Resources for educators, facilitators, teachers and students of Mathematics and Statistics July 21st  2014 CENTRAL NORTH - Mathematics and Statistics Resources
Jim Hogan - - 027 461 0702 - based at Central Plateau REAP, 73 Titiraupenga ST, Taupo, NZ
Coming Events
On Line Resources
Workshops Teachers
Previous INDEX Pages 2002 - 2014
My Book
This will be an ongoing event until Oct I am guessing. I want to put some better organisation into the work done since 2002 when I became a Mathematics Advisor with Waikato University. The contracts terminated at the end of 2012 and I taught mathematics in a school in 2011. My job with Team Solutions, Auckland University began in April 2012. The future? At this stage it all ends on 31st DEC 2014.

Hence, time to revise while I have a chance. I like images, style, colour and simple. The internet has become a very fast, connected place so plenty of links, modern, future and past. I have felt many times that I live in the future. So that is where this site is positioned... the future.

Working this website
Use the connecting links in tables, pages generally go down when you get there, there are no rollover or surprises, no strange links or hidden tricks, what you see is what is get. I am trying to teach myself PYTHON so all that may change, but not for a while. All files are virus checked and everything is generated on a Mac Platform.

What you really learn in school...
Enjoy learning and teaching mathematics. After 40 years of teaching (and learning) I am not entirely sure what I taught or what was learned in my classes. I know that at first I learned more than my students. I suspect that perseverance, problem solving, fun and enjoyment, curiosity, asking why and being independent, a skeptic and fairly dogmatic, taking full responsibility for my own mistakes and always trying to repair any damage was up front. Simple is a good word and not always easy. We can all do anything! Being reflective, keeping a journal, being an inquirer, having a deep passion for achievement and understanding.  If you happened to be in my classes at some stage, send me an email and tell me what you are doing. I like those updates. It keeps me going and reminds me the success.

GOLF RESOURCE - Here is a .csv file of my first 97 games of 9-hole golf. I wanted to know if i was getting better at golf so I trimmed of the first 20 and last 20 games. These are compared in a this iNZight file and to me confirm an improvement of 3 stokes. Every now and then I excel and win. I have more ideas about learning mathematics through golf. I know all golf clubs would welcome junior involvement so give this some thought. Your class, or a group, could measure their golf, do an intervention and then re-measure to evaluate. More on this in RESOURCES under ACTIVITIES in the menu navigator above. Good info on handicapping and golf on DOTGOLF.

BOPMA CONF 21st NOV 2014 - More comingGoogle "stanford online" How to Solve Maths
Data - Keep an eye on student credits so that numeracy is gained, 10 cr in NCEAL1. Do an Inquiry into your teaching. We do write and read in mathematics so please take care about setting out, language and use of symbols, graphs and equations.

I can only recommend the following. It is a must for every person on this planet, especially parents, grandparents, teachers and students not necessarily in that order. Thanks Jo. Thanks Standford.
Google "stanford online" and look for "How to Learn Mathematics".
The first seven sections are:
1, Introduction,
2. Maths and Mindset,(your mind grows)
3. Mistakes & Persistence,(we learn by mistakes, persistence is everything)
4. Teaching for a Growth Mindset, (probablem based learning)
5. Conceptual Learning, Part I: Number Sense, (models)
6. Conceptual Learning, Part II: Connections, Representations, Questions, (being curious)
7. Appreciating Algebra. (actually we all do algebra).

The concepts behind mindset are very useful to all levels, unfortunately the course is not free anymore, now US$125. However you can see all the videos from last year's course on youtube though. Search youtube for "jo boaler how to learn math: Session 1.1" for the first video. There is close to 90 videos in the series.

There is another course starting in June called How to learn maths for students which is free and may be useful the link is

Another site from Jo Boaler where she is trying to put forward her ideas is [2] which could be worth visiting otherwise google "Jo Boaler" or "Carol Dweck" for stuff on mindsets

FROM National Workshops
I have the latest version of the Backmapping here. I want to finish all the standards and add resources and more ideas. Work in progress as other work take precedence. Maybe July break will give me time.

A couple of website you need to explore. Google "BTwaters" for probability games. Actually all these are in my latest CN News. Earlier in the term I sent out this News. Earlier in teh year I sent out this T1 News. The National News's are elsewhere on the internet but here is Term 2 Nat.

