## An unusual way to teach plotting straight line graphs…

Image via Wikipedia

I bet you’ve not seen this one before…

There is a linear relationship between air temperature and the number of times a cricket ‘chirps’ per minute. What an interesting idea for a lesson on plotting straight line graphs!

After putting across the idea of the relationship, and motivating the pupils by explaining how the next time they are out and about in the countryside and want to know what the temperature is they can work it out by listening to crickets, give them this worksheet which gets them plotting the linear relationship between degrees fahrenheit and chirps per minute. The worksheet is quite scaffolded and I took some artistic (mathematician’s) license to adjust the coefficients of the equation so that it was more appropriate for secondary school pupils to work with. After working out their table of values and plotting the straight line graph they are given questions that assess their ability to interpret the graph.

If degrees Fahrenheit means nothing to you (because like me, you are English) then you can move the lesson on by giving the pupils this worksheet that gets them plotting the degrees Fahrenheit to degrees Celcius temperature conversion chart. Note the slight increase in pitch with the decimal number coefficient and the negative axes. There are some more interpretation questions to follow once they have completed plotting the graph.

A really nice plenary to this lesson is to get a pupil up at the front and get them to do cricket chirping noises with the rest of the class counting how many they made in a minute. The class then have to use the graphs they have plotted to work out the ‘temperature’ in both degrees Fahrenheit and Celcius.

Great fun and a bit different than teaching this topic from a dry textbook…

## How fast are the planets?

Which planet is travelling the fastest in its orbit? Which is slowest? Is there a link between distance from the sun and how fast the planets travel?

Start by asking the students to come up with what information they would need to work this out. You can then take their ideas and if necessary lead them to working out each planet’s speed by doing the distance travelled in it’s orbit (assume circular orbits) and the time taken for one complete orbit (a planetary year).

You can Google the orbit radii and planetary year times in the lesson. Get them to convert the units; if the distance is in km, get them to convert to m; if the planetary year is in earth years, get them to convert to seconds etc. They could even use standard form to work with the large numbers involved.

This idea came from watching Mr S teach a lesson which was based on using pi in real applications. In fact, the task uses many areas of maths including speed = distance / time, units conversion, compound units and standard form.

An engaging using-and-applying investigation for a high-attaining group. Cheers Mr S!

## The Fibonacci Sequence in nature

Image by lucapost via Flickr

As the end of term draws near we are all looking for lessons to inject a bit of fun into the last two weeks of term. I need some display work for my classroom so am getting the pupils to create posters about the famous mathematician Fibonacci.

After introducing the Fibonacci Sequence, I then showed the pupils this presentation which shows where it turns up in nature. We also talked about Fibonacci and how he was actually called “Leonardo of Pisa” and how he brought the base ten number system to Europe. We also drew some Fibonacci spirals and then looked at the shape of a Nautilus.

The pupils were astounded by the presentation and it really inspired them. One of them even asked me “did God use the Fibonacci Sequence when he built all the universe?”! One of them then said “Sir, we are made up of Fibonacci numbers too; we’ve got 1 nose, 2 hands, 5 fingers etc…”. He then said he was going away to look at animals and see if they have numbers of limbs and features that were Fibonacci numbers. Isn’t this what we are aiming for in our pupils? Initiative, enquiry, curiosity, questioning. Great!

They have all gone away super keen to find out more about the great man and to gather things to put on their posters next week.

## What does the cube look like?

I created this worksheet based on a problem on the excellent NRich Maths website.

The pupils have to use their skills of visualising 3D shapes to draw patterns on the faces of a cube net after deciphering where they should go by looking at 3D views of the cube. To scaffold the task an actual cube net is also included so they can build what they think is the right solution. There is a nice extension for the future engineers who have excellent visualisation skills.

I found this to work well with medium-to-high attaining year 7 and 8 classes.

## Marathon Man Bearings

Image via Wikipedia

In 2009, comedian Eddie Izzard ran 43 marathons in 51 days around the UK. He endured blisters, losing a toenail and damaging an ankle ligament. He also had daily ice baths which, in his own words, were “to stop your legs inflating to the size of an elephant”! After running over 1100 miles he returned to Trafalgar Square on 15th September 2010.

