Monday, 7 August 2017

Making Connections

If  algebra is about seeing patterns and making connections, how can we connect number, geometry & algebra?

One approach... think about the number 180;
  • 180 degrees on a straight line
  • 180 degrees is the sum of the interior angles in a triangle
  • 180 degrees in a semicircle
  • 180 is an even number and a multiple of 10
  • 180 in standard form looks like this 1.8 x 10 ^2

Is 180 a happy or an unhappy number?

  1. What pairs of numbers add up to 180?
  2. How many different pairs can you find?
  3. What patterns can you see?
  4. How do you know if you have found all the pairs?

A spreadsheet is one way for students to experiment :

Use the View> Show Formula option to introduce students to the algebraic logic behind spreadsheet formulae

How could we draw this?
How else could we draw this?

How could this be written using symbols?
120 + 60
or 120 + 60 = 180

Target 180
Two numbers add to 180. If I know one number what could the other number be?
Use a table like this as a starter/energiser  for a lesson

How else could this idea be represented ?

A picture maybe?

Using symbols and text?
120 + ? = target   or 120 + x = target 

In this case the target is 180 so we could write :
120 + x = 180

What would this equation look like if the target number changed?
What does this tell us about the values that x can take?

Other ideas might involve rectangles , perimeters,  area 

What other ways can we connect algebra, geometry & number?

Monday, 10 July 2017

20 years on

As we embed the changes to 91027 and prepare for a changed format in  91028 I wondered how things used to be...

From the 1996 School Certificate chief markers report.

In the first paragraph it was noted  that there was a "continued requirement for candidates to interpret information,  to explain, describe and justify their mathematics clearly and concisely"

I discovered investigation tasks in exams are not new -
In 1996 candidates had to  carry out an investigation to discover what length and width of a box would give the greatest base area.
To find a solution they could chose their method and were offered a table or grid as a guide.

School Certificate 1996

These investigative type questions first appeared in 1995 and these was one in each paper up to the introduction of NCEA.

I have scanned the questions and put them in the shared 91028 folder  

You will see there is a folder called GIVE ONE GET ONE that all teachers can add a question to - this is the quickest way we will build a useful resource. Please be careful to not delete any of the files in this folder

It seems we are singing the same song as our 1996 colleagues when it comes to algebra. The report noted basic algebra techniques were poor - these included
  • expanding
  • factorising
  • changing the subject and 
  • solving equations
It was recommended that students should be exposed to problems that are challenging enough to not be solved by guess and check and while rote learning of processes allowed students to pass the exam they did not prepare them for higher levels of mathematical understanding

All was not doom and gloom, the chief marker reported there were many "excellent examination papers and a large number of candidates were well taught and had a rich range of mathematical experiences throughout the year"

Monday, 19 June 2017


Each winter the stars of Matariki and Puanga signal the end of one year in Aotearoa, and the beginning of the next. Traditionally Mäori have recognised the rise of Matariki as a time to celebrate and prepare for the new year.

Matariki  takes place on the  25th June however  the Matariki celebrations have begun.
To see what's on check out the Matariki Festival 2017 website.

Matariki gives us an opportunity to enrich students’ mathematical experiences in a meaningful context.

Click here for a an integrated unit from NZMaths 
The unit begins with an investigation into some of the mathematics of astronomy associated with the rising of Matariki and learn where to look for the stars at the beginning of Matariki. As students work through the unit they learn about the significance of whakapapa, our family tree, and the mathematics of our descendants as they go back generations.  They discover the algebra behind a famous tukutuku design and finish off using percentages to help them build kites.

More resources

  • Make rewana bread using the recipe on this page
  • Click here for instructions to make a Manu taratahi

Thursday, 6 April 2017

Jump Start

  1. What do you do for students who arrive with significant academic gaps?
  2. How you will identify them?
  3. How you will you know you have made a difference?

This post highlights a recent discovery that will help  address question 1, that is a book written by Suzy Pepper Rollins,   Learning in the Fast lane, 8 ways to put ALL students on the road to achieve academic success.

Suzy argues that we spend too much time focussing on  filling the gaps rather than  moving forward. In otherwords we spend far too much time remediating rather than accelerating students.
 "instruction that aims to catch up lagging students or fix all their past problems ends up providing classroom experiences that are not compelling, rigorous, or engaging. Such instruction may inadvertently widen rather than close achievement gaps."

