Maths on Holiday

We have seen many great pictures on Twitter recently tagged #mathsonholiday.

Looking back over some previous posts, I thought I would check and update some holiday-themed posts.

An Italian holiday included a visit to the wonderful National Cinema Museum in Turin – see the Mathematics in the Movies post.

National Cinema Museum, Turin- Photograph by David Young
This image has an empty alt attribute; its file name is milan-cathedral.jpg
Milan Cathedral – photo by Sophie Young

Visiting Milan and wandering around the lovely Cathedral (one of the largest in Europe) I was struck by the geometry all around!

Some interesting sites on Mathematics and architecture:

From Maths Careers, see Interesting Buildings Based on Mathematics and from Tripbase, 9 Most Mathematically Interesting Buildings in the World.

The Tripbase article includes the cathedral in Barcelona Designed by Antoni Gaudi. 

Barcelona - Cathedral
Barcelona – Cathedral – photo by David Young

For some further reading Plus Magazine has an article on Perfect buildings: the maths of modern architecture by Marianne Freiberger.

Buildings

A great resource on TES for when we get back to school is Laura Wilson’s Plans and Elevations, a PowerPoint of images showing plans and elevations of some famous buildings.


Holiday Pictures

All photographs by David Young, taken in the attic space of the Casa Milà Barcelona a building designed by Antoni Gaudí, constructed between 1906 and 1910.

cosh x Desmos image

Imaginary Exhibition

Surfer

I do like to keep my eye open for mathematical pictures hence: (see Tetrahedral Numbers on Mathisfun)

Neuwied Schloss cannons Photograph by David Young
Neuwied Schloss Cannons –  Photograph by David Young
Bottle sequence
Barrel holding equivalent of 200,000 bottles

…..

The Mercier champagne barrel which contained 200,000 bottles of Mercier Champagne, Mercier Champagne House, Epernay France

Algebra Resources

Back in March, I wrote, Number Resources, still very much a beginning and a work in progress, I have been reorganising pages. Making things easy to find is a never-ending task! Having written this blog since 2009, many older posts are still very useful – I want to make those easier to find.

Hence some new pages, the first created was Number under GCSE (14-16). This shows GCSE content and links to some favourite posts, also to sites that are particularly easy to search by topic. Further posts and resources and sites will be added, this is quite a project, but watch this space!

I have now added Algebra which brings some posts together such as:

Algebraic Notation


Factorisation of Quadratic Expressions

Lyszkowski’s method

Simultaneous Equations

White Rose Maths – Exemplar Questions

Iteration

Transum Mathematics – Iteration

Proof

Activities to help learn reasoning and proof

Links to sites that are particularly easy to search by topic for Algebra are included, including some brilliant Underground Mathematics questions to challenge your GCSE students.

Underground Mathematics Algebra Review Questions (old O/AO level).
Some favourite tasks to challenge your GCSE students:

Resource typeTitle
Review questionTwo values of x that differ by 5 satisfy x2 −12x + k = 0, what is k?
Review questionHow small can this triangle be?
Fluency exerciseQuadratic solving sorter
Review questionCan we solve these simultaneous equations of degree 1 and 2?
Review questionCan we simplify these algebraic fractions?
Review questionIf we know two values satisfying a quadratic, can we find the quadratic?
Rich exampleQuadratic grids
Building blocksWhich quadratic?
Review questionCan we find the three inequalities that define this region?
Review questionCan we solve these simultaneous equations that involve reciprocals?
Package of problemsName that graph
Building blocksGradient match
Fluency exerciseMultiple manipulations
Review questionWhen are these quadratic inequalities true together?
Building blocksA tangent is …
Review questionWhen are the coefficients of a quadratic equal to its roots?
Many ways problemTwo-way algebra
PhET Interactive Simulations, University of Colorado Boulder, https://phet.colorado.edu

If you like the old exemplification examples – there are still some great questions, these have been added to the following pages:

Algebra Exemplification Examples

Algebra – Exemplification Examples

Watch this space for further additions to all these pages.

Mathematical Miscellany #69

A compilation this week:


From Julia Smith (@TessMaths), have a look at this wonderful collection of Mathematical Hooks.


In Mathematical Miscellany #68 I included From Complete Maths (@LaSalleEd) this brilliant 128-page Task Booklet from Jonathan Hall (@StudyMaths). The tasks which aim to promote mathematical thinking and behaviour in the classroom have been designed to be used with an appropriate model or manipulative. (See also NCETM’s Using Mathematical Representations at KS3.)

Note the playlist, Tasks on the Complete Maths YouTube CPD channel where Jonathan Hall is sharing his thoughts on some of these tasks. He recently shared this on Negative Combinations:


From Sparx Maths, have a look at their Transition Booklets, one for Year 6 to 7 and one for GCSE to A Level; these booklets are free whether you have Sparx Maths or not. The Year 6 to 7 booklet with over 130 questions is based on the Year 6 DFE/NCETM ‘ready to progress’ guidance from June 2020. The GCSE to A Level booklet uses over 120 questions taken from 11 key topics on Sparx Maths. Answers can be obtained by completing a form with your school details.


