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Video and documentation to help you catch the vision of working like a mathematician. A mathematician's work begins with an interesting problem. Explore:
  • Principles
  • Problems
  • Teaching Craft
View on screen, or download if you wish, but please acknowledge the source.

 

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LIBRARY

Adventure of the Sphinx An Ocean of Possibilities Billiard Ball Bounces
Bob's Buttons Cars In A Garage 1 Cars In A Garage 2
Changing The Triangle Four & Twenty Blackbirds Growing Tricubes 1 & 2
Haberdasher's Problem Hearts & Loops 1, 2, & 3 How Does it Feel to Work Like a Mathematician?
Lunching With Jumping Kangaroos Move Around My Professional Learning 1, 2 & 3
Potato Olympics 1 & 2 Potato Olympics Oath Pub Menu PD
Teaching Craft with 4 Arm Shapes Truth Tiles 2 Yellow to Blue
Working Like A Mathematician

 

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Adventure of the Sphinx

Dani and Alex introduce you to the amazing investigation by Pam McGifford's Year 8 class at Cressy District High School into the remarkable properties of a shape called the Sphinx. You will discover unexpected connections between shape, pattern, measurement and algebra and you will be stunned by the competence and confidence of these young people who are Learning to Work like a Mathematician. Perhaps the most amazing thing of all - or perhaps not if you have ever been captivated by mathematics - is that the students did most of their problem solving, as a group, on their own during Mrs. McGifford's absence. Pam had introduced the problem to them using Sphinxes made by her husband. When she returned to school and saw what her children had achieved and the confidence and enthusiasm with which they expressed it, she encouraged them to publish their work 'just like a mathematician would'.

  • Learn more about Tas166, Sphinx in its cameo and the Sphinx Album.
  • Maths300 members can find out more about this investigation in Lesson 25, Sphinx.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 8:40)

 

An Ocean of Possibilities

First presented through the web site of the Association of Teachers of Mathematics (ATM), UK, this video introduces an alternative vision of mathematics education that is driven by the Working Mathematically Process identified by mathematicians. The video was produced in conjunction with the article An Ocean of Possibilities, published in Mathematics Teaching 217, March 2010, by ATM.

  • Learn more about Task 216, Square Pairs.
  • Maths300 members can find out more about this investigation in Lesson 140, Square Pairs.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 2:15)

 

Billiard Ball Bounces

Billiard Ball Bounces is a Maths300 lesson which doesn't grow from a task. But as Matt Skoss shows us in this video made at a professional development session, it can start very practically on the floor. All you need is a set of cards about 20cm square and a length of coloured cord. The cards are used to make a 'billiard table' of any size, in this case 6 x 5, and the cord traces the path of a ball hit from the bottom left pocket. The challenge is to predict the number of bounces before the ball 'drops' into a corner pocket.
  • Maths300 members can find out more about this investigation in Lesson 55, Billiard Ball Bounces.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 1:13)

 

Bob's Buttons

Bob's Buttons has many solutions and each one has to satisfy two conditions - a solution must be able to share between 4 and have 2 left and share between 5 and have 1 left. Jamie and Jack, Year 5, Ashburton Primary School, show how satisfying one condition can be transformed into satisfying the other.
  • Learn more about Task 123, Bob's Buttons.
  • Maths300 members can find out more about this investigation in Lesson 10, Bob's Buttons.
  • Non-members have access to three sample lessons (all with software) at the same address and one of these is Lesson 10, Bob's Buttons.

