Ratonga Tautoko for education advice

Waikato and Bay of Plenty Regions

SNP 2006 Resources




July 4th 2007 update GO BLACK BOAT!

May Day and all is well. I hope Term 2 brings joy and happiness to everyone. Good luck to the ducks and the Black Boat. May the All Blacks stop injuring themselves and the Warriors and the Silver Ferns win every game.

> Term 2 2007 Newsletters Math News here! Posted to schools a week or so ago.

> Later this year in September the revised 'draft' curriculum will be in your schools for final approval. I have seen the first draft of the revision and feel teachers will appreciate the more carefully worded rewrite. The achievement objectives remain quite open with the emphasis on developing mathematical thinking and communication skills. These two key competencies are the real reason for learning and teaching mathematics. Support material is being generated and will be available for 2008. Do not throw out previous schemata!

> The NCEA L1 revision submissions last year by teachers indicated the fragmentation of mathematics in the current standards did not allow the connectedness of mathematics to be emphasised, explored or examined. Teachers also reported too many standards. I was quite surprised by the magnitude of the changes suggested in the review which has been posted to all schools a few days ago. HODs will have to be on the ball to respond by 21st May but considered response is needed by everyone. Force the effort please.

Basically there are six new standards suggested:-
- each worth more or the same, total 24 credits as before. One external is worth 6 credits.
- demonstrate an understanding is the new expectation which is in line with draft curriculum, CAS and SNP projects
- assessment questions can now be from across strands (remember only three strands in the new draft curriculum)
- very little if any has been removed so you will need to choose a course as before to suit student needs
- there are alternative CAS standards for the CAS project students in number and algebra
- there are three external and three internal standards
- there is one learning criteria for each of the Achievement, Merit and Excellence parts.
There are no sample assessments or questions yet to help clarify expectation or the standard and no existing assessments will be suitable without significant alteration.
What does this do to your Year 11 courses? Has the student motivation issue been addressed? Good luck and keep your head on! BUT REPORT BY OR SOON AFTER 21st MAY 2007.

> A NEW DVD Resource for ESOL or English as Second Language teachers. I will write about this in my TERM 3 news as I do think it is useful not only for the non-English speaking students. Most of us from time to time discover a wee surprise addition to the classroom and from my experience over the last 30 years of teaching feel a bit imposed upon, miffed and/or quite unprepared to attend to or accept the challenge and extra work these students generate. This resource clarifies and exposes needs with practical suggestions and one to one teacher, student interviews and classroom examples. For these students it is not the mathematics that is the primary is the language. There are 156 languages being spoken by students in NZ schools in 2007. How would you cope with three Year 11 Bolivian students in your class?

> SNP - Mathematics Resources. If you are wanting independent work for better students or practice work for your slower students you may well find suitable tasks on the website under project material, SNP. Click here to go there. If you have tasks that would be suitable or would like to write tasks then please tell me. This is becoming a very good collection of a lot of clever work all with teaching notes and discussion.

> I am running two courses later this year. Problem Solving and Thinking in Mathematics. The first develops the ideas from "Lighting Mathematical Fires" by D Holton and C Lovitt (1999). The second is an unravelling of current research about how students develop mathematical thinking and exposes the issues of higher level thinking. Our SNP data shows Year 10 students reach a plateau and only 20% or so emerge with what I call multi-dimensional thinking. Many of our Year 13 students remain as multiplicative thinkers and achievement is limited by this feature. I am focussing my spare moments this year on how to break this mold. Test yourself...The front tyre on my bike lasts 60,000 km and the rear tyre lasts 40,00km. If I swap them around a bit how far could I get out of one set of tyres? How many swaps do I need? When do I swap? What colour is the bike?

> Hi Deb and is the Farmer Brown Powerpoint for you. You have inspired me to add more to the series. The powerpoint can be used with teachers to explore solving proportional problems or students to explore alternative solutions at different Year levels.

From Last Time

Powerpoint 768k from Waipuna, National Numeracy Facilitators Day used in my session on Developing Proportional Reasoning. I have removed the pictures so it is smaller. I need to add your contribution to the summary diagram and will get that done later this week. The other resources are all available as i indicated at the other session from Thank you to everyone who took part in these two sessions. Very useful.