In my post on Proof I included some Geometrical proofs. We could treat this diagram as a goal free problem; what is the diagram showing you? This idea came from Colin Foster’s article –Trapezium Artist: Some thoughts on the formula for the area of a trapezium where he discusses a Year 8 lesson on area. Colin Foster states “The formula for the trapezium stood out as being the only one that wasn’t immediately ‘see-able’. With thought, those for the triangle, rectangle, parallelogram and kite could all be seen to be correct at a glance. That got us thinking about different ways of proving the formula. We were seeking something not only believable but striking enough as an image to stick in our minds. All our methods involved converting to simpler shapes”

“I have ended up quite keen on Method 6”

For an animation to illustrate this, see Trapezoid Area (2) from Tim Brzezinski.

…and in case you are wondering about Trapezid Area (1)


George Stone (@DrStoneMaths) is producing one slide summaries of interesting educational research papers.

For research summaries – see also the reading pages Research – Mathematics Learning & Teaching including easy to digest research on Mathematics education from Cambridge Mathematics (see their Espresso page), and Research – Learning & Teaching which includes Research in 100 Words from Chris Moyse and summaries of educational research from Tom Sherrington.


Reading

The reading series of pages is devoted to various reading materials – many of which are free!

A post for students is on Mathematics for students; note this book is currently free on Kindle:

GMAT Foundations of Math – 900+ Practice problems (see also GMAT Math Practice).

For a limited edition bargain on Kindle, I see Thinking Better: The Art of the Shortcut from Marcus du Sautoy for 99p.

Looking at the Books (free) page, for puzzle fans perhaps try Henry Ernest Dudeney’s puzzle collection.

Mind Hurdles

Looking at the free Kindle offerings, these include Mind Hurdles: Mystery Number – a set of ‘number mysteries’, one or more of which would make a good lesson starter and Henry Ernest Dudeney’s – Amusements in Mathematics a puzzle collection (with solutions). The first set of puzzles will offer a trip down memory lane for those who remember money – pre-decimal! There are several categories of puzzles available.

And do make sure you have Colin Foster’s KS3 books in your collection.

Colin Foster - Instant Maths Ideas
Colin Foster – Instant Maths Ideas

Colin Foster’s KS3 Instant Maths Ideas (3 books) are now freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is a Reader in  Mathematics Education in the Mathematics Education Centre at Loughborough University. Read Colin’s blog here.

Summer Maths 2022

Nrich will again publish a challenge a day throughout the UK summer break. Every weekday from 18 July to 2 September, a new interactive game or puzzle will appear on this Primary page and this Secondary page. Once students have tried the day’s challenge, they will be able to compare their approach to previously published students’ solutions.

Nrich – What Numbers Can We Make Now?

Also, from Nrich, remember there are many interactive games and puzzles.


Transum Mathematics

Perhaps try some curve stitching on Transum. Also, on Transum, you will find School Holiday Maths Activities; this collection has many activities to encourage students to continue their learning during the holidays. These are categorised, and we have a lovely mixture of learning, puzzles, and games to make students think. There is a great deal of choice here. See also the full list of all fun maths activities.


Try these brilliant GeoGebra puzzles from Daniel Mentrard, also his 64 geometric puzzles.

Puzzles – Daniel Mentrard

Perhaps try Tangram on Mathigon.
How many of the different shapes can you make?

Nrich also have a Tangram activity for students age 7 – 11 or for 5-14 years olds try Tangram Pictures.

Nrich Tangram Browser

I do enjoy puzzles, and the summer break offers time for more! Try the series of pages, Puzzles & Games available from the top menu.

Index

To highlight just a few resources from this large collection, Algebra includes the lovely SolveMe mobiles puzzles.

Or, for a rather different approach, try Shuttle Mission Workshop from Math Playground, here students build and solve their own visual math puzzles. Play Shuttle Mission Pro first to practise.

Nrich features on many pages, including reading; Nrich has many excellent articles on the use of games in the classroom; hence a Reading page.


Math Playground – PEMDAS Exhibit

On Number, Math Playground, PEMDAS Exhibit provides great practice for order of operations. Touch an operation to form that part of the operation.


On Geometry of course follow Catriona Agg who regularly posts new puzzles and has made her collection of screenshots freely available.

Catriona Agg

Following each puzzle, you can find a discussion on the puzzle. Have a look at this puzzle and discussion for example.

In response to this puzzle, you can see various solutions, including an Autograph file created by Rob Smith. Rob has this up to change both squares and you can move also move a point on the smaller square.

Another brilliant Geometry puzzle author is Ed Southall who made 40 puzzles available to celebrate his 40th birthday last year; he has also provided slides for teachers. Check his Geometry Cheat Sheet.


On Probability and Statistics try…

Guess the Correlation
Guess the Correlation – Omar Wagih

The collection includes from Cambridge PhD student Omar Wagih, ‘Guess the Correlation‘, a rather addictive game with a purpose – Omar Wagih is collecting the data on the guesses collected and using it to analyse how we perceive correlations in scatter plots. Select About to read the rules and further details.


The Underground Maths page includes several resources on puzzles and games.


Underground Maths – Equation Sudoku

From Underground Maths try Equation Sudoku for example.

We can write down equations:
c+g+k=17

f+g+a =19

m+k+c =16

and so on.

As always on Underground Maths, we have suggestions, a complete solution, and printable/supporting materials.