A quick blog to share free set of pie chart resources, require no-prep printable downloads, that we produced when NumberLoving joined up with LittleStreams in collaboration.
The worksheets produced by Littlestreams help introduce how to calculate angles in order to construct Pie Charts. Once pupils are able to construct, you can move them into completing the NumberLoving Treasure Hunt. This requires pupils to interpret pie charts; finding amounts from pie chart sectors and includes questions like those included in Higher EdExcel and AQA GCSE 9-1 Maths papers.
The two resources can be downloaded for free using the links below;
This is a quick blog about Foldables, an alternative to revision notes. Foldables are fairly new to me, since last summer anyway and I love them! The fact that pupils can revise not only when completing them with notes they can then revise from then by being ‘tested’ by a friend or testing themselves; makes them a win in my book. I also print each foldable on colour paper and get pupils to stick to a large piece of A3 piece of paper. Pupils then take these home and complete the poster for interactive revision at home!
First time I used foldables with a class, we made shutter foldables and we made them from scratch. I just gave pupils the blank pieces of colour paper, I then thought it would take just 30 seconds to describe the process of folding and cutting as shown in the picture on the left. It wasn’t that straight forward, but we got there.
This pdf Foldables by Dinah Zike is full of ideas of different foldable styles and instructions on how to build. Check out the layered book on page 17 for advanced foldables!
For my classes I’ve found that lesson time is used most efficiently and productively when I print both guidance on the folding of the foldable (where to fold, cut and glue) but also by giving them diagrams or prompts for each window which they then have to complete for the given topic!
Here is a picture of NumberLoving’ Naming Parts of a circle foldable in action, available here. As you can see it has been printed on bright paper (use same colour for formula, same colour for rules etc), they can be glued into class or notebooks or revision posters.
Pupils could be encouraged to glue their revision foldables on to a poster, alongside the simple revision idea of attaching an envelope to the poster to hold any flash cards created by pupils, providing another on the spot testing or interactive element to the revision.
I’m always adding to my foldable bundle, check it out here or click the image below.
This is a premium bundle of 14 foldables, as I create new foldables I add these to the bundle, which means once purchased any additions will be yours for no additional cost.
**UPDATED with Table of Values section below and mixed to improper conversion
Efficient Calculator Use
The need for pupils to be comfortable and confident with their calculator by the end of their KS4/GCSE studies is not new, but the new 9-1 specification has brought to my attention some new methods (not necessarily functions) that would benefit pupils in being able to perform using and navigating their calculators efficiently. As we follow the AQA 8300 specification many of this appear repeatedly in the practice papers. You might also be interested in our blog Can you Pay my Bills? 9-1 GCSE blog post, which looks at the bank statements, invoices and pay calculations as seen in the AQA practice papers. Any of the calculator methods described are not to replace understanding or written methods, in fact they are based on a mastery of techniques, particularly when considering remainders.
The new 9-1 specification AQA calculator papers include questions such as this calculation below. When performed correctly this would result in an improper fraction and pupils would be required to change to a mixed number.
I couldn’t understand why so many of my students were getting this wrong. So I asked a pupil to show me how they were entering this in the calculator and it turned out the problem was entering mixed numbers! The pupils were using the primary fraction button (red arrow) and using the ‘back’ button to insert the whole part before the fraction! The calculator would then interpret this as whole multiplied by the fraction part!!! When in fact they need to use the secondary function (green arrow) in order to insert the mixed number correctly.
These questions will give answers as an improper fraction and pupils may need to convert to mixed numbers (depending on the question requirements). Using the S>D function would give the whole part; instead use the shift button to activate the mixed to improper (orange arrow to left).
Although I have shown pupils this function in the past I have been reluctant to push it’s use because pupils need to complete prime factor decomposition for the non-calculator paper. However, increasingly expressing a product as its prime factors or finding the HCF/LCM is present on the new 9-1 calculator papers. To use this function, input the number for example 225, enter, then shift “FACT” and the calculator will express as a product of it’s primes. This was Q 24 from paper 2 of the foundation AQA practice set 3 which required pupils to express 225 as a product of it’s prime factors, this is awarded two marks. Pupils will save time if they use this function and that time can be used to complete the HCF/LCM part of the question.
