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!
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.
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.
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.
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.
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.
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.
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.
Is that pasta really a Sine Curve?
*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.
*How do you buy 2,000 marbles (ball bearings)? Do you count them? You would buy them by weight.
*Any more suggestions?