Simultaneous Equations

MathisFun Easter Puzzle

MathisFun Easter Puzzle

An Easter puzzle from MathisFun – as an excuse for solving simultaneous equations. We could of course use algebra. Using the notation, h, q and t for the egg Horace wants, the egg with the small square pattern and the egg with the stripey pattern respectively.
We have:
h + 2q      =550 (1)
h + q   +t =600 (2)
—-2q  +t =500 (3)
Subtracting equation (3) from equation (2) gives
h−q=100 (4)

(1)−(4) gives 3q=450 so q=150 and h must be 250 ($2.50).

We could check our solution on WolframAlpha of course:

Select image for WolframAlpha query

Did you know that you can easily invert matrices and solve simultaneous equations using Excel?

Excel sim equations & matrices

Select image for Excel file

Select the image or this link for the Excel file. Excel simultaneous equations

To enter the MINVERSE function in the example above, select cells C7:E9, enter the MINVERSE function as shown then press CTRL + SHIFT + ENTER; similarly to enter the MMULT function in this example, select cells H7:H9, enter the MMULT function as shown and then press CTRL + SHIFT + ENTER. (Using formulae like these demonstrates a neat Excel technique, to learn more see MrExcel on Array Formulae).

For notes / examples / tutorials on Simultaneous Equations try the mathcentre resources or this workbook from Plymouth University. For more on solving three equations in three unknowns for older students see Simultaneous Linear Equations from AJ Hobson’s ‘Just the Maths’

Since it’s Easter an updated version of the best Easter Eggs of all – from WolframAlpha.

If you want some more puzzles, MathisFun has plenty more, or try some of the puzzles here.

 

 

 

 

Box Plots

Box&Whisker - WolframAlpha

Box&Whisker – WolframAlpha

Box Plots show summary information for data – the box shows the median and quartiles and the whiskers are extended to all points which are not outliers.

A very clear description for younger students can be found on BBC Bitesize. For A Level Students the Centre for Innovation in Mathematics Teaching includes Box Plots in Chapter 3 of their Statistics text (page 26 of the pdf file, which is page 76 of the text).

Box Plots are particularly useful when comparing one or more distributions;

CIMT notes

CIMT Statistics Text

To help older students think further about about outliers and skew, have a look at this excellent illustration of Nobel Prize data from Plotly. Who is that outlier for the Nobel Peace Prize?!

Plotly - Nobel Prize winners by field

Plotly – Nobel Prize winners by field

Note that it is possible to display points with Box Plots in Plotly, the following data and charts demonstrates skew well:

Data

Box Plots & Skew

You can learn more about Plotly for graphing and sharing your data here: Learn and explore Plotly 

Valentine’s Day is coming…

Desmos Valentine

Click on the image and then on the slider!

Desmos Valentine instructions

Why not send your mathematical friends (or anybody else!) a Desmos ValentineThe wonderful team at Desmos have made their brilliant math-o-grams available earlier this year….and watch out for new designs coming soon.

The math-o-grams are really easy to create; why not give it a try? Just select your design, add your message and share!

 

 

Regression

If you want to check your calculations for a regression line and see the line then Excel and WolframAlpha are both very easy to use. In Excel – just add the data, insert a chart – choose Scatter, then add a trend line.

Regression Excel

…or let WolframAlpha do all the work for you (including a plot)!

WolframAlphaRegression

WolframAlpha Regression

You could also use Desmos. Their video gives clear instructions:

For another example with an A Level question (using the same data as for Excel and WolframAlpha above) check this slideshow.

Try this least squares demonstration on GeoGebra.
GeoGebra least squares

Transum Maths Puzzles

Colleen Young:

Transum Pu Wiang TrophyIf you enjoy puzzles try Pu Wiang from Transum

Update: 19 is the new record!

Originally posted on Mathematics - Games:

Transum Tweet Select Image for Transum’s Pu Wiange puzzle

I couldn’t resist this counter moving challenge – happy to report that I scored 20! Evidence in the image!
Pu Wiang

You can try more puzzles from Transum here.

There are plenty to try, all are attractively presented and easy to use. Fun to do but these puzzles will help students practise a variety of mathematical skills.

Some of these puzzles would make good lesson starters, for example the Magic Square puzzle or Prime Square.

Note – this has been added to the Puzzles page.

View original

Desmos on Android

This slideshow requires JavaScript.

The best graphing calculator around is now available on Android (free).  Get it on Google play here. (Desmos iOS apps have been available for some time).

Maths students everywhere get this app! It’s great for younger students as it is easy to use for learning about graphs but has the sophisticated features that older students need. From simple linear graphs to polar or parametric curves – Desmos does it all!

There are several examples in the slideshows here to show you the syntax you need on Desmos if you are unfamiliar with it.

It’s Christmas time!

So,Nrich Advent time to relax and what better way to relax than with a puzzle or two?!

On Nrich you’ll find a collection of advent calendars a Sudoku for each day perhaps? (Solutions are supplied if you want them). Or a tangram? Maybe you want to play a game? (Clearly the year doesn’t matter for an Advent Calendar!)

Plus Magazine also have an Advent Calendar where you will find some of their favourite books and other mathematical toys.

For many more games and puzzles, see this collection including a challenging logic puzzle from Coolmath Games – can you set the circuits to light up that Christmas tree?! If any of you have any little relatives they might enjoy Top Marks’ collection of their favourite Christmas Activities.

Perhaps you could make your Mathematical friends some cards! Why not put a Desmos tree on the Desmos Christmas treecover?! Note this is simply a collection of lines and circles, as you can see from the syntax it is very easy to restrict x or y values. (For more on getting creative with Desmos, see Graph Art).

Staying with the subject of cards you can practise your coding skills with this Scratch project with a very clear tutorial on how to make a greeting card; not a great work, but I did enjoy playing with Scratch: here’s one I made earlier!  If you are feeling creative you might like these Christmas fonts.

On the subject of coding and Christmas trees you might enjoy  Holiday Lights where you can use coding to light up a holiday tree outside The White House. Holiday Lights comes from Google as part of their Made With Code initiative. Note that Google’s Blockly is being used for the code.

For some rather more advanced coding, there’s a rather nice Christmas tree generator here; select Auto Generate and sit back and admire the tree! Note that for any Scratch project you can ‘look inside’ and see the coding – a good way to learn more syntax.

Christmas Tree Scratch

Scratch project by vidarfw02

Wishing students (and their teachers!) everywhere a very Happy Christmas.

Spirograph

Spirograph by Nathan Friend

Inspirograph by Nathan Friend

As a child my Spirograph was definitely a favourite toy so I was delighted to find this digital version, Inspirograph by Nathan Friend. Try altering the gears so that the fixed and rotating gear are the same size, or make one size a factor of the other, make the two sizes have a common factor, or not! Investigate. You can change the colours too and create a work of Art! For some more Spirograph resources including from the awesome Desmos graphing calculator see this post. Spirograph