20 random iPad Maths Apps that help cover all areas of curriculum

Around this time last year, I wrote a post about the lack of engaging Maths apps on the iPad that went beyond “skill and drill” number activities. Since then, developers have introduced a greater range of apps across all areas of the Maths curriculum that can be used to enhance the Maths teaching and learning in your classroom. Here’s a selection of 20 apps that cover Number and Algebra, Measurement and Geometry, and Statistics and Probability ( these are the Content strands (CS) Australia’s Mathematics curriculum has been categorized under ). They also cover the proficiency strands (PS) of Understanding, Fluency, Problem Solving and Reasoning. I’m sure other countries’ curricula are similar in many regards and you will be able to make the connections.

Undecided (free at time of writing)

A handy tool for probability experiments, Undecided comes with customisable dice ( up to six) with number of rolls, last roll and sum of rolls data, Heads/tails coin toss with cumulative tallies, a 1-10 spinner ( wish it was customisable) , Rock/Scissors/Paper and Short Straw simulations and a random number generator with customisable maximum number beyond thousands (although it’s time consuming to go beyond 1000).

CS  -Statistics and Probability  PS – Reasoning

Decide Now! (\$0.99)

Does what Undecided doesn’t with spinner. You can create/edit unlimited numbers of spinners with any types of categories and combinations of categories. Minimum number of sections is 10. If you add less than that, it intelligently uses ratio to created the segments. Great for probability experiments, especially for increasing and decreasing chance of random events to occur.

CS  -Statistics and Probability  PS – Reasoning

DragonBox+ (\$6.49 – expensive for multiple copies)

Despite the cost, which would be prohibitive for some schools with limited budgets, this is a clever app for building conceptual understanding of the principles for balancing algebraic equations. Presented in a game format, it builds up from simple to complex as you play through 5 levels and 300 individual puzzles. The object is to be left with a single object on one side by applying inverse operations to object on both sides. The final level introduces the alphanumerical symbols associated with algebra.

CS – Number and Algebra       PS – Understanding, Problem Solving, Reasoning

Dartfish EasyTag (free)

This app allows you to create data collection tools using panels as recording buttons for categories and and subcategories you create. Each time you touch a panel, it begins tallying results. It collects category totals and tracks the elapsed time by whole seconds, minutes and hours. Not only useful for data collection and statistics, but can be used as a simple timer as well. Results can be exported by email as a csv file which can be opened in Excel (not  iPad spreadsheet programs), although it records labels rather than numbers so editing the spreadsheet is necessary for tallying results.

CS – Measurement and Geometry, Number and Algebra  PS – Fluency, Reasoning

Pattern Blocks (\$0.99)

A simple app that can be used for many purposes. The drag and drop geometric shapes can overlay translucently to create fraction models, supported by the grids. Tessellations can be created effortlessly and rotations can also be done. At junior levels, shape patterns can easily be created and continued. Relationships between different shapes can also be explored.

CS – Measurement and Geometry, Number and Algebra   PS – Problem Solving, Reasoning and Understanding

Room Planner (free)

Created with House planning in mind but can be applied for many measurement tasks. This app allows you to create and edit individual rooms or entire house plans. Each element ( room, architectural element or furniture) can have its dimensions adjusts though simple touch and drag, elements can be freely rotated and final plans can be viewed from all angles and views in 2D and 3D. Area and Perimeter investigations can be implemented and concepts of space can be explored through placing objects within the rooms. Text can be added and in 3D mode, creativity is encouraged though applying colours and textures for realism. Scale can be explored by creating models of actual rooms.

CS – Measurement and Geometry  PS – Problem Solving, Understanding and Reasoning

A simple but engaging equation building game that builds understanding of order of operations rules. A target number is randomly selected and 5 dice are provided to use as the values to generate equations to reach the target. IT provides a whiteboard for experimenting with possibilities before dragging the numerals and operation symbols into place. There are options for using some or all operations and brackets to allow for different ability levels.