Click the photo to begin the video. (Time ... 0:36)

 

Cars In A Garage 1

Jessica & Madeleine, Year 4 at Ashburton Primary School, Victoria, explain how they know that three cars can be parked in three garages in only 6 ways. The critical element of the explanation is the recognition that two cars can only be parked two ways in two garages - this way or that way.
  • Learn more about Task 2, Cars In A Garage.
  • Maths300 members can find out more about this investigation in Lesson 128, Cars In A Garage.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 0:17)

 

Cars In A Garage 2

Compare Cars In A Garage 1 with this explanation from William also in a Year 4 class at Ashburton Primary School, Victoria. He also understands the element critical to all combination theory challenges.
  • Learn more about Task 2, Cars In A Garage.
  • Maths300 members can find out more about this investigation in Lesson 128, Cars In A Garage.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 0:37)

 

Changing the Triangle

A child in Year 5/6 at Rangebank Primary School, Victoria, explains how to change a triangle into a rectangle.
  • Can your students reconstruct the vital unspoken elements of the demonstration?
  • Can your students extend the 'aha' moment implied by the video to discover how to calculate the area of triangle?
This Investigation Guide might help. The mathematical content in the investigation is embodied in Task 187, Triangle Area, from the Mathematics Task Centre and Lesson 44, Area of a Triangle, from Maths300. The Maths300 lesson also supplies software.

Click the photo to begin the video. (Time ... 0:11)

 

Four & Twenty Blackbirds

In this Year 7 class at Trädgårdsstadsskolan, Sweden, the teacher explains the problem at a central table using a fishbowl strategy. The table is a courtyard and around the perimeter there are eight feeding platforms, one at each corner and one at the midpoint of each side.

Twenty-four blackbirds land so that there are nine along each side. How are they arranged?

Video 1 shows that this story shell has captured the students' interest. The conversation is in Swedish.
Video 2 is later in the lesson when Sofia, Maria & Annika explain, in English, how they can find every solution.

  • Learn more about Task 62, Four & Twenty Blackbirds.
  • Maths300 members can find out more about this investigation in Lesson 62, Four & Twenty Blackbirds.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click a photo to begin the video. (Time ... Video 1 = 0:32, Video 2 = 1:57)

 

Growing Tricubes

This class of trainee secondary teachers at Högskolan Malmö had discovered that Tricubes can grow reasonably easily by powers of 2. They had made Size 1, Size 2 and Size 4 by working together.
  • But what happened to Size 3?
  • If there is a Size 3 could we predict the number of Tricubes to make it?
  • If we have that number, is it possible to make it?

Video 1 shows the struggle to try to build Size 3.
Video 2 is just a few minutes later when it has been achieved.

But that just leads to asking more questions...

Click a photo to begin the video.
(Time ... Video 1 = 1:43, Video 2 = 0:47)

 

Haberdasher's Problem

The original puzzle was to dissect an equilateral triangle to make pieces that could be rearranged as a square. That puzzle was solved by Henry Dudeney in the late 1800s and these Swedish teacher trainees have the pieces that result from the dissection. However, it is clear that the challenge of using these to make both the square and the equilateral triangle is non-trivial. When achieved, it is the tip of the iceberg which then interests students in the original challenge and develops into a history of mathematics lesson requiring significant geometry.
  • Learn more about Task 146, Haberdasher's Problem.
  • Maths300 members can find out more about this investigation in Lesson 86, Haberdasher's Problem.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 0:31)

 


Video 1                        Video 2


Video 3

Hearts & Loops 1, 2 & 3

Nick and Owen, Year 4, Ashburton Primary School, are learning to work like a mathematician. First they become interested in a problem, in this case a problem from topology related to open and closed curves. If they can separate the heart from the loop, then both curves were never closed.

For a mathematician, solving a problem is not enough. A mathematician must be able to explain the solution.

Nick shows us that he can separate the pieces (Video 1). Owen shows us that he can reconnect them (Video 2). Then Owen introduces Nick (Video 3) who, with his hands behind his back, teaches the teacher how to separate the pieces.

Click a photo to begin the video.
(Time ... Video 1 = 0:23, Video 2 = 0:11, Video 3 = 1:18)

 

How Does it Feel to Work Like a Mathematician?

