Animated Math from Pixar Math in a Box

A career as an Animator is one of the math-related careers in my freebie PDF 21 Seriously Cool Careers that need math. So I was really excited when I heard that the animation superstars at Pixar had teamed up with the genius math folk at Khan Academy to bring an interactive learning experience called Pixar in a Box, showing how math is used to animate our favorite cartoon characters.

Pixar in a Box

Pixar in a box in a box aims to

…show you how the concepts you learn in school are used to tackle creative challenges we face during the making of Pixar films. Along the way you’ll also learn a lot about Pixar’s filmmaking process….

Topics covered include:

Art&Story

Modeling

Rigging

Surfaces

Sets&Staging

Animation

Lighting

Rendering

 

Pixar in a box topic

Each topic includes a design activity (suitable for those  ages 10 years+) followed by a math activity, some of which are suitable for 10 year olds and some which will need middle school or high school math knowledge. The Educators Guide gives suggested grade levels for each activity, as well as some additional offline activities.

There’s an active comments section under each video, where students can ask questions and there are math exercises to complete based on the particular math topic linked to the design activity(with links to additional instructional math videos).

This is a great resource for both keen mathematicians and those who are always asking “When will I need math?”

Check out the Pixar in a Box introductory video below:

An Insider’s Guide to Thinkster Math (formerly Tabtor)

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2 years ago Thinkster Math contacted me on my Maths Insider email, asking if I’d like to review their new iPad based math program. After testing it with 2 of my kids and exploring it using my 20-years-of-math-teacher-experience, I wrote the blog post Is Thinkster Math a Real Alternative to Kumon?

After publishing the post, Thinkster Math, who are based in the US, offered me a position to work with the families from Europe, Asia and Australia who had signed up for the program, many after reading my review. Over the past 2 years I’ve had the pleasure of working with amazing families from around the world who are using the Thinkster Math program to guide their kids to math success.

Other programs and resources are definitely available and I’ve written about a whole heap of them here on Maths Insider, but in this post I’m going to offer an Insider’s guide to the Thinkster Math program and tell you how you can use even just the Thinkster Math 1 week free trial to kick start your child’s math learning.

How to get the best from Thinkster Math’s 1 week trial

Many families are attracted to Thinkster Math because of the  chance to try the program without paying(tuition centres like Kumon don’t have free trials). Make sure you make full use of the Thinkster Math trial by following the tips below:

Use the Thinkster Math trial straight away

My big tip for Thinkster Math’s trial is to sign up when you have at least a few non hectic days. Your free 7 day trial will begin straight away once you’ve signed up and your child will have the chance to try a sample worksheet, take a diagnostic test, try some worksheets based on the questions they got wrong on the test and even speak to their instructor. Those families who get straight on with the Sample and Diagnostic test, worksheets and conference with the instructor will have a real insight into their child’s math learning gaps as well as into the Thinkster Math program and will be in a great position to decide whether Thinkster Math will work for their families.

Ask for the trial to be extended

Some families sign up and don’t get round to completing the Sample or Skills Assessment or they complete those but don’t get round to trying the worksheets or speaking to the instructor. In that case, it is possible to get your trial extended for a few more days by contacting the Thinkster Math support team.

Use the insights the Thinkster Math program gives you

Even if you decide to not subscribe to the Thinkster Math program, if your child has completed the Skills Assessment, you’ll be able to see exactly which math topics your child has weaknesses in through the progress report chart built into the Thinkster program (see below).

Inside the Thinkster Math instructor app

Thinkster Math instructors have an app,  which we use to provide us with insights into each students math learning and to share our insights with students and their families.

As a Thinkster Math instructor, I can give written feedback and step by step solutions for each question, by either writing in the worked solution or providing corrections to the student’s working out. The picture below shows the instructors writing in red.

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As a Thinkster Math instructor, I can see at a glance which topics each student is struggling with (those in red), which topics each student is confident with (those in green) and which topics each student understands, but is still making errors on (yellow topics).These insights help me to decide what work to assign to my students. Parents and students can also see the progress report on their Thinkster Math account.

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As a Thinkster Math instructor, I grade and send feedback on each of my students worksheets. This is a screenshot from the Thinkster Math program. Students and parents can easily see the instructor’s feedback.

