A new puzzle to consider

Recently, a friend introduced me to this game/puzzle, and I wanted to be sure to share it with you.  It might be a great thing to use your PTO money or ask a generous parent to pick up for the class.

The only problem I really have with this game is its name: Genius Star.  I hate for that to cause students to believe they aren't capable of solving it, or vice-versa, that if they are able to solve it, it makes them a genius! 

This puzzle explores spatial relationships which for so many of our students can be a challenge.  It also offers students the opportunity to distinguish pieces they should prioritize as well as a trial in perseverance!

Here's how it works:

Roll the die that come with the game:

Lay the little white triangles onto the corresponding triangles on the board:

Now, I usually solve these on my own, and I don't recommend that it becomes a racing game, but students then take the 11 game pieces and place them on the board to cover in the star.

Students can compare their solutions to see what they did the same or different.

Students can also reflect on what made the puzzle challenging or easy. 

The box comes with two black trays to solve the puzzle on, but you could maybe get more than one game so that more students could work to solve. I find it quite fun, and it highlights the spatial skills of math.  The company makes other similar games that will show up when you follow the above link to this game.

Students can solve the puzzle in pairs and discuss their findings, they can investigate the dice and the regions of the board that each one covers, they could create their own puzzle numbers that they think are unsolvable and ask classmates to prove them wrong, they could create fractional questions about the puzzle or its pieces, or you could use two solutions for the same numbers as a same/different discussion. It seems to me like there are a lot of ways that this little puzzle could be used!

Let me know in the comments if you have found or find other ways to use this puzzle in the classroom!

Removing Ability Grouping while increasing Problem-Solving

One of the biggest missteps that occurs in math core instruction is people trying to organize it the same as they do their reading workshop.  

Traditionally in reading workshop, students are grouped by reading level and then called to the teacher to read and discuss a text at their level.  The teacher's small group instruction is really concentrated during this time when meeting with a small group of students away from the rest of their classmates.

In math workshop, we do not recommend this kind of grouping for students often.  In fact, through the work of Peter Liljedahl, more and more teachers are reading and using the research around VRG: Visibly Random Grouping. In his book, Building Thinking Classrooms in Mathematics, he explains how he realized students are more successful this way.

Visibly Random Grouping can be intimidating to some teachers because it means that they have to give up some of their control.  Not like let the room run crazy loss of control, but letting students work with whomever they match with.  Teachers have spent a lot of time organizing and reorganizing their groups for activities.  The thought of just letting it be random might be a lot.  However, once teachers begin to use VRG, they tend to love the results.

To begin with, the students should witness that the grouping has been random. There are apps that group students randomly(even Dojo), but you can always use playing cards, popsicle sticks, birthdays, or any other method that helps them see that you did not intentionally choose who was going to work together. Liljedahl's research shows that groups of 3 work best in most grades to get all students thinking.  In the primary grades, he recommends groups of 2.

Here are some of the benefits of VRG:

• Increased engagement
• Improved collaboration skills
• Reliance of students on each other more than on the teacher
• Improved student ability to work with anyone and recognize the strengths that classmates possess
• Better flow of learning with students not just sharing in their group but also with others in the room: the feeling of being on the same team
• Perception of the students that the teacher believes they can do it.  They don't have to be placed with a student who can "pull them along" or one that they need to support. No matter who they are with, they will be able to access the problem and move forward.

As teachers begin to move towards more use of VRG, they will find themselves removing labels from students.  This subtle shift in thinking will carry over into the students' views of each other, too.  This video by Jo Boaler offers somemre insight into the benefits of heterogenous grouping.

There are many teaching shifts that Liljedahl discusses in his book.  Visibly Random Grouping is one that is a great first shift for all teachers, and it will help when they decide to give a Thinking Classroom a try.

March is Full of Palindromes this Year!

 As we approach the end of March, we come close to multiple school days which are palindromes. From 3-20-23 to 3-29-23, our dates will be palindromes, and they may offer opportunities for you and your students to explore palindromes!

Students of all ages can look more closely at palindromes! I am going to focus on explorations with numbers, but your students might enjoy finding words that are palindromes, too. Here are a few books you might share with your students:

Some of your students may get caught up in noticing individual words that are palindromes, but some may enjoy the word play involved in sayings and phrases that are palindromes.  At either level, it is word work that many students find FUN!

For math explorations, you might not explain to your young students what a palindrome is, but let them discover!  

• Using your pattern blocks as a visual, you can give students numbers to "create" and allow them to notice what makes these numbers special.  For example:

If you display the pattern blocks to represent different digits, then you can dictate numbers and ask students to create them.  Can they identify the pattern that makes palindromes special?  Can they see with the March dates how they are palindromes?

• Ask your students to find all of the palindromes between 0 and 100.  What do they notice about two-digit palindromes? Is there a pattern in 3 digit palindromes?

• Will there be other palindromes this year?  How about next year--What palindromes will there be?  Is there ever a year without a palindrome date?  What can your students find?

• Finding palindromic numbers Math For Love has a great lesson exploration opportunity where students search for different levels of palindromes. It offers a way for students to add, look for patterns, and have fun with numbers--all in one activity!

I hope you and your students find some time to explore the fascinating patterns and elements of palindromes in our words and numbers!  You might want to consider ending with this Weird Al video, Bob, which is made entirely of palindromes.