# Autograph Newsletter 12 – Don Steward Puzzles

 Welcome Welcome to the twelfth Autograph Newsletter! Each jam-packed edition looks at a specific topic in mathematics and how Autograph can help engage students and enable them to understand the key concepts better.
 Introduction One of my all-time favourite mathematics blogs is Median, created by Don Steward (donsteward.blogspot.co.uk). The range of activities and the levels of depth, challenge and imagination are simply outstanding. The vast majority of my ideas for lessons and activities these days come from this blog and the equally outstanding NRICH. Many of the rich, intriguing activities that Don creates lend themselves very well to being analysed on Autograph. I am always keen to ensure that students first tackle the problems on pen and paper, and then Autograph is used to test theories, answer questions, and embark on wonderful extensions. Below you will find a selection of my favourite puzzles from Don’s website, with accompanying Autograph files. I hope you and your students enjoy them, and thank you to Don for creating such a wonderful resource.
 Diagnostic Question Usually we have a Diagnostic Question in this spot, but for this special edition of the newsletter we are instead going to have… a puzzle! Project this on the board, encourage your students to develop a systematic way of solving it, and challenge them to explain their method to their peers. Encourage them to compare each other’s answers and methods, and describe the merits and flaws with the different techniques. For a full discussion of the problem, grids to print and the solution, click here.
 Free Online Autograph Activity Leap Frog Leap over the three points on paper first. Once you have noticed something, try to explain it. Then turn to Autograph to look at the puzzle in more depth. These Autograph activities do not require the full version of Autograph to run them. You just need to install the free Autograph Player (you will be guided through how to do this), which means you can use these activities in the classroom or set them for your students to do at home.
Further Puzzles
The following ideas for puzzles are also taken from Don Steward’s website. Try them on paper first and then turn to Autograph to look at them in more depth. Click on the image to download the individual Autograph files.
Idea 1 – Extending Leap Frog
One way of extending the Leap Frog puzzle above is to think about what happens if you leap half way towards each point instead of twice as far.
 • What do you think will happen? • Try this out on paper first, with each member of the classes starting with their points in different positions • What seems to be happening? • Which students have similar outcomes? Which have different? • Get your students to keep the three points in the same position but try another starting point • When you have some predictions, use the Autograph file • Drag the three points and the starting point around and observe the effect on the path and position of the leaps • What is happening here? Why? • You can add more leaps if you like by creating vectors (see the Handy Tip at the end of this newsletter) • What will happen if you leap ¾ of the distance? • How about 1.5 times the distance?
Idea 2 – Four Lines
This classic geometry puzzle works particularly well on Autograph, and Don has added a second pattern that I had never seen before!
 • Can you use four connected straight lines to go through each of the 9 dots in the first pattern? • Drag the points on the green dashed line around to experiment • When you have cracked this, try the same for the heptagonal pattern… and when you figure out how to join these up with four connected lines, please let me know how! 🙂 • Finally, can your students create a similar challenge?