Welcome to 2007! I remember thinking as a child in the 1960's that I would be my parents age in 2007. Well here I am and it feels OK. I did think that the issues of starving India, African famine, wars, fusion energy and a few other problems would be all but gone but that is another story.

My latest o7 Term 1 newsletter is here! Two megabytes so be warned. It is not for a slow connection. I did post a smail mail copy to all schools.

Comet pics , all .jpg below. I took all these pictures, what a beautiful sight and it is still with us. When the moon gets a little less bright we will continue to see the Mc Naught Comet. This is the first very persistant and obvious comet I have seen. Halleys Comet i saw but it was not as vivid as this one.
Comet 1, Comet 2, Comet 3, Comet 4, Comet 5, Comet 6, Comet 7 , Comet 8 , Comet 9, Comet 10

I have about 70 pictures and will take some more when the full moon resides a bit.


Here is a proportional reasoning paper i am enjoying at the moment. The website

has a huge resource of valuable work to explore. I recommend it to develop this very important aspect of learning.


All the best to everyone and enjoy teaching thsi year. Start the year with data and finish the same way.




Thank you for everyone for supporting the conference. Over 160 teachers present and about 40 or so presenters and trade displays some of whom were also teachers. Here is Neil Marshall's paper he presented on High Level thinking. No other papers available at this stage. Good evaluation feedback and it is noted we need time for lunch! The next BOPMA Conference is in November 2008.






Mini Conference Day 14/10/2006

Thank you to the Wellington Mathematics Association teachers who gave me such a warm reception and inviting me to talk as a keynote on 14th Oct. A Saturday! Wow and what a braod range of workshops from which to choose. Thank you for the book tokens as well. I have a target book for those by Simon Singh. The powerpoint I used is here, and the material I used in my workshops is here, here , here, and here I have a couple of other independent activities that you may be interested in here and here. These and others are all available from the wesite under SNP project resources, activities.

The books I referred to and some others were:-

  • The Curious Incident of the Dog in the Night Time by Mark Haddon..."The dog is dead" "I got that far" said the policeman.
  • I's About Learning (And It's About Time) edited by Stoll, Fink and Earl. Professor Louise Stoll was in NZ in 2005 and spoke around the country. "We do not have a knowledge problem...we have a use of knowledge problem." Picture attached.
  • Also:-
  • The Music of the Primes by Marcus du Sautoy "1 2 3 5 7 11 15 22 30 ...What are the next three?"
  • The Tyranny of Numbers by David Boule. "Whay counting can't make us happy." "The speed of London traffic 1900; 12mph. Speed of London traffic 1996; 12 mph"
  • and do not overlook these two old favorites from that year 1994. mathematics Volume 1 and Mathematics Volume 2. Pictures attached.

These books all changed the way I viewed education and thinking. I have a few others when you have finished them. Simon Singh for example has some curious views. I see the lastest collection of papers is about to be published by the Ministry of ED. Keep a lookout for this booklet of papers.

A fascinating Magic Square for you is here. Instructions included. I challenge you to find another solution. lastly we should all note that Friday the 13th Oct 2006 was a very special Friday teh 13th. The 13/10/2006 digits all added to 13. When did this last happen? Clue one can remember it!
Thank you again everyone.

Two new independent activity resources for teachers Years 9,10
Number in Statistics and Number in Probability. Many more of these on the website under SNP Project Materials...Activities. These resources are designed for small groups to work independently and then report back to the teacher or class. They can be used with all levels but tend to be more suited to the able students. Assistance would be needed with lesser mathematically enabled students but is still a realistic task. Most tasks develop patterning and algebraic thinking through problem solving and investigation.

Math HOD Day Tauranga and Hamilton Resources
The Darft Curriculum Powerpoint Used.
Calculus 2005 Answers .ppt
Laurenson File L1L2 PERFORMANCE
Laurenson File US/AS Levels
Reading Key Competencies
Four Questions Feedback
R squared .ppt
Pics for Matt, one, Two, three
Difference Two Squares
Prime Numbers

Thank you...JIM

Maths Week! Yippee

So what do all the numbers on a completed
SUDOKU puzzle add up to?

