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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Equations of Tangents and Normals

My Year 12 Maths Methods students are now applying their differentiation skills to applications. Student D. has requested a worked solution to this question:

For the function y = loge (2x+3) , find the equations of the tangent and normal at the point on the graph where x = 0.


My students often ask why the text answer is not in the form {y=mx+c}. I explain that they adopt the convention of writing solutions without fractions or negative numbers where possible. I personally prefer the standard y=mx+c and my students do to.

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Resources ….

spirit duplicator

As a young first year teacher in 1980, I had many things to learn.

I started searching for and making resources to help my students learn. The smell of methylated spirits from using a spirit duplicator is still a vivid memory.

Then I had to decide how to file these valuable resources for future use?file-cabinet

My filing cabinet soon was overflowing with worksheets, tests, homework, etc. But finding that fractions test master could sometimes take a while. Ten minutes before 8C Maths and half the contents of my filing cabinet would be scattered all over the office floor!

GlobalInternetThe invention of the computer and photo-copier has sure made teacher’s preparation a lot easier. We can now collaborate and share with teachers all over the world. Teaching blogs and websites now provide teachers with a vast amount of resources.

One of my new favourites is “Resourceaholic” by Jo Morgan. She labels her posts “Maths Gems” and I highly recommend that you investigate her website here.

Jo Morgan

Upon checking the hard drive on my nearly worn out Lenovo L420 laptop, I find that I have over 28000 files in my ~MATHEMATICS folder!

Mathematics Directory

 To find a particular file, the search function is invaluable. However, I decided a logical folder naming system was important too. Here is a snapshot of it:

Maths Folders

I am also experimenting with using “Notebook” to organise my resources. How do you keep all your Maths teaching documents organised and easily retrieved?

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Emotional Blackmail Backfires

I tried a new strategy to try to motivate my Year 9 Maths class. It went like this:

1. Friday morning. I meet my year 9’s at the door. As usual there are stragglers.

2. I tell the class that I am going to show them a video. “It is not directly about Mathematics. We will discuss it after the video finishes.”

3. Video: Anna Clendening sings Hallelujah on America’s got talent. (Latecomers are told to wait outside until the video finishes)

Anna Clendening

4. I wipe a tear from my eye. “Please give me a chance to recover – this video always makes me cry!”

5. Class discussion initiated: “This video always makes me very emotional – who knows why?”

6. Trent says “Because you are soft Mister!” (backfire)


7. Class erupts in laughter and I am lost for words but manage a smile.

8. Finally, I get myself under control. I pause and look each student in the eyes. I say (in a quiet, serious voice) ” I get emotional because Anna gave her best performance ever, after fighting depression and anxiety. As a teacher, I want you, my students, to give your best performance in our classes. I want you to be the best you can be.”

9. The students are quiet as I hand out the days work (basic numeracy skills) and ask them for their best work.

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Spaced Practice and Mathematics

There is plenty of support for the notion that spaced practice will help consolidate information into long term memory. For example John Hattie’s work where it rspam5anks 12th in his table of effect sizes with a value of 0.71.


So perhaps unlike the food product shown, Spaced Practice and Mathematics is good for students!


So based on this belief, I have begun to make up some S.P.A.M. sheets aligned with the Australian Curriculum.

You can download 10.01 here.

Please leave a comment about the usefulness or otherwise of this type of assessment.

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SWPB and Yu-Gi-Oh Cards

Schools are generally much more positive environments than they used to be. Our school community (including students, teachers, parents, principal class, cleaners and visitors) has many opportunities for positive, constructive interaction.


will-press-lever-for-food1Our aim is a ratio of six positives to every one negative. Of course the verbal comment giving recognition to effort, work process and product, and good work habits are still our mainstay. But we now add to this postcards sent home and raffle tickets.

This token economy system uses operant conditioning to reward positive behaviour on the spot with a special stamped raffle ticket. Students may redeem these at the end of the week at a shop stocked with various goods.


I wondered whether students would see “Dungeons and Dragons” type trading cards as positive rewards. Z became very excited telling about a card game called Yu-Gi-Oh. He said he would bring his cards in next lesson. I talked to a younger Maths teacher who knew all about the game and told me you could make your own Yu-Gi-Oh cards online. Here are some of the cards I made:

01 Accuracy Des Koala

Student T. had just finished five scale drawings and had measured lengths and angles accurately. I announced to the whole class that T. had been awarded the “Accuracy Des Koala” Yu-Gi-Oh card. T. put Des Koala proudly on her work desk with a big smile.

07 Goblin Worker

Student S. always works hard in class, asks questions, uses good manners and has excellent work habits. I announced to the class that S. had earned “Goblin Worker” I again got a positive reaction from the class and the Year 10 student concerned.

04 Hippopotenuse

Student J. had finally mastered identifying the sides of a right triangle. He was pleased to get the “Hippopotenuse” card.

Some brainstorming in the Maths staffroom resulted in the following card which we hope a lot of students will want because of its design, power, and the difficult? challenge to get it!

02 Mathematician

It is early days in trialling this reward system, but feedback from students has been great so far. Some of the students want to design their own cards. Other students have stories they want to tell about trades, games, best cards, etc.

I enjoy creating the cards. I hope they encourage students to improve their Maths skills and work habits. The cards I have designed so far are:

01  Accuracy Des Koala                   08 Homework Hedgehog

02  Mathematician                           09  LOL Cat

03  SohCahToa                                   10  OnDemand Test Magician

04  Hippopotenuse                          11  OnDemand Penguin Soldier

05  Fraction Learner                        12  Correction Des Kangaroo

06  Power Spell Maker                   13  Grapha, Dragon Lord of Dark World

07  Goblin Worker                            14  Punctual Possum

What do you think of this idea? What methods of positive reinforcement do you use?


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