A mathematician's work begins with an interesting problem. Kathy and Steve are certainly interested in the problem Squound which was presented to them in a workshop. Join them in the middle of their muddle to get a sense of what your students need to experience if they are ever to learn how to work like a mathematician. Then investigate the problem for yourself - it will take a while - and come back to watch the video again to reflect on how it feels to work like a mathematician. Consider too the features which have made it more likely that these teachers would be fascinated, captivated and absorbed by Squound.
  • Learn more about Task 139, Squound.

Click the photo to begin the video. (Time ... 4:25)

 


Video 1                        Video 2


Video 3                        Video 4


Video 5

Lunching With Jumping Kangaroos

Three secondary schools decided they could best support change in their maths departments by funding long term professional development for key teachers. They chose a 6 day program, Engineering 'aha' Moments in Algebra, from Mathematics Centre, and two or three teachers from each school to participate. This video sequence shows the teachers choosing to eat their lunch while working together on the Jumping Kangaroos task. Perhaps evidence in itself of the success of the course.
  • Video 1: Playing with the initial problem (Time ... 2:30)
  • Video 2: Success, peer teaching, what happens if...? (Time ... 6:33)
  • Video 3: Collecting class data, developing an hypothesis (Time ... 0:17)
  • Video 4: Discussion, consensus (Time ... 2:33)
  • Video 5: Oh no! there's more. (Time ... 0:22)
Learn more about

Click a photo to begin the video.

 

Move Around

Jamie Kemp, St. Francis of Assisi Primary School, Calwell, explores Move Around, an activity from Calculating Changes with Year 6 and Year 3 students. The children learn heaps about numbers on the number line, place value - even decimals - and Jamie learns heaps about teaching. This could be the best 11 minutes of professional development you have ever experienced.

Click the photo to begin the video. (Time ... 10:54)

 


Video 1


Video 2                        Video 3

My Professional Learning 1, 2 & 3

In three short videos three teachers explain what they learnt in a full day course titled Learning to Work Like a Mathematician. The description of the course was:

For a mathematician to start work they must first have an interesting problem. Their work involves applying reasoning, questioning, justification and communication processes in the pursuit of a solution. Therefore when we view the school curriculum as learning to work like a mathematician, we begin with problems - genuine problems with unknown answers, not repetitive exercises with expected answers - and select teaching craft designed to fascinate, captivate and absorb learners.

The course was included in the 2015 Annual Conference of the Association of International Schools of Africa in both a primary and a secondary version. These videos were made voluntarily at the end of the Primary day.

Click a photo to begin the video.
(Time ... Video 1 = 1:09, Video 2 = 0:13, Video 3 = 1:07)

 

Potato Olympics 1

Anne Mullans, St. Patrick's Primary School, Murrumbeena, produced this inspirational video to stimulate their Potato Olympics adventure in 2008. That year also happened to be the official human year of the potato, but to potatoes every year is the year of the potato, so the video remains very relevant to any Olympic year. Use it as is, or get inspired and create your own 'video-duction' to this event.

Potato Olympics derives from the work of one Swedish teacher recorded in this article, Potatis Matematik, published in The Classroom Connection, Vol.4 No.2, April - June 1996. From there, various teachers from many places have played with the idea of using potatoes as a concrete teaching aid and, somewhere, the idea of Potato Olympics, as described in Anne's video was born. Maths300 Lesson 67, has collected many of these ideas and includes fabulous Classroom Contributions from Year 7, Luther College, Victoria ... Year 5/6 Kingston, Tasmania ... and Fregon School in very far outback South Australia.

Click the photo to begin the video. (Time ... 1:14)

 

Potato Olympics 2

Created and mounted to YouTube by Chairo Christian School, Victoria, this video provides insight into one school's interpretation of the Potato Olympics challenge. Also, Sue Gibson, Mount Dandenong Primary School, Victoria, has written with equal excitement about her experiences at:

Click the photo to begin the video. (Time ... 3:41)

 

Potato Olympics Oath

On behalf of their decorated potatoes, Mel Ferguson's Year 5 class, Mt. Carmel School, Yass, New South Wales, swear their Potato Olympics Oath and begin another day of competition. You can see some of their spudletes in action in Potatoes in Action.

