About Dots and Boxes

Dots and boxes is a classic pencil-and-paper game which goes by a variety of different names including dots, boxes, pigs in a pen, the game of dots, or dots and dashes.

The game was originally named “la pipopipette” when it was published in the 19th century by Edouard Lucas, a French mathematician.

Instructions and Scoring

Like the original dots and boxes game, this is a paper and pencil game for two players. Take turns drawing a line from one dot to another on the grid. If your line completes a box, write your initials in the box and take an extra turn.

Each completed square is worth one point. Earn an additional bonus point for each 2025 in your squares. Once the grid is completely filled, the player with the most points wins.

I would recommend placing this puzzle in a dry erase pocket when using it in your classroom.

More Seasonal Versions of Dots and Boxes

I am currently working on creating more seasonal versions of the classic game of dots and boxes. Here are some other versions I have posted:

• 
  2025 Dots and Boxes Game
• 
  Christmas Tree Dots and Boxes Game
• 
  Fall Dots and Boxes Game
• 
  Hanukkah Dots and Boxes Game
• 
  Kwanzaa Dots and Boxes Game
• 
  Math Symbol Dots and Boxes Game
• 
  Snowflake Dots and Boxes Game
• 
  Thanksgiving Dots and Boxes Game
• 
  Veterans Day Dots and Boxes Game
• 
  Winter Dots and Boxes Game

Instructions

You can think of this 2025 maze worksheet as a single maze or four separate mazes. This idea is that you start solving the maze in the upper right corner by entering the 2.

Solving the 2 maze will lead you to the 0 maze which must now be solved. Continue until you have traveled through all of the digits in 2025.

For years, I have used hidato puzzles in my classroom, and they have always been a HUGE hit with students. I recently learned how to generate shaped hidato puzzles.

Have a different shape of puzzle your students might be interested? Send me an email, and I might be able to make it happen!

What are Hidato Puzzles?

Hidato Puzzles (or Hidoku Puzzles) are the creation of Dr. Gyora M. Benedek, an Israeli mathematician. The Hebrew word “hida” means riddle. In a hidato puzzle, you are given a grid with a selection of the numbers already filled in.

Your task is to fill in the missing numbers so that each number connects to the next number either horizontally, vertically, or diagonally. 1 must connect to 2, 2 must connect to 3, and so on.

When I use Hidato Puzzles with students, I often have them draw in the lines between the numbers in order to help them check their solutions.

2025 Hidato Puzzle Instructions

Fill in the missing numbers in the number-shaped grids so that each number connects to the next number either horizontally, vertically, or diagonally.

This 2025 puzzle is actually four hidato puzzles in one!

For these specific puzzles, students are arranging the numbers from 1 to 47 in the two-shaped grids, the numbers from 1 to 52 in the zero-shaped grid, and the numbers 1 to 51 in the five-shaped grid so that consecutive numbers touch either horizontally, vertically, or diagonally.

You could definitely think of this puzzle as making a “chain of numbers.”

Four Levels of Puzzles and Printing Options

These 2025 logic puzzles are available to download in four different levels: Easy, Medium, Hard, and Challenging.

As the levels progress, you are given fewer and fewer numbers on the grid to begin with. This means that much more logic is required to solve the puzzle.

For most students, I would recommend starting with an easy level puzzle unless your students have solved numerous hidato puzzles in the past.

What are Factor Tree Puzzles?

I first learned about factor tree puzzles in 2018 when I attended a Math Teachers’ Circle Summer Workshop with Dr. Harold Reiter.

In Dr. Reiter’s version of these puzzles, each variable stands for a unique digit. You must determine the values for each digit so that the numbers form a valid factor tree where all circled numbers are prime.

These puzzles, while fun, are VERY CHALLENGING because you do not even know the starting number of the factor tree. I decided to make an easier version of these puzzles to help celebrate the new calendar year: 2025!