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As a Thinkster Math instructor, I can see my students’ working out, how long they’ve spent writing, thinking and erasing. I can even “playback” their work. This shows me how the student has approached answering each question.

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My favorite part of my work as a Thinkster Math instructor are one-on one coaching calls I have with my Thinkster Math  students. During these calls we review how their work has been going and preview upcoming work. I also teach strategies for any tricky work they’ve met or are about to meet and we discuss and sort out any problems related to the math they have been working on at school.

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The Thinkster Math Parent Insights app

This week Thinkster Math have released a new Parents Insights iPhone app to help parents easily keep track of their child’s Thinkster Math work and activity. The video below gives an overview of the Thinkster Math Parents Insights App which uses intelligent technology to provide further insights into your child’s learning:

 

I hope this post has given you an great insight into “behind the scenes” at Thinkster Math . For your 1 week trial and 10% off for 3 months, use the referral code mathinsider1 or sign up from the following link: Maths Insider Thinkster Math discount

5 More Fascinating Science and Math Podcasts

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I highlighted how cool math podcasts are in my post here on Maths Insider, Listen Up! 8 Fascinating Podcasts to Spark a Love of Math in Your Teen. I still listen to podcasts in my car but recently Mr Maths Insider bought me a waterproof bluetooth speaker which I use to listen to podcasts in the shower (too much info??). Since then, I’ve discovered more cool science and math podcasts which I share below. Some are great for young kids and some will inspire teen mathematicians. Check the descriptions below. You can also click on each of my favorite episodes right here in the post!

1. Brains On – great for kids

Brains On by Minnesota Public Radio describes itself as a  podcast featuring science for kids and curious adults. My younger kids like listening to Brains on episodes as they fall asleep at night. Great for kids and adults.

Maths Insider pick: Numbers

The questions we have about numbers are uncountable – but here are a few of them: Where does zero come from? How is there more than one kind of infinity? What is it like to do math when numbers have different colors – and personalities? click below to listen to the Numbers episode.

 

2. The Infinite Monkey Cage – British wit + science

The Infinite Monkey Cage is a British podcast science podcast which describes itself as a “Witty, irreverent look at the world through scientists’ eyes. The show is presented by Professor Brian Cox and stand up comedian Robin Ince. This podcast does make me chuckle and is great proof that scientists do have a great sense of humor. Great for teens and adults.

Maths Insider pick: Numbers Numbers Everywhere

Although many people fear maths and will admit to dreading  any task that requires even basic skills of numeracy, the truth is that numbers really are everywhere and our relationship with them can, at times, be oddly emotional. Why do so many people have a favourite number, for example, and why is it most often the number 7? Click below to the Numbers, Numbers Everywhere episode.

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3. Planet Money – short, sweet and always interesting

On NPR’s Planet Money, you’ll meet high rollers, brainy economists and regular folks – all trying to make sense of our rapidly changing global economy. Each episode of Planet money is relatively short (about 15 – 20 mins long) and it’s one of the few podcasts that i listen to where I like to make sure i’ve listened to every episode as they are always really interesting regardless of the topic. Great for pre teens, teens and adults.

Maths Insider pick: The Long Run

Stories about a $50,000 loophole, what neighborhoods mean for kids, and what the Six Million Dollar Man would cost today. This is my favorite podcast episode in this post! Click below to listen to The Long Run episode.

4. Science Weekly – serious science simplified

The Guardian’s science team brings you the best analysis and interviews from the worlds of science and technology. I only discovered this podcast recently thanks to fellow Thinkster Math (formerly Tabtor) Tutor Dan Cox who shared it on his Delta Maths Facebook page. So far, I’ve only listened to the episode below, but I’ve already picked out some other episodes of Science Weekly to listen to. Great for pre teens, teens and adults.

Maths Insider pick: How maths can change your life

Mathematician Jordan Ellenberg argues that maths can help all of us become sharper thinkers. This episode has some cool insights and discussion focusing around how everyone needs math. Click below to listen to How maths can change your life.