This is a fascinating story and one that you can use to inspire your pupils! Read more of this post

## Pure inspiration- nature by numbers

This has to be one of the very best videos I have ever seen to show the beauty and power of maths. Just imagine all the ways you could use this to inspire the kids.

## Rotational symmetry- synchronised swimming

Further to our post “Symmetry the fun way: B-boy dancing“, Mr Williams suggested a great idea of using synchronised swimming as inspiration for a lesson about rotational symmetry.

Here is the Japanese Team in full flow at the Sydney Olympics:

There is an excellent routine at about 2 mins into the video which has some fantastic rotational symmetry in it. You could freeze frame the video here and use it to demonstrate the concept.

There are endless possibilities you could go on with from here: could they design their own synchronised swimming pattern/ routine and draw it or act it out on land, get them in the pool for a cross-curricular link if you have one or could they do some research for a homework to find as many pictures showing rotational symmetry in sports and other applications as they can? Great fun.

## Making 100

Pupils write out the digits 1 to 10 like this:

1   2   3   4   5   6   7   8   9   10

The aim is to create an expression that equals 100 by putting as many + – X and / signs between the digits as they like. You might like to demo one like this:

1    2   3 + 4   5   6  X 7 / 8 – 9 = 123 + 456 X 7 / 8 – 9 = 513

Obviously this one is too high but it does illustrate the method. You can decide whether the pupils must use BODMAS or not (I’d suggest they do!) and whether they are allowed to put brackets in as well.

There are many solutions and you might like to post them in the comments section below when you find them!

Thanks to Cat for this engaging little starter. It might make a brilliant homework too!

Have fun!

## Who is the best England batsman? An investigation using the mean, median, mode and range

Cricket isn’t everyone’s cup of tea but this lesson idea hasn’t failed to motivate any class that I have tried it on.

The idea is simple- look at the real world batting scores of England batsmen and use the mean, median, mode and range to decide who is the ‘best’ batsman. Each group of pupils are given these worksheets which list the scores, explains the task and also contain pictures that they might like to stick on a poster next to their statistical analysis and interpretive reasoning. Read more of this post

## Taboo words

Thanks to Sarah for this brilliant way to assess understanding of concepts and maths vocabulary.

Split the class up into groups of 4-6. Each group gets a set of small cards which each have on them one maths related word. The first thing they have to do is write on each card, under the math related word which is at the top, three words that people will not be allowed to use when describing the top word. For example, if the top word is circumference then three words the team could write underneath could be circle, perimeter and length. The idea is to make the describing of the top word as tricky as possible. The words that they can’t use when describing the top words are called Taboo words.

The sets of cards are then passed onto another group and one person in the group gets 1 minute to describe as many of the top words as possible to their group colleagues without using the taboo words. The teams get a point for each correct word they guess. Each team has a go and the scores added up at the end to identify the winning team. You can do a tie-breaker round if necessary.

There are lots of variations you could do of this game and it does seem to really engage the kids and is an excellent way to revise key vocabulary and assess conceptual knowledge.

## Height vs arm length- are they related?

Here’s a great little investigation into whether a person’s height and arm length are related. The pupils get a copy of this worksheet and have to use a metre stick to measure the height and arm length of ten of their class colleagues to the nearest cm. After recording their results in a table they draw a scatter graph and answer the questions at the bottom of the worksheet to think about whether there is a correlation. They could be encouraged to share their findings and justification with the class in a discussion in the plenary.

You’ll need metre rulers or tape measures and graph paper for this lesson in addition to the worksheets. Enjoy!

## Mathematics can be cool

Professor Brian Cox isn’t just a nerdy particle physicist. Years ago he was the keyboard player for the famous music group D:Ream which made the hit single Things can only get better. Here is a link to a great little 5 minute video the BBC did with him at The Science Museum where he talks about his life, his work and the big ideas in maths and science.

It’s a great way to show your pupils that not all mathematicians are just mathematicians and that there are big links between the worlds of maths and science.

Thanks to Ben for suggesting this idea.