This function can also help with questions requiring pupils to identify larger prime numbers as seen in Q3 of the Foundation AQA practice set 4, paper 3. If it is a prime number for e.g 97, after using the FACT function 97 would be displayed; therefore it is prime.
Table of Values
I had totally forgotten about this function, thankfully my Twitter colleagues @MrCarterMaths and @Mathematical_A reminded me!
Select mode (green arrow) which will give the four options seen on the display. Select option 3 : TABLE. You are then prompted by f(x) to enter the function, enter the function using the ALPHA key and the bracket key with the X (red arrows). Ensure pupils check carefully that they have entered this correctly. You are then prompted with “START?” followed by “END?”, both referring to the range of values of X in the table, e.g. from -2 to 5 (remember to us (-) for minus two), press enter after each. The final prompt is “STEPS?”, i.e. what is X going up in (most often one). Then a table of values is given in a vertical format. @Mathematical_A has mentioned that the new FX991EX has dual tables!!
Here is one of the treasure hunt cards requiring remainder to be found, again this was originally poorly answered by my pupils despite it being on one of the calculator papers. This style of question is seen in the AQA foundation practice papers, for example Q12 from paper 3 of set 3.
Below is the method we show pupils to tackle this efficiently; this slide is taken from our Walking Talking Mock.
Scientific calculators can be used to set a number of decimal places (using shift>set up>6. Fix), however this is not something that I choose to show pupils; they should be able to round correctly and there’s too much of chance they don’t change it back! So instead it is good ‘exam technique’ to insist pupils write down the whole answer and then round as required. Again a slide from our walking talking mock on the left demonstrates these calculator paper tips.
To help refine pupils calculator paper skills we have produced some resources for use with a scientific calculator and knowledge of skills such as Pythagoras’ Theorem, Trigonometry etc. Therefore this resource is best used once you’re confident pupils have the range of skills on the topics listed below.
9-1 Calculator Use Resources
The first new resource is our 9-1 Efficient Calculator Use Treasure Hunt activity differentiated to two levels; amber and green. The amber level covers the following topics; finding remainders, calculating with fractions, improper to mixed, area of fraction of circle, product of primes, Pythagoras, Rounding. The green level covers Trigonometry, remainders, compound interest, density, rounding, area of sector, scales, conversions, using formula. Each of these require pupils to round correctly i.e. decimal places or significant figures.
Check out our Treasure Hunt blog post for different ways to use treasure hunt activities in the classroom and beyond.
The second resource is our 9-1 Efficient Calculator Use Worksheets which includes two worksheets to complement the first resource to make a full lesson or use as homework. Worksheet 1 covers six topics (powers/roots, place value, remainders, primes, fractions and percentages). Worksheet 2 covers three overall topics but each progresses in challenge (use of formula, right angled triangles i.e. Pythagoras’ theorem and trigonometry, circles (arcs/sectors).
Effective use of department time, this is a daunting task for a newly appointed head of department! So like most when I first took this responsibility I made sharing good practice (SGP) a permanent agenda item as one way of continuous professional development. However, I soon realised that this wasn’t meeting the needs of professional development for the team, all of which were at different stages of their career. The sharing good practice item too often had become one member of the department “sharing a resource” they have used or ‘found’ recently. For many reasons I decided to keep the format of SGP (rota basis throughout the department). So instead of replacing it, I added other activities to department meetings that I felt actually resulted in discussions of good practice in terms of the teaching of Mathematics. In this post I describe three tried and tested strategies for keeping the objective of deeper understanding at the forefront of your departments’ planning and preparation.