5. The Story Collider – live science storytelling

According to Story Collider, “Science surrounds us. Even when we don’t notice it, science touches almost every part of our lives. At the Story Collider, we believe that everyone has a story about science—a story about how science made a difference, affected them, or changed them on a personal and emotional level. We find those stories and share them in live shows and on our podcast. Sometimes, it’s even funny.” I’m a fan of story telling podcasts such as This American Life and The Moth, so the Story Collider podcast with its mix of science and story telling is a favorite listen of mine. Great for teens and adults.

Maths Insider pick: Your Favorite Number: Alex Bellos is surprised that people ask him what his favorite number is, so he decides to ask everyone what theirs is.

Take a listen to the math podcasts above. Which ones did you like? Tell me in the comments below.

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Does Your Daughter Lack Math Confidence? She’s Not the Only One.

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A recent study by the OECD (Organisation for Economic Cooperation and Development) has highlighted the problem of girls’ lack of math confidence. From the report:

Girls “lack self-confidence” in their ability to solve mathematics and science problems and achieve worse results than they otherwise would, despite outperforming boys overall

Girls do worse at math and sciences than boys, even though they do better in other subjects. This gender gap occurs in the majority of countries who took part in the PISA (Programme for International Student Assessment) tests, but the gap in the UK, the US and Western Europe was much more noticeable.

A spokeperson from the OECD criticized the teaching of math in the UK which he says was “simple math wrapped in complex words,”compared to Asian countries where complex math is taught earlier and from first principles.

The report goes on to say that this gender gap is not because girls aren’t as clever or able as boys, in fact they do better than boys in reading tests, but their poor performance is due to a lack of confidence in their math skills and their belief that they won’t need math for their future careers.

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As the mother of a 15 year old girl, these results sadden me, but I know that looking at the make up of the advanced math groups in her school, the majority of the class are boys, with only 5 girls out of 20 in her class and only 6 girls out of 25 in my 14 year old son’s advanced math group.

The OECD also looked at data from parent questionnaires and found that parents were much more likely to expect their sons to work in careers that needed math than their daughters.

What can we parents of girls do to lift our daughters from the bottom of the math confidence pile?

Show them cool careers that need math

Photo: Mashable.com

Photo: Mashable.com

Research from the Universities of Pittsburg and Michigan found that many women who have strong math ability, also have strong verbal ability and therefore have a wider choice of of career options. Make sure your daughter is aware that, if she chooses,  she can use both her math and verbal abilities in many of math and science based careers.

Share cool math videos

9 Ted Math Talks

Who doesn’t love a funny or inspiring video? Make a point of sharing some cool, well-made math related videos with your child. You won’t go wrong with Ted Ed math videos and there are some really cool math and science You Tube channels out there. And don’t forget math related podcasts

Keep up with the latest math education research

The Pisa (Programme for International Student Assessment) tests whose results formed the basis of the girls and math confidence study, take place every 3 years. In between test years, researchers worldwide dissect the the test data to produce findings which parents can use to support their own children’s learning. Quality news websites such as the Guardian, The New York Times and the BBC are good sources for finding out about the latest math education research. Of course, Maths Insider also highlights research based ideas to help you help your child with math.

Let them read math

Research (and personal experience from my 4 kids) has shown that girls love reading books more than boys do. We’ve managed to sneak a few math books onto our daughter’s bookshelf over the years. You can find some engaging math story books in the Maths Insider Amazon store in the side bar. Also check out my blog post Go Read Some Math.

Find out what your daughter really thinks about math

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Kids, especially as they get older, are often experts at hiding their true feelings. After reading this post, you’re more likely to look out for signs which indicate the level of your daughter’s math confidence. A casual chat in the car, or at the dinner table will yield more insights. You should also check out my “How Confident is Your Child at Math?” quiz here on Maths Insider.

 

As a biased math fanatic, I’d love it if every child loved math, and as a mother of 4, I’d be content if my own children loved math all the time. In reality, that’s just not going to happen. However, as parents, we want our children to be confident in all their subjects at school, and especially in the core subjects of math and English. We also don’t want the fact that our child is female, to mean she has fewer future career options. The advice above will help raise the math confidence of your child, whether it be your son or daughter, but the research shows the problem is more acute for our girls.

 

How Can I Help You Help Your Child With Math?

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It’s been over 2 years since I blogged here on Maths Insider! So the first thing I’ll say is I’m sorry! I’ve still been connecting with Maths Insider readers through my Maths Insider Facebook page but have neglected those of you who have been coming over here for advice on helping your child with math.