Latest July Newsletter from moi. Here

You might like to read the report from ERO on The Quality of Teaching in Years 4 and 8:Mathematics. The newspaper made it sound attrocious.

A little problem for you all... What is the ratio that is exactly halfway between 1:1 and 1:2? The answer is 5:7. Now that is obvious isn't it! Try finding halfway between 1:2 and 2:3.

Congratulations to the winners of my competition in the last newsletters. I decided to give an HP CAS calculator to both entries. Well done and thank you Lewis (TGC) and Christine (TNT). I am keen to here from schools committed to being involved in SNP for 2007 and 2008.

Here is my latest newsletter and one from Massey, Anne Lawerence as well. Good notes in the Massey one about dates and scholarship. The problem in my newsletter can be solved in many ways. A good challenge for your students is to find out just how many! I have 8 distinctly different ways which I may share with you here in a few weeks.

BIG reminder to visit the website for good workshops on stats. I think these are of use to students and teachers. Here is the amazing Rice Uni link.

Three Files of Work for Independent Group work with Instructions and Tecaher notes.
Double Double, The 1 That Got Away and More Powers Investigations

The Dot and the Line by Norton Juster
I rediscovered this little book first published in 1963 and republished in 2001. The author I note is now retured and conducts a support group for negative numbers. An abmirable and possibly rewarding venture. The story is about a line who is deeply in love with a dot. The dot is distracted by the squiggle however and ignores the line. The miffed line learns to to be very creative and so demonstrates to the dot a superior cleverness over the squiggle which woos the dot forever more.


Another fascinating book is MATH CURSE by Jon Scieszka and Lane Smith. In this book a student refects on experiences with learning mathematics in Mrs Fibonacci's class. The story becomes a nightmare of problems with an answer that equals a whole through which the student escapes. The problems in the book are Year 9 type problems and all have answers which encourage creative thinking skills.

This book and others, eg Lineland, Flatland, Alice in Wonderland, Through the Looking Glass add that extra dimension and variability to a mathematics classroom making the subject more accessible and fun. Search for these on Amazon and email to me your favorite books for mathematics.

Curiousity for Classes?

I'm Dot in Place

is an anagram of

Decimal Point

I wonder how many other mathematical words and phrases rearrange into similar meanings?

I noticed in a visit to a school a large "Hundreds Board" about 5m x 5m painted on the courtyard along with a wide range of other shapes, squares, circles, lines and letters. The hundreds board was a copy of the "Snakes and Ladders" board and when I stood on it with a numeracy teacher we both saw the possibilities of "doing" mathematics on it. Do your school grounds have opportunity for students to do mathematics in their play?

NCEA - Nat Cert of Maths - MAP - unit standards and achievement standards. Keep an eye on the JUST UPS from TKI. There is a discussion paper about "residuals" in Statistics that would be worth while sharing in a department meeting. Residuals are a way to confirm agreement with a model of a situation in Level 3 Statistics. National Certificate of Mathematics should be a major goal for the Year 12 students. Likewise MAP 2006 (NZAMT website) now includes unit standards and is alligned with Nat Cert and NCEA. MAP 1,2 and 3 is for the students who from the numeracy project we can identify as adders or pre-multiplicative thinkers.


  Counters, Adders and Groupers.

Here is a lesson about how students learn mathematics.

The NZ Numeracy Project has established through research that students learn mathematics in a progressive way. They begin solving problems with basic counting strategies, through additive strategies and thence to grouping strategies and groups of groups strategies. This represents an increasingly complex thought process development as the student matures and gains experience of life situations. The teacher has the job of ensuring this process happens by monitoring the progression and creating appropriate instruction for each student.

Counting is a zero dimensional process. Adding builds on numbers in a 1 dimensional way. Multiplying or grouping is an array or 2 dimensional thought process. Powers of numbers, mathematical proof, analysing data, creating solutions, vectors, trigonomery all represent multi-dimensional thought which if a student is not sufficiently prepared for in multiplicative thought will forever remain a mystery. These are the students that struggle in Year 11, 12 and for whom National Certificate of Mathematics and MAP are appropriate.

