by Sharon Derbyshire | Apr 17, 2017 | Lesson Hooks, Number, Revision, Teaching Ideas & Tools |
**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.
Fractions
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).
FACT Function
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 a video tutorial from @GuideCalculator on this function and you might also be interested in using the table function to complete trial and improvement (although not explicitly on the new specification, it could fall under iteration).
Remainders
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.
Rounding
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).
What calculator tips do you give your pupils? Get in touch @numberloving or NumberLoving’s Facebook page.
Check out our free and premium resources in our Store.
Photo Credit: Calculator Scientific by Fornax (Own work) is licensed under CC BY-SA 3.0 via Wikimedia Commons
by Sharon Derbyshire | Apr 12, 2017 | Number, Revision, Teaching Ideas & Tools |
A quick hello to all readers! It has been a while, we have been busy behind the scenes creating new resources to meet the new 9-1 specification.
Bills and Statements, Debits & Credits, Task Cards is one of our latest resources which is designed to cover all money related questions as seen on the new 9-1 specification GCSE, in particular on the AQA exam board. This resource includes 5 Bill Statement, 4 Pay statements and 4 Bank statement task cards, instructions and solutions. Here is an example of one of the task cards, in this task card pupils are required to find the missing balances from the bank statement, ensuring pupils understand ‘debit’ and ‘credit’.
To complete this resource we have designed this quic and simple starter resource, included in the download. Pupils answer questions on mini-whiteboard. In doing this activity first with my class I was able to introduce terminology such as debit, VAT and recap calculating pay (see the example below)
Check back soon for our next blog on calculator use resources!
Get in touch @numberloving and follow our Facebook NumberLoving Page
Check out our free and premium resources in our Store.
by Sharon Derbyshire | Mar 24, 2016 | Geometry & Measure, Revision, Teaching Ideas & Tools |
A quick post about one of the four transformations- Translation!
Hook
Play Girls Aloud’s song “I can’t speak french” or “I like to move it” from Madagascar as pupils enter the classroom. Or turn it into a quick game of name the lesson topic instead of name that song.
Translation Mystery
Pupils use the clue cards to plot two shapes and translate them both twice, labeling each vertex and dis-ciphering the code. This mystery consists of two different difficulty levels (easy and hard). The easy cue cards describes each translation using words and pupils can plot the shapes on a 1-1 coordinate grid. The hard version requires pupils understand translations given as vectors. Download the full resource and solutions from our store here.
We’d love to hear how you hook your pupils in! Get in touch @numberloving and follow our Facebook NumberLoving Page
Check out our free and premium resources in our NumberLoving Store.
by Sharon Derbyshire | Mar 9, 2016 | Algebra, Events, Games & Puzzles, Geometry & Measure, Number, Revision |
It is nearly Pi Day, March 14th (3.14), so to celebrate try some of our resources from the seasonal Pi Day bundle. This bundle consists of three resources described below.
Pi Day Relay Race
A set of 16 relay race questions suitable for able KS4 pupils. The questions are progressively difficult, starting with the basics (see picture) to solving problems involving area, circumference or volume.
Print one set of questions for each group on different colours. Each group has a team captain, they retrieve the question from the front , taking it to the team to answer. Once they are confident they’ve got it correct they return it for marking. If correct they get 10 points and the next question. If they are wrong they can have a second attempt for 9 points.
Pi Day Collect a Joke
The pupils must calculate progressively difficult fractions of amounts (suitable for KS3 pupils), each answer gives a letter spelling out the punchline to the Pi Day joke. This resources includes ‘red herrings’ for quick self and teacher assessment. This resource is free to download as part of try before you buy!
Pi Day Mystery
Pupils are challenged to use the clues to plot all five circles and find the point of intersection. They will need to use and inverse the formulas for the area and circumference of a circle, as well as some Pythagoras’ Theorem.
Each resource includes instructions, ideas for support/extension and solutions.
All three are available in our Pi Day bundle
Check out this blog “Plan a Pi Day Party” by Gary Hopkins for Educational world for more great ideas and resources to celebrate Pi Day.
Get in touch @numberloving and follow our Facebook NumberLoving Page
Check out our free and premium resources in our NumberLoving Store.
by Sharon Derbyshire | Feb 28, 2016 | Events, Revision, Teaching Ideas & Tools |
A quick blog about different strategies and resources to get your class and classroom exam ready!
Displays
Command Word Display
Print this NumberLoving display for your classroom and use it to reinforce the meaning of command words. They can displayed along side the meaning and it also a good activity to remove the command word and ask the pupils to state the command word given the meaning.
Exam Countdown Display
Print and laminate this exam countdown display, displaying the most appropriate length of time, whether it be months, weeks or days. Using a whiteboard pen this can easily be updated so the countdown to exams is clear for all.
Exam Practice
Training to Triple read
Encourage pupils not only to read the questions but to triple read the question, each time with a different purpose;
- Highlight the figures in yellow (numbers or words e.g half)
- Highlight command words in green
- Read again “aloud in your head” with emphasise on those words
Do this as part of your teaching, highlighting in two colours, modelling by reading aloud with emphasis on command words. It will soon become part and parcel of pupils’ approach to questions.
Start from the back
Little change with the potential of a big impact on pupils’ resilience and mindset. Starting from the back when pupils are more focused and moving towards the front of the paper and the easier questions. Very relevant if working on papers in class, start from the back so pupils can get support from peers, the teacher etc.
However we are not fans of death by past paper, check out our post “Anything but more past papers” for alternative revision techniques.
Walking Talking Mock
This is large scale modelling; modelling as a teaching strategy is simply put as ‘thinking out loud’. Therefore modelling for pupils the thought processes when approaching problems. Pupils will increasingly take this role of modelling, guided and refined by the teacher. The walking-talking mock is described by the Guardian here as the “new initiative intended to boost students’ exam technique”. In brief it is a large scale version of modelling, highlighting exam technique and key exam words, the lead teacher hints, modelling thought processes related to the mock paper in front of the pupil, question by question in the exam hall. Dragonfly Training give a good description of how they ran a walking-talking mock here or check out Kristian Still’s blog here, this is another good example of how to approach the walking talking mock.
Key Skills Builder
As mentioned in our post some topics keep on coming up so it is important that these skills are embedded in pupils’ practice. We discuss exam warm ups as a way of reinforcing and revising vital topics. Check out the blog here.
Has anyone used these strategies or other strategies? We would love to hear you views! Get in touch @numberloving and follow our Facebook NumberLoving Page
Check out our free and premium resources in our TES NumberLoving Store.
by Sharon Derbyshire | Feb 3, 2016 | Revision |
It’s getting to that time of year where we start to think about year 11 revision, but it’s sometimes hard to know where to start. Obviously you speak to your class and you analyse their mock papers but beyond that it’s impossible to revise everything. So, as a starting point I decided to analyse all the AQA Linear Maths papers from the last 4 years to see which topics were a good bet. Here are the top ten topics from higher.
And the top ten topic from foundation.
These results should make for an interesting discussion with your department, there are certainly things which I have never considered revising in detail (like money) but which should offer a good pay off for students. Obviously these results need to be taken with a good dose of common sense too!
If you are with OCR there is a similar analysis available on TES here shared by m34maths.
Get in touch @numberloving and follow our Facebook NumberLoving Page
Check out our free and premium resources in our Store.
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.
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.
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).
