**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).
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!
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.
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!
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.
The class is split into eight groups and each group is given a bell. Each bell is numbered, if the answer to the question is the same as their group’s bell they should ring the bell. At first the pupils are likely to be too slow to recognise the tune and therefore you may need to go back the beginning and repeat to here the tune. It is an ideal activity for a short plenary.
In this version of the game the order of the questions is important and should follow the same numbers as the tunes provided on the tun sheet. You set some of the pupils a challenge to come up with questions relevant to the topic studying which give the answers to follow one of the tunes provided with the bells.
This bidmas-bells-twinkle-twinkle resource contains questions which if played in the correct order will play the tune “twinkle twinkle little star”.
Another adaption would be to group pupils and give each group a bell. All pupils will be given an answer card, and for each answer card there is a question. The order of the questions is again important. Use the interactive display board to pose a question to the class, if pupils have the answer to the question the ring the bell. The trick here is to first make the questions and answers, one for each note of the tune. Then assign each question card to the corresponding bell by numbering the question card. Then group all the cards for each bell, mixing them up so the order isn’t clear.For example if the tune was 1, 2, 2 (the numbers on the bell) a pupil from the group with bell one would need the answer to question 1 and pupils from the group with bell 2 would need the answers to question 2 and 3! This is slightly more complicated to prepare but worth it. My top tip is to label the back of the answer cards with which bell number it belongs to!
They can also add fun to quizzes or team games, not as tuneful but great fun!
About the Bells
The bells are called handbells and are sold in sets. You can buy them from here and many other places, always check that they come with a handy tune sheet.
We hope you find the ideas useful and we would love to hear your feedback on how the ideas work for you. Get in touch @numberloving and check out our free and premium resources in our NumberLoving Store.