What does a teacher do to determine if a student is a counter, an adder or a grouper? The answer is look and listen. Ask the student a question and listen to the explanantion of the student in answering the question. How advanced is the thinking of the student. Some questions are better than others for this purpose.

The question "How much do I pay if I buy 48 bales of hay at $5.50 each?" is beyond the counters and early adders. The more advanced adders can get an answer but it is the multipliers who will see ways to use number knowledge to invent a solution from numbersense rapidly. The use of either the calculator or the vertical algorithm give no information as to how a student is thinking and is not a foundation for building senior mathematics.

Once a teacher accepts that students learn in this progression the monitoring; the lesson matrial; the assessing of learning; and the reporting on learning all become issues which must be resolved. Does a teacher accept the same answer to an area problem from a counter, an adder and a grouper for example?

The categories or stages the NZ Numerfacy project classifies students are very broad and blurry but are useful indicators. It is wise to remember this as students will change their thinking depending on variables ranging from the difficulty of the problem to the time of day and if it is raining or not.


FROM Last Update.

I went to the CAS training days in Auckland in March. It is interesting to see how closely aligned the CAS and the Numeracy projects have become. The main push in both is effective teaching and learning for all students. One of the activities we explored was the old Yak problem with a row of Yaks represented by matches trying to walk and leap past an opposing row of Yaks. Starting with 1 each side and recording the walks (steps forward) and the jumps then increasing the difficulty to 2 each side and so on. A curious power rule emerges.

Here is a cool file. I call them magic cards. Instructions on the file.

I have deleted OD data from this page but if you still need to see last years index page go to the bottom of this page.

Gordon has asked me to ensure all teachers know that NZAMT Olympiad Committee offer a certificate in problem solving to all secondary students throughout NZ.This is an excellent opportunity and follows on from the Calc/Stat Scholarship training we all enjoyed last year. Gordon mentors each student by marking and coaching the papers personally. This is an NZAMT initiative.

#3 NZAMT Writiing Panel Report CHCH 2006
I have just had three very interesting and busy days writing new assessments for the NZAMT website. There are not so many new assessments this year but they were all checked quite carefully to see if they met the standard and have been modified accordingly. I rewrote 5258 which is the "Use of expected values" Level 3 standard. The old one was a bit off the track.

I have to recommend to any teacher interested in assessment that the Writing Panel is an excellent opportunity to learn practical assessment writing. There will be another session in Week 3 january 2007. Book it in as part of your PD. The olympiad meets then as well as Development Band developers and MAP rewriters. The many Olympiad students are there as well. Good networking opportunities with fellow teachers, lecturers and professors. We only had nine writers this year and to overview all unit standards in three days is a big ask for this number.

MAP has been rewritten and is a recommended option for the lower achieving students in Years 11, 12 and 13. The modern school systems means you will get students with little math ability in these years and they are your responsibility. What do you do with them? The National Certificate in Mathematics is a good option but is realistically a Year 12 award. The Year 11 students sees no reward for effort in Year 11. MAP gives an award with a grade and it now includes the easier Unit Standards as assessments along with other investigations that may well not be an NCEA type option. The same adjustments have been made for Year 12 and 13. For detailed information including enrolment and critical dates go the the NZAMT website. Mathematics students now have MAP, NCin Maths and NCEA to aqchieve for qualifications.

On that note please do not over assess. Construct a suitable course with each of your students and have a scheme and teaching practice in place that is sufficiently flexible to ensure success.

#5 Curriculum UPDATE.
Information will be coming to you in JUNE from NZQA to begin the consultation process. I seriously suggest there are no scheme rewrites until you have spied the the anticipated revisions. Add flexibility to your scheme or learning programmes but keep away from major time consuming updates.

BOPMA Mathematics Conference, NOV 24th, Friday 2006, 9am to 3pm.
Rotorua Convention Centre. Costs for non presenting teachers is $45 per head. If you present a workshop there is no charge for you attending. Tea/Coffee on arrival, morning tea, lunch and afternoon snack will be provided.