2025 Factor Tree Puzzle Instructions

For this 2025 Factor Tree Puzzle, you must find the missing values to create a valid factor tree for 2025. Each variable stands for a unique digit. Circled numbers are prime.

Puzzle Instructions

Cut apart the provided pieces and assemble them into a 3×3 square so that the puzzle pieces match along each edge to form the new year – 2025!

Options for Printing and Prepping the Puzzle

There are several options for printing and prepping this puzzle.

The easiest way to distribute this puzzle to students is to print the page with the puzzle pieces, have each student cut out their own pieces, and let them build their square grid on their desks.

If you plan on reusing the puzzle pieces from year to year, I highly suggest running the pages through a laminator first to make the pieces more durable.

If you are giving each student their own copy of the puzzle, this is entirely unnecessary. Just print on some pretty, colorful paper and GO!

If you are looking to display the resulting work or if you would like students to keep their work in a folder or notebook, you might want to print the next page in the PDF file which includes a 3 x 3 puzzle grid for students to build their solution upon or glue their pieces on after solving.

In my opinion, this page is most useful for those who are opting to display or keep the resulting solved puzzle. If you are reusing the puzzle pieces with different classes, I would just put the puzzle pieces in bags and forego the printable template.

If you are working with younger students or with a population of students who needs a bit of starting place for their puzzle solving, there is another version of the grid in the file that shows which puzzle piece belongs in the top left corner of the square.

Including this piece of information will drastically reduce the amount of time it takes older students to solve the puzzle, so I would be very discerning about whether your students need this scaffolding or not.

Ultimately, you know best what your students need. When I first started sharing puzzles I created for my classroom 8 years ago, I never imagined that they would be used in so many diverse classrooms around the world.

Puzzle Instructions

Arrange six of the twelve provided pentomino pieces to completely cover the rectangular grid. Four of the pieces will contain holes. These holes must be placed to reveal the number 2025 at the center of the grid.

Pieces may be rotated or flipped, but the pieces may not overlap one another. Six pieces will not be used.

Puzzle Pieces

This puzzle uses a standard set of twelve pentominoes pieces with a single hole cut in eight of the pieces. The solved puzzle will use four pentominoes pieces with holes in them and two standard pentominoes pieces.

I used my Cricut Maker 3 machine to cut the pieces out of Astrobrights cardstock and punch the holes out of the pieces.

Cricut used to have an easy way to share their Design Space files with others, but unfortunately I cannot share the file I created with you because Cricut has changed their terms of use. No files including uploaded images can be shared, and I uploaded the images of the pentominoes pieces into Design Space. Ugh.

You can still cut out the pieces on your own cutting machine, but it will require a bit more work since you will have to remove the background from each image/hole and resize the pieces so they print properly. Each pentomino piece should be made up of 1 inch squares.

Don’t have a cutting machine? You can still print the pieces on cardstock and cut out the circles by hand. Take a single hole punch and punch a hole onto the circle you are trying to remove. Then, you can continue to use the hole punch to punch out the rest of the circle or you can use scissors to cut out the rest of the circle.

Ideas for Using the Puzzle in the Classroom

I will be putting this 2025 Pentomino Puzzle out as one of my puzzles of the week alongside the 2025 Yearly Number Challenge and the 2025 Digit Grid Puzzle I shared earlier.

Fun Fact: My “Puzzle of the Week” has really turned into “Puzzles of the Week” because so many of my students have become eager puzzle solvers. They get very sad when they solve all of the puzzles early in the week and don’t have anything to challenge them for the rest of the week.

I don’t dedicate any class time to these puzzles of the week. I just hang the puzzles on my dry erase board. Students grab the puzzles off the board as they come into the classroom and take them to their tables to work on. Groups often see other groups working on puzzles which inspires them to give that puzzle a try the next day.

Students are puzzling before class, between classes, and in odd moments in class like the daily announcements. Some students also work on puzzles if they finish early and don’t have other work to work on.

Modifying the Puzzle for Younger Students

I created this puzzle with secondary students in mind since I personally work with juniors and seniors in my high school math classes.