CS – Number and Algebra PS – Fluency, Problem Solving, Understanding and Reasoning

Foldify (\$2.99)

Its whimsical nature and cost makes it appear superficial use of technology but it allows for an engaging exploration of 3D objects and nets. Can also be used to create patterns on dice faces that can encourage logical reasoning in building patterns.

CS – Measurement and Geometry PS – Reasoning and Problem Solving

Geoboard  (free)

Simply put, it is a Tech based Geoboard that allows for wide ranging angle and shape explorations as well as quick creations of arrays to build understanding of multiplication and division. Can also support fraction and decimal exploration with careful manipulation. Shapes can be rendered transparent or translucent for easier viewing and comparison.

CS -Measurement and Geometry, Number and Algebra   PS – Problem Solving, Understanding and Reasoning

Geometry Pad (free; \$6.49 full features)

This app allows for exploration of shape, angles, co-ordinates, area, perimeter, circle properties,algebraic expressions on graphs and linear graphs ( functions in the paid version ). Free version is still quite functional but paid version has some compelling upgrade features for higher level mathematics.

CS – Measurement and Geometry, Number and Algebra    PS – Understanding, Reasoning

MyScript Calculator (free)

A screenshot doesn’t do this app justice. In a nutshell, this app converts your handwritten scrawlings into equations and calculates the answers. Recognises indices/roots, trigonometric functions, percentages and fractions as well as basic operations. YOu can edit equations on the spot by crossing out and replacing numbers and symbols and equations automatically update as you increase and decrease values on either side. Blank spaces are replaced with calculated values. A great app for exploring equations as well as a very functional calculator. Does have limits, which you will find as you explore but its free so explore at will.

CS – Number and Algebra    PS – Fluency, Problem Solving, Understanding and Reasoning

Friends of Ten  (\$0.99)

A handy app for exploring subitising and the visual conceptualisation of 1-10, important number skills to develop in younger students. This app has six activities using Tens Frames to develop build to ten, how many and more than/less than.

CS – Number and Algebra   PS – Fluency and Understanding

Tens Frame Snap Lite (free)

This game based app consolidates the skills developed in Friends of Ten above using a 2 player Snap game.

CS – Number and Algebra   PS – Fluency and Understanding

(\$1.99) (My Maps – linked to Google Maps account – free but harder to use)

Using Google Maps as its base, this app allows students to build routes along maps by dropping waypoints along the way. It generates distances and estimated times along the route and between points and you can compare bicycle, car and walking routes to the same locations. It also creates instructions which can be tested by actually going out and following the routes created. The distances and times can also be tested by actually going along the route as well. Routes can be shared via email, Twitter/Facebook and printed.

CS – Measurement and Geometry, Number and Algebra     PS – Problem Solving, Reasoning and Understanding

(free)

An app that provides manipulatives to explore the relationships between fractions, decimals and percentages. Limited to values from 1/2 to 1/12s ( no 1/7s or 1/9s)

CS – Number and Algebra    PS – Fluency and Understanding

Counting Board (free)

A simple but effective counting aid. Either show or hide numbers. Create visual number patterns. Use to develop count on/count to/ count backward strategies for counting, addition and subtraction. Has an option to say numbers as they are tapped.

CS – Number and Algebra    PS – Fluency and Understanding

Fraction Division (\$0.99)

A very specific skill set for an app but great to see a conceptually difficult operation ( division of fractions) explained in a concrete way. I know teachers who don’t understand how to divide fractions or explore the rote learnt reciprocal concept. This app definitely helps

CS -Number and Algebra   PS – Fluency, Problem Solving, Understanding and Reasoning

Numbler Free (Free! – paid app \$0.99)

A fun way to explore equations and practise calculations. Basically, this is a number based version of Scrabble. YOu are given a selection of tiles with numerals, operation symbols and an equality sign. The object is to make equations with the tiles you have and/or the tiles already on the board.  Easy to play, challenging to finish. Encourages experimentation by trying to score the highest possible score. Free version only allows for one player versus computer. Paid version allows two player game.