How do students feel?
sourced from

A colleague  likened this to someone falling off a boat while out on the harbour sailing. If someone who can't swim falls overboard , you don't jump in and teach them to dog paddle while the boat sails away, you haul them aboard and teach them to dog paddle as you keep sailing.

Acceleration comes with the usual logistical challenges - which students, who will teach them and when will we do this. Acceleration in this context is meant to be an enriching experience for students and  designed to encourage thinking, build vocabulary and scaffold missing pieces as they learn alongside their peers.

Learning in the Fast Lane is an essential guide that identifies eight high-impact, easy to use, research-based instructional approaches that will help you
  1. Generate thinking, purpose, relevance and curiosity
  2. Clearly articulate learning goals and expectations
  3. Scaffold and practice pre-requisite skills
  4. Introduce and practice key vocabulary
  5. Apply the new concept to a task
  6. Regularly assess and provide feedback (ie: formative assessment)


    read the first chapter of Learning in the Fast Lane  online here .

    listen to a podcast with Suzy Pepper Rollins  here

     watch a webinar  here

    Check out the effect of some of the evidenced based strategies that form the pedagogical basis for the Learning in the Fast Lane model here. An effect size of 0.4 or more is considered significant.

    Get Learning in the Fast Lane from Kohia Teachers Centre Bookshop

    Monday, 30 January 2017

    One word 2017

    A new year is synonymous with New Years resolutions that are never followed through. This year I came across the #onewordtrend2017. Rather than a a new years resolution i would find a New Years word.

    One of my words for 2017 will be resilience. 

    Resilience because I believe it is one of the most important things we need to teach our students 
    Resilience as the new PLD environment means navigating uncharted waters.

    Jo Boaler's setting up positive norms in the maths classroom offers a kete of ideas for building belief and developing resilience in students. 

    In the document these 7 key ideas are shared with supporting strategies to help set students up for a year of successful learning

    1. Everyone Can Learn Math to the Highest Levels. Encourage students to believe in themselves. There is no such thing as a “math” person. Everyone can reach the highest levels they want to, with hard work. 

    2. Mistakes are Valuable Mistakes grow your brain! It is good to struggle and make mistakes. 

    3. Questions are Really Important Always ask questions, always answer questions. Ask yourself: why does that make sense? 

    4. Math is about Creativity and Making Sense Math is a very creative subject that is, at its core, about visualising patterns and creating solution paths that others can see, discuss and critique. 

    5. Math is about Connections and Communicating Math is a connected subject, and a form of communication. Represent math in different forms eg words, a picture, a graph, an equation, and link them. Colour code! 

    6. Depth is much more important than Speed Top mathematicians, such as Laurent Schwartz, think slowly and deeply. 

    7. Math Class is about Learning not Performing Math is a growth subject, it takes time to learn and it is all about effort.

    I particularly liked one of the ideas from #2, Mistakes are OK

    To illustrate that mistakes are valuable  get students to
    1. screw up a piece of paper and throw it at the board with the feeling they have when they make a mistake.  
    2. retrieve the paper and colour in all the lines. 

    Tell them how these lines represent synapses firing and brain growth from making a mistake. 
    Have them keep the piece of paper in their maths books or put them on the wall as a reminder  

    What will your one word be ?

    Tuesday, 29 November 2016

    Teaching Financial Capability in NZ schools

    The personal financial management unit standards have been reviewed and are now found under Financial Capability.
    Read the review here

    What's happening in NZ Schools around Financial Capability ?

    To find out I attended Sarah's workshop at the BOPMA conference day: 

    At Sarah's school they have trades & services academies however there was still a group of students who were not well catered for.  

    Maths for Life, a Level 2 course is based on the Financial Capability standards.

    Maths for Life students completed the following standards from the framework to credential their learning

    US 28094 – produce a balanced budget
    US 28092 – analyse states of personal financial income
    US 24695 – taxation
    US 28093 - describe financial responsibilities of utilising tertiary study funding option
    US 28097 Banking ( didn’t get to this)
    US 24699 – smart goals
    US 28095 - investment
    US 28096 – insurance

    there were 17 students in the class and they worked pretty much at their own pace throughout the year.

    The Services Academy used Instant resources which are "amazing but way too wordy for my students"

    Sarah turned to the Young Enterprise Scheme resources for her Maths for Life students.
    The Workbooks and Hot Topics became the core resources

    1. Students were  engaged for longer learning important life skills– budgeting, tax, funding tertiary study
    2. All the standards open book so students could work at their own pace - this was particularly important as many of her students were out of school on a regular basis completing trades and gateway course
    3. Students gained 12 credits towards their Level 2 qualification. 

    What did the students say?
    Topics were relevant
    Skills will be useful- they are life skills
    100% recommend course to others 

    Going forward:
    Level 3 is in the in the planning
    28098 – evaluate options to increase personal income
    28100 – develop a plan to achieve a long term personal financial goala
    28104 – analyse impacts of external factors on personal finances
    28102 – demonstrate understanding of risk and return for a personal investment portfolio
    28101 – create a long term investment portfolio 

    What is out there to help ?

    Westpac – offer a financial programme which they run in schools, contact Julia Jackson to organise something in your school

    BNZ – Tauranga Girls College students visited a BNZ branch organised through an education officer based in Auckland. 

    Bamzonia – pre-prepared resources - have a cost associated

     Instant Education: prepared resources - have a cost associated

    NXZ Virtual share trading 

     NZ Teachers have started a closed group on Facebook to ask questions share ideas and resources for teaching these standards

    Search Teaching personal financial management in NZ on Facebook and ask to join. If you are not a registered NZ teacher message admin and request access. Alternatively share your thoughts via the comments below.

    STAR funding may be available for this course as Financial Capability falls under Core Generic standards.

    Monday, 24 October 2016

    Exam Ready

    "Giving students the information they need to pass exams is the beginning of the process"
    Christine Ward

    In preparing our students for exam we  tend to focus a lot of attention on preparing students with the content  but often pay little heed to how they feel and how we can help alleviate the stress.

    Where will they be sitting the exam?
    Will they be in a familiar classroom, the hall, gymnasium at another school?
    How do our students practice for the feeling of sitting in the space they will be sitting the exam in?
    How do we prepare them for the unfamiliar?

    Reading time
    Once upon a time exams began with 10 minutes of reading time where pens had to be left on the desk.
    My observations of students beginning exams these days is that almost all pick up their pens and begin answering question one as soon as the supervisor says they can start.

    Taking time to read the entire paper before starting to write can give students the time they need to become calm and clear their heads. It gives them time to think about the questions.

    And remember to check the Formula Sheet for clues

    I know we all tell our students to read the paper before they start but how often do we actually practice this with them.
    The most common response from students is "i don't have time", after practicing they might be surprised.

    Where to start?
    Question 1 is not always the best place for everyone.
    Students should find the question they feel most confident with and begin here.
    This could be decided during a second reading time - again students need to practice doing this
    How many times have your students practiced making a plan for an exam paper then followed through on their plan? and then made a plan and followed through in the allocated time?

    Should I show all my working?  YES
    While reading they should also check for any specific instructions, e.g. 1.6 is likely to have instructions like “All working for calculations must be shown”,"give reasons".

    What about short answer questions?
    Chance and Data (1.12)  could have short answer questions. Sometimes a structure is a useful guide to keep the thinking going and avoid going blank".

    They  could try SSA to help structure their answers
    Statement, answer the question
    Support your statement with evidence.  this is because..... 
    Apply, provide an example. For example ....

    or WWW
    What do I see (statement)
    Where do i see it (give specific evidence)
    What does it mean or why might it be the case ( apply)

    What if I go blank? 
    Distract yourself  (only for a moment), drink some water 
    Relax, take 3 deep breaths 
    Doodle - make notes in margins or a blank piece of paper
    Use a structure 
    if none of these work move on to your next question & come back to this one later
    The worst thing you can do is start to panic, because as they say ‘stress makes you stupid’. You won’t be able to think clearly.

    What if I get writer’s cramp?
    Practice writing before the exam
    Try gripping your pen loosely
    Put your pen down & have a rest for a few minutes (there is time to do this) Flex your hand in between questions.
    Sometimes a fatter pen can help

    Share your best tips in the comments