So what has Maths Insider been up to for the past 2 years?

1) Working with Thinkster Math (formerly Tabtor)

For the past 2 years,I’ve been Thinkster Math‘s instructor for International students looking after families everywhere from the UK to Europe to Asia and lots and lots of Thinkster Math families in Australia and a few in New Zealand. Thinkster Math approached me after I reviewed the Thinkster Math program here on Maths Insider. As a Thinkster Math Instructor, I’ve been helping families guide their children to math success using Thinkster Math’s iPad based system.

2) Homeschooling!

The other thing I’ve been doing is I’ve started homeschooling one of my four kids. I’ve been homeschooling my 8 year old son for the past year and am pleased to announce that we’ve both survived our first year of homeschooling! The math has been straight forward thanks to Thinkster Math and another cool math resource that I’ll talk more about later, but finding out how to guide my child to homeschool success in English, History, Geography etc has put me in the position of being an anxious parent searching Google, blogs and Facebook pages to find that secret sauce. All this searching has made me realise that a blog such as Maths Insider is still a valuable resource which I need to keep adding to.

The Maths Insider legacy still continued

During my blogging hiatus:

Teachers and parents have still been downloading the 21 Seriously Cool Careers that Need Math resource to give kids math inspiration.

Families have read my eBook – The Ultimate Kumon Review and have been able to find out if the Kumon programme is right for their child.

I’ve also had people joining the 31 Days to Faster Times Tables membership site and using the worksheets, audio and video guides to get their kids over the Times Tables hurdle.

About Kumon

And I’m back!

Over the next month I’m going to give you a behind the scenes look at the Thinkster Math program, so you can see what tools I’ve been using there to help kids improve their math. I’ll also show you exactly how to use Thinkster Math’s 1 week free trial to identify your child’s math strengths and weaknesses.

I’ve got a blog post in my drafts box about Girls and Math Under-Confidence. It’s based on academic research and also on my daughter’s personal experience, as well as on my experience as an math educator for the past 20 years.

I’m bursting to write a review post about Life of Fred Math because it really is quite the most quirky, wonderful and inspirational series of math textbooks I’ve ever come across.

I’m also toying with the idea of writing about my experience as a Kumon franchisee. I get lots of queries from people who are interested in running a Kumon center, so an in-depth and honest post  on the topic seems to be needed.

Over to you!

When I grow up I'm gonna invent a machine that eliminates all math homework

Apart from these ideas, I’d love to hear what questions you have about guiding your child to math success!

You can add your question here, in the comments, below this post or email me directly at caroline@mathsinsider.com

Looking forward to hearing from you!

How to Solve a Physics Problem (FUNNY!) plus Mental Math Tips

I saw this cool comic strip below, by the funny folks at Saturday Morning Breakfast Cereal (SMBC), a few weeks ago on Facebook , and spent a good few minutes cry-laughing (is that a thing?) Even my daughter in the midst of wrangling with quadratic equations in preparation for a math test, joined in. You see, even for seasoned math teachers, math lovers and professional scientists and mathematicians, arithmetical errors are all too common when problem solving.

how to solve a physics problem

As part of my role as Instructor for International Students at Thinkster Math (formerly Tabtor), I was given 5 math worksheets at Grade 5 and 6 level to test and report back on any errors or inconsistencies before the worksheets were released onto the student app. Needless to say I made 1 or 2 (or 5) mistakes across the set of worksheets!

If you’re a parent of a child who’s struggling with arithmetic, you might not yet be able to see the funny side of  SMBC’s satirical cartoon, but take heart that mental math mistakes happen to the best of us.
I’ve added some links below to some blog posts here on Maths Insider which will help polish your child’s mental math skills ready for the day when they need to solve that tricky physics problem!
How do you help your child with Mental Math?

Check out These Challenging Online Math Tools for Gifted Kids

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This is a guest post by Joseph Rodriguez

While many educators agree that it is essential to improve the quality of math education in our public schools, a debate persists about how it should be done. Do we work with the students who are struggling, so that they can do better? Or do we push the students who are excelling, so they can move on to even greater things? Budgets are tight and many schools are pushed to decide one path or the other. Fortunately, many online resources can challenge gifted math students with new coursework and an outlet for their ingenuity. Here’s what you should know if you’re an educator or parent in need of inspiration.