CS – Number and Algebra PS – Fluency, Problem Solving, Understanding and Reasoning

Logic Puzzles HD (\$2.99)

I love Logic Puzzles. This app provides are large selection of puzzles to complete. While not easy to categorise under COntent strands, the logical reasoning developed throough these puzzles is essential for higher order thinking. I have successfully taught 7 year olds how to solve ( and create ) these types of puzzles which has encouraged thinking, problem solving, creativity and logic.

PS – Problem Solving and Reasoning

Others prefer SurveyMonkey but PollDaddy has its own iPad app that gives you a simple way to COLLECT data based on surveys created online. All you have to do is link the app to an account, download the survey and it creates an easy to use, question by question survey on the iPad. You can review the results and upload the surveys once done.

CS – Statistics and Probability

As you can see, most of these apps are free so you can easily try them out to see what you can do in your classrooms with them. The paid apps won’t exactly break the budget if you download one copy to try. While many have physical, old school versions that can be used instead ( just like they were pre-iPad), I am of the opinion that the iPad version are more user friendly are allow for more possibilities and instant, repetitive use.

Let me know what you think about these apps or maybe suggest some other apps I have left out.

xiPad + yApps + zAirServer = Engaging Algebra

Algebra gets a ‘bum rap’. Then again, it has a lousy public relations manager. Whoever came up with the whole ‘letters and symbols’ campaign should be sacked. Yes, opening up to Exercise 7D and solving 50 variations of 2x + y = -7 is n0t anyone’s idea of fun. But as I said, Algebra needs a new PR campaign.

DISCLAIMER: I’m just a Primary/Elementary teacher without any official qualifications in High Level Mathematics – No Masters, no Ph.D, just an A+ Average in High School/College Maths and 25+ years teaching kids to enjoy,not stress about, Maths. I may be completely off base with the great mathematical minds out there in what I’m about to describe regarding Algebra but I make no apologies. my students get it this way – including the Year 7-11 students I’ve tutored at home to relieve the confusion caused at their schools. (WARNING: Bear with me, I’ll take a while to get to the point of this post’s title – skip ahead if you want to ignore my Algebra rant!)

Now we have that out of the way, back to my message for today. I have a certain belief about Algebra. I define it as a systematic way of organising, recording and explaining your mathematical thinking using numbers and symbols/letters instead of words and pictures. Where we seem to get lost is that we go straight to the symbol without developing the thinking through the words and pictures/objects. We provide no context or purpose; just a meaningless string of equations with Xs and Ys that need to be solved. I see Algebra as problem solving support, not equation solving.

Last week, I was called in to take a Grade 6 class to release a teacher for planning ( the usual release teachers were unavailable). Maths was on the agenda for the day and I had worked with some of the other Grade 6 students on a similar lesson earlier in the week as a support for some of the high achievers. This time, though, I was on my own and in control so I applied my full tech+Maths kit to the group of students I had for that session.

The lesson/task that preceded this actually had fractions as its focus. One of the teachers had introduced a task involving a a building pattern for shading in grids to make fractions.

The lesson was differentiated to allow for a range of responses. Some needed to build the patterns with counters to discover anything. And then there was “Sheldon” ( not the boy’s real name) whom I walked in on to find him showing his mate the formula for the relationship between square and triangular numbers! When I confronted “Sheldon” to explain his formula and why it worked, he didn’t know how. So began my challenge and the rationale behind the lesson I’m about to recount. In the end, Sheldon actually discovered the key to this lesson I led in the class I took later in the week.

SO…this fraction lesson turned into a pattern and algebra exploration. All the children were able to discover the growing patterns in both number sequences and could describe the change. Square number differences increased by +2, the triangular number differences increased by +1. But that additive thinking was as far as they got. They needed more support to think multiplicatively, to think ‘Algebra’.

Enter (finally we get to the title of this blogpost!) the iPad and AirServer. Yes, I could have done all of this without the technology. I had done so earlier in the week with my small group of advanced students. But the engagement and ease of use was no comparison between the ‘sheets of paper and coloured marker’ group and the iPad and AirServer. If you are unaware of AirServer, I explained its significance in a recent post. Basically it projects multiple iPad screens onto a computer connected to a projector/iWB.

