Tag Archives: math

Instant Graphs

22 Apr

This post is in addition to creating instant bar charts and pictograms using Post-It notes check out the previous post. Post-it notes are great for collecting information and instantly organising that data into a bar chart or pictogram to find the mode, median and range (if applicable).

Pie charts demonstrate proportions of amounts or a population, to ensure pupils understand this it is vital that they observe some basic proportions represented in pie charts. For example half choose red, a quarter blue and a quarter green.

I always introduce pie charts in this way using pie chart wheels. Pie chart wheels are easy to make. The Instant Pie Chart Template  can be downloaded  with intructions.

Print the pie chart template on four different colours, cut out and then secure the wheels  in place using a pin and piece of card at the back.

Pupils adjust the colours by spinning to represent the results in the Power Point. Then ask pupils to give their own results that could be represented, or not if only  four colours are available.

I always ensure I have red, amber and green in my pie chart wheels as they then double up as an assessment for learning indicator. Pupils display red when they require help, amber when they feeling more confident and green when they are confident and need more of a challenge.

Tallies and Pictograms

Another of my favourite data handling activities is to use music when reminding young year 7 pupils of how to tally. Pick a top ten hit with a repetitive song, as the song plays pupils have to tally the number of times the word is said!

Try it with Cheryl Cole’s “you have to fight for this love” and you have yourself a real challenge. Discussions can then be held about the modal word.

Check out our post on using post-its for instant pictograms on the classroom windows!

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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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Can you Pay my Bills? 9-1 GCSE

12 Apr

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 and moving all resources to our new TES NumberLoving online store.

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 FREE Bills, Statements, Quick Fire Starter Questions starter resource. 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!

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AQA Maths Topic Analysis

3 Feb

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.

Higher

And the top ten topic from foundation.

Found

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.

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3-D Shapes in more than 3-ways

3 Nov

In this post I have pulled together lots of different ways of studying 3D shapes, with my new favourite ‘Pull-Up’ shapes. For each activity I have linked it to my favourite nRich tasks, check out their collection here.

Fold-Up for the Notebook

imageimage

This great idea from Pinterest, means pupils can have this 3D shape in their class books but it still folds flat!  I believe this idea originally came from Hooty’s Homeroom blog, check out their website here for full instructions.

n-Rich Pyramid N-gon

The base of a pyramid has n edges. In terms of n, what is the difference between the number of edges of the pyramid and the number of faces? Check out this nRich task here.

Construct and Hang-Up

mobileUsing toothpicks or wooden skewers as edges and midget gems or marshmallows as vertices most 3D shapes can be built.  These make great 3D shapes for display but also useful for when exploring trigonometry and Pythagoras’ Theorem in 3D.  CIMG0057Midget gems will go hard and therefore will withstand the test of time on the classroom windowsill. Check out our blog post ‘Sweets, cocktails sticks and 3D shapes’ here.

imageNRich Cube Paths Puzzle

Use tooth picks and midget gems to construct a skeletal view of a 2 by 2 by 2 cube with one route ‘down’ the cube.

How many routes are there on the surface of the cube from A to B?
(No `backtracking’ allowed, i.e. each move must be away from A towards B.)

Pull-Up

image imageOften the building of 3D solids leads to some not so pretty and poorly constructed shapes, partly due to ‘accidentally’ cutting tabs off and mostly due to poor fine motor skills. I recently read Liz Meenan’s article for the Association of Teachers of Mathematics, who had experienced the same and in her article she talks about pull-up nets.

The nets are constructed pretty much as usual, however there are no tabs but instead small holes in strategically
placed corners. A thread is then looped through these holes in order, pull on the thread to pull-up your 3D shape.

Check out the full ATM article by Liz Meenan here.

imageNet Profit- add some challenge to the pull-up cube activity with this nRich task.

The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube? More questions and solutions here.

Pop-Up

20121024-224955.jpg

I absolutely love making the pop-up Spider for a Halloween activity. The pop-up spider is a dodecahedron painted black. Check out our blog post here for this and other Halloween maths ideas.IMG00133-20111104-1331

Alternatively, get pupils to construct equilateral triangles using a compass, therefore create the net for this pop-up octahedron. Check out our post ‘A lesson off-never’ here for further details.

n-Rich Dodecamagic

dodecamagic

Here you see the front and back views of a dodecahedron which is a solid made up of pentagonal faces.  Using twenty of the numbers from 1 to 25, each vertex has been numbered so that the numbers around each pentagonal face add up to 65. The number F is the number of faces of the solid. Can you find all the missing numbers?

