (+2, ÷2) x becomes the subject of the equation and ultimately becomes solved with x=8.5









Common errors become obvious earlier. Students decide what operation needs to be done and see what that operation would do. Take this common case:

The student has multiplied by 2 before they have subtracted. They can instantly see their mistake (the LHS of the equation looks more complex rather than simpler so the student starts again. The second attempt subtracting 5 gets them closer to making x the subject of the equation.

For many of us, this is how we learnt to transpose equations - a little trial and error. Lots of practice. Lots of heartache. Lots of looking at the back of the book.






The students found using the calculator fun... and the calculator only gave them guidance - not just solving the answer. It was a mix between the old inverse operations method (change the sign/change the sign that causes all sorts of difficulties when fractional terms/multiple terms are introduced) and the balancing method. To be honest, I've never found the 'scales' explanation that typically accompanies the balancing method useful - but the CAS introduction way I think may have real promise.

The other great thing is that they were recording their answers really well on paper.

For the above example I would see (with equals signs aligned):

2x-2=15
2x-2+2=15+2
2x=17
2x÷2=17÷2
x=8.5

To see mid tier students lay out work like this rather than
1) 8.5
was fantastic.

Here is a link to other CAS calculator posts.

Talented students and self confidence

If a talented student at the start of year 11 wants to leave your class what do you do?

It's a question I don't know the answer to and is a difficult one.

Paths I've taken in the past have included:
a) Discuss their choices and investigate their motivation for leaving
b) Direct them to school counsellors
c) Do nothing

Invariably before now I have been sucked into option a). This last time I've decided to do c). Whether it is peer pressure, lack of support from parents, lack of confidence in your abilities, interference from other learning areas to bolster numbers, laziness or poor work ethic; students feel compelled to make changes at the start of year 11. It will be interesting to see what they will do. I know though that I can't in all honesty tell them that they will pass if they think the grass is greener elsewhere. I'd much rather have those students that are enjoying themselves in the new courses.

The pall cast by students wishing to leave really dampens my enjoyment of classes as I was really looking forward to working positively with them. I suppose it's just the ups and downs of working with adolescents.

The main course affected seems to be the year 11 3ab MAS course. The introduction of new content seems to have spooked a few students. I am concerned that the MAT only students this year will struggle in 3C MAT next year without the additional practice provided by 3AB MAS. It is only guesswork at this stage.

Maths backgrounds for worksheets and Powerpoint

As an upper school teacher, we sometimes ignore the requirements of appearance of our materials and focus on presenting quality content. This is evident in the material available on the web.

When I get a moment I like to (in the words of my wife) make things pretty and spend the time to ensure there is a background on worksheets, a powerpoint slide with a coloured background and the like.

One site I like to use is http://www.brainybetty.com/. There are some great free backgrounds there for Powerpoint. I really like the orange one and have used it a lot.

Here is a background I made for a recent certificate for the summer school using the MSWord 2003 equation editor.

Have no fear the image is bigger. Just click on it, right click the image and save it. Here's a simple way to make it a watermark in Word 2003.

1. Open up a Word document.
2. Go Format->Background->Printed Watermark
3. Select the Picture Watermark option
4. Click Select Picture
5. Find where the background is saved and select it
6. Change the scale to 200% (or to whatever works for your image unless you want a tiled image)
7. Ensure the washout checkbox is selected
8. Click apply

Voila. A professional background for your MSWord 2003 document.

Sometimes you will find the washout selection too light for your printer. In that case you need to insert the picture, send it to behind the text and increase the brightness of the picture to a printable level that doesn't interfere with the readability of the text. This is the way I usually do it as my printer is temperamental but it makes it a bit of a cow to work with the page.

Here's how it turned out.

Getting fired up about the start of term.

Yes, another PD session today . The time left for planning was great and I am feeling ready to start the new term. The work done at the end of last term has made this easier than expected thus far. Our TIC provided input on the course and directed worthwhile changes. Programmes and daily plans are written for the three year 10 streams my yr 11 1B/C classes, 3A/B MAT, 3A/B MAS and yr 12 Modelling with Mathematics. Yay!

We're all pretty keen to get started and even the most cynical of us are looking forward to what the year can bring without last year's threats of industrial action. Let's get on with the job of teaching.

The PD material was of dubious standard with a part time presenter condensing a week long course into 1.5 hrs to a group of 60 teachers from different learning areas. The topic of course was literacy, which meant another rehash of primary strategies, collaborative learning and.. you guessed it.. graphical organisers.

We were asked 'how we knew that students were engaged?' with a range of answers from 'if a student is looking at you (culturally inappropriate in many cases)' to 'actively answering questions (disposition/culturally inappropriate)'. No answer was given by the presenter (I think her answer was discredited before she had a chance to supply it). Doodling notes on the page was deemed a valid method of note taking. We again were informed that the 2 squillion genre's were a necessary part of learning and teaching.. a focus on breadth of learning over depth again. The change in emphasis from version 1 to version 2 of First Steps is a shame as the original First steps had focus and is still a valuable teaching tool as it gave students a foundation to learn other genres. Despite being a Maths teacher I own copies of both the first and second editions of First Steps.