National Workshop feedback.
Big thanks to all 74 Hods and TICS who attended Ham, Rot and EIT Nat Workshops. Great feedback.
Best quotes...
"Hogan you better with age!"
"Hawkes Bay Math Assoc will be restarted"
"We need to do this more often (workshops)"
"Now for Year 9 and 10!"
"OSEM is a good idea"
What is on your wish list? "TIME!"

Files used today (slightly more finished!)
1. Session 1 .ppt. This has a few notes in the foot of teh slide whcih may help unpack it all.
2. Session 2 .ppt. This is about Backmapping from Year 12 to Years 7/8 and attempts to capture key learning and resources. i will post a collection from the three regions in a spreadsheet which may well help with developing learning programmes.
3. Pathways .ppt
4. Differentiation
5. Literacy
6. INQUIRY...Six steps
1. I notice, 2. I noticed because... 3. Data to support 4. Options 5. I choose to do 6. Do it! 7. Data after 8. Reflection ....what did I learn.
7. MISC a writing template
8. Liz Sneddon Resources - Search on Census@Schools 
9. Jake Wills - Google his website

Ok, Hamilton Workshop 23 people
, and a big thank you to everyone, amazing the talent and resources we have in teachers. Support Waikato Mathematics Association and share your knowledge and skills!
Files from today and answers to the Stickies.
Sticky 1
"Do you mean that students can bring their 'note book' into an assessment." ANS = The comment of a student generated formulae sheet being OK simply replaces the formulae sheet given to students in the past. There is no reason NOT to extend that to a page of examples, formulae and whatever else the student might like. However my view supports Pam at Sac HRT saying "We should expect students to remember something!" I suggest you try it and see what happens. Let students generate a HELP SHEET and trial it as an inquiry to see if it unduly affects outcomes.

"Can Vocational Assessments from VP website be used for academic classes." ANS = Yes of course. They are an assessment in a specific context. Many of the NZAMT tasks I wrote  for 91026 are no different and include a reference that this would suit a certain pathway. Dif out Geology 91030 and see how that fits Primary Industry Mining or Engineering.

"For making an inference is it individual sample size or combined sample size that determines the n=30 so 1/3rd or n=100 so 1/5 of OVS?" ANS = The sample is of a certain size and determines that decision. Remember that rule is only a guide, a suggestion to follow. Hence taking a sample of 40 means I would use 1/3 rule but if my sample is say 90 I would be happier to make a finer decision of 1/5th OVS cf DBM. See C@S inference documents.


What's up Doc?
- I think the Standford-0nline "How to Learn Maths" course by Jo Boaler is worth every cent of the $125 fee. I did this last year when it did not cost. Well I did tell you at the time! We need a similar course in NZ for all teachers and parents. I am working on that.

- Youth Guarantee now has a certificate for each of the petals like Primary Industries. Students just need  numeracy, literacy, 60 NCEA L2 and some Sector Related credits (see YG website) and there is your certificate to help  the student get access to a job. Good idea and another prod in the right direction in the right place.

- nzmaths forum is still active but activity has slowed. I wonder what this means? I still see a need for the forum based on the questions but perhaps teachers are getting familiar with the revision.

- Last years wine harvest was excellent with "24.6 Brix in the vat" grapes. This has created a deep red, full bodied, 14.5% alc wine full of dark berry flavours. It is only 30 days out of ferment and is a pleasant delight to sip. The wine will develop more character, clear, and become a best ever. Very happy with it. 2013 was pretty spectacular but this one is potentially better.

- remember all aspects of PPDAC have to be in evidence in a student assessment response.

- A "cheat sheet" is OK for internals. The key here is NOT TO TELL STUDENTS HOW TO SOLVE THE PROBLEM. A cheat sheet might be all the formulae a student needs, worked class examples, setting out examples and notes on how to use the calculator. An assessment with a new task is not invalidated by any of these notes. It may well help a student reviser and study! Try and see if the results are much different!

- I have heard recently of cases where "we just change the numbers in the assessment and practice this for a couple of weeks then do the assessment." That is totally unprofessional. Do not do it. A programme of learning based on standards is bad enough but passable, based on assessments is unacceptable. A learning programme should be based upon the NZC and students assessed when ready. There is no time limit for assessments unless practical situation (like large school) demands an efficiency.

