Functions – an update

function-builder

I have updated a post on functions with the excellent PhET simulation, Function Builder

The post includes several excellent resources for teaching functions. See also this further post aimed at older students.

PhET Simulations look excellent, I will be exploring more of these. I have used the Projectiles Simulation with Mechanics A Level students and have posted on this for students on Mathematics for Students. There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for iOS also for Android.

PhET Balancing Act working nicely on my phone!
balancing-act

 

Mathematical Miscellany #5

Twitter can be useful for alerting one to resources / news, note the first two items.

Problem Solving – an open access (free) book which looks at research on Mathematical Problem Solving.
Problem Solving

Note this page for a large collection of free Mathematics books.


Tools for Maths Teachers J HallJonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. Note that you can show solutions for the GCSE questions – there is a link at the bottom of the page for each question.
JHall site


The page on Apps has recently been updated, there are fuller descriptions of the various apps and note the addition of Summaze2 from MEI and Sigma. A wonderful example of a free app – Maths to make you think, visually attractive and no irritating adverts trying to make you buy the premium edition!

Sumaze Integral


In Mathematical Miscellany 4, I mentioned the excellent Linar Equations Calculator; for an excellent way to illustrate the balance method of solving linear equations, try this manipulative on Mathisfun, this is very simple to use and does not require the user to log in.
Mathisfun Algebra Balance


tickUK Results 2016 – a new page has been created which I will update as A Level & GCSE results / news comes in. As I do each year, I will provide links to the results statistics and grade boundaries for the various examination boards.

Note my Twitter Examinations list. Check this for announcements / news. (You do not have to be a Twitter subscriber to use the list.)


Whilst this is Mathematical Miscellany #5 I have been writing these compilation posts for quite some time. They were at one time ‘Thoughts this week…”. Previous posts are all filed under the category (note the Category menu on the right) Mathematical Miscellany.

Apps

I thought I would create a page for apps I come across which I find useful; these are mostly available for  Android as well as iOS. Just a small number currently, but these are all free and work very well.

Apps - Mathematics

Apps – Mathematics

Mobile Puzzles – Algebra

Mobile Puzzles

Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit solveme.edc.org to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.

Menu

Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:
Master Level

Note the menu in the corner of each puzzle page:
Play Menu

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

create equation
Note that you can then drag a heart to subtract a heart from both sides:
puzzle demo
Note that under settings you can choose to show numbers in the mobile as in the illustration. If the solution is correct, the mobile will balance.

On the other hand….
puzzle demo wrong answer

 

PhotoMath

PhotoMath

PhotoMath

PhotoMath is a free camera calculator phone app available on Android as well as iOS and Windows. To use point the camera towards a printed mathematical expression and the app gives the solution, step ­by ­step solutions are also available. The problem types are limited to those shown in the examples here and it can be a bit tricky to focus the camera sometimes, particularly where problems are very close together on a page but this is rather clever! The app has handwriting recognition.

photomath-examples

Photomath Examples

Experimenting, I have found that the app works if you point the camera at a screen, so one could zoom to an appropriate size first. Try these equations in the Year 7 text on CIMT for example:

CIMT Linear Equations

CIMT Linear Equations

PhotoMath-solving-explanation-Android

Select for video demonstration

Select for video demonstration on Vimeo

Desmos on Android

This slideshow requires JavaScript.

A happy day! Desmos comes to Android and I now have the best handheld graphing calculator I have ever had! As you would expect of Desmos, it just works! Get it on Google play here. (Desmos iOS apps have been available for some time). I will certainly be asking students with Android phones to get the app.

You will find a series of Desmos Slideshows here, (these have been written with students in mind) and more on Desmos on this series of pages.

Photos by David Young

Cubic

Things I Learned This Week: Sep 8

This week in class…
  • In my first lesson with each class I have been talking to my students about being gritty and green!  The green refers to our engagement with learning assessments where we traffic light students green / amber / red for their engagement with their learning. They certainly all listened and understood the message and clearly want to do well.
  • I have used the name cards I described here; I printed the address of my homework blog on one side for them to see and note and they wrote their name on the other. I find these really helpful, seeing the name beside the student means you can use their name when you talk to them and I already know many names. I collect them in at the end of the class, providing another opportunity to use their name thanking them for returning the card. (The ‘cards’ are actually folded A4 paper.)
  • Diagram - T SherringtonI read Tom Sherrington’s post “Empowing students to own their learning solves maths problems“; a great idea to start with a diagram with no labels at all as a way into a problem. I tried this with Year 10 (very able students) in their first lesson, presenting them with only Tom’s diagram and was very pleased indeed with the outcome. I didn’t even give them the question – just the diagram (a small copy each) and we started by deciding what the question might be. We quickly got onto areas as a possibility so then answered Tom’s original question ‘what fraction of the shape is shaded?’. The class happily discussed how to solve the problem and a student asked ‘can we write on the diagram?’ which of course was perfect – absolutely they could write on it. We solved the problem, revising some basics and had the discussion about what to do when you don’t know what to do! I will certainly use diagrams with no labels again.
New Discoveries
  • Numbers AndroidNrich now have modules for STEP preparation which look excellent. Note also their related resources such as preparing for university.
  • The wonderful Desmos graphing calculator keeps getting better and better and now has animations.
  • I tried an Android app I rather like, Numbers which is similar to Countdown. Use the given numbers to achieve the target. There are over 200 levels. I’m not sure the levels have a lot to do with increasing difficulty – look at level 61 here for example – this is much easier than some of the earlier problems. When I first started playing I didn’t realise you could click on intermediate results as you see in the illustration here and actually managed several levels without doing do! Dave Gale has written a post on the app here. I think I’ll try some of the problems this week with my Year 7 class when we discuss order of operations because we could write out the solution on several lines as in the app but then discuss how we could write the solution with brackets. I really want this on my interactive whiteboard (as well as my tablet and my phone!)
  •  Maths News
 
Miscellaneous
  • I have written before on Jane Hart’s Top 100 Tools for Learning, the 2013 list is now published.
Blog Updates 
….and finally 
Thank you Doug Belshaw, I enjoy your Thought Schrapnel every week.