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The 5-4-3-2-1 Challenge

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There are 40 engaging math puzzle problems to solve in the 5-4-3-2-1 Challenge. Your job: to see how many of them are even possible!

5-4-3-2-1 Challenge

This puzzle is just one of many free printable number challenges that I have created for my own classroom and am sharing with you!

Be sure to check out my entire collection of free printable math puzzles.

free printable number challenges for the math classroom.
first week of school activities

Looking for more first day of school activities and puzzles for your classroom? I have a giant blog post dedicated to 40+ activities for the first week of school.

Here’s a few examples of some of these engaging activities for the beginning of the school year.

Puzzle Source/Origin

On Sunday morning, Nancy Swank tweeted me a link to a puzzle on NPR’s website from master puzzle author Will Shortz.  

This shouldn’t come as a surprise because Nancy is the entire reason why NPR spent an entire day in my classroom in 2014.

I followed the link and started reading the puzzle.  Within about a minute, I knew I HAD to do this puzzle with my students this week.  

5-4-3-2-1 Challenge Instructions

I decided to rename this puzzle the “5-4-3-2-1 Challenge” in order to use it in my classroom.

Instructions to 5-4-3-2-1 Challenge.

Use the digits 5, 4, 3, 2, and 1. The digits must remain in that order. Place the four arithmetic signs – plus, minus, times, and divided by – between the digits and as many parentheses as you like around the digits.

How many numbers from 1 to 40 can you get? It is important to emphasize to students that some of the numbers may not be possible. It is their job to find out which ones are and which ones are not possible!

Resources for Using this Puzzle in the Classroom

5-4-3-2-1 Challenge Posters

In the same style as my Yearly Number Challenge Posters, I made a set of 5-4-3-2-1 Challenge Posters.  After students find a solution and get it checked, they can write the solution on the poster and sign their name next to it.  

These posters are designed to print on 11 x 17 cardstock.  I use this cardstock for so many posters in my classroom!

5-4-3-2-1 challenge poster 1
5-4-3-2-1 challenge poster 2
5-4-3-2-1 challenge poster 3
5-4-3-2-1 challenge poster 4

To keep things organized, I pre-typed the 5 4 3 2 1 part of the solution.  Students will only have to write in the mathematical operators and parentheses.

Since the challenge is to find as many numbers from 1 to 40 as possible, I designed the posters to hold the solutions to 10 numbers each.  

Dry Erase Pocket Template

To help students solve this puzzle, I decided to design a template for students to slide into their dry erase pockets.  This lets them draw and erase and repeat over and over and over as they work through the puzzle.

5-4-3-2-1 challenge dry erase pocket page.

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.

student working on 5-4-3-2-1 challenge puzzle.

MATH = LOVE RECOMMENDS…

dry erase pockets

I cannot imagine teaching math without my dry erase pockets! They instantly make any activity more engaging and save me countless hours at the copy machine since I can use the same class sets of copies year after year.

Here are my current go-to recommendations:

Laminated Activity Strips

If you don’t have dry erase pockets, I also made some 5-4-3-2-1 strips that could be printed and laminated.  Then, students could write directly on them with their dry erase marker.

5-4-3-2-1 challenge laminated strips.

Answer Tracking Sheet

By the time I had made all of these resources, I decided I wanted something to help me keep track of all of my solutions.  

I had started working on this puzzle briefly while waiting for Sunday School to start, but my answers were just jotted on random paper in random order.  I needed a way to figure out which numbers had solutions and which didn’t.

5-4-3-2-1 challenge worked on by student with answer key document.

So, I came up with this 5-4-3-2-1 answer tracking sheet:

5-4-3-2-1 number challenge worksheet

Digital Version of 5-4-3-2-1 Challenge

Ms. Tish has created a Google Sheets version.

Tweet with Link to 5-4-3-2-1 Challenge in Google Slides.

Puzzle Solutions

ANsWer key link

Puzzle solutions are available on a password-protected solution page. I do not openly post the puzzle answer keys because one of my goals as a resource creator is to craft learning experiences for students that are non-google-able. I want teachers to be able to use these puzzles in their classrooms without the solutions being found easily on the Internet.

Please email me at sarah@mathequalslove.net for the password to the answer key database featuring all of my printable puzzles and math worksheets. I frequently have students emailing me for the answer key, so please specify in your email what school you teach at and what subjects you teach. If you do not provide these details, I will not be able to send you the password.

Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, or as fun activities in their workplace. Just give me enough details so I know you are not a student looking for answers to the puzzle that was assigned as their homework!

Sarah Carter teaches high school math in her hometown of Coweta, Oklahoma. She currently teaches AP Precalculus, AP Calculus AB, and Statistics. She is passionate about sharing creative and hands-on teaching ideas with math teachers around the world through her blog, Math = Love.

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9 Comments

  1. Well, I am almost done. Not sure if you want it posted where I am stuck- certainly not giving any spoilers on here! But it was fun- I wonder how long it will take my students?

  2. Thanks Sarah. Was just looking for something new for my "puzzles" bulletin board. I just introduced students the graphing calculators and that the calculators "know" order of operations. So I'm going to have my students do this on the dry erase templates, then show me the solution on their new calculators to drive home the point:)

  3. It was fun watching this take off on the #MTBoS! (P.S. I use heavy duty sheet protectors for inexpensive dry erase pockets – they work well!)

  5. By Sunday afternoon I got all but a handful of the integers in the 30s. Will Shortz stated that all are possible except 39. Will you be posting solutions? I tried a "systematic" approach (instead of an unrelated series of trials, which did not pan out. To post a system would be interesting.

  6. The files are no longer available to download. Would you be able to email them to me?

Comments are closed.