- I am getting to be a very strong advocate of my HOW TO SOLVE A PROBLEM (see below) procedure. It is in reality a subject specific literacy strategy which helps the student make sense of the problem and gain the standard. An added trick I have discovered is after reading the problem and drawing a picture of it, draw a line through the picture showing the order in which you will proceed. "Imagine grabbing each end of this line and straighten it". This is the way the solution should appear on your page. This is the strategy! Do the calculations and answer that problem to gain Merit at least. Add more information, some critical reflection or improvements and that is sufficient for Excellence.

- iNZight is totally worthwhile and should be the first port of call for all students. I have seen other software and it can all be done on Excel but just get of the bandwagon and use the easiest software in the world. Designed for NZ. Google "iNZight software" for latest version.

- There are some interesting signs of life about math education in 2015. I will post any movements ASAP.

Now FEB 19th. It appears that NCEA results for L2 are increasing. See NZ Herald 18th FEB, page 5
NZ Herald 19/1/14 page 5

This is good news. The cause is difficult to establish but it is the game we are playing and it appears we are winning. I think it is a real increase which has resulted from putting a concentrated effort into the area of need.

Problem Based Learning.
Here is a problem that you can challenge anyone from about Year 7 to Year 97.

The inside square touches the circle and so does the outside square.

What is the area of the rectangular shape between the two squares?

Circle, square out, square in

Problem based learning causes learning. It requires a strong relationship between the students and the teacher and all believe in learning together. I would set up a group of 4 students and present them with the problem. The lesson would proceed on something like fractions or area or trigonometry but the problem would remain tabled. It is not important that a problem like this is solved NOW. It is important that a student or group group of students think about the solution. When an answer is agreed upon the next most important step is that it is presented to a peer group. This is what mathematicians do. I ask another for an opinion or assurance in a difficult problem just as Sir Andrew Wiles did in sealing a prove of Fermat's Last Theorem. At a different level of course but in exactly the same way. I wonder what this problem would be in 3d? Ahhh.... now I have to investigate!

Here are 5 steps that can be used to frame "How to solve a Problem".
1. Understand the problem.
2. Draw a picture of the problem.
3. Think up a strategy to solve the problem
4. Do the calculations
5. Present your solution to others.

I developed a powerpoint last year about this How to solve a Problem. I will update it a little this year but actually it is all I need to say. This approach to mathematics, and all other problems, causes reasoning and structures reasons for why you decide on a path. I have good student feedback on how this approach helps. Giving a reason and being able to explain is MERIT. This causes student achievement and this in turn causes engagement and NCEA L2 85%.

Geometry can be a bit tedious depending on how you teach the subject. I love all aspects of geometry. I continue to learn about it. I have invented a puzzle which I am calling "The Nine Towers". 3d printers have allowed me to make the shapes easily. I have made wooden and plastic versions of different sizes but it takes time. If you have a 3d printer and would like the files then please email me at I developed the shapes on the software at While I was using this very straighforward 3d CAD system it occurred to me that this would be a fun way to teach 10 to 14 year old students all about angles, transformations, measures, scale and shapes. Present a problem like "Make a set of SOMA blocks with 2cm cubes" and let them go.

A solution can be saved and sent to a 3d printer (just look on-line or buy one). I would ask students to explain in mathematical language the shapes and transformations, how they are connected or made and how to solve a few of the many puzzles. An extension is to create a new puzzle and sell a million copies for $1 each. I would like to do that so ask about my "Nine Towers Problem".

Enough for now. I have updated my pages!
Coming...2 innovative courses for  Year 12 and Year 13.
Another Problem
Seventeen or Bust Update I am on the 6th check and none have been primes to date. My computer has been hot now since Xmas 2012 and iterated a few billion times, (10,000 every 0.001 seconds). We must run out of numbers at some stage.

Cheers for now.

A new year and a new SSAC contract.
Just listening to the Prime Minister on 23rd Jan at West Auck business (see for the archived video.. Executive principals, Expert Teachers, Lead Teachers and Change principals all with a broad purpose of increasing student achievement so young people make better contribution to NZ and Family. Using the existing expertise and sharing that knowledge and skill around to other struggling schools is well founded. Mathematics, science, technology and digital technology were mentioned especially. These subjects are key to the future in NZ and I am fully supportive of this initiative. It is not cheap and will cost around $350m over the next couple of years. No mention of where that puts advisors like me but I will no doubt find out. A critical and telling indicator of performance is the OECD measure of mathematics where the PM stated our 15year olds are now ranked 23rd as compared to 4th in 2002. We have NCEA now, new then, SNP during that time, an economic low NZ wide but are emerging with a very positive outlook for the future. We now have a strong Pathways link, our national workshops this year will involve backward planning for the 85% Public Service Goal of all 18year olds in 2017 amongst other effective ways of lifting achievement for priority groups. All good news really for education. Google "OECD reports" and look for nz education, "Pisa study" to find how we did in mathematics. I think we did  OK but our students are able to do better and from last year I know if the will is there we can make these students improve to Merit and certainly achieve more...see my newsletter out soon.

Great technology, fast internet, clever social websites and our students are tech savy and have smart phones and mini computers like ipads. It is now very important we incorporate these technologies and websites into our classrooms.

One teacher I spoke with recently had used a private Facebook Group with her Year 13 Statistics class. One student photographed her notes and homework tasks on the white board using an iphone and had these posted on Facebook as the class was leaving. She commented that she now has a whole year of Stats Notes. The group allowed students to co-operate on homework and discuss concepts and issues. Her class appreciated a place to work together and most students actively took part. The resulting engagement and success changed what lessons became, what use the classroom became and how internet content resources could be incorporated. This in mathematics is quite remarkable and I can see how science, history and geography, technology and art could also use these methods.

This year is another year of what is called INDEPTH work in schools needing help, ideas and resources to increase student achievement for target students. Most schools identify literacy and numeracy as key indicators of performance.

I will upload thsi and edit it over the weekend.
Cheers and hope you have a great year.

NZAMT Conference 13 • Wellington • OCT 1 to 4
I am running two sessions.
1.Creating a Culture of Mathematics
This is about pushing the flag of mathematics higher. Making school and staff aware that mathematics is a highly valued context and bringing mathematics to a "talked about" position. The visual nature of aspects of mathematics are beautiful and artful. The problem solving aspect such as the AMC competition is enjoyable and challenging. The playground is a wonderful place to explore mathematical shapes for play. Connecting mathematics with location, science, IT and sport and always being on alert for the opportunity to encourage, make real, and have fun. That is our topic.
Main Culture ppt

2. Accelerating Multiplicative Thinking
"Keeping a robust and unrelenting focus on turning every student into a multiplicative thinker" is paramount for every mathematics teacher. There were many lessons we learned from the Numeracy Project years and this message was my favourite. Breaking counting and addition habits by reinforcing the use of multiplication, using problems that are best solved using multiplication, pushing factors, multiples and primes, always generalising results and memorising facts. Multiplication is about thinking of at least two things at once and is a big step up from linear or additive thinking.
Main Mult ppt,

Learning and Teaching of Calculus
How do you teach the concepts? From fundamental ideas? Rule driven? Here is a survey. Complete and flick back. Only a few people handed back surveys so can not really do much. Was hoping to have a get together about teaching and learning of calculus, the forgotten child.

CN National Workshop #2 • Getting Connected June 18 to 21

Tauranga Tues 18 AM, 143 Durham ST; Waikato Wed 19 PM, St Peter’s School; Napier Thurs 20 PM, EIT Taradale R101; Gisborne Fri 21 AM, SSS Bright St

Napier Thurs 20 PM, EIT Taradale R101;       Gisborne Fri 21 AM, SSS Bright St. Session 1, Session 2, GM Progressions, NA Progressions, 2.6 Prep EXT, 2.7 Prep Ext, MOError link, Geogebra link, Lets Talk reading.

Here is an updated file. A GeoResource. It is a task to themeasure  Girth of the Earth. Orignially it used the GPS system and now it uses Smart Phone apps as well.
Measure the Girth of the Earth Resource, .

Some learning files for you.
From Whangarei and Waikato  Jumbo.
Weight by SEXSession 1 iNZight for Beginners, Trout Sample, Session 2 iNZight Advanced, another trout sample and Session 3 was a hodgepodge of many ideas. Here is another important one. There are 23 others in this folder and if you are interested then please send an email to discover what is there. All Trout here. I just added a rand column and sorted on that to randomly mix a dataset, then selected 20 or 30 or 40 (sample size) from somewhere in the data. The original data is actually a sample of the estimated 1.5 million trout over 45cm in Lake Taupo at that time of the year but for the purposes of learning in the classroom treat the 1000 fish caught as the population and sample from that. That way you can know about the population  DOC has many Target magazines with more information.

