{"id":1114,"date":"2026-03-02T09:51:16","date_gmt":"2026-03-02T09:51:16","guid":{"rendered":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/?p=1114"},"modified":"2026-02-26T09:52:22","modified_gmt":"2026-02-26T09:52:22","slug":"magic-maths-mind-reading-number-tricks-and-mathematical-thinking","status":"publish","type":"post","link":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/2026\/03\/02\/magic-maths-mind-reading-number-tricks-and-mathematical-thinking\/","title":{"rendered":"Magic Maths: Mind-Reading, Number Tricks, and Mathematical Thinking"},"content":{"rendered":"

Magic Maths: Mind-Reading, Number Tricks, and Mathematical Thinking<\/span><\/b>\u00a0<\/span><\/p>\n

\"Avatar\"Kellee<\/p>\n

Charlotte Lighter and\u00a0Kellee Patterson\u00a0<\/span><\/b>
\nThe Open University at Maths Week\u00a0Wales\u00a02025<\/span><\/i>\u00a0<\/span><\/p>\n

What do you get when you mix number tricks, curious minds, and a sprinkle of mathematical magic? A room full of excited primary school\u00a0pupils!<\/span>\u00a0<\/span><\/p>\n

As part of\u00a0<\/span>Maths Week\u00a0Wales\u00a02025<\/span><\/b>, we ran a public engagement session\u00a0for primary children across\u00a0Wales,\u00a0called\u00a0<\/span>Magic Maths.\u00a0<\/span><\/b>Our session was<\/span>\u00a0<\/span><\/b>designed to spark curiosity and mathematical thinking in young learners. The session was full of \u201cthink of a number\u201d (THOAN) tricks\u00a0–\u00a0those classic puzzles where you follow a series of steps and end up with a surprising result.\u00a0<\/span>\u00a0<\/span><\/p>\n

Behind the magic was some serious mathematical thinking, drawn from ideas explored in\u00a0our very own\u00a0<\/span>Open University Mathematics Education modules<\/span><\/b>.<\/span>\u00a0<\/span><\/p>\n

\"Sign<\/span><\/p>\n

Your turn!\u00a0A Magical Number Trick<\/span><\/b>\u00a0<\/span><\/p>\n

Let\u2019s\u00a0start with a little magic of our own. Try this:<\/span>\u00a0<\/span><\/p>\n

    \n
  1. Think of a number between 1 and 9<\/span><\/b>\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ol>\n
      \n
    1. Square it<\/span><\/b>\u00a0(multiply it by itself)\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ol>\n
        \n
      1. Add the number you first thought of<\/span><\/b>\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ol>\n
          \n
        1. Divide by your original number<\/span><\/b>\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ol>\n
            \n
          1. Add 17<\/span><\/b>\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ol>\n
              \n
            1. Subtract your original number<\/span><\/b>\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ol>\n
                \n
              1. Divide by 6<\/span><\/b>\u00a0<\/span><\/li>\n<\/ol>\n

                We will using magical mind-reading to guess your answer!\u00a0<\/span>\u00a0<\/span><\/p>\n

                \"Two<\/span><\/p>\n

                Have a go before scrolling down \u2026 (No peeking!)\u00a0<\/span>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                ,<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                .<\/span><\/b>\u00a0<\/span><\/p>\n

                \u00a0<\/span>Your answer is\u2026 3!<\/span><\/b>\u00a0<\/span><\/p>\n

                \u00a0<\/span>Did it work? Try it again with a different number.<\/span>\u00a0<\/span><\/p>\n

                Still 3?\u00a0<\/span>\u00a0<\/span><\/p>\n

                That\u2019s\u00a0the magic of mathematics,\u00a0and\u00a0it\u2019s\u00a0not just a trick. There\u00a0is\u00a0a powerful\u00a0mathematical\u00a0idea behind it:\u00a0<\/span>doing and undoing<\/span><\/b>.<\/span>\u00a0<\/span><\/p>\n

                \u00a0<\/span><\/p>\n

                Unmasking the magic: How does it work?\u00a0<\/span><\/b>\u00a0<\/span><\/p>\n

                Let\u2019s\u00a0look at another \u201cthink of a number\u201d trick. This time see if you can work out what is going on and how we are able to work out\u00a0your starting number.\u00a0<\/span>\u00a0<\/span><\/p>\n

