Dominotion (part 1)

I love the satisfaction you get from creating something. Like a new blog post. But creation requires effort.

As Mathematics teachers, we create lessons for our students. The content of these lessons can come from many sources. eg. Videos, worksheets, games, text books, puzzles, card matching, etc.

One of my most successful methods of creating original content is to start with “material”. eg. cards, blocks, dominoes, dice, cardboard, paper, etc.

My most recent purchase was a double 15 set of dominoes from a “Games World” store in Perth.

double 15 dominoes

The first questions that come to mind are:

  1. How many dominoes? (don’t show students the tin)
  2. Total number of dots?
  3. What size rectangles can be made?


Another application is to use dominoes to represent fractions. For example find equivalent fractions, sort fractions in ascending order, etc. Any other ideas – I would love to hear from you.

Stay tuned for (part 2) of this post where I introduce a new game called “Dominotion”.


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Hidden Figures


I have just watched the film Hidden Figures. It tells the story of three African American women mathematicians at NASA—Katherine Johnson, Dorothy Vaughn, and Mary Jackson—who were instrumental in “doing the math” that allowed John Glenn to be the first American to orbit Earth. The film is based on Margot Shetterly’s book, Hidden Figures.


If you are a Maths educator or student you should definitely watch this film. It breaks the stereotype that men make better Engineers/Scientists/Mathematicians. I already know that this stereotype is wrong, because I have worked with and still work with excellent female Mathematicians and Mathematics teachers.

But seriously, watch the movie, it is damn good. Be prepared though for many reminders of colored segregation and discrimination in the 1960’s.

For a much more comprehensive review, check out Science News for Students.

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Maths Warmups

Many Math Blogs have good ideas for starting a Maths lesson. For example:

  1. WODB
  2. Would You Rather
  3. Always, Sometimes, Never
  4. Transum
  5. Solve My Maths

When I started teaching Maths (37 years ago!) my mentors impressed on me the importance of getting a lesson off to a good start. As a result, my students know that as soon as they sit down they are expected to start work.

Apart from forming good work habits and learning Maths, this immediate use of a “warmup” allows the teacher to complete his/her admin duties. For example: roll marking, checking uniform and equipment, deal with late arrivals, read daily bulletin, etc.

Although I use WODB, Would You Rather, etc., my preference is for 10 quick questions. These should be graduated in difficulty from easy to challenging.


I have nearly finished creating “50 Warmups for Secondary School Students”. One of my students contributed two drawings – a boy and a girl character as shown above. She named them Mandy and Drew! Below is a sample – let me know what you think?


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Playing Mathematically

Anybody who knows me, can easily see I have a passion for playing games. A fellow teacher starts each school day trying to beat me at “Stop or Dare”. At the end of a teaching day Maths teachers and the odd English teacher gather for a game of “Liar’s Dice”. WHY?

  1. Playing Mathly CoverIt’s fun (we laugh and shout)
  2. It’s relationship building
  3. It provides practice in basic arithmetic

I have now gathered over 100 games that I have tried in the classroom. Three are originals invented by yours truly: domino squares, operation golf and salute the king.

Click the image at right to download.

Hope you enjoy playing. Let me know your favourites!

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2016 Bring It On

clip-art-gardening-188910As usual during the summer holidays I get sick of gardening and housework and can’t wait to get back to school. Fortunately, I have 90 Mathematics teaching blogs in my RSS reader.

These give me plenty of inspiration, as well as teaching ideas and resources.

Here are 5 that have “caught my eye”:

1. Add Em Up Review Activity by Sara Vanderwerf. Her goal is to get students talking about Maths! Make sure you check out her 1 to 100 activity also – a great way to get group work going with a new class.

2. Putting Stats Projects into Practice by Amy Hogan. We are implementing common assessment tasks this year. This post gives great advice on ten important features of doing Projects in the classroom.

3. Visual Patterns and Coding by Adrian Pumphrey. I intend to continue using the excellent Visual Patterns website and now I will add some programming with Skulptor and graphing with Desmos.

4. Creating a Positive Learning Environment by Mo Ladak where he gives 22 great strategies to help achieve this. Well worth a read!

