To use demonstrations of those wonderful applets such as Building Houses that work on modern browsers, go to the Numworx Secondary Education Site. To use the resources without saving any work you can simply Login as Guest. Whilst a guest login has restrictions you will be able to explore and use resources, many of which make excellent demonstrations.
A site very well worth exploring.
To find the resource so many teachers know as “Building Houses” select Old, then Secondary Education and then Geometry.
The Cube buildings exercises include 4 sets of 10 exercises to keep everybody busy! The last set of 10 involves building structures given only the silhouette – quite a challenge. It takes a little bit of pratise to become familiar with the mouse controls, a left click adds a cube. To delete a cube hold the left click button and press the right click button also.
Access Maths – Starters On Access Maths you can now find a whole library of Starters covering Algebra, Sequences, Probability, Geometry and Number. The Starters have been designed to be used in the final term with a top set year 9 in the author’s school. These starters could be very useful for GCSE in Years 10 and 11.
I frequently recommend Andy’s excellent resources, recent resources include his pyramid puzzles, currently available, he has puzzles on Indices, Expressions and Calculations (designed to be done without a calculator).
I’ll end this collection with a little listening – literally a little listen from the Learning Scientists who include Bite-size research in their podcast collection. Their latest episode, Bite-Size Research on Seductive Details, looks at the details we include in our teaching that are not necessarily relevant for understanding the topic but make the lesson more interesting – a good idea? Some further research into how you present new information to students.
Under Activities, you will see a favourite of mine, I often recommend Transum resources, Graph Match has various levels of activities in which a number of linear, quadratic, reciprocal and other graphs must be matched up with the given equations. Note too ‘More Graph Activities‘ including this lovely Advanced Level starter.
Transum – Graph Match
A recommendation under worksheets comes from CIMT, Chapter 13 of their GCSE material, is on Graphs and section 13.11 is on graphs of common functions is a very useful summary.
CIMT GCSE – Graphs
Note too, the Topic Tests, such a valuable resource as we have tests providing excellent coverage of the specification. Included in the Higher Topic Tests is one on Further sketching graphs.
AQA Topic Test – Further sketching graphs
There are two recommendations for (free) TES resources which we can see from the reviews have been very well received.
Included in the detailed content statements on the material which must be included in A level specifications in further mathematics which makes up approximately 50% of the total content of A level further mathematics, we see the section on Further calculus.
Given that this is a compulsory topic, teachers of Further Maths can usefully look at specimen and practice materials for all the examination boards. We can also use technology to demonstrate and check answers. Additionally there are many useful resources offering notes and examples which are freely available.
WolframAlpha can very easily be used to check any volumes of revolution and also gives a clear visualisation of the solid formed; note the option to show the surface or solid formed.
Dr Frost – Further Calculus
On Dr Frost’s site, Further Calculus can be found here.
CIMT – Further Calculus
The A Level notes from CIMT include some useful notes, activities and exercises for Further Mathematics, if we look at Chapter 8, Further Calculus in the Further Pure Mathematics section the we see that the chapter includes Volumes of revolution. We also have reduction formulae which is included in the optinal content for AQA, Edexcel and OCR Specification A.
For more notes, examples and exercises, not just for Calculus but many parts of the Further Maths specification, as well as CIMT, try AJ Hobson’s ‘Just the Maths’ or the Helm Project.
(For easy reference these notes have been added to the Teaching Resources page for Further Mathematics.)
Improper Integrals – University of Pennsylvania
Looking for resources on Improper Integrals, I came across this from the University of Pennsylvania, a clear presentation with worked examples.
Edexcel have a SolutionBank and GeoGebra interactives for their various texts for Maths and Further Maths freely available online. If we look at Core Pure Mathematics Book 2 for example, you can see the various chapter links. These take you to the interactives for each chapter and to full worked solutions for each exercise. Looking at Chapter 4 for example on Volumes of Revolution, we can see two GeoGebra Interactives allowing exploration of volumes of revolution around the x and y axes.
Edexcel Geogebra Interactive – Volumes of Revolution
It’s that time of year again and we can play the 2020 Year Game in our January lessons. You can preview the 2020 game now, full rules are here. Can your students use the digits in the year 2020 and the operations +, -, x, ÷, sqrt (square root),^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100? My students have always been curious about the double factorial function.
Excel has a function for computing double factorials, illustrated here.
I like to show my students a few examples and see if they can work out what is going on!
Have a look at this articlefrom Wolfram Math World or have a look at this article on Ask Dr Math. Note the relationship between the double and single factorial functions.
A great idea for a starter on return to school from Alex Bellos’s Monday Puzzle, note the end of the solutions post here where Alex Bellos describes a new New Year challenge from Inder J Taneja, a retired maths professor from Brazil; can your students write 2020 using only single digits? Solutions are provided for the digits 1 to 9.
Once again, Manan Shah has provided us with some puzzles to keep us busy, 20 in fact to keep us all busy!
We can also look at WolframAlphawhich provides further information on the number properties of 2020 including what 2020 looks like in historical numeral forms. We could use the various WolframAlpha queries 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.