First: Why the importance in the Teaching of Mathematics One of the key message from “Mathematics: made to measure” (read it here) is our responsibility to enable all pupils to develop a conceptual understanding of the mathematics they learn, its structures and relationships and fluent recall of mathematical knowledge and skills in order to equip them to solve familiar problems as well as tackle creatively the more complex and unfamiliar ones that lie ahead. The Ofsted 2012 descriptors found on page 30 of this summary of Mathematics’ reports (another good read) are certainly still relevant when discussing teaching approaches with your department. One element for outstanding quality of teaching is; “Teaching is rooted in the development of all pupils’ conceptual understanding of important concepts and progression within the lesson and over time. It enables pupils to make connections between topics and see the ‘big picture’”.
The Bigger Picture
This is a simple concept in which you ask the department to work in pairs during department time, to consider particular topics/skills on three different levels.
1. Method; what is the method, the skill in its most basic form? Are there any generalisations (known by some as rules grrr)?
2. Understanding; How do you teach for understanding? How do you lead the pupils to make their own generalisations?
3. The bigger picture; What are the applications? Are there any links to other topics?
This really is a great for unpicking your departments’ approaches to individual topics in detail. Often revealing gaps in staff knowledge and understanding (particularly NQT/RQT’s), and can even reveal if staff have been oblivious using and teaching tricks just because they were taught that way. How many of your department now how to conceptually explain the division of a fraction by a fraction. This NumberLoving resource, download for free from here, includes a number of examples such as operating with indices,operating with fractions, standard form and a blank grid (probably the most useful) which you can adapt to suit any topic coming up in your scheme of work.
How do you teach yours? This second approach requires some forward planning, and forethought from your department members. Prior to the meeting give each member of the department a “How do you teach yours” sheet on the topic you will be discussing. Here is an example of what this might look like for the topics of multiplication and division.
As you can see the department members are asked to complete each indicating how they would teach the pupils, prior to the meeting. Once at the meeting methods, approaches are discussed and debated. This naturally leads to an agreement of what is the best way to teach for understanding. Once agreed on the best approach this can be documented as shown in the example on the right.
This department activity could easily be adapted for any subject area. I have provided three examples of “How do you teach yours” to help get you started. Download it for free here.
Department Reading This can be done with any text or report which you feel will aid discussion. With a pre-determined focus direct the department towards the book/report, or even better provide a paper copy in their tray. Department should read this in preparation for the meeting.
Nix the tricks As described on the website this book is “filled with alternatives to the shortcuts so prevalent in mathematics education and explains exactly why the tricks are so bad for understanding math”. I would highly recommend providing each member of your department with this book. This makes for both a great discussion point and a handy resource for alternative methods. I have also found it useful as a point of referral when during work samples I have observed potential teaching of tricks and not of understanding. This book can be purchased online or downloaded as a pdf for free from the Nix the Tricks website here.
I hope this has provided some ideas of how to promote continuous professional development rooted around the effective teaching of mathematics!
Colour by number is a well known childhood activity and in most cases requires no maths other than number recognition. Take for example this Halloween Scarecrow picture, which I have completed online using the Color It by Numbers website here. As you can see each number represents a particular colour and once finished the image is more defined.
In this type of activity pupils must answer the questions and then shade all the squares with that answer with the colour indicated, resulting in a Halloween picture. There are two different Halloween MathArt resources available in our Halloween Bundle.
To add further challenge and set a homework task, I use a blank and much simpler template such as this pumpkin picture taken from Coloritbynumber.com here, and ask pupils to create their own question with the correct answers placed in the grid. Pupils will need to group the questions by colour.
You could ask pupils to create a set of questions limited by topic area for example; BIDMAS, solving equations, area, perimeter, evaluating formulae, alternatively pupils could create it based on a number of topics recently studied. Their work (when checked) could then be given an a starter of homework activity for another class. Here is an the example I show the pupils;
We love relay races as a great team and review activity, check out our blog post here about how to run a relay race. A collection of relay races for all occasions, not just Halloween, can be downloaded from here made by Chris Smith @AAP03102.