If you are working with much younger students, you can modify this puzzle by removing some of the pentominoes pieces that are not in the solution. As the puzzle is written, 6 pieces will be in the solution and 6 pieces will be unused.

To make the puzzle VERY easy, only give your students the six pieces needed to solve the puzzle. My husband was able to solve this version of the puzzle in around 30 seconds, so I would suggest including at least one or two distractor pieces to make the puzzle a bit more fun and challenging. Last year, my then-four-year-old, on the other hand, spent 5 minutes on the easier version before giving up.

Previous Year’s Versions

2024 Pentomino Puzzle

The 2024 Pentomino Puzzle is available to download as a convenient PDF file and an editable Publisher file. In order to edit the Publisher file, you will need to make sure you have Microsoft Publisher installed on your computer.

PDF

2024 Pentomino Puzzle (PDF) (1747 downloads )

Publisher (Editable)

2024 Pentomino Puzzle (Editable Publisher File ZIP) (731 downloads )

ZIP Folder of Pentomino Piece Images for Creating a Cut File

Images of Pentomino Pieces for Yearly Pentomino Puzzle (ZIP) (907 downloads )

2025 Digit Grid Puzzle Instructions

Arrange the strips in the provided grid to form the digits in 2025. The strips may be placed horizontally and/or vertically on the grid.

When I first started creating these puzzles in 2023, I didn’t specify that the strips could be placed horizontally and/or vertically, and I ended up with a lot of teachers emailing me saying that the puzzle was impossible.

If your students are struggling to solve the puzzle, you might re-emphasize to them that the pieces can be placed horizontally and vertically on the puzzle grid.

There are actually two different versions of the grid to choose from. The first version (shown above) includes a blank grid for students to build 2025 on top of.

This is great for promoting spatial reasoning in students as the have to look at the 2025 grid at the top of the page and think about what they need to complete the grid for the puzzle.

If you are working with younger students or with students who need a bit more help, there is an additional version of the puzzle grid that has 2025 marked out on the grid in gray squares.

This version is also suggested for teachers who want to have the activity take a bit less time. If you are using this as one of several activities during a class period, every minute counts!

Two Puzzle Versions

On top of there being two versions of the board to print, there are also two different levels of this puzzle: Level 1 and Level 2.

Level 1

The easiest version of the puzzle has 11 strips that students must place on the puzzle grid to form the digits of 2025. The strips come in two different sizes. Most of the strips are 1×5 rectangles, but four for the strips are 2×5 rectangles.

Level 2

The slightly more challenging version of the puzzle has 15 strips that students must place on the puzzle grid to form the digits of 2025. In the advanced version, all of the strips are 1×5 rectangles.

Printing and Prepping the Puzzle

This puzzle is designed to fit on letter-sized paper, but you could also scale it slightly to print on A4 paper if you aren’t in North America.

I highly recommend printing both versions (basic and advanced) and trying them out before deciding which version would be the best to use with your students. Or, you could print both versions and let students choose which version to attempt.

I printed my puzzle pieces on colorful Astrobrights paper to make them “pop,” but you could just print them on regular copy paper as well.

Using the Puzzle in the Classroom

This would make a great welcome back activity for the first day back after holiday break to help celebrate the new year.

I will also put out the 2025 Yearly Number Challenge as one of my puzzles of the week. It too is a yearly tradition in my classroom!

I have recently been posting my puzzle of the week in a Charles Leonard magnetic pocket that I picked up from Amazon. It hangs on my dry erase board, and it can hold a surprising amount of weight. I’m very impressed with them.

Previous Year’s Versions of the Digit Grid Puzzle

2024 Puzzle

The 2024 Puzzle is available to download for free in two convenient formats: PDF (non-editable) and Publisher (editable). In order to edit the Publisher file, you will need to make sure you have Microsoft Publisher installed on your computer.