Mathematics news Term 2 National News and Regional News.

Student Voice imageStudent voice is important in course design, feedback about learning their(student) learning and your(teacher) teaching. I like and have trialled successfully "journalling". This was essentially allowing for a 5 minute slot at the end of a class period and training the students to reflect, record and otherwise ponder their learning. Starter questions may be used [ "What do you now need to learn?" How do I help you learn? ]. I insisted on full sentence structure, neatly written. I would collect these and ponder them. Students asked surprising things like, "Can you teach me how to remember my facts Sir?" "I still think that is a silly way to add fractions!" "Can I see you this afternoon Sir, I have to ask you something". Yum, just love those ones...Yeah Right!. There is also student voice when another person gets some questions answered as was doen in teh Attol project. "What are you learning?" "Why are you learning this?" "How will you know when you have learned it?" "How does your teacher help you learn?" Other questions like "How do you help you learn?" "Do you have a learning space at home?" Too mnay questions....overload.

Workshop imageNat Workshops coming up.
From the news.
At the term 2 national workshops middle leaders will have the
opportunity to discuss current issues and trends. Topics will include:
• Revisiting NCEA Level 3 – tasks/resources/pedagogy
• External examination preparation – subject specific literacy
• Writing and editing assessment tasks
• Course design including SOLO and ALIM
• Progressions – preparing junior students (Y9 and 10) for success in
NCEA L1, 2 and 3 in number/algebra – measurement/geometry.

I am employed under the Secondary Student Achievement Contract with the Faculty of Education, Team Solutions, University of Auckland.  The contract is targeting Maori, Pasifika and Special Needs students; and be working indepth with some schools; and be working with Middle Leaders; and will be developing focus investigations; and providing some needs-based workshops. This year 2013 the focus is INdepth. Schools who have volunteered or those that have been identified as needing help.  I will report successes.

LOMAS HUGHES TESTS for fast ID of CL level in NZC Number. Test 1, Test 2, Test 3, Test 4, Answer Sheet 1, Answer Sheet 2, Answer Sheet 3, Answer Sheet 4, Marking 1, Marking 2, Marking 3, Marking 4, Bonus Chapter on Negative Numbers.

Download, install and use iNZight. Register and use the nzmaths Blog Latest National and Regional newsletter.

Have you considered data from a physics experiment as a sample? Then bootstrap it to get estimates? Data from an experiment is a sample from an infinite population.
Look at this. I am "pretty sure" the  slope is in the interval [0.25, 0.34] or is it 0.29±0.05. Is this a cool way to get error estimates? This connects Statistics and Physics.

Sample data image

National Workshop 1 Resources
Agenda, the grand plan
This session develops the idea and stresses teh importance of being an inquiry focussed teacher. Students do not always fit the expected. The Year 9 students are not at Level 4 ready and willing to enter Level 5 NZC; they are all over the curriculum. Is my approach working effectively. Am I prepared to move my practice. How can I help improve achievement? This is inquiry learning.
.ppt used
Reading 1 by Dr Graeme Aitken, AU
Reading 2 by Mike Fowler
Reading 3 Teachers as Learners
Blank Sheet to set up your inquiry
My inquiry example
How to solve a Problem powerpoint i am using this year in INdepth work.
Reading from Professional Engineers Newseltter April 2013. They use a similar method.
The homework is to construct and do an inquiry, write it up and be prepared to report in Workshop 2.

The powerpoint used.
Y9 marks resource
Class data spreadsheet
Sample data to show variation of ability
Sample assessment resource used and you should have a look at your own data to see if it can be seen with better eyes. This could be an inquiry. The connections to inquiry are fairly plain to see.
LOMAS HUGHES TESTS for fast ID of CL level in NZC Number. Test 1, Test 2, Test 3, Test 4, Answer Sheet 1, Answer Sheet 2, Answer Sheet 3, Answer Sheet 4, Marking 1, Marking 2, Marking 3, Marking 4, Bonus Chapter on Negative Numbers.