The presenter put us in a lineup and instructed us to stand from engaged to not engaged. She then asked us 'Did we feel engaged by PD opportunities? and to position ourselves accordingly in the lineup. I stayed where I was which was on the disengaged side. As I had been critical of earlier answers (and was sitting under the presenters nose) she asked me why I felt disengaged from PD sessions. I said that I rarely encountered worthwhile PD (to which I embarassingly received a clap from staff). Yep.. that's me.. survival skills of a bunny on a freeway.

More seriously I would add to that PD's are rarely well prepared as they inadequately take into account prior learning (no more bloody graphical organisers!), show little awareness of the requirements of staff (we had staff from every learning area), have no follow up or action points (this may be more of a management issue), take too long to tell too little and generally are just not good value for money. She rightly guessed I was a maths teacher as I was critically evaluating the value of PD sessions.

On just the value for money point.. 1.5hrs x 60 people at an average of $70,000 per year conservatively cost the school $3,000 in lost wages. That's a projector installed for each of the teachers in Maths which would benefit 150 students every year or a new set of text books for a classroom. It has an opportunity cost of our students having a more cohesive programme that could have been developed. I would be interested to know how many graphic organisers are actually used in classes or how many teachers use the text supplied.

I don't accept that we should be grateful for any PD given and accept mediocre presentations. If we waste 90 man hours of training time, it is a criminal waste. We cannot stay professionals and not continue to learn our craft. Without good PD opportunities we cannot grow at our optimum rate.

I took away one point from the PD, an interesting example on the use of questions to promote discussion on a subject. It was ok but explicit teaching would have imparted the same knowledge (drink water if in the desert) in 1 minute rather than through a round of discussion. I can see how it could be useful and is another tool to use in the kit bag. It also explains why a number of my alternate lessons work..

The materials presented by the principal were great in that they allowed teachers a chance to vent concerns in a healthy environment. In another session it was interesting to hear that 360° reviews were contemplated and rejected (where teachers review performance of management and vice-versa). It's difficult to see the benefit of inexperienced management staff reviewing inexperienced staff. It's all a bit silly really when experienced staff exist to perform the teaching review within the school.

It was raised that we needed to communicate better with like schools and embrace some of their successful strategies. This is a great idea - unfortunately one rarely possible. It would be good to see long term strategies that lead to teachers on loan to adjacent schools for terms, semesters or for the year, further developing our abilities and bringing back learning to our schools.

It was nice to hear that many teachers thought our mathematics summer school was a worthwhile first attempt. It will be interesting to hear the anonymized results when they are handed to admin by students on the first day back. These trailblazing year 11 3A MAS and MAT students are the bleeding edge of our new maths students and for them to succeed would be great for them and the school.

Only time will tell.

Understanding reports in WA

I am often asked to interpret reports of friends children and explain to parents what the report really means. I am no expert on writing primary reports but I am critical of the lack of transparency in school documents and the degree of technical literacy required to understand them.

Reports are one of those things that have been bastardised by bureaucracy and politics. To be honest their usefulness is limited in their current form unless you are a teacher or bureaucrat. Even as a teacher, the variance of grading between one teacher and the next is too great making the data unreliable and thus is rarely referred to. Here are two cases that recently presented themselves.

Scenario A
Student is in year 7, has been given an excellent report. He has a level three in Maths and English and is finding school boring and too easy.

Q: Is my student doing ok?
A: Probably not. If they are level 3 and finding school easy then they are not being extended enough. Asked student to record what they did today in paragraph form (not dot points). Spelling accuracy was limited. Student was writing without an understanding of conjunctions, limited punctuation and was writing very slowly. Student could not recall last book longer than 10 pages read. Student could not recite 4 or six times tables. Student had limited understanding of order of operations.
Remedy: Indicated that parent needed to take greater interest in performance of student. Suggested student complete homework at kitchen table each night with parent assisting and providing additional examples to complete. Indicated a few books that the student may like and indicated that parents reading with them would be a good idea. Suggested methodology for learning tables and order of operations.

Level 3 is the minimum level a student should be getting in year 7. You would expect students to be completing a variety of level 4 tasks in year 7. Sadly many teachers are only teaching level 3 material. This is very evident when talking to primary teachers at PD through their lack of understanding of level 4 tasks in mathematics.

Scenario B
Student is in year 4. He is the top of their class in mathematics and performed well in NAPLAN testing. He has been given a B. The student is distressed as they expected an A.

Q:Huh? How can this be?
A:Back in the day when we were students, results for a class were scaled to a normal distribution - each class had a few A's, a few more B's, lots of C's, a few D's and a student or two earmarked for being held back. Sadly this is no longer the case. If a teacher does not teach the 'A' material (for whatever reason defined by that abomination smartie chart), an A will not be given, the same goes for B's, C's, D's & E's. In this case this is what has happened. NAPLAN testing at this level is more IQ testing than progress testing which is why this result was consistent with student and parent expectations.
Remedy: I supplied printed copies of progress maps and pointers for mathematics and links to sample items for the next NAPLAN test. Suggested parents consider looking at level of student and work at assisting student understand material at the next level.