Programme: Keynote from Auckland University lecturers on Modern Trends in Mathematics; Just where do our math graduates go? This will be followed up with workshops in modern studies such as Bio-Mathematics, Modelling and Learning Algorithms.

Teachers are hearby invited to submit briefs on workshops they would like to prepare for this conference. Include needs.

The 2004 Conference was attended by 167 teachers and about 20 presenters. All agreed it was an excellent effort. Let's do it again.

#7 Secondary Numeracy Project 2006
I continue to be amazed by the misinformation that I hear from teachers about this project. It is not primary mathematics. It is not for low achievers only. It does not require a huge purchase of equipment. All current teachers of mathematics can learn these different ways to teach. I am offering 2x1.5 hr sessions as Introductory Numeracy PD. If you want me to organise a visit and workshop then please call me on 027 278 5458 or email me to

This year I have 9 teachers in 13 schools running the programme with Ministry funding and my help. The new schools are Te Awamutu College, Otarahonga College, Hamilton's Fraser High School, Hillcrest High School and Putaruru College.The second year schools are Tauranga Boys' College, Tauranga Girls' College, Edgcumb and Kawerau Colleges, Taupo-Nui-A-Tia and Tauhara Colleges, Reporoa and Rotorua Lakes Colleges. You may contact the HOD Maths in any of these colleges for independent and honest updates.

I am looking at 2007 now as well. If your school is interested then please contact me. I will be running Introductory Numeracy sessions in all schools who have already contacted me. Selection of participants for 2007 depends on regional balance and need.

Get this resource from for statistics. A lot of good data ready for use..

Another cool website I was reminded of....

WAIMAT have a website! Visit

Visit a really interactive encyclopeadia at
Visit the National Library of Virtual Manipulatives for some math applets...really really useful.
Here is a cool fraction site. Does fractions >1 which is a nice change.

CHECK in with Mathsweek Developments.

JOBS...Quite a few important HOD jobs available in the region. Check the gazette or subscribe at


I found the Mindreader again!
AND here are two .pdf files for



Numeracy Project

 NZAMT Conference 2007

WEBSITES and Other Resources for Teachers

Mathematics Advisor Newsletters
Term 2 2003
 Term 3 2003
Term 4 2003, Survey Numeracy
Term 1, 2004
Term 2, 2004
Term 3, 2004
Term 1, 2005
Term 2, 2005 and Survey
Term 3, 2005

Term 4, 2005 and Survey
Term 1, 2006
Term 2, 2006
Term 3, 2006

Term 4, 2006
Term 1, 2007

Term 2, 2007

Ministry of Education
TKI NCEA Internals etc

Numeracy Project
Statistics New Zealand

Problem Solving
Sample problems for Years 9/10

Graphing Calculator Software
Math Archives in UK
Maths on Line in NZ

KaleidoTile Software for Macs
ENC Ed Resources
CAST Statistics Simulations - MU
Mersenne primes
Amicable, Happy and Rare Numbers


Modeling in 3D
3D Models Templates

Calculator Sites

MORE Resources
Teachers at WORK
EFOFEX Software

Hope you enjoy these

Free Software
Account for your Department Dollars
Time Diary for Advisors and Teachers

Curriculum Document
Mathematics in the NZ Curriculum 868k
Frist Draft of New Curriculum

Mathematics Associations
Maths. Assoc. of Victoria (OZ)

NZAMT - Unit Standard Assessments
Caterbury Maths Association

Three Teaching Tips.

Give me Another!

Students understand when they can ask you a few similar questions.

Give me another, and another, and another.

2.3 is a number between 2.1 and 2.45. Give me another.

Ask the Answer!

Instead of asking what is the area of a 6x4 rectangle...


I have an area of 24 sq units. What does the shape look like?

This is a much more powerful and investigative question with many more answers.

How do I make it easier; how do I make it harder?

For a game or warmup activity ask the question, How do I make it easier and how do I make it harder? For example the simple warmup activity for a group of
"Count the next 20 numbers after 89" could become easier if we started at 1, or 10, and harder if we counted in 37s or 7, or start at 2.3 and count in halves, count backwards from 87 in 5's.

Apply this skill to all activities and you will have an endless source of new ideas.

2005 DEC Index Page Archive

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