 # MathTech Review: Math Tricks

## In this month's MathTech Review, we looked at the Math Tricks app and identified how you can use it in the classroom to explore different strategies for tackling difficult arithmetic problems and developing your students' number sense.

Lachy Fitzpatrick
Co-founder and CEO

### Introducing Math Tricks

Although I did cringe a little when I was first told about Math Tricks (I have not come across many ‘brain training’ apps for which I would remove the quotation marks around ‘brain training’) I decided to give it a go and keep an open mind.

The basic format of the app is that it explains a math trick and then provides the user with automatically generated questions to practice. An example of an automatically generated question on Math Tricks.

At first, I was quite underwhelmed by the explanations of the maths tricks. Although they were nicely colour coded and somewhat easy to follow, they failed our fundamental assessment at Math Mate: ‘Is this teaching the mathematical concept or only a trick to memorise the concept?’.

Naturally, my next step was to enter full-blown skepticism of the app and to test whether the supposed ‘math tricks’ even worked. I thought I’d start with their cover trick: double digit numbers multiplied by 11. You can see my working below as I picked apart their algorithm to see the maths behind the tricks. A photo of my working out when checking the Math Tricks algorithm. Note that Math Tricks uses underscores to indicate number concatenation (eg. 1_2_3=123).

All of a sudden this app got a lot more interesting! It elicited my curiousity to find out why this trick worked. The best bit was that there were a whole lot more tricks for me to explore!

This opened up opportunities to adapt the use of the app to exploration and discussion activities. The speed, and by proxy, the ‘power’, of the tricks presented are good enough to get students interested. Coupling this with careful content selection and well facilitated discussion, and Math Tricks becomes a useful tool for developing students’ number sense and conceptual understanding of arithmetic.

### Using Math Tricks in the classroom

It turns out that all the ‘tricks’ that Math Tricks explores, take advantage of patterns or arithmetic properties (eg. simplifying multiplication through decomposition 32x3=32x2+32x1). This makes Math Tricks a useful learning tool as the tricks can be pulled apart to reveal their inner mathematical mechanics.

• Sparking students’ curiousity from the simple question ‘Why does this trick work?’. This is then a good setup for a facilitated exploration for an answer to this question with many mathematical discoveries to be made along the way.
• Explorations into the limitations of these tricks and why these limitations exist can be launched for more advanced students to sink their teeth into. Sometimes students will even find that the tricks only need a slight modification to abstract them to be useful outside of their initial limits (eg. multiplication of two-digit numbers by 11 can be abstracted to multiplication of n-digit number by 11 relatively easily).
• Students’ mental arithmetic skills will improve and in particular the flexibility with how they go about deploying these newfound skills. This is contingent on exploring the mathematical concepts behind the tricks.
• Students' appetite and ability to identify patterns in maths will grow. There were numerous classes of problems that I had always put in the ‘hard’ bucket for evaluating mentally that were not as bad as I had thought. An example is squaring numbers between 10 and 19 which you can see below.
• The unmasking of these tricks as maths that students are familiar with should help empower them to be more curious about why other maths concepts work. The trick for squaring numbers between 10 and 19. Have a go at working out why it works mathematically!

### What does Math Tricks cover?

Math Tricks sports an impressive collection of different play styles. I mostly spent time in Training Mode where I can choose particular skills to practise. We think this is the best place for students to spend most of their time as they have control over what trick they are learning.

Training Mode provides tricks for: addition (2 tricks), subtraction (3 tricks), multiplication (35 tricks), division (17 tricks), squaring (17 tricks), exponentiation (9 tricks), nth roots (6 tricks), and percentage (18 tricks). Topics for Training Mode.

Outside of Training Mode, there is also Single Game, Joint Game and By Heart.

Single Game provides a couple of different time modes plus a mode with no time limit. Here students can challenge themselves to set high scores. When students struggle with a problem they are able to see where they need to go in Training Mode to better learn the trick.

Joint Game is a fun little ‘player vs player’ format where students can play with each other on the same device. Students are competing to finish each problem first with the first person to 10 points winning the round. The screen setup for Joint Game with room for a player on each side of the screen.

By Heart is a drilling tool for times tables covering 1x1 to 100x100 and every combination in between.

### Words of caution

With all this in mind, Math Tricks is a long shot from a perfect app, especially if its use isn't orchestrated by you as the teacher. The following are some words of caution when using Math Tricks.

• Math Tricks Pro is not a free app (\$6) and the free Math Tricks has very obnoxious ads that will practically render the app unusable after the first 5 minutes.
• As with any technology, the effectiveness of its use does come back to you as the teacher. With Math Tricks I would say this is particularly important! If the tricks are not used as stepping stones to discussions around the maths concepts lurking beneath, then the students will likely just try and memorise the tricks.
• The time investment to run an activity investigating the actual maths behind a trick is quite high both from a preparation perspective as well as the class exploration-discussion time. Identifying the levels that will deliver the desired learning outcomes is a ‘must’ for your lesson prep and we’d encourage caution towards assuming that if students are doing more work on the app they will by default be achieving learning outcomes. Remember, the value of Math Tricks is primarily in the exploration and discussion that it can be used to generate.
• The content is not adaptive and there is a lot of it. This means that if students aren’t guided to the content then they may dive into content that is too hard, discouraging them from further using the app and potentially reducing their confidence in their maths ability generally.
• Training Mode content is all timed content meaning that students don’t have the opportunity to practise without time-pressure.
• It would be great if they expanded their content to include negatives numbers. This is more a missed opportunity for them though.

### Conclusion

Math Tricks is an app surprisingly packed full of learning potential. Although it could be dangerous if not used thoughtfully due to the lack of mathematical rigour in the trick explanations, a facilitated unpacking of the tricks in the classroom will provide a great platform for building curiousity and having valuable mathematical discussions.

We’d encourage you to have a look at the free version and judge for yourself if it could suit your class’s arithmetic needs!  