2024 Puzzle (PDF) (6836 downloads )

2024 Puzzle (Editable Publisher File ZIP) (1753 downloads )

2023 Puzzle

The 2023 Puzzle is available to download for free in two convenient formats: PDF (non-editable) and Publisher (editable). In order to edit the Publisher file, you will need to make sure you have Microsoft Publisher installed on your computer.

2023 Puzzle (PDF) (6560 downloads )

2023 Puzzle (Editable Publisher File ZIP) (2951 downloads )

What is the Yearly Number Challenge?

The 2025 yearly number challenge goes by a variety of different names. You might know it as the 2025 Number Challenge, 2025 Year Game, 2025 Math Challenge, or just the 2025 Challenge.

Whatever you choose to call it, the goal of this math challenge is to use the digits in the current year (2025) exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers 1-100.

What Mathematical Symbols or Operations Are Allowed?

Ultimately, remember that this challenge can be whatever you need it to be. Feel free to change the rules to meet your students’ needs!

Extra Challenge

Want even more of a challenge? How many numbers can you find if you keep the digits in order each time?

NCTM calls this the “Year Game” and encourages students to keep the digits in the original order whenever possible. I often find the challenge is difficult enough without encouraging this restriction.

2025 Challenge

When I use the yearly number challenge with my high school math students, I challenge them to find mathematical expressions for as many of the numbers between 1 and 100 as possible. I have created a free printable sheet for them to fill out as they find solutions for various numbers.

Some years it is possible to find more numbers in the challenge than other years.

Depending on the age and math ability of your students as well as the amount of class time you would like to dedicate to this activity, you may wish to only have your students find a subset of the numbers.

For the past couple of years, I have ended up creating 6 different versions of the yearly number challenge that you can print and use with your students. Challenge your students to find the numbers 1-10, 1-20, 1-30, 1-40, 1-50, or 1-100 using the digits in 2025.

I would suggest printing off the challenge sheet with all 100 numbers on it and then try to find as many solutions as possible using the type of mathematical operations that you expect your students to use while solving. Once you see how many you are able to solve on your own, you can then decide which level of challenge will be appropriate to your students.

I also highly recommend checking out my free printable 2024 puzzle (2025 Version COMING SOON!!) that involves reassembling the digits in 2024 using horizontal and vertical strips of paper. It’s trickier than it looks at first! Over 5000 teachers used the 2023 version of the puzzle in their classrooms, so I can’t want to see what everyone does with the 2024 puzzle.

2025 Math Challenge Answer Key

I am currently crowdsourcing an answer key for the 2025 Number Challenge. If you are a teacher looking for the 2025 Challenge answers or would like to add the answers your class has found to the answer key, send me an email at sarah@mathequalslove.net. I look forward to hearing from you!

Be sure to include information on what/where you teach so I can be sure that you are a teacher and not a student searching for answers!

Additional Resources and Ideas

Introducing Students to Factorials

I published some information on how I introduce students to the concept of factorials in 2022 when I blogged about the 2022 Challenge.

I actually kicked off class with an ACT question featuring factorials. The majority of my students have never encountered factorials before, and I knew that we would have much more success with the challenge if we were able to capitalize on the fact that 0! = 1.

We worked through the ACT problem, I taught them the word “factorial,” and then I challenged them to use their new understanding of factorials to determine the value of 0!.

After revealing that 0! is 1, I told them that this fact might come in handy today and handed out the 2022 Challenge worksheet.

In 2019, I took a slightly different approach to introducing the concept of factorials. We started by trying to complete this chart.

We started by trying to complete this chart as a class on the dry erase board. It was interesting to hear students’ theories evolve as each new answer was revealed.

Ideas for Motivating Students to Complete the Challenge

Bulletin Board Puzzle for Early Finishers

The first few years I ran this yearly challenge (2016-2018), I posted it as a bulletin board in my classroom for early finishers to work on throughout the month of January. Or to be honest – until I got around to changing the bulletin board!

It always brought great joy to me to see groups of students clustered around the bulletin board (or dry erase board) while discussing that year’s number challenge.