1. Challenge Math Online


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Challenge Math is meant for students in grades 2-6 who have shown great talent for mathematics and who are eager for an extra outlet. It’s set up with two semesters of coursework, a fall and a spring, which can be done separately or together. It focuses on problem-solving strategies suitable for their age group, including diagrams, lists, logic, and learning how to work backwards from a solution. An early start on cultivating a love for math can go a long way in a child’s education, and learning how to solve problems logically is a useful skill in many contexts.

2. Math Zoom

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Math Zoom is another rigorous, yet fun, math course for students who have demonstrated an excellence in the subject. It has both an in-person and online options, and both provide training for students who would like to enter into mathematics competitions. Like many of these courses, they focus on areas of math and problem solving which go beyond what the typical classroom can provide. In addition, they offer a deep level of analytical, logical, and problem solving training which can help them when taking advanced high school or university level math courses. The Math Zoom academy provides training and coaching to push gifted students into their full potential and help them experience the brilliant world of mathematics firsthand.

3. Omega Math

Omega Math is affiliated with Woodbury University and offers online math courses for both credit and non-credit options. It has a full range of class levels, from basic math skills all the way up to Calculus III. For people who love math and want to further their understanding of it at any level with the option of getting extra college credit, this is a great resource. It is entirely online, so the learning can happen on your own or with help from the online tutors, and upon passing the course, a student will have a college transcript and list of credits when taken with the credit option. There’s even a business calculus option for those interested in learning how calculus can relate to real world business problems. More info on great careers for math wizzes can be found at  thebestcolleges.org

4. Alumcus

Art of problem solving math

Alumcus is a free online set of mathematics courses designed to get harder as the student learns more and becomes capable of more advanced calculations. Also, if a certain topic becomes harder to pass, there are more problems which can be added into the curriculum to give extra practice. There are built-in progress reports, so everyone can see where they’ve done the best and where they need extra work, to give the student a genius-level degree of understanding what they know and what they’ve improved upon.

Math carries with it very important problem solving and logic skills which can be applied to anyone’s life. It is very important, therefore, that students with a gift for math develop their skills as fully as possible, or that talent will not be properly strengthened.

Joseph Rodriguez writes all about math and education. His recent work is on the best Masters programs in Math in the US.

 

Holiday Math and More

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If you’ve read my Thinkster Math vs Kumon blog post a few months back, you’ll know that I’ve been working with Thinkster Math (formerly Tabtor), the personalized iPad based math program. I’m Thinkster Math’s instructor for many of their international students, and I’m also recording instructional videos which accompany each of the Thinkster Math worksheets as well as writing articles for their blog.

As a result, It’s been a bit quiet here at Maths Insider but after the holiday I’ll hopefully be back here with a vengeance.

I’ve still got plenty of ideas to share with you on Maths Insider over the next few months but in the meantime, here are some of the articles I’ve written recently over at the Thinkster Math  blog about holiday math, Kumon and Thinkster Math:

Want to Give Your Child a Math Boost this Holiday Season? Here’s How!

Fun, family, festivity and math? Believe it or not, the winter holiday period is the perfect time to give your child a boost in their math. Take a look at these 8 practical ideas to keep your child’s math skills fresh this holiday season………..

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Advice from an ex Kumon parent

We’ve been asking our Thinkster Math parents to give us feedback on the program. This is the text of an email that one new Thinkster Math parent sent us last week……..

Yes, America Agrees! Math is the Most Important Subject of All

Tabtor holiday math

Math has never been seen as the coolest subject on the block, with math lovers being called geeks, nerds and worse! However, there’s no escaping the fact, even amongst the haters, that knowing your 1, 2, 3’s and your X,Y,Z’s is important.

And America agrees!

This week Gallup released the results of a poll which asked,

“Which school subject has been most valuable to you in your life”……….

Thinkster Math vs Kumon. An Insider’s Perspective.

A few weeks ago, I wrote a post on my Maths Insider blog comparing Thinkster Math to Kumon Math. I used to run my own Kumon centre in the UK and 2 of my own children worked through the Kumon program for several years, so I’m in a unique position to compare Thinkster Math’ innovative math program with the well established Kumon program……..

Naturally the articles above are all written to promote Thinkster Math, but I hope you’ll find plenty of helpful information in them to help support your child’s math.

Educator.com – A Great Math Program for Self Motivated Teens

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This is a guest post by Stephanie from houstonnanny.com.

For those who need a math education program that can allow high school students to work at their own pace, Educator.com may be what you’re looking for. Subject material from basic math skills to more advanced forms of linear algebra are present and ready for you to explore, as well as science and computing courses. While there are some materials that can be tested for free, a subscription is needed in order to take advantage of the courses at this website.

Educator.com

How Detailed are the Courses?
Each course is divided among several sections each carefully going through various aspects of the material. Videos are accompanied by notes, sometimes practice questions and downloadable slides in order to allow you to work on your specific section offline. Each section also provides an area that allows students to leave comments about each lecture.

Each section can have several hours’ worth of video content that students can watch in order to learn the material. Since this is a work-at-your-own-pace environment, you can watch these videos as often as you wish in order to help you retain the knowledge.

What Kind of Interaction Can be Expected?
The content provided at Educator.com is geared more towards the self-starter who is able to learn well from watching video. There is no interaction within the courses save for the comment section that every student has access to. Although there are a few quizzes that can be useful to help you determine if you are understanding the content, the actual interaction regarding the material is quite nominal. If you thrive on social interaction to achieve a common goal, Educator.com may not be the best of choices.

How Professional are the Lecture Providers?
Those that provide the video content of the website are seasoned professionals in his or her field. The video delivery is well performed and is spoken in a clear and understandable tone. Each professional seems to be well versed in his or her topic and provide detailed information. During the lecture, you can see the speaker on the right while he or she is working the content on the left in a larger window. While this gives the sense of interpersonal connection, the video can easily be paused reminding you that it’s not a live stream. Check out the sample video below:

What is the Cost of this Education?
Educator.com has several plans for those that may be interested in learning at his or her own pace through video content. While some may view the subscription plans as steep in comparison to other online educational materials, the quality of the content you will be receiving could be worth your investment.

Educator.com has a wide range of material covering math, science, programming and more. Each is quite detailed and can be broken down to specific areas of need. Whether you are looking for a brush-up on your mathematical skills or need in-depth tutoring and knowledge, the courses available can help you accomplish your goals. As with all work-at-your-own-pace themes to education, your success using this site will be ultimately determined of your own level of commitment. Keep a strong momentum and you will be successful learning additional mathematics.

Author Bio:

Stephanie has many years of experience as a nanny. She has always loved children and has continuously been involved in childcare activities. Currently she is one of the writers for houstonnanny.com. If you want to get in touch with her, you can email her at stephanie. Houstonnanny @ gmail. com.

 

Pretend Mind Reading – A Way Of Learning Algebra by Lawrence Ball

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This is a guest post by Lawrence Ball

Here’s a way to pretend you read someone’s mind.

It’s also a way to get familiar with algebra.

I want you to do some calculations for me, are you ready?

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  • Think of a number between 1 and 5, don’t tell me what it is, but remember it for later. OK? Got one?
  • Now double it. OK?
  • Now add 10.
  • Now halve it (or divide it by 2 – same thing)
  • Now take away the number you started with.

Your answer is 5.

Well it should be, if it isn’t you made a mistake!

Lets try another one.

  • Think of a number between 1 and 5

The reason I keep it between 1 and 5 is because if you try this on someone who’s not so good at arithmetic, and they make a mistake, then it backfires on everybody, so keep the numbers small, many adults make mistakes on this, and younger humans too.

Anyhow, again

  • Think of a number between 1 and 5, (don’t tell me what it is, but remember it for later. OK? Got one?)
  • Now, multiply by 3. OK?
  • Now add 12.
  • Now divide it by 3.
  • Now take away the number you started with.

Your answer is 4.

Lets do one more, to show you more how the numbers can be varied each time, in fact you can make these up as you go along, which is what I am doing at this moment.

  • Think of a number between 1 and 5, don’t tell me what it is, but remember it for later. OK? Got one?
  • Now multiply by 5. OK?
  • Now add 10.
  • Now divide by 5.
  • Now take away the number you started with.

