How will you celebrate Pi day in your classroom? Pi day lands on a Saturday this year 2020 but we plan to celebrate a day early on Friday March 13th. Here are some ideas including a free download from NumberLoving.
Beauty of Pi Use this video below to demonstrate the beauty of Pi or download the app by Fraser McKay and Chris Smith from their PiWire site here to explore Pi and other numbers visually.
One Million Digits of Pi Display as a list here or a rap video by AsapScience for just the first 100 digits in the video below.
Pi Day Dingbats These are great for form time; say what you see! Download this PowerPoint presentation shared by Lloyd here.
Pi Day Puzzle Free Download Two different puzzle styles, one is a straight forward pi-doku based on Sudoku but only using the digits 314 and the second is a reasoning puzzle similar to GCSE area/percentage question with no dimensions.
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.
The new 9-1 GCSE continues to cause a lot of teachers I know some sleepless nights! The thing which worries me is not so much the new content but the style of the exam papers. It is clear via the specimen and four set of practice papers published so far that they are much less routine and less accessible than the current specification. Again, this isn’t really an issue in itself, I welcome the challenge and problem solving, I just hope I have been able to provide my students with the skills they need.
The main challenge I’m facing with my students is developing their resilience as well as the tools in their problem solving arsenal. I’m a great believer in the simplest solution being the best one and so to tackle my concerns I’m simply trying to expose my pupils to as many different problems as frequently as possible. Above is a picture of how students can “Plan for QWC” using this window overlay. The aim of the overlay is to help pupils breakdown the complexity of the problems; not always useful but has been for most students in the beginning.
Here are just some of the resources I’m using;
AQA have released a set of 90 maths problem solving resources, download from here.
These short problems from nrich make great starters across ages and abilities. They can also be used by tutors during form time if you don’t already have a numeracy programme. There’s a good deal of variety in terms of style of problem and difficulty.
This free problem solving booklet from La Salle comes with teacher notes, I’m using problems from it as homework tasks for years 7 and 8 but it could easily be linked into your SOW for use in lessons.
The premium bundles from NumberLoving are developed specifically with the new GCSE in mind. The mysteries in particular help to develop resilience and thinking skills.
When students are working on problem solving tasks I have a rule that they can’t ask questions for 5 minutes (you can get some good timers here). I’ve found this really helps them to start thinking for themselves and exploring different options. I also have a list of strategies on the wall in my room which can sometimes help them get started (see below).
Problem solving strategies
Draw a diagram or picture
Make a model
Try to spot any patterns
Can you solve an easier problem (make the numbers easier)
Write what you know on the diagram
Can you form a right angled triangle?
Try a number and see if it works (trial and improvement)
Make a list or a table
Don’t obsess over what you’ve been asked for, focus on what you know and what you can work out
Can you express anything using algebra?
What topic is this assessing, think about what you know on this topic
Hopefully if I keep at it my students will become more confident and independent mathematicians and therefore as a matter of course they are able to succeed at the new GCSE. I’d really like to hear other ideas and resources people are using, get in touch @numberloving and check out our free and premium resources in our Store.
This blog post has been sat in drafts for over 12 months! Thankfully in that time there has been a wealth of resources created and shared, too many to include in this post. I have tweaked this draft a little and published, thanks for the encouragement from Twitter Colleagues @ColleenYoung and @mhorley
Revision Pong Those that are regular party goers have probably played this game in a social yet competitive environment and adapting it for the classroom is quite easy and flexible in the way it’s played. You just need a set of plastic cups (numbered), a ping pong ball and a set of questions (also numbered).
It can be played as a team game (I recommend no more than 3 per team to avoid down time). If team gets the ball in a cup say number 4, they then answer question 4 to gain points, I give 10 points for correctly answered questions. In order to keep the other team, team B, involved they can also be calculating the answer to “steal the points” if team A get it wrong or alternatively gain bonus points (I award 5). Team B would have to prove to Team A they got it correct by showing their calculations (I provide each team with mini whiteboards).
These great resources from @JR-Maths-Resources are not only beautifully presented and cover a range of topics, they are differentiated from fluency in the centre to reasoning and finally problem solving as the outside layer. I use these either daily as quick starters (they take around 10 minutes) or as short homework task.
Again some experimentation has led me to believe the best option here is to number the jenga pieces and use with a corresponding set of questions.You can see in the picture on the left that I do have a set of jenga pieces now dedicated to solving equations, but since numbering the pieces I’ve got a lot more use out of them! The game is played in the same way as the Jenna game, the only addition is that pupils must answer that question before they can remove that piece (if numbered, version on the left pupils would answer after removing it, if they get it wrong they go again). This can be differentiated, identifying the level of difficulty on the question card.
I create a revision carousel using a variety of different tasks, one at each of the stations for the topics in the carousel. The timer is set for 7 minutes at each station and pupils rotate through the stations in groups of 3-4. At each station they either answer the questions or taking part in the activity for example Fan & Pick. Therefore a verbal but brief explanation of each station is needed, and reminder notes on how it is played at each station also helps the carousel run smoothly.
Here is an example of a carousel I ran with 6 minutes at each station.
One of our favourite ways to revise, which we love is to use our revision foldables, check out our blog post Fold it to download it Revision Resources and click on the image below for our premium bundle of revision foldables.
**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).