I designed the bulletin board version of this puzzle to be printed on 11 x 17 cardstock.

The 11 x 17 poster templates have spaces to write a solution and the name of the person that came up with the solution next to each number. Even though I haven’t updated the bulletin board versions in several years, you can easily download an older year’s template and update the instructions to use the current year’s digits. Everything else can stay the same.

I decided to add visual reminders of which operations are allowed to spice up my bulletin board a bit.

I made space on one of the posters to include the instructions to the puzzle. This meant that students could get started solving the puzzle without any guidance from yours truly.

Though, I usually make it a rule that ALL solutions must be verified by me before being added to the posters!

You and your students will love watching the bulletin board fill up with solutions. I found that as the bulletin board started to fill up, more and more students became invested in the puzzle and wanted to join in and help.

The bulletin board files I have made over the years are available to download at the bottom of this blog post. You will need to update the year to match the current calendar year.

Class Period Competition

One year, to give my students a bit of extra motivation to engage with the activity on the first day back from break, I decided to pit my classes against one another in a contest. I told them whichever class period found the most solutions to the challenge would win cookies.

Apparently, teenagers love food because I found that my students were engaged and quite competitive. My afternoon class even went as far as to compile all of their results on the dry erase board to make sure that students weren’t working on numbers that had already been solved by another group.

They also argued that their class was at a disadvantage since they had half as many students as some of my other classes. They wanted me to change the rules to make it ratio based, instead.

Group Competition

Back in 2019, I decided to take the yearly number challenge which I had previously just used with early finishers and turn it into an entire class activity where different groups of students were competing against one another.

I walked the entire class through a slide presentation to introduce the activity.

I gave them a list of some of the possible mathematical operators to get their brains moving.

In the past, I would post the challenge, introduce it to my students, and let them fill out as many solutions as possible. As the first day would progress, the challenge would get more and more difficult as the easier numbers that could be achieved by simple addition and subtraction with maybe a little multiplication thrown in were already claimed.

I needed to keep six entire classes of students engaged, so I decided to have each class start the challenge from the beginning. That’s when I got the idea to pull out my 100 number chart that I purchased last year from Amazon.

Then, I spent some quality time with the paper chopper and some cardstock to cut out a different colored set of squares for each of the six groups that my desks are arranged in. I sized these squares to be the same size as the 1-100 cards that fit in my 100 number chart.

Groups would work together to find as many expressions as possible to equal numbers between 1 and 100. When a group found an expression for an unclaimed number, they would bring their solution up to get it verified.

If it was correct, they would place one of their squares of cardstock on top of the number to “claim” it for their team.

By the end of the 50 minute period, the board would look something like this:

In some ways, this activity structure was better than my bulletin boards of the past. And, it also left some attributes to be desired. Let me try to reflect.

Adjusting this to a group-based competition did have some unintended consequences.

Some groups were WAY more hyper-competitive than I expected.

One group had one of their team members permanently stand next to the 100 number chart so that as soon as they figured out a number and got their solution checked they could mark it with the color for their team. This meant that this student was not doing any math at all which was not my intention.

I attempted to combat this by requiring in another class period that only one person from each group was allowed out of their seat. This solved the prior issue but created another.

One student from the group would tend to spend the entire time running answers up to my desk and getting them checked before marking off their numbers on the chart. This meant that there was still a student who was primarily doing no math at all.

Still yet another downside to the competitive team nature of this activity was that some groups tended to give up entirely as they realized JUST how far they were behind the other teams.

Some students started trying to play games on their phones instead of participating in the activity because they knew that their group was NOT going to win.

To combat this in the future, I might have students remove the cards from the chart after solving them and have them place them in a small box or basket for each team.

This way, everyone can still see what numbers remain unsolved, but they can’t easily see how far ahead or behind they are from the other teams.

I really appreciated the fact that making this into a group activity ended up engaging a vastly larger percentage of my students than my previous use of the activity with early finishers.