We started with creating the fraction grids using the iPad App Hands On Maths Color  Tiles ( I reviewed this and others in the Hands On Maths collection last year ). Again, we could have hand drawn grids or made them with counters but I had the students more engaged by getting them to make 1 grid each using Color Tiles and getting multiple students to project their grid onto the whiteboard using AirServer. This took 1 minute instead of 10 and allowed us to move straight into discussion with all the visuals needed on the screen – created by students, not me.

We then discussed the three properties visible in these tiles – side length, square size and the shaded (red here) area ( they hadn’t recognised them as triangles yet). I introduced the problem solving strategy of ‘Make a table’ – a strategy that should be embedded in their thinking by now, but it wasn’t. I created the table on my iPad and projected it on the screen. The students then created their own tables, using Numbers, on their iPads and filled in the side lengths, square sizes and shaded areas. Once they had the numbers in tables, they could start looking for relationships in numbers across the properties, rather than just look at the isolated number sequences. It was at this point that some students were able to recgognise that the shaded area numbers increased by adding on the next side length.

I wanted them to see what type of numbers they were creating with the shaded areas – most still didn’t realise. This time I went back to old school methods –

counters. AirServer and my iPad still played a role. I asked the group to use the counters to create the sequence of numbers in the shaded area column in rows. As they began, some weren’t sure what to do. Instead of telling them what to do, I used my iPad’s camera to spotlight pairs who were building triangles onto the screen, thus giving support to others who needed a hint. Every group then wanted their triangles on the screen as well! This idea of spotlighting using iPad and AirServer can work in many ways to maintain engagement – kids like to be on show and recognised .

Once this was done, the students realised they were creating square and triangular numbers and that there was a relationship between them. Children started to recall the rule we had discovered – square the side plus the side then half it gave us the triangular number. But I posed one final challenge – why does this work and how can we show it with our tiles to explain the relationship? Back to Color Tiles we went. We recreated our two coloured square tile pattern. Then we added an extra column/side length. Bingo! The students recognised that this created two equal halfs, a red and yellow half- two triangular numbers!

4×4 Square with extra column of 4 results in two equal shaded areas- triangular numbers!

The final step in the process now was to put all of these theories into one explanation and come up with a formula – finally Algebra was coming into play. The important thing here is that they were thinking algebraically all along – I just didn’t tell them because Algebra is such a dirty word. Now they were quite excited that they were doing algebra.

I asked them to take screenshots of the tiles and the table and import them into Explain Everything. Then we looked at the table again. I explained that the only difference between what we had been doing and algebra was that we needed to replace our words and ideas with letters and symbols. What was the starting point? The side lengths. What will we call them – we decided on s ( could have been x,y, l etc). What is the square number? s x s or s^2. What did we do next? +s. Finally we halved the total ÷2 . With all these symbolic represenations students were able to create a formula for finding a triangular number: (s^2 +s)/2

Now thinking they were expert mathematicians, the students were able to record their understandings in Explain Everything AND find any square and triangular number without creating a long sequence. And they got it because we started with the thinking and investigating, not the formula that “Sheldon’ told us about. By the way, he worked this out independently and actually helped out my thinking with the idea of adding the extra side to the square grid – that’s the first time I had visualised the two triangular halves. This shows that our high achieving students can support the learning in the class – they just need a biy of guidance in their thinking, He was happy with knowing the formula. Now he UNDERSTANDS the formula and why it works. His discovery helped the less able students to also understand the thinking behind it all. And the iPad, the apps  and AirServer kept them engaged long enough to get there.

Oh, one more thing. I mentioned earlier context and purpose. I put this whole task in the context of a tile designing company. I talked about how the construction of Federation Square ( a modern structure in the City of Melbourne laden with geometric designs ) was not a random design. It was very mathematical. I put to them the scenario of customers wanting a design like the one we investigated created at a size of their own choosing. As employees of the company, we needed a method for quickly calculating how many of each tile we would need – the formula we discovered would get the job done.

