1. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

Building THINKING Classrooms

Peter Liljedahl , Assoc. Professor , Faculty of Edu, Simon Fraser Uni, Canada, has developed a revolutionary way of teaching maths.

He wants students of all levels to get the Aha! Experience in maths class. I met him at the ICME 13 congress in Hamburg.

His research, which extends across 600 Year 7 – 10 maths classrooms shows that his approach is very successful.You will find many examples of his recommendations at the Vertical Non-Permanent Surfaces hashtag or VNPS Twitter feed here.

This is what he recommends:

 

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1. DEFRONT THE CLASSROOM

Students stand around the walls working. Desks allow anonymity and this means students can avoid thinking. Some call this approach 360 maths, but that’s just the beginning.

In the 360 Math Classroom the desks aren’t needed.

More info on TEACH here. More on 360 Maths Classroom here.

But wait, there’s more to this.

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2. USE WHITE BOARDS

White boards proved to be the best non-permanent surface. Students scribbled calculations on the boards and wiped them off. They worked across the surface.

Some teachers even stood tables on end to get enough white board surfaces.In the following youtube clip teacher Lindsay Chinn is piloting 360 degree maths on  whiteboards.

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3. USE RANDOMLY SELECTED GROUPS

Frequent and visible random selection was very successful. Students accepted the fairness of this approach. And teachers devised all sorts of means of randomising groups. They gave students numbers and drew numbered marbles out of a bowl or pulled names out of a bag.

The groups should consist of 3 or 4 members to be effective.

Jacob, Morten, Philip and Shania attempt to calculate

where one of them should lie on the floor

to land an m&m from an m&m cannon in their mouth.

This is from fab Jes Jorgensen’s maths class in Denmark.

And here is the youtube clip in Danish.

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4. PROVIDE OPEN ENDED MATHS TASKS

Here is a numeracy task recommended by Peter Liljedahl.

Here are some students from Mylene Abi-Zeid’s 1P Math Class in Ottowa, Ontario, Canada

working in a decentred classroom on Vertical Non-Permanent Surfaces. You will find Mylene’s Twitter feed here.

CELL PHONE PLANS

Students must pay for their own cell phone plans. There are three plans Pay As You Go, Basic Plan and Easy 4 U Plan. Costs are defined. Students must write an explanation that will convince their parents this is the best plan for them.

You’ll find open ended maths tasks for all levels here.

Plus some card tricks here.

And an excellent summary of Peter Liljedahl’s revolutionary ideas here.

2. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

IMAGINARY

IMAGINARY is a German website where ART and MATHS combine. It is AMAZING.

Schools, museums, students, anyone can download interactive Computer Programs like MORENAMENTS (below) to create art, maths demonstrations and public exhibitions. IMAGINARY also contains maths/art films, an art gallery, programs for printing 3D-sculptures, maths texts and exercises, and more.

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It is FREE.

It is written in ENGLISH.

Here are a few highlights picked by Mathspig, but you have to explore the website yourself.

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SURFER

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 SURFER is a program that allows you to put in any equation and test the resulting 3D image. There is a brief video explaining how it works and you can download the program here.

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WORKSHEETS

You can download worksheets for every school level, but get ready. Here is a worksheet for 5-7 year olds. But why not? Five year olds can look at sheet music without running away screaming, why not show them ALGEBRA too?

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Mathematicians Just Wanna Have Fun

The following videos show mathematicians having fun! If your middle-school students think maths is ‘boring’ show them just one of these videos.

 

Explore IMAGINARY. Enjoy.

3. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

Mathspig tried the m&m Algebra Challenge in her ICME 13 Workshop in Hamburg.

BUT … I bought PEANUT m&ms. OH Nooooooooo!

They were the WRONG SHAPE. Deformed m&ms bounced everywhere. All I could do was collect the m&ms in my gloved hands and hand them out to the workshop participants. They seemed to enjoy the failure.

But Mathspig does not give up that easily.

Here is the m&m ALGEBRA CHALLENGE with PLAIN m&ms.

The Great m+m ALGEBRA CHALLENGE

Method:

1. Open a packet of PLAIN m&ms. (Wear white Gloves like the m+ms)

2. TIP onto table. (Put a few books around the edge to define an area.)

3. Sort the m&ms into:

…m -UP pile.

…m-DOWN pile.

4. REMOVE the m-UP pile.

5. PICK up m-DOWN pile and TIP again.

6. REPEAT until only 1 m+m is left.

The pattern should follow the exponential equation here:

Did it work? Check it out below.

Who knew one family packet had 366 m+ms?

You’ll find a worked ‘theoretical’ example here.

Here’s the ANSWER:

Try it. Middle school students have to see

that applying maths in the real world can be tricky but logical.

And a lot of FUN too.

4. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

So camera’s on. Open this link in

Firefox or Chrome.

Let your middle school

students play with this amazing website

but show them the Mandelbrot and other equations.

This is maths!

WOW!

More Crazy Maths Selfies on pinterest.

5. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

Algebra! Many students struggle with algebra because they see no point doing it. But here is the best fun with algebra you’ll ever have. It is so counter intuitive that you have to see the algebra to believe this trick. Mathspig tried this exercise out on school teachers at her ICME 13  workshop in Hamburg and this is the result filmed – with a few lighting wobbles – on an iphone.

Detailed explanation here.

6. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

Dutch Artist, Theo Jansen’s Strandbeests or Beach Beasts are the most mystical, magical mechanical beasts to walk the earth. And the maths involved is mind boggling with respect to accuracy.

Once again (See 10. Funky, Fab and Fantastic) you can see the maths at work here, but getting it right is tricky.

Here are some of his bigger creatures in action:

But you can build your own Standbeest from a kit that you buy online. This is a wonderful ‘maths’ challenge. And cost is $US10-20 or less. Here is the Strandbeest built by Mr Mathspig.

But you will really appreciate how hard it is to immitate animal movement if you try to construct ONE LEG in balsa wood or icecream sticks. Mathspig took the dimensions of our small Strandbeest (written in mm on each strut) and created this gif using Gifcreator here. Can you make a beast leg walk?

You can see a more detailed design of the Strandbeest leg here.

7. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

The Maths Mystery Box is a great treasure chest to take into maths classes. It can be used an an extension exercise or to engage some disengaged students.

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The IDEA is to use concrete objects and write a maths problem to go with the object. (See examples below) The appeal of the MATHS MYSTERY BOX is that it involves CONCRETE THINKING, sort of.  All text books involve ABSTRACT thinking, which some students do not like.

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A student picks a maths problem from the box. A problem can be simple or complex. But it is not just a maths problem. The student gets to hold an object in their hand. They have to devise their own method of approach. And they must be resourceful. ie. use equipment at hand eg. their phone as a stop watch. Students like this activity. Even maths teachers like this activity as Mathspig found out at her workshop in Hamburg.

This is what the graph should look like.

Bob the Beetle moves very fast and students have to use available tools eg. phones to calculate his speed.

You’ll find the answer here.

Safety Lecture: Do not flick at anyone. But it is fun.

 

8. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

One reason why students think maths is a waste of time is because they do not see it in their world. It’s not just middle school students. We are all maths blind.

Here is the challenge. At the beginning of your next maths class:

Ask your students what ‘mathsy’ thing they have on them and see what happens. Mathspig started her ICME 13 Workshop with that question and maths teachers from around the world struggled to answer. Here is what happened.

More ideas below.

Note: I missed the significance of ‘Standing on the Shoulders of Giants’ Quote. It was from the great mathematician Sir Isaac Newton, 1776.

More Maths on or around you: 

*food snacks: nutrition information, calories, cost.

*medication: recommended dose, concentration eg. 5 mg, quantity, cost.

*room temperature: weather forecast.

*Light Bulbs: Watts, brightness (lumens, inverse quadratic function)

*Flooring: Wood (parallel lines), carpet (tessellations), coefficient of friction (Don’t want people to slip in the wet).

*Windows, doors: Hinges (Fulcrum, Effort as a Hyperbolic function), opening/closing door is an equation of a circle, angles, fly screens (pattern), windows (pulleys sometimes), handles (knob or lever impacts on effort)

Table/desk/chair: Based on statistics to fit majority of students.

Leaning back on chair: Centre of Gravity. Watch out. 

Sharpening pencil: Circular motion, sharpness of blade reduces force needed. Why?

Pens, books dropping on floor: Good old gravity. Works every time. Quadratic fn.

Fonts: Size. Based on statistics for readability. Watch the small print.

Jewellery: Geometric shapes & patterns, but also symmetry of diamond facets, weight of diamonds in carats, purity of gold in carats (different carat).

Zips: Interlocking pattern hopefully not interlocking with your skin.

Heating: Flow rate, cost, vent locations.

Architecture: Of building involves length, height, area and cost. 

External Noise: Wall thickness. Sound proofing.

Rubbish: Recycling. Why do it?

Tights: You buy them using a height weight graph on the back of the packet. 

9. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

Here is a fabulous idea for prompting students to ‘see’ maths in the world. This activity was designed by Axelle Person Faughn, North Carolina University (Below).

The idea is simple.

Ask students to take pictures of maths they see in their lives. The photos below were taken by Axelle’s students.

Alternatively, you can give students an equation and ask them to find a picture representing that equation. Axelle gave Mathspig a slip of paper with the words ‘Demonstrate limits’. I sent back a picture of curly hair and a link to the equation of a helix.

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Is that pasta really a Sine Curve?

 

10. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

Maths today is invisible.

It is hidden, most often, behind screens in computer code. But every so often some magical machine arrives that makes maths visible.

Look at the Marble Machine (below) by Wintergartan a Swedish folktronica band, then ask your students ‘what maths was involved making this machine?’

It didn’t just happen. Some suggestions below.

Maths involved:

*length of xylphone keys. These will be accurately measured to produce the correct note. Ditto width and thickness.

*rate of rotation of gears, wheels

*parabolic path of marble falling on xylophone keys

*ratios of gear wheels

*statistics. The marbles do not always bounce indentically off the keys. So the cup needs to be big enough to capture – what?- 99.99% of the bouncing marbles. I think less. You can count the number of marbles – ball bearings – that have escaped. You can see them on the floor at the end of the video. So you can calculate the % that escape.

*timing (Each element of the machine has to be timed to create the musical effect. Not chaos.)

*Engineering Maths: Strength of laminate. This will have been tested by the manufacturer. Laminates have a much greater tensile strength than one piece of wood.

*Computer Cutting: A program exists to accurately cut out those wheels from a laminate.

*Cost

*How do you buy 2,000 marbles (ball bearings)? Do you count them? You would buy them by weight.

*Any more suggestions?