You might like to make a dodecahedron (pop up or not) and write the numbers at the vertices.

Check out the n-Rich task here.

n-Rich Magic Octahedron

imageIn a Magic Octahedron, the four numbers on the faces that meet at a vertex add up to make the same total for every vertex. If the letters F,G,H,J and K are replaced with the numbers 2,4,6,7 and 8, in some order, to make a Magic octahedron, what is the value of G+J? Click here for the website and access to solutions.

Build-Up (Virtually) with Building Houses

This can be used on the interactive whiteboard to build with ‘virtual’ cubic cubes by pupils or teacher. The shape can be rotated to consider different views (side/front elevation etc). Check out the website here. Colleen Young has a great blog on the use of this app, check it out here.

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Mathematical Shapes Calendar, Origami

3 Jan

2013New Year, New calendar

Inspired by David Mitchell’s Mathematical Origami book , I started to think what about using an origami dodecahedron as a calendar! A quick search revealed it had been done!

Todd’s place will produce rhombic calendars in different languages, with or without guidelines, you can also change the font and colours too. However you will need to save as a PS file and then use the online converter detailed on the site.

cal2009small

Another great website with a wide variety of 3D shape Origami calendars are available from this website CDO. The site is in Italian but also has printable in English and other languages. I found the guidelines on the printouts very useful.

This video below shows how to make one of my favourites and not just because it looks great but I also think it would be interesting to ask pupils work out the surface area of the completed shape.

To increase the difficulty pupils could use pencil and compass techniques to construct each of the faces and then construct! Great for extra curricular maths club!

Inspired by my colleague Sister Mary-Anne I have been thinking how else to use flexagons, and have found these on the Origami Resource Centre with a calendar based on a pentahexaflexagon by Ralph Jones.

dodecaflexCheck out their website for templates like this (to the right ). Scroll down to Flexagon Calendars to download the 2013 printable worksheets to make your own and there are also links to video instructions.

Happy New Year to all Number Loving Readers from Sharon and Laura! Get in touch @numberloving and check out our free and premium resources in our TES NumberLoving Store.

Pushing the Sudoku Boundaries!

16 Dec

Try these numberloving favourites!

I was first introduced to Sudoku as a NQT ten years ago and found this puzzle right up my street. I am sure many of you know how to complete a Sudoku puzzle, this article concentrates on puzzles beyond the basic Sudoku. For beginners click here for hints and tips on the classic puzzle.

So what happens when you breeze through [most] sudoku challenges found in newspapers and magazines alike? Or you maybe simply looking for a new logic challenge! Well I recommend the samurai Sudoku. As you can see this joins five classic sudoku to get your brains really working.

Click here for a daily samurai Sudoku, or tap into its archives and puzzles can be printed (myself I prefer to print as a break from the computer). Or there are many books like The Times Samurai Su Doku available through online bookstores.

Way beyond the classic Sudoku is Kuboku a 3D Sudoku cube game created by Creaceed this app, available for £1.49 (at time of publishing). The video below gives a demonstration of Kuboku, don’t forget you get extra Kuboku points if you can complete it faster. You will be interested to know there is no sound in the game, unlike the video!

For a 3D Sudoku in 2D try this flip pad, also known as Tredoku. Tredoku keeps to the same rules as classic Sudoku with the added dimensions or corners which need to be considered whilst completing. Some printable Tredoku available here.

Also don’t forget killer Sudoku, in this game not only do the digits 1-9 have to be placed in the same way as classic Sudoku but you are only given guidance on the total of groups of numbers. Therefore knowing combinations of digits for a given total is helpful. This is an example of one online playing site, there are many available. I use that particular site as its archives are easy to navigate.

New to myself, and frustratingly yet to fully master is the greater than and less than Sudoku, as shown on the right. Again the ultimate goal of placing digits 1 to 9 are the same, however the only hints you are given are the inequalities < or >. I found A day in the Life‘s blog helpful and need to dedicate time to completing one of these over the Christmas break. Play online here, or some print and play here.

The Bermuda Triangle Sudoku game, is a nice twist, with triangle placement of the digits 1-9 as well as colour coordination. Luckily the sound can be muted once the game has begun by clicking on the word sound in the top left corner.

Many of these variations named above are available online, or as a downloadable app for those with a smartphone and on the move. Here is a list of recommended websites for Sudoku. If you have an favourites to add to the list please your comment, authors of Numberloving are always looking for a new puzzle challenge!

Merry Christmas!

Numberloving does not endorse any product or site, we merely blogging about our favourites. There are of course other sites/books/sellers to get these services.

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