Powerpoint used to check your knowledge of jobs and Pathways petals.
Stds to Pathways spreadsheet to put your own courses in and see whcih Pathways they favour.
Youth Garantee Link to see how standards are connected to future employment
Careers Link to check out what jobs pay
Future Job Link, Ministry of Business Innovation and Employment. We do not need 400 designers every year in New Zealand!

Power point used
Teaching Randomness and a few other things
Understanding TRUE probability
Jail Break and a couple of other things for learning about probability
There are a huge number of resources around probability and statistics. See Census at Schools and Google "NLVM", "Starter of the Day",  "" and others!

Effect Size for Dummies
Timperley on Evidence

and explore sound files on, go and look for cool recordings.

That is about it for the time being. The following is from last year and at the bottom references to a lot more and previous 10 years. Discover "Ask the answer", "If you can't model it, do not teach it."

Cheers, enjoy being a teacher.

This is a popular resource, has assessments (2013) written around the context and is fun.
taupo fish pic
          14lberTAUPO TROUT and INFERENCE • Workshop 3/4 OCT/NOV 2012
Here are the files I used in this workshop. You can use all data, modify and use ideas and resources. Not all fish are as big as this beauty and in 2012 they might be a bit few and far between! The big lake is a pretty good fishing spot nevertheless.
Main document - Lake Taupo Trout description and progressions Year 9 to 13. Sample assessments and answer schedules. Teacher PD questions.

All trout data has been formated as .csv files.
Trout Data 1993
Trout Data 1994
Trout Data 1995
Trout Data 1996
Trout Data 1997
Trout Data 1998
Trout Data 1999
Trout Data 2006
Trout Data 2007
Trout Data 2011
Excel sheet of all trout.
Fathom file of all trout.
Pictures for making the box and other cool art.
Art 1, Art 2, Art 3, Art 4, Art 5, Art 6, Art 7, Art 8, Art 9, Art 10
Fish for cutting up and putting into the box for sampling
1993 data, 1999 data, and 2011 data. More availble on request.
Confidence interval caution reading!
Dot plot, box whisker sheet for data cards and hand sampling
Marion's Inference .ppt, see also this website
Jim's .ppt
Reading about bootstrapping
and there are more files if you need. I will try and keep these updated.

BOPMA LogoBOPMA Biennial Conference Nov 23rd 2013
Theme "it is all about the thinking" and Website
BOP Polytrech, Windermere. $40 per head , presenters free. Morning tea and lunch provided.
I have mailed out a registration document and here is a map of BOP Poly. Planning is progressing well.

The keynote speaker is the NZAMT Bevan Werry Speaker Naomi Ingram (more on I have tried to encourage as many local teachers as possble to contribute and share their knowledge and expertise. Amazingly this has worked well. Also the Mathematics Department from Auckland University are sponsoring and running workshops for us. NZQA and possibly ERO will hold forums. There are 11 trade displays at the moment. BOP Poly is providing the venue which I think was last used in about 1998 or there abouts. Invoices will be emailed to schools as soon as registration returns are recieved, payments by bank direct credit to BOPMA. BOP Poly is catering for everyone. We will be attempting to video sessions and make them into downloadable sessions for dept PD. Topics include randomisation, bootstrapping, courses, unlocking thinking, algebra resources and ROGO.
Latest National and Regional news and the old ones.
Term 4 2012 National, details of Road Show and statistics help in Term 4.
Term 4 2012 Regional
Term 3 2012 National
Term 3 2012 Regional
Term 2 2012 National (first one in new contract)
Term 2 2012 Regional (first one)
Two reallly important documents to be familar with and use.
Evaluation at A Glance
This is a synthesis of 25 reports and clearly identifies three key issues to raise student achievement.
1. Being student centered
2. Embracing NZC
3. Engagement.

Literacy and Mathematics Y9 and 10
If you do not believe that data helpds, read this.
______________________ Klein Project, is about  "a sense of connectedness between the mathematics of the teachers’ world and contemporary research and applications in the mathematical sciences." It is refreshing to be thinking mathematics instead of assessment, pathways, organising students and managing management. Take a look at this sight and freshen your classroom with some interesting problems in mathematics. I took an immediate affinity to the oranges problem having written a resource about the patterns that the balls form when stacked in this way a few years back. These are still on under SNP activities but here is the resource [Math Investigations]. The Klein Problem is about finding how to stack spheres in the most densely packed way. It has been solved by the way.