Algebra need not be hard. It’s just logical thinking written down in an organised, symbolic way. Taking students through the right process can demystify it all. And it doesn’t hurt to use a bit of tech like my good friends the iPad and AirServer to help them along the way.

What are you doing to make Maths real in the classroom?

spikedmath.com

Mathematics – you either love it or you hate it. There seems to be very little middle ground in this area of thinking. The lovers can find something fascinating in any challenge involving the world of numbers, statistics, shapes and measuring. The haters switch off as soon as you announce ” Please get out your maths books” and go into a quivering near foetal position at the mere mention of the word ‘algebra’.

So where have we gone wrong? Is it just that Maths is too hard for some people? Or have we failed to make it relevant so the doubters just switch off? If we did a better job at showing how important Maths is to real life – that it doesn’t just exist within the confines of a lifeless text book divided into 12 chapters and 120 Exercises of mind numbing practice drills –  would we, along with an injection of teachers who truly love and understand Maths, finally produce a generation of mathophiles (if thats even a word)?

What are you doing to make Maths real in the classroom ( and beyond where it should be)?

• Are you taking advantage of the simple beauty of Lego blocks to teach arrays, number patterns, counting and  visualization?
• Do you rely on all those exercises in the textbook or do you show how Trigonometry and functions can be used  to build ramps, staircases, find out slopes;Test and adjust the water flow of a slope on a roof or a pipe; discover The effect of a ramp’s slope on the distance of a jump; work out whether throwing a ball on a steeper angle increases the distance it travels; test the physics of Angry Birds and other similar games?
• Are you using ratio to alter recipes to cook for more or less people or for changing the taste of a sauce?
• Do you just learn about the properties of different shapes or do you explore how different shapes fit into a space more efficiently and how this can impact design?
• Are you buying all of your class/school supplies or getting students to organise surveys to find out parent/their preferences, do research on costing of supplies, table or graph results, compare costs of home purchases versus school purchases, investigate savings and what money could be used for instead?
• Do you organise school events or have you thought about students working together to organise the costing of events like graduation parties, excursions, transport options, fundraising events?
• Does your school block or encourage free fantasy sport online competitions which develop money management skills?
• Do you go on excursions to local shopping centres to buy resources and look for the best prices and possible discounts?
• Do you use worksheets about statistics and percentages or do you keep statistics about school sports events as real data to monitor performances?
• Do you use Maths text books for examples or do you collect infographics from newspapers, news programs and websites so children have relevant, recent data to analyse?
• Do you just serve up pages of algebra exercises to complete or do you demonstrate how algebra can be used as an efficient way to solve real problems, create formulas for simplifying work practices or show the usefulness of algebraic formulas in spreadsheets?
• Are you still making graphs about favorite colors in the junior grades or are you teaching them that graphs can represent information from questions that make a difference to their lives ( that doesn’t have to be as deep as it sounds)?
• Are you teaching students how to manage budgets, are you showing them how interest rates impact on their spending? Do they understand credit card debt?
• Are you involving them in every mathematical possibility in a school day from helping out in the canteen, collecting and counting fundraising money, being timekeepers, sorting out notes in the office, conducting daily surveys of relevance, cataloging books, tallying fines or costs of replacing lost books in the library, helping the PE teacher measure results in athletics carnivals or repaint the lines on sports and games fields out in the playground?
• Are your students building resources that involve accurate measurements like puppet theaters, book boxes and doll houses for the junior grades? Do you just draw plans to scale or let the children build scale models of real objects they measured?
• Do you let your students take control of the layout of your room so that they can apply location strategies learnt in class?
• When considering guest speakers to come to your classroom, do you just think authors and campaigners or do you think about builders, engineers, businessmen or others that can share Maths in the real world?
• Do you see that organising collaborative discussions with classrooms around the world provides an opportunity for teaching time concepts?

The list can go on forever. I would love to hear from you about what you are doing in your classrooms to make Maths real, relevant and exciting. One idea would be sufficient or more if you want. I’ll add your ideas to my list ( and give you credit of course). Maths is too important to be feared. We have to show our students its worth. Join the conversation.