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How Far Can YOU Climb? – An Activity by Frank Tapson

Last week, I ran across an activity by Frank Tapson called “How Far Can YOU Climb?” (page 34).

The premise of the puzzle is quite simple.  Form the longest chain possible by moving horizontally or vertically from one number to an increasing number.

Here are Frank Tapson’s instructions:

I printed off a class set, and we slid them into our handy dry erase pockets.  I firmly believe that every classroom in the world could benefit from a set of these dry erase pockets!  

If you don’t have a classroom set of dry erase pockets, you could also use heavy duty sheet protectors. But, I highly recommend investing in a classroom set of the pockets since they are so much more durable.

My students got really into this activity!  As students finished their first chains, they called out the scores to the class.  When someone realized their score was higher/lower than their peers, there were corresponding shouts of excitement and frustration.

I think this is a fitting task for practicing problem solving strategies with students.  Some students would erase their path and start over entirely from scratch if they messed up.  Other students would just back up a few steps and test if continuing their path in another direction would result in a larger score.

I got MOST excited when one of my students suggested we should find the highest value on the game board and work backwards towards 1 since that would surely give us the highest score possible.

The student who took that route eventually decided it was impossible to make a route between the lowest number on the board and the highest board.  I haven’t played around with it enough to know if that is indeed true.

Some students in another class saw these puzzles setting on my podium, and they begged to take one with them.  Of course you can take a math-y puzzle with you!

As I was writing this post, I made an exciting discovery.  Remember the giant number line poster I have in my classroom?

This number line was made with a printable I found online.  It turns out that file was created by Frank Tapson!  His website full of resources is a true treasure trove.

Digital Version of How Far Can You Climb

Kathy Henderson has created a digital version of How Far Can You Climb in Desmos Activity Builder.

Puzzle Solutions

I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.

Anonymous

Wednesday 31st of January 2018

I used this during some extra time with 6th graders today --- 72!!! Their technique was to work backwards (and I didn't even mention that idea to them). Most of my 6th graders were completely into this activity for 30 minutes - until I said we had to move on. Some didn't want to give up! Love it!

Anonymous

Thursday 18th of May 2017

Hello. I am a student and I have tried the puzzle. I have succeeded in making it from the lowest to highest number, but I want to know what the highest score possible on this puzzle is. Thank you for sharing this puzzle! By the way, I got a 72.

Unknown

Sunday 24th of February 2019

I found one 80 long, this was given out in my class recently.

Anonymous

Thursday 18th of May 2017

Sorry. I got a 75 now.

Unknown

Friday 3rd of March 2017

It is possible to reach 300 , the best way is to try working backwards

Sarah Carter (@mathequalslove)

Tuesday 18th of April 2017

Great to know!

Anonymous

Thursday 16th of February 2017

My boss got me some dry erase pockets!!!! I printed this puzzle on cardstock and slid them all in and now I have an entry task for tomorrow for all my classes! FYI- I bought a bag of 15 pair of white socks at Walmart a few years ago. They make great whiteboard erasers. I put a whiteboard pen in each sock and now the students just have to get a sock (with pen) and a dry erase pocket and they are all set to write and erase. I keep them all in a file crate at the front of the room and the kids all know how to distribute them and put them back. -snapdragon

Sarah Carter (@mathequalslove)

Friday 3rd of March 2017

Yay for dry erase pockets! And, the socks are a GREAT idea! Thanks for sharing!