Here is an Overview of Sec Numeracy Project for you. PD! It has been here since 2005!
Please join this free blog. Today I answered a question concerning "1.7 Conditions of Assessment". I answered "re Conditions of Assessment on the TKI website for aligned standards.The term "free from unnecessary constraints" should be read with the sentence following which states "Collection of evidence for this standard could include, but is not restricted to, an extended task, an investigation, or a more formal activity." [Note the same sentences are in the C of A for each standard.] The intention was to free up assessment form the more common and traditional 1hr test. The next sentence "In all cases authenticity of evidence needs to be considered." puts a damper on this freedom but most of your suggestions above are OK. Reality means "open book is fine", "formulae of course are accessible", computers and technology (iphone/ipad) could be used, "tick sheet may well tell them solutions so perhaps is not appropriate, access to practice papers should be of no use to students if they are solving a new problem. Hence make sure the problem is a genuine and new problem to be solved. The mathematical thinking is being assessed. A = straight forward, M = justified solution, E = correct and well justified, presented and perhaps extended solution; all in general of course. Authenticity means "this student" did " this thinking"." This is an example of the information sharing of which the blog is capable. Please please use it!

Ngatea, Hauraki Plains TOD
Resources June 15th 2012

Files, Links, Ideas and Notes from TOD at Hauraki Plains School as promised.

Workshops by Jim Hogan
1. Probability Progressions.ppt used. NOte 6.8 mb. Email me if you want the pic free verison. I want to add more detail for Level 1, 2 and 3 probability as well. That may happen.
2. Numeracy .ppt used. This is the small no pic version, the other is 18.4mb. email if you want that.
3. Breaking the stick problem.
4. Book 9 Numeracy for long run simulation and Monte Hall problem. Google for these as well.
What you said about Prob and Numeracy.
WK2 feedback and Numeracy Stat.
Good to see resources and understanding feature. Likewise problem for Numeracy WK.

Workshops by Sandra Cathcart
1. Algebra Powerpoint used.
2. Files supporting Algebra
    - algebra bingo
    - algebra language loopy
    - algebra loopy
    - algebra substitution integer
    - algebra substitution whole
    - algebra race
    - bubble substitution
    - Coaster Problem .ppt
    - Collecting like terms loopy
    - four in a row algebra
    - four in a row MULT template
    - match up algebra
    - Strategic Solving Part 1
    - Strategic Solving
    - Substitution Game
    - Writing Algebraic Expressions
Wow, that a lot of files. I think some ofthese are also on the SNP website,
3. Progressions in Statistics Powerpoint
4. Files supporting Statistics
    - 01 Kiwi Capers
    - 08 Kiwi Capers
    - Growing Scatter
    - How kids learn ... reading
    - Hungry or google "Hungry Planet"
    - progressiosn L5 to L6
    - Shape Stats Activity
    - Sheep
    - stats shape.doc

Resources used in the CLUSTER MEETINGS May 2012
Feedback of Needs! Needs feedback WK1 HB ASS NOTE!

Files, Links, Ideas and Notes from Workshop 1 in Central North as promised.
1. Powerpoint used. .ppt
2. Noel's Problem. This is good for advanced algebra Year 10,11,even 12 students. It is a geometric investigation into the relationship between the hypotenuse of a right angled triangle, its area and its perimeter.
3. Tataiako Files. Diagram, culturally responsive teachers and readings, self assessment.
4. Pathways Matrix Page 1, Matrix Page 2, BOTH
5. 2.9 AME steps and the standard
6. 2.14 AME steps and the standard
7. How to solve a problem wall display and a sheet for students.
8. My Learning in Maths, a file for students voice
9. My SCHEME and course outlines.

1. Justin's files (HOD Trident HS) Send him an email and say thanks.
    - Pathways example
    - Year 11 MCAT .ppts for practice
        - Page 1
        - Page 2
        - Page 3
        - Page 4
        - Page 5
        - Page 6
    - Bonus for Year 7/8/9/10 programmes
        - Times Tables Beep, TT Shrink, Timesnake. The first two are .ppt for recall practice. The Timesnake are cards, bent in half so the answer is on the back. Students show teh question to a partner and check their answer.

Feedback Wordle
Feedback WK 1

Fairly obvious what went on in Cluster 1 workshops!

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