It may sound ok to define 'A' material and provide an 'A' consistent with students across the state until you consider that in some low socioeconomic schools if grading was done consistently with curriculum framework directives, no student would get higher than a C for the first years of schools whilst they caught up to their contemporaries in more affluent schools. Even gifted students (but lacking environmental support) get discouraged as they try to overcome their lack of support at home and get C's despite making large jumps in knowledge and applying themselves. Although the idea of A-E grading was good, the application was poor. For low ability students in lower classes - they may never get higher than a D despite a great work ethic and working at a level consistent with their peers.



The solution? Provide normalised results for each class on reports (allowing students to get grades in relation to their peers) and use NAPLAN tests to show progress in relation to other schools with expected ranges for university and TAFE entry. Duh!

(Addendum 30/1/2008: It is interesting to note that the West had an informative article on just this topic today.. details of the article can be found here (half way down the page) by Bethany Hiatt titled "Parents need lessons on the grading system". Yes I am being positive about a media article - must be the optimism and endorphin spike associated with the start of a new year.)

Trigonometry and CAS calculator I

During exams last year we noticed that those who had CAS calculators were not using them for Trigonometry problems. During summer school we sought to rectify this. To start with we looked at properties of triangles.

Students stated that the calculator would give no solution when solutions existed. This sounded doubtful but I had a good idea where they were going wrong.

I started with the following. Take three lines, 4cm, 2cm, 1cm. Now obviously this can't make a triangle. Right?




No matter how we change the angles at A & B they cannot form a triangle. This was to inform students that a no solution result in their calculator had meaning.

So now we had a look at a problem that they were having difficulty with.

In their work pads they had written A=x, a=5cm, B=72°, b=72 and labelled the triangle correctly. So far so good.

They could tell it was a sine rule problem but had difficulty entering it into the calculator. Where did the sin, cos, tan buttons go from the calculator?

The first thing to do is find the sine function. Open the soft keyboard, select the mth tab and press the Trig button at the bottom of the keyboard.



Next enter the sine equation with the substituted values. They needed the fraction template inside the soft keyboard under 2D






Hitting execute at this point gives no solution. Huh?

Well.. we still have to solve for x. So highlight the equation and go to the interactive menu (in the menu bar at the top of the work pane), select Advanced and then solve. The Equation should be there and the variable listed should be x.



After a rather long wait a huge expression appeared with a strange looking answer.

I'll rekey it here as the whole answer does not appear on the work pane on the calculator.

{x=360.00.constn(1)+137.209, x=360.00.constn(2)+42.791}

The answers are the two bits in red (at this point we had a bit of a chat about the ambiguous case with the sine rule). To get to the answer you have to navigate with the style and the left/right arrows at the edges of the equation.



So the answer is x=137° or x=43° (0 d.p.)

We then drew these triangles to give students a better understanding of the ambiguous case.

In the next example we'll look at the perils of rounding and go back to the case above with the impossible triangle.


Here is a link to other CAS calculator posts.

Solving Simultaneous Equations using the Classpad 330

There are a number of ways of finding where two lines intersect. Let's solve this example.

"Where do the equations y=x and y=-2x+3 intersect?"

One way to find the solution is to solve the two equations algebraically using simultaneous equations.

First open and clear the main work pane.



Press the blue Keyboard button and bring up the soft keyboard. Select the 2D tab.

You should be able to see a button with a bracket and two small boxes (circled below in red). Press it.

You should see the simultaneous equation template in the main pane.
(Update 1/6/2010: Press it twice to add a third equation line!)

Click on the first box and type y=x

Click on the box below it and type y=-2x+3

In the third box to the right of the vertical line type x,y (the variables we wish to solve).

Hit the exe button.

The answer (x=1, y=1) should appear.

Here is a link to other CAS calculator posts.

Classpad 330 and Normal Distribution

Normal distribution problems can be done quite simply on the Classpad 330, but the method seems a little weird.. perhaps I haven't found a menu yet, or completed an update.. but here's how I did it for the following problem.

"A packet of mince contains 500g of mince. Suppose the actual weight (x) of
these packets is normally distributed with a mean of 512 grams and a standard
deviation of 8 grams. What is the probability of picking a packet between 504
and 520g?"

Firstly open the main window and add the list editor from the toolbar.

Opening the list editor should make the Calc menu appear in the menubar at the top of the window.

Select Calc->Distribution. This will make a popup appear with some options

The Type dropdown needs to say Distribution.

The second dropdown should say Normal CD. After that is selected tap Next. A new dialog box will appear.

For our problem the lower bound is 504, the upper bound is 520, the standard deviation is 8 and the mean is 512. Tap Next when this has been entered. The answer will appear with a probability of 0.683

Tap the graph icon in the toolbar to view the distribution.

Viola!

Here is a link to other CAS calculator posts.