                  \n
                • Think of a number\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                    \n
                  • Double it\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                      \n
                    • Add 10\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                        \n
                      • Half it\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                          \n
                        • Subtract 3<\/span>\u00a0<\/span><\/li>\n<\/ul>\n

                          Now remember the answer!\u00a0\u00a0\u00a0<\/span>\u00a0<\/span><\/p>\n

                          \u00a0<\/span><\/p>\n

                          During our live session, we asked the children to tell us their\u00a0final answer,\u00a0and we were then able to tell them what number they started with\u2026 magic right?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          Or is it maths?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          Have a go at following the steps\u00a0above\u00a0and see what you notice.\u00a0<\/span>\u00a0<\/span><\/p>\n

                          Try another number. Is there a pattern?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          Can you generalise by describing the relationship between the starting number and the\u00a0final answer?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          In this example the answer is not always the same, unlike in the first trick when the last two steps always led us to 18 divided by 6\u2026 which always gave 3, in this example the answer is linked to the starting number you chose.\u00a0<\/span>\u00a0<\/span><\/p>\n

                          Have a go yourself before scrolling down.\u00a0<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          .<\/span>\u00a0<\/span><\/p>\n

                          Did you spot that the\u00a0final answer\u00a0is always 2 more than the number you started with?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          So,\u00a0if you started with 4\u2026 the answer you got would be 6, with 5\u2026 the answer was 7 etc\u2026\u00a0<\/span>\u00a0<\/span><\/p>\n

                          We could generalise and say if the starting value\u00a0was\u00a0n, the answer would always be n+2.\u00a0<\/span>\u00a0<\/span><\/p>\n

                          But why\u00a0is this?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          Can we look at what the trick asked us to\u00a0<\/span>do<\/span><\/i>, and\u00a0<\/span>undo<\/span><\/i>\u00a0the steps to understand how the trick works?\u00a0<\/span>\u00a0<\/span><\/p>\n

                          When working through this with young learners, we used a numerical example to help us work through the steps. You could also use algebra.\u00a0<\/span>\u00a0<\/span><\/p>\n

                            \n
                          • Think of a number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – our starting number is 6\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                              \n
                            • Double it\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12 (2×6)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – doubling this gives 2 x 6\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                                \n
                              • Add 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 22 (2×6+10)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – adding 10, gives 2 x 6 + 10\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n

                                Note we are recording the operations and keeping track of them. If we just write down the answers at each step (6, 12, 22) it will be\u00a0very difficult\u00a0to spot what is happening and how the trick works.<\/span>\u00a0<\/span><\/p>\n

                                  \n
                                • Half it\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 11 (6+5)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – halving it means we have 1 x 6 + 5\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n

                                  This is\u00a0an important step. We had doubled six and now we are halving that, bringing us back to 6. This is an example of undoing an operation. We are using the inverse operation here. Doubling and halving (or multiplying by 2 and dividing by 2).\u00a0<\/span>\u00a0<\/span><\/p>\n

                                    \n
                                  • Subtract 3\u2026\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a08\u00a0 (6+2)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – subtracting 3 we have 6 + 2\u00a0\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                                      \n
                                    • The answer is\u2026.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 – our *starting number + 2<\/span>\u00a0<\/span><\/li>\n<\/ul>\n

                                      Note: We chose to keep the 6 as it is, because this was our starting number, and take 3 from the 5. This is so that we can generalise later by changing the value of 6.\u00a0<\/span>\u00a0<\/span><\/p>\n

                                      To generalise we could use a box, or a letter to\u00a0represent\u00a0the starting number.\u00a0<\/span>\u00a0<\/span><\/p>\n

                                      This might look like this:\u00a0<\/span>\u00a0<\/span><\/p>\n

                                        \n
                                      • Think of a number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 n<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                                          \n
                                        • Double it\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2n\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                                            \n
                                          • Add 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2n + 10\u00a0\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n
                                              \n
                                            • Half\u00a0it\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 n + 5\u00a0\u00a0<\/span>\u00a0<\/span><\/li>\n<\/ul>\n