Hypothesis testing: practical activities

Can your pupils tell the difference between own-brand and branded products? Will they improve their time taken to complete a maze with practice?

Lots of ideas from CIMT and Nuffield.

Quick response codes

Make a treasure hunt, provide a link to extension work, and more using QR codes:

http://teachery.net/how-teachers-can-use-qr-codes/

Shared by one of my pupils - a song about finding the mean, mode and median of a set of data.

http://www.youtube.com/watch?v=QH2obAPwfqk

TED-Ed

As well as the brilliant TED talks, you can now access TED-Ed: short animated lessons, with supplementary material, on a variety of topics.

Super-fast addition

Ask the class for two numbers, for example 3 and 5, and use these to generate 10 terms of a Fibonacci-esque sequence:

3, 5, 8, 13, 21, 34, 55, 89, 144, 233

Ask someone to add these up with a calculator while you add them up in your head.

What is the quick way to do this?

Folding polygons from A sized paper

From Motivate:

Be a paper mathemagician!

Multiplication tricks, part one of many

Squaring a two-digit number ending in 5

The last two digits will always be 25.

To get the first digit(s), take the tens digit of your number and multiply it by the next integer.

Example: 45²

To get the first two digits, multiply 4 by 5 (the next consecutive integer) to get 20. Last two digits are 25. So

45² = 2025.

Dubious proofs, part two

Theorem:

A cat has nine tails.

Proof:

No cat has eight tails. A cat has one tail more than no cat.
Therefore, a cat has nine tails.
(from Math Humor)

Magic mindreading maths tricks

A brilliant way to practise numeracy and algebra!

"I think of a number... add 5... double the result, subtract three.. now take away twice the number you first thought of... what have you got?"

See all over the internet (!) and http://www.iwbmathstraining.co.uk/index.php?option=com_2j_tabs&Itemid=24 (A9: Number Magic)

Mathematical hats for very low temperatures

Klein Bottle Hats (http://kleinbottle.com/klein_bottle_hats.htm) : not only nifty mathematical objects themselves, but the sales page includes some intriguing sentences -

Warm in the winter? Yes, indeed! They may be single-sided but they're double-walled, so your head enjoys twice the insulation of a standard ski-hat. There's two layers of wool between your head and that cruel winter wind. Works down to minus 40 degrees (F or C, your choice) !

Fun Stuff For Calculus

Includes the Quadratic Formula song.

http://www.calculus-help.com/funstuff/

BBC Learning Zone: Class Clips

Thousands of clips, arranged by stage and subject, with ideas for how they can be used in lessons:

http://www.bbc.co.uk/learningzone/clips/

Maths Bingo

V useful for quick revision.

Basic version: ask pupils to draw a 4 x 4 grid (mini whiteboards, rough book...) and choose 16 integers from 1 to 20, writing one in each square. You then ask questions for which each of these is an answer; these can be varied according to topic/ability etc. Keep a note of the questions you have asked. First pupil to cross off four answers in a row shouts "Bingo" (or "Hurrah for Sums" or similar).

With prep version: prepare lists of questions and answers in advance and give pupils a list of possible answers to choose from.

The Nonagon Song

I love this song! Via Kate Nowak.

http://www.youtube.com/watch?v=z5m8BWk5LoQ

 

Positive and negative numbers: Connect Three

A good game for practising positive and negative numbers (from nrich):

http://nrich.maths.org/5911

More or Less

Podcasts of More or Less are available via the Radio 4 website:

http://www.bbc.co.uk/podcasts/series/moreorless

Some great demonstrations of how statistics can be used to answer questions and solve problems.

Make a scratch-off card

A tutorial for making scratch-off cards (like lottery scratch cards):

http://artmind-etcetera.blogspot.co.uk/2009/05/how-to-make-scratch-off-lottery-tickets.html

Would be fab for a treasure hunt or for generating interest at the beginning of an activity...

Secret function: what's my rule?

This is based on a UK Mathematics Trust activity from the Team Maths Challenge.

Draw an input/output table on the board. Choose a function, but don't disclose it!

Fill in several non-consecutive 'input' numbers in the table. For one or two, write down the corresponding output (using your secret function).

Ask pupils for the output numbers, one input at a time. They should not disclose the rule. If they are correct, write it down and move on to the next input. If they get it wrong, ask the next student to have a go.

After several correct numbers, ask for the secret rule. 

Transformation golf

A favourite of our maths department!

http://www.mathsonline.co.uk/freesite_tour/gamesroom/transform/golftrans.html

Dubious proofs, part one

Let

x = y

Then

x² = xy

Subtract y²:

x² - y² = xy - y²

Factorise:

(x + y)(x - y) = x(x - y)

A bit of cancelling gives us

x + y = x

Let x = y = 1, so

1 + 1 = 1

Convinced?

Random name picker

From Classtools, this nifty device allows you to input a class list and then choose a name at random.

http://www.classtools.net/education-games-php/fruit_machine

1089

Via Cut-The-Knot, a magic trick from David Acheson:

http://www.cut-the-knot.org/Curriculum/Arithmetic/S1089.shtml

• Take a three digit number (e.g. 602).
• Reverse it to get another three digit number: 206.
• Subtract the smaller from the larger: 602 - 206 = 396.
• Reverse this number, and add it to the answer obtained: 693 + 396 = 1089.
• Now try with another three digit number. What do you notice?

and a couple of follow-up questions:

• Can you explain it?
• Are there any numbers for which it doesn't work? Why not?

Height

xkcd: Height