However, a trade-off was that my students weren’t necessarily learning from one another as much as they have in the past. This was because previously, students would write their solutions to each number on the bulletin board.

Often, students would take a solution for one number and end up tweaking it slightly to create a different number. Usually, this would involve adding a factorial symbol to a 0 to produce a 1 or something similar to that.

Frequently, students would see a solution written on the board and ask a question about it, thinking it was incorrect. This made a great teaching moment.

If I do this again, I might write 1-100 on the dry erase board and have students write their solutions next to each number as a step in the process. This keeps the competitive aspect while still encouraging students to learn from one another. It’s also easily erasable between classes.

Previous Year’s Challenges

Looking for printable versions of previous year’s challenges? I have kept the previous versions available below.

2024 Challenge Worksheet

2024 Yearly Number Challenge (PDF) (5458 downloads )

2024 Yearly Number Challenge (Editable Publisher File ZIP) (1564 downloads )

Puzzle Instructions

Cut apart the provided pieces and assemble them into a 3×3 square so that the puzzle pieces match along each edge to form snowflakes.

Options for Printing and Prepping the Puzzle

There are several options for printing and prepping this puzzle.

The easiest way to distribute this puzzle to students is to print the page with the puzzle pieces, have each student cut out their own pieces, and let them build their square grid on their desks.

If you plan on reusing the puzzle pieces from year to year, I highly suggest running the pages through a laminator first to make the pieces more durable.

If you are giving each student their own copy of the puzzle, this is entirely unnecessary. Just print on some pretty, colorful paper and GO!

If you are looking to display the resulting work or if you would like students to keep their work in a folder or notebook, you might want to print the next page in the PDF file which includes a 3 x 3 puzzle grid for students to build their solution upon or glue their pieces on after solving.

In my opinion, this page is most useful for those who are opting to display or keep the resulting solved puzzle. If you are reusing the puzzle pieces with different classes, I would just put the puzzle pieces in bags and forego the printable template.

If you are working with younger students or with a population of students who needs a bit of starting place for their puzzle solving, there is another version of the grid in the file that shows which puzzle piece belongs in the top left corner of the square.

Including this piece of information will drastically reduce the amount of time it takes older students to solve the puzzle, so I would be very discerning about whether your students need this scaffolding or not.

Ultimately, you know best what your students need. When I first started sharing puzzles I created for my classroom 8 years ago, I never imagined that they would be used in so many diverse classrooms around the world.

Jumbo Version of Puzzle

I printed copies of the puzzle and hung it in a magnetic pocket from Charles Leonard on my dry erase board at the front of my classroom. This way, students can grab a copy of the puzzle and take it back to their desk to work on it.

There are also jumbo-sized puzzle pieces available to print at the end of the PDF file. These can be printed so students can work on the puzzle in small groups.

Disc magnets can be applied to the pieces so they can be hung on a magnetic whiteboard or other magnetic surface.

What are 6×6 Sudoku Puzzles?

6×6 Sudoku puzzles are a simplified version of the traditional sudoku puzzle (usually played on a 9×9 grid) that are intended for kids between the ages of 6 and 10. They can also be used as an introduction to sudoku puzzles for older kids and adults.

I also like using 6×6 sudoku puzzles with older students as a brain break activity or class starter since the amount of time needed to solve a puzzle is substantially less than the 9×9 sudoku grid puzzle.

The goal of a 6×6 sudoku puzzle is to complete the 6×6 grid so that each row, each column, and each outlined 2×3 rectangle contains exactly one of each number or letter used in the puzzle. In this case, each puzzle features letters form a Christmas-related word.

Printing Options

These 6×6 Christmas sudoku puzzles are formatted 4 puzzles to a page. You can print a single page for your children/students to work on, or you can print an entire packet of 12 puzzles.

Additionally, these puzzles are leveled as EASY, MEDIUM, and HARD. The easy puzzles include more clues to help the puzzler get started. Thus, they require less logical thinking to solve. The hard puzzles feature the least clues and require the most logical thinking.