Also, Leah Taylor, St. Anthony's School, Wanniassa, ACT, confirms the involvement and learning Mel experienced in this PowerPoint summary of her Potato Olympics experiences.

Click the photo to begin the video. (Time ... 0:27)

 


Video 1                        Video 2


Video 3                        Video 4

Pub Menu PD

Six teachers, one workshop and a Pub Menu produced 'aha' moment after 'aha' moment for these teachers who chose the Give Them A Choice workshop at the Association of International Schools of Africa (AISA) 2015 conference in Cape Town. You can't imagine how joyful they felt about their workshop selection. You have to watch the videos to see it and hear it. The first three in the set capture each group as they thrill to their problem solving success. In the fourth one Yvonne sums it up. This was the most excitement about numbers she has ever felt in her life!
  • The tasks on the menu were Truth Tiles 1, Crosses, Magic Squares, Steps, Number Tiles, Fay's Nines
  • More information about offering students a choice can be found in the article Menu Maths & Other Models for Making Mathematicians in Web Papers.
  • Maths300 members can find out more about each investigation in the lesson of the same name. Each of these whole class investigations is supported by software.
  • Members will also find an article on Menu Maths in the Professional Learning link of their site.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click a photo to begin the video.
(Time ... Video 1 = 1:35, Video 2 = 1:08, Video 3 = 1:18, Video 4 = 0:28)

 

Teaching Craft with 4 Arm Shapes

Two colleagues explore a little teaching craft using Task 154,
4 Arm Shapes. The video was made by the Association of Teachers of Mathematics, UK, and was first published in Mathematics Teaching 223, July 2011.
  • Visit the journal page of the ATM web site for the latest edition of Mathematics Teaching.
  • Learn more about Task 154, 4 Arm Shapes.
  • Maths300 members can find out more about this investigation in Lesson 40, 4 Arm Shapes.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 09:59)

 

Truth Tiles 2

Truth Tiles 2 begins with a simple equation, namely:
+ - =
Using just the digits 3, 4, 5, 6, 7 we are asked to find solutions. Blair and Alexander, Year 5, Ashburton Primary School, using tasks for the first time, offer a perceptive explanation that not only shows some solutions, but suggests an approach that will help to find all solutions.
  • Learn more about Task 17, Truth Tiles 2.
  • Maths300 members can find out more about this investigation in Lesson 168, Truth Tiles 2.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 2:52)

 

Yellow to Blue

Bella, Emma, Amy & Beatrice, Year 6, Camberwell Primary School, describe their insightful algorithm for changing yellow to blue. The problem uses plugs with a different colour on each side. The challenge is to begin with four yellow plugs and by turning over all except one on any turn, to change them all to blue. You might like to try it yourself first because it isn't as easy as the girls make it look. Instead of plugs use four scrap of paper with a cross on one side of each.
  • Learn more about Yellow to Blue which derives from Task 132, Red To Blue.
  • Maths300 members can find out more about this investigation in Lesson 127, Red To Blue.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 0:54)

 

Working Like A Mathematician

Eric The Sheep is used as a an example of what it means to work like a mathematician. The video, produced for the ATM YouTube channel in May 2012, emphasises becoming interested in a problem, collecting and organising data and making and testing hypotheses. Follow up the video by exploring the Task Cameo of:
  • Learn more about Task 45, Eric The Sheep.
  • Maths300 members can find out more about this investigation in Lesson 17, Eric The Sheep.
  • Non-members have access to three sample lessons (all with software) at the same address.

Click the photo to begin the video. (Time ... 6:23)

 

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