Central Tendencies Puzzles

Central Tendency Puzzle templates for you to check out. I’d love to hear some feedback on these.

Data management is becoming an increasingly important topic as our students try to make sense of news, social media posts, advertisements… Especially as more and more of these sources aim to try to convince you to believe something (intentionally or not).

Part of our job as math teachers needs to include helping our students THINK as they are collecting / organizing / analyzing data. For example, when looking at data we want our students to:

  • Notice the writer’s choice of scale(s)
  • Notice the decisions made for categories
  • Notice which data is NOT included
  • Notice the shape of the data and spatial / proportional connections (twice as much/many)
  • Notice the choice of type of graph chosen
  • Notice irregularities in the data
  • Notice similarities among or between data
  • Consider ways to describe the data as a whole (i.e., central tendency) or the story it is telling over time (i.e., trends)

While each of these points are important, I’d like to offer a way we can help our students explore the last piece from above – central tendencies.

Central Tendency Puzzle Templates

To complete each puzzle, you will need to make decisions about where to start, which numbers are most likely and then adjust based on what makes sense or not. I’d love to have some feedback on the puzzles.

Linked here are the Central Tendencies Puzzles.

Questions to Reflect on:

  • How will your students be learning about central tendencies before doing these puzzles? What kinds of experience might lead up to these puzzles? (See A Few Simple Beliefs)
  • How might puzzles like these offer your students practice for the skills they have been learning? (See purposeful practice)
  • How might puzzles like this relate to playing Skyscraper puzzles?
  • What is the current balance of questions / problems in your class? Are your students spending more time calculating, or deciding on which calculations are important? What balance would you like?
  • How might these puzzles help you meet the varied needs within a mixed ability classroom?
  • If students start to understand how to solve one of these, would you consider asking your students to make up their own puzzles? (Ideas for making your own problems here).
  • How do these puzzles help your students build their mathematical intuitions? (See ideas here)
  • Would you want students to work alone, in pairs, in groups? Why?
  • Would you prefer all of your students doing the same puzzle / game / problem, or have many puzzles / games / problems to choose from? How might this change class conversations afterward?
  • How will you consolidate the learning afterward? (See Never Skip the Closing of the Lesson)
  • As the teacher, what will you be doing when students are playing? How might listening to student thinking help you learn more about your students? (See: Noticing and Wondering: A powerful tool for assessment)

I’d love to continