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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.

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 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).

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.

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

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Four Pictures One Maths Word

17 Mar

Inspired by Reflective Maths blog here and Mr Collins post here I got my thinking cap on and came up with the following maths versions of the latest craze!

VOL

All of these can be downloaded for free, get it here; 4pictures1word

It would be great to hear your thoughts or suggestions on improving the four pictures and/or sharing your ideas!

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

NumberLoving’s 1st Birthday!

26 Oct

Wow over 160, 000 visitors this year! Myself and Laura are made up to be celebrating the success of Number Loving in its first year!

Our Top Ten Posts

1) Mathematical Fortune Tellers; using this childhood game to practice Maths

2) Do or Die with Dice; Many games to play with dice, my favourite practising place value by playing Nasty.

3) Nets to Catch Angry Birds; Studying nets, volume or surface area by making these 3D shapes in the form of angry birds.

4) Treasure Hunts; Get pupils up and out of there seats

5) Pimp your classroom; Looking for inspiration then look no further for ideas on interactive displays

6) The Author; here I am, I have worked hard to build up our website and appreciate all the great feedback I have received! Laura Rees-Hughes also co-authored NumberLoving from 2012 to 2016.

7) Maths Top Trumps and Other Games; The Top trumps, one of most successful resources for spicing up practising a skill.

8) Numeracy Coordinator Making the Role Count; Our ideas on how to successfully build the numeracy role and raise the profile of numeracy in your school.

9) Dance Maths; Every department needs a set of numbered dance mats, great for plenary or even open evening.

10) Cooperative Learning; Tools and resources; Ideas and resources built around the Kagan approach to cooperative learning.

Here are some of favourite posts that haven’t made the top ten but are definitely worthy of a mention;

1) Tick or Trash; Our latest resources added to the TES store, tick one answer and trash the other.

2) Outdoor Learning; Using the school building and trigonometry skills out and about the school site.

3) Teaching Loci; Using outside spaces and the pupils themselves to teach loci

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

Maths Party!

15 Apr


Maths and party are not two words you often hear in the same sentence but party games provide us with some great ways to engage students in the classroom. Here are a few of my favourite ideas:

Pass the parcel:

A simple idea which is great for a starter. this works very much as the party game but each layer has a question selotaped to it, before students can unwrap their layer they have to answer the question! In the past I have asked each student to write a question on a slip of paper as a plenary, then I use these questions in the pass the parcel the following lesson. I have done this with GCSE groups too and used exam questions cut up from a past paper. Students to the left and right can peer mark the answer to check it is correct! I have my classroom organised into five tables so I make five ‘parcels’ so each table has one to pass around, but you could adapt this depending on how your room is set up. All you need is some music and a prize for the middle and away you go!

 

Balloon modelling:

Balloon modelling is an exciting venture for anyone, old or young, this PowerPoint “Welcome to the fun fair!!” takes you through the steps needed to make a balloon dog. Students have to measure their balloon (bought cheaply from homebargains, be sure to leave a 10cm section at the end which is un-inflated) then work out and mark the fractions on (starting from the end which is tied), then they fold and twist. It really is simple and makes a great fun lesson when studying fractions of amounts, it could be adapted to work for percentages or ratio. You could also extend the idea and get students to investigate making some of their own models! The video below shows how to make the twists, if you have younger students you may want to do this for them:

Four corners

This is great for types of shapes or number types. In each corner of the room you have a picture of a shape or a number hung up. You call out a property such as ‘four vertices’ or ‘square number’ and students must go to the corner which fits that property. If students go to the wrong one they are ‘out’ and should sit down, you can make it progressively more challenging by having several conditions they have to meet.

Simon says

This is a classic which can be adapted for practising drawing shapes, you give an instruction – for example ‘simon says draw a horizontal line 4cm in length’ and students have to do it, you continue on in this way until they have constructed a shape, the catch is sometimes you give an instruction which does not start with ‘simon says’ in this case they should not follow it. Get ready for chaos!

Keep tuned as this week I will also be blogging about dance maths… Get in touch @numberloving and check out our free and premium resources in our TES NumberLoving Store.

Joking around in Maths? Collect a Joke!

5 Apr

The joy of laughter is not to be denied even in the learning environment. I like to think pupils are laughing with me when I crack my latest mathematical based jokes, even with comments like “Miss, that’s your worst one yet”, I know they enjoyed it really!

 

We have developed a few ideas of how jokes can be used in the classroom to motivate and engage learners, as well as creating a great atmosphere!

1) Collect a letter

This is a slight adjustment to a normal worksheet with each answer there is an accompanying letter and the next question.
Changing numbers to and from standard index form

2) Hunt a joke
This can be the easiest way to liven up a activity which at NumberLoving we call “bog standard worksheet” into a motivating and engaging activity.

Simply take the answers in order, to any worksheet and match them each with a word (if enough words, letters if not) on laminated cards that have been placed on the walls around the classroom. When pupils have completed their work and had it marked they can then move around the rooms collect the words or letters in the order of the answers to form the joke or secret message.

Check out this simplifying surds worksheet, which is differentiated to three levels of difficulty, hunt cards and solutions.

3) Treasure hunt

You may have already seen our treasure hunt resources. This is a slight adaptation, in which with each treasure hunt card a word from the joke or a letter to punch line is added to each card.

For a healthy supply of those all important mathematics jokes check out this forum discussion on the TES as well as this previous post on maths jokes.

My favourite “What did the zero say to the eight?”

Punchline; “Nice belt”

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

Beautiful Reflections

8 Feb

Mirror mirror on the wall. Who is the fairest of them all?

Beauty is often linked closely with the symmetry of the face meaning there are many applications in the classroom!

Reflecting faces

For the hook to my reflection lesson I created a short investigation into beauty of the rich and famous! Some stars with a symmetrical face (Angelina Jolie) and some stars not so fortunate (Wayne Rooney and Susan Boyle).

Find a portrait photo of the star (or pupils can investigate their own face) and paste the photo into Power Point three times. The first gets left as it is, the second they crop to just show the left side of the face, the third the right side of the face.

Then make a copy of each half face, select one of the half faces and in the picture tools go to rotate and flip horizontal. They can then compare the reflected celebrities with the original! Here is a Power Point of some of the famous faces I looked at with my year 7 class.

Please note your school’s policy regarding photography of pupils.

On-line web cams like this one are great for school laptops with built-in cameras, pupils can look at their face using the symmetry camera. Be warned this is not something to do at the beginning of your lesson!

Substituting into expressions

On the topic of beauty this is another activity I use when studying substitution into expressions. Students have to measure lengths on the faces and sub into the expressions, the closer to 1 their answers the more ‘attractive’ the face (the expressions are all based on the golden ratio). I ask them to find the mean of all their answers and then order the celebrities. Measuring lengths, substitution, calculator skills, surds, averages and ordering decimals, so much Maths and they won’t even realise! You could of course ask them to do it with their own faces but in my experience this quickly descends into chaos!

You could even start with this video from the BBC or this video all about the golden ratio presented by none other than Carol Vorderman!

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

 

Post-it addict?

20 Jan

A pupil informed me recently that she’d counted 132 post it notes on the walls of my classroom. It was not until this moment that I realised I may have a problem. They say the first step in solving a problem is admitting you have one so here goes, my top uses of post-it notes in the maths classroom.

Thoughts and Crosses

Anyone who reads Mr Taylor’s Blog will have read about this great idea, a grid of questions which increase in grade or level as you move up the grid. Whilst there are a variety of ways you could use these they are a great way to bring competition as well as differentiation into your lesson. I made this one on solving equations and got students to work in pairs, they each got a different colour of post-it note and had twenty minutes to cover as much of the grid as they could. To claim a square they had to have a fully worked solution to that question on their post-it. They really enjoyed this and it was interesting to see which questions they chose. Next lesson I am going to give them the grid back with someone elses solutions (which I will have removed) and they will have to re-match the solutions to the correct squares.

What am I?

This popular party game can easily be used in the maths classroom. Students work in pairs and each write something on their partners post-it, this is then swiftly attached to their partners forehead, they take it in turns to ask each other yes/no questions to reveal what is on the post-it. This can work for loads of topics but here are a couple I have tried:

Number Types – pupils have to write a number between one and 100, you will find students questioning about factors, multiples, primes, odds and evens without even realising it!

Shapes and their properties – pupils have to draw a shape (works for 2D and 3D), students quickly realise they need a range of questions beyond ‘have I got four sides?’ and will be asking about parallel lines, lines of symmetry and equal angles before you know it!

Fill in the blanks

An idea for a starter is to have some questions on the windows (or board) with numbers or words missing, as students come in they get a few post-its and have to fill in as many blanks as they can. Using the windows is a really good way to engage students, often they become a bit desensitized to the IWB.

Bar Charts or pictograms

Post it’s are great for doing bar charts, all you need is a blank axes and a question. Each student records their response on a post it and then sticks it in the correct position on the graph, this works just as well for pictograms if you get some post-its which are fun shapes. You can then have a discussion about labelling the axes and scales etc.

Plotting lines and curves

A fun way to teach plotting lines and curves is to allocate each pair of students an ‘x’ value, they must work out the corresponding ‘y’ value and write it on their post-it. They can then all plot them on a set of axes the board and you can discuss the pattern etc.

Peer assessment

In my experience students really like assessing each others work if you give them some pupils speak level descriptors. It’s hardly groundbreaking but I often ask them to write their assessments on post-its, they have two each, one for the level with a reason which references the criteria and one for how they could have reached the next level.

Feedback on books

I sometimes have the problem of students not reading feedback in their books so I mix it up a bit and occasionally give them feedback on a post-it on the front of their book, they will read it straight away as it is different.

Afl strategies

Post-its are great for lots of AFL strategies. You can ask students to write ‘one thing you have learnt’ and ‘one question you still have’ on post-its and then stick them on a wall or window. These can be reviewed by you to inform your planning and they can be reviewed at the end of the next lesson to see if students questions are now answered.

Another nice AFL activity is to ask students to write their name on a post-it and place themselves on a scale of confidence which refers to the objectives of the lesson (this can be on a wall or on the board). You can review this as often as you like to see if students are making progress, especially good if you are being observed and need to evidence progress in a short space of time.

Secret questions

I love the secret question! Before the lesson you stick a post-it under a chair with a question on, this can be about anything for example ‘give me three key things you learnt last lesson’. At some point in the lesson you shriek ‘secret question’ and the students have to all check under their chair, the chosen one has to read out the question and an answer (remember to give them some thinking time!).

Happy post-it-ing! Get in touch @numberloving and visit our TES NumberLoving store for free and premium resources!!

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