Posts Tagged ‘exercise’


Mean, Median and Coffee: Busting an Urban Myth

April 21, 2017


A Fun Maths Exercise.

Students count steps.

No units of length used. 

You can find the free pdf worksheet  (included below) here.

Other fun middle school math(s) worksheets in the Hot Heels series at TpT include

Unit Rates, Angles, Ratios and Algebra.

There is a lot of maths and science behind coffee sloshing in a coffee mug. ‘The human stride has almost exactly the right frequency to drive the natural oscillations of coffee’ explains fluid physicists at the University of California at Santa Barbara. You will find their full explanation here.



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

October 10, 2016


Funky, Fab and Fantastic INTRO

mathspig-at-icme-hamburg-2016Mathspig 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.



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.


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

September 20, 2016


Funky, Fab and Fantastic INTRO

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.


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

August 26, 2016

Mathspig Funky, fab & Fantastic 8

Funky, Fab and Fantastic INTRO

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.

August 26, 2016

Mathspig Funky, fab & Fantastic 9

Funky, Fab and Fantastic INTRO

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).

Mathspig Maths Selfies 1

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.


Mathspig Maths Selfie 2

Mathspig Maths Selfie 3


Mathspig Maths Selfies 4

Is that pasta really a Sine Curve?

Mathspig Maths Selfies 5



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

August 23, 2016

10 Funky, fab and Fantastic

Funky, Fab and Fantastic INTRO

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.


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

*Any more suggestions?


Lego Fractions

January 15, 2016

Here is a post on Lego Fractions by New York Grade 3 teacher Alycia Zimmerman. Surprisingly I found this on an art website.



Mathspig found this Lego Maths so much fun she thought she’d try some more. Here is the result:

Lego Mean, Median and Mode

Lego Algebra