Tag Archives: learning

New Store

17 Apr

Hello all NumberLoving readers!

Sorry we have been away, we have been busy getting married and setting up our new store NumberLoving TES and NumberLoving TpT! This is a quick post to let all our readers and followers know there will be a 20% sale from tomorrow 17th April until midnight Friday the 21st April.


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Navigate to Calculate in the new 9-1 Specification

17 Apr

**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).


 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 VALUES.pngTable 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).


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).


What calculator tips do you give your pupils? Get in touch @numberloving or NumberLoving’s Facebook page.

Photo Credit: Calculator Scientific by Fornax (Own work)  is licensed under CC BY-SA 3.0  via Wikimedia Commons

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How do you teach yours? Dept. CPD

16 Feb

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?
how teach blankThis 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.

how you teachAs 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.

imageDepartment 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!

Thank you for reading! Get in touch @numberloving and follow our Facebook NumberLoving Page

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Spooktacular Colour by Numbers

30 Oct

Colour by number is a well known childhood activity and in most cases requires no maths other than number recognition.

paint by number completepaint by number blank






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.

To add difficulty to this activity each number can be replaced by a question with that numerical answer. For example this pumpkin colour by number requires students to solve the equations to find the value of x. Each answer is then one of the five colours. This worksheet can be downloaded from Education.com, which is a free account based website.

I am still not satisfied that there is enough challenge for all pupils, in which case I use a blank template such as this bat picture below taken from Coloritbynumber.com here, and ask pupils to create their own question with the correct numerical values for which ever topic is most relevant. blank bat

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.

Other Halloween Activities we Love

Relay Races

halloween relayWe 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.

Skeleton Rotational Symmetry


Check out our post on making some Halloween decorations using rotational symmetry here.

Witches Brew

witches brew

Check out our blog here.

Thank you for reading NumberLoving!

Sharon and Laura

Get in touch @numberloving and check out our free and premium resources in our TES NumberLoving Store.


Witches Brew, Ratio, Proportioning and Costings

5 Oct

Double, double toil and trouble;
Fire burn, and cauldron bubble!

Another of our Mathematical Halloween themed activities is using ratio and proportion to make witches brew.

The Brew

Download the recipe sheet I used with a low ability year 7 group here; Witches brew Recipe Sheet.

I renamed some basic ingredients to make them more disgusting sounding! Stagnant pond water = lemonade, pumpkin puree = orange juice, pink poison = cranberry juice, dash of blood = grenadine.

Any non-alcoholic recipe can easily be used as a witches brew, make it more ghastly by adding jelly snakes, eyes or other gruesome sweets available at this time of year! Check out this post by Emma Salk for non-alcoholic cocktail recipes.

The Lesson

Download this creepy cocktails starter activity of quick fire questions; Creepy cocktails ideal for low ability year 7 pupils, which recaps finding halves, doubles and thirds of amounts. Following which pupils then make the cocktail, using the recipe sheet (above) to find the measurements for one drink and then use Price List Witches brew to work out batch costs.

These resources were designed for low ability pupils, they can easily be differentiated by requiring students to work with more complex ratios, or requiring more precise measurement.

Numeracy Across the Curricular Links

Many links with the food technology department, adapting recipes and using the measuring jugs!

Further Ideas

Why not dress up and make an event of it by also making the pop-up 3D spiders (our next blog post soon to come)!

This idea can easily be adapted for Hawaiian themed beach party if you study ratio and proportion in the summer time. Check out the crazy cocktail resources, also available for free download from Number Loving’s resource shop.

We hope you like our ideas and would love to hear how they went in your school!

Mathematical Whodunit?

30 Sep

Halloween is such a fun time of year and it’s great to try and bring some of that excitement into your classroom, I’ve never found a really good Halloween themed resource so at Number-Loving we set about trying to make some!

To kick things off we have a Mathematical Whodunit, this is born out of my love (and unbeaten record) of the board game Cluedo.

The setting is the hotel ‘Spooksville’, the victim is the elusive ‘Mr Black’ and there are six suspects.

The idea is that students work in groups of 5-7, each assuming the identity of one of the characters. They each get a character card which gives them answers to three questions. On their turn they can ask a fellow player one of these question. There’s also a pool of general evidence for students to look at to help them in determining who the murderer is.

The task is quite complex so depending on the class you may need to structure it for them – e.g. tell them for the first 10 minutes they have to find out about the crime itself, then for the next ten they have to find out who had a motive, then who had the means and finally who had opportunity. But if your class are quite used to mysteries and open tasks then you can probably just leave them to it! The Maths is mostly functional and includes:

  • Interpreting time in 12 hour and 24 hour
  • Maps and scales
  • Speed, distance and time
  • Reading timetables and mileage charts
  • Reading bank statements
  • Applying logic and working methodically

In the resource I have summarised a few alternative ways to play – one idea being to get members of the department dressed up as the characters and play the game at an open evening or collapsed timetable day.

I haven’t used this with a class yet – I’m going to save it for my last lesson before Halloween, if anyone does use it I’d love to hear how it goes. You can tweet us @laurareeshughes and @numberloving. Check out our free and premium resources in our TES NumberLoving Store.

Mathematical Taboo!

17 Sep

We have been a bit quiet on the blog since the Summer but we’re now back with lots in store for the new academic year!

To kick things off how about a game of taboo? Taboo is a really simple, fun and occasionally frustrating game where you have to describe a word to your partner without using the three ‘taboo’ words. These are an amazing way of consolidating key words and concepts as well as promoting communication and team work!


This works well if students work in fours and  split into two teams of two. Team one have say, two minutes to get through as many words as they can with one member describing and one person guessing. Whilst this is happening team two are timing them and keeping a close eye on the ‘taboo’ words to make sure they are not used. Once the time is up the teams swap over.

In the style of many of our resources these cards are differentiated. Each set comes with 8 green and 8 red cards. The words are taken from the key vocabulary in the national strategy, the red cards are words from year 7 and 8, the green cards are words from year 9. Students could split the cards into two piles and pick which one to play with or you could direct them, I often suggest they get 2 points for a green word and 1 point for a red word. So far we have 6 sets on Number Loving covering key topics.

Variations on the game

Once a word has been guessed additional points can be gained by guessing what the ‘taboo’ words are on the card

Students get blank versions and make their own with the key words from a specific topic or unit!

Get in touch @numberloving and check out our free and premium resources in our TES NumberLoving Store.


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