On Transum Mathematics, we now have Equatero which John Tranter created having seen the TV game show, Lingo.
The rules are simple – find the calculation – any numbers or symbols in the correct place are shown as green, any numbers or symbols that are correct but in the wrong place will be yellow and any numbers or symbols that are not included in the calculation will be red. Rather an addictive game – but plenty of thinking! This has been added to the Number collection in the Puzzles & Games series.
It’s really helpful when sites have a clear ‘What’s new?’ type section or you can easily search by recent additions and/or subscribe to a newsletter. Just a few examples from the many excellent sites for Mathematics:
On Transum see Breaking News where you will find information on new and updated resources. Current news includes the resources mentioned above, Equatero and Vocabero.
On Dr Austin Mathsselect New from the Menu, I see some more of her always high quality resources – I’m a fan of Fill in the Blanks (as well as all her other resources!) For a whole collection of Fill in the Blanks type resources from various sources, see this post.
I must start this post with something Dan Meyer said at the MEI Conference 2021 that really struck a chord with me, he said “There are no mistakes or misconceptions, just takes and conceptions.” Dan Meyer mentioned WW Sayer who said:
Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong’. Rather he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole art of teaching.
For a starter addressing common misconceptions try the excellent Classic Mistakes resources by Nigel Hopley.
A superb resource to use in class (or for students to use at home) to address misconceptions is of course Craig Barton’s and Simon Woodhead’s Diagnostic Questions site. The site has many thousands of questions with carefully designed multiple-choice responses to address common misconceptions.
The Insights feature is so helpful for learning about misconceptions, suppose we look at a White Rose Quiz on Algebraic Notation, for example, looking at the Insights we can see for any question the number of responses for each option from the many students who answered this question.
From NCETM, these videos and resources for teaching Key Stage 3 maths topics include common misconceptions and pitfalls; looking at Directed Numbers for example we find slides and a pdf support document including as illustrated here, “What things typically go wrong?”
Some years ago a website, counton.org which is now no longer available published a very useful document on misconceptions. In 22 sections, in each section misconceptions are given along with the correct version. Further explanations are also provided and also follow up exercises with answers.
The above pdf document includes all 22 sections. The first 8 of these documents, by Ilan Samson & David Burghes, are on the CIMT website.
Malcolm Swan’s excellent ‘Improving Learning in Mathematics‘, includes a section (5.3) on exposing errors and misconceptions. An activity suggested there is to let your students become examiners and mark the work of others, this works very well, I have highlighted some excellent resources for this on the ‘Spot the mistake!‘ page.
On the SERP website before see MathByExample and AlgebraByExample which is a set of Algebra 1 assignments that incorporate worked examples and prompt students to analyze and explain. These resources can provide prompts for discussing common misconceptions.
From Michael Pershan, see his Math Mistakes site, to quote the Author:
The purpose of this site is to collect, organize and make sense of the mistakes that students make while doing math. I’m also increasingly interested in using mistakes to help us create worked examples that students can learn from.
It’s that time of year again and we can play the 2022 NCTM Year Game in our January lessons. Full rules are here; that’s a lot of 2s, multi-digit numbers such as 20, 220, or 0.22 are accepted for 2022 though note that students are encouraged to find solutions using only the single-digit numbers 2, 0, 2, and 2 rather than double digits like 0.2 or 22.. , students are also encouraged to challenge themselves to use the digits in the order 2, 0, 2, 2.
Playing this with younger students has been an opportunity to introduce the factorial function, and we tend to stray into double factorials as students are curious. A good exercise in algebra for your older students – can they find a relationship between the single and double factorial functions?
2022 is also an iban number – this has amused me for a long time – get your students thinking outside the box with the iban sequence: 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 100, 101…
We can also look at WolframAlphafor further information on the number properties of 2022 including what 2022 looks like in historical numeral forms. We could use the various historical numerals examples to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.
The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.
For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.
I do enjoy puzzles and the Christmas break offers time for more! During the Summer of 2021, I incorporated a series of pages, Puzzles & Games on this blog, available from the top menu. Since then new additions can be found in all categories; you can see from the index that you can try puzzles and games by category as well as access collections.
To highlight just a few of this large collection…
Nrich features on many pages including reading; Nrich has many excellent articles on the use of games in the classroom; hence a Reading page.
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.
Here’s a recent puzzle you can see with many replies:
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.
Algebra includes the lovely SolveMe mobiles puzzles.
For the last few years, I have made Christmas Cards for students using Chalkdust resources, MatthewScroggs has designed the 2021 Chalkdust card. You can use an interactive or pdf version. The 2021 card contains 14 puzzles.
Recently published, is this year’s official Christmas card from Director, Sir Jeremy Fleming. Each year the card contains a festive brainteaser, this year’s card has seven puzzles that have been specially designed for 11 to 18-year-olds. GCHQ is encouraging everyone to test their skills and see if they can complete the challenge.
For more puzzles, a search on the GCHQ site returns many puzzles to keep you busy! We can also search onChristmas, this search returns cards and Christmas puzzles from earlier years.
For arts and craft lovers – construct a Christmas card from Clarissa Grandi on Artful Maths. I see for 2017, Clarissa used Spirograph, a great idea for Christmas cards. As a child, my Spirograph was definitely a favourite toy, if you don’t have a Spirograph set you could use this brilliant 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! Now there’s an app too – Spirograph on your phone!