Your answer is 2.

Now, welcome to algebra…..

Lets see how this pretend telepathy actually works.

I often teach this at the beginning of learning algebra, partly as a way of entertaining my students, why not have fun learning?

We start off with a number we don’t know. Now in algebra, its actually useful to have a way of referring to something we don’t know. It might seem strange to you, but that’s what we do. This is a stage removed from maths so far, which we now refer to as arithmetic. Algebra is a kind of maths where we deal with not only numbers that we know like 6 or 3.2 or a quarter, but also numbers we don’t know (at least not yet). We use letters, often x, or another letter.

In this number trick, I think “x” when I consider your chosen number, and when I ask you to double the number in the first one, I don’t know what number you have now, but I do know that whatever it is, its twice the number we started with, so at this point in the trick we have

2x

twice the number we don’t know. We still don’t know what it is.

Then I ask you to add 10. In algebra we represent this as

2x+10

We still don’t know what the number is at this stage, but we do know, that whatever it is, it is twice what you started with, with 10 added on extra.

Now here’s the clever bit. What we now do, is halve the number you’ve got now, the 2x+10, and we can do that by halving the 2 pieces separately. Half of twice the number (2x) we don’t know is just the number (x), and half of 10 is 5.

x+5

Now this is clever because no-one really notices that the 10 and the 5 are connected (unless they know the trick), so we now take away the number you started with, which is the x, and guess what – you’re left with…

 5

Apparent magic.

No matter what you started with, any uncertainty has now been removed. We now know exactly what the number you finished with is.

That’s how the first one works.

Now, lets look at the other 2 versions I created. Again you think of a number between 1 and 5, we write

x

A number we don’t know.

I’m very fond of this little phrase I tell my students, it makes them laugh (and me too). x is a number we don’t know, but we can still talk about it, even though we don’t know what it is!

Its easy to forget what x and these letters mean, we can end up with a pile of mumbo-jumbo and turns into a lot of nothing, if we forget the richness and clarity of what we’re doing.

Then I ask to multiply by 3, because I don’t know what the number is, (in fact you could have a whole roomful of people with different numbers). Its now three times the number you started with.

 3x

Now I ask to add 12, so we have 3 times the number I don’t know with 12 added on extra.

 3x+12

Now, cleverly we divide by 3, by dividing the 2 pieces separately. 3x divided by 3 is x. 12 divided by 3 is 4.

 x+4

Then, we say take away the number you started with, (the x), and your answer is

4

Give people plenty of time to do this, as you’re trying to impress people, particularly people who don’t know the trick, you want to make sure the answer comes out right, because if someone sees this for the first time they can get a real fun shock at this point.

Lastly, again you think of a number between 1 and 5, we write

x

times by 5

5x

add 10

5x+10

divide by 5

 x+2

Then, we say take away the number you started with, (the x), and your answer is

 2

I hope that clarifies this trick, what you have to realise is that the number you multiply and divide by must be the same – 5 in the last case – otherwise its not going to come back to x at the end. The number you add on needs to be a number that that number goes into – in this case 10 must divide by 5, you couldn’t add 11 and have the answer come out to be a whole number.

You must always remember to take away the number they started with at the end. It may help to remember you have one of each of the 4 operations, a times, a plus, a divide and a minus, in that order.

For more clarity see my video on this trick:

Mind Reading by Algebra from Lawrence Ball on Vimeo.

If you havn’t seen this before I hope you found this interesting and fun, and hopefully now, or soon (you could always reread to clarify) you can play this trick on your friends and family, and even better your maths teacher which might impress them no end, and may even cause a creative diversion in the classroom.

Lawrence Ball, London, UK    July 4 2013

Find Lawrence on Adrian Beckett’s Maths tutoring site. 

Lawrence Ball is (http://www.lawrenceball.org) a long-term maths tutor (but also composer and musician), with a history of helping with motivation and difficulty, as well as with maths material. He has tutored privately including extended royal family, and all 4 children of Lady Helene Hayman, and has had big success in helping pupils with dyslexia.

He has developed ways to teach basic arithmetic which are innovative, and that promote relaxed concentration. He lives in North London.