5. Learning Mathematics: the struggle, the tools and the way forward by Michaela Epstein. This up and coming star Aussie teacher is a product of the fantastic TFA program. Watch her presentation from the Transform Ed conference.

20 more sleeps………..zzzzzzzzzzz

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Multiplication Tic Tac Toe in 3 Acts

Multiplication Tic Tac Toe is a great game because it:

  1. is easy to learn
  2. requires minimal equipment
  3. provides lots of practice of multiplication facts
  4. requires logical thinking

ACT ONE – Constructing the Game

Provide a pair of students with a multiplication-tic-tac-toe-blank. Get them to write in the first 9 multiples in each part of the board.

The obvious advantage to doing this is the practice at writing multiples and developing an understanding of the game board.

ACT TWO – Playing the Game

This is the main event! Lots of games needed to improve multiplication facts and developing game strategy.

For game rules see artofmathstudio.

ACT THREE – Analysing the Game

Get students to colour in the board as follows: blue represents “quadruple plays”, yellow’s represent “triple plays”, oranges represent “double plays”, and white represents “single plays.

tic tac toe coloured

Get students to explain their strategies for winning the game (written or verbal).

Do you think that the “3 Act” structure lends itself to all games or only to this particular game?

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Hulk Smash!

How important is a “hook” into a lesson? Imagine this:

A teacher runs across the room, jumps in the air and falls to the ground with his fists punching the floor, yelling “hulk smash”. For greater effect he would have a hulk mask and hulk hands like my 3 year old grandson!


Then onto introducing the lesson (Volume of Prisms) and using Hulk vs. Red Hulk worksheets by mej – solvemymaths.

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The Quilt


Sun streams in,

as young minds do battle.

Youth blossoms with potential,

but struggles with meaning.

A quilt hangs in all its glory,

with names adorned from the past.

A link exists,

which brings great sadness.

Oh life, Oh death,

What does it mean?

When once you sat,

In this very room.

Of what did you dream,

Why did you leave so soon?

Jeff Trevaskis


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A Challenge to all Mathematics Teachers


Steve Wyborney on his blog – I’m on a Learning Mission – recently challenged educators to:

Think deeply about what you believe about every student’s learning potential.  Complete this sentence and post it.

“I believe…”

I replied:

“I believe that students are waiting for teachers to show them: the beauty of Mathematics, the aha moment when understanding dawns, and the intrinsic motivation that comes from persevering and finally solving a challenging problem”.

My challenge to educators is to think creatively about taking a risk and changing their teaching practice. Complete this sentence and post it.

“I wonder what would happen in my Mathematics class if …..”

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If Solving Simultaneous Equations with Matrices is the Headache…

I really struggle to think of catchy headings – so I stole this one from Dan Meyer!

My Year 10’s are currently learning Matrices – operations, determinants, inverse matrices, etc. Because this group of students “loves” forming groups and solving problems, I decided to flip the lesson (Japanese style) and start with a problem.

To give the reader some context, 3 out of 7 groups had solved the “Tourists & Guides” problem in about 30 minutes, which I found on Mike Lawler’s blog.

tourists and guides

So I wanted to give my students a big headache, before giving them the aspirin or perhaps paracetamol? Here is the problem:

Three students go into a shop and make purchases. Katie buys 3 packets of chips, 2 cans of drink and a chocolate bar and pays. $10.65. Mark buys 4 packets of chips, a can of drink and 2 chocolate bars and pays $12.60, and Tony buys 3 packets of chips and 3 chocolate bars and pays $10.95. Determine how much each item costs.

Within minutes I had a buzz of noise as students began the problem. From the students point of view:

  1. The problem did not look too difficult – money, chips, drinks and chocolate.
  2. It is real world – students often buy these items.
  3. A simple strategy – trial and error – can be quickly employed.

After 30 minutes, I started to hear groans and comments like “we are only 5 cents off”. After 45 minutes, many students gave up and went off task. At this stage I promised to show them how to use an Inverse Matrix (learned previous lesson) to quickly solve the problem (with the use of a ti-Nspire CAS calculator). Aspirin time!


Student B however, was determined to solve the problem on his own – which he did in a seperate room, taking about 90 minutes in total.


  1. I don’t plan on giving students many problems that they can’t solve in future!
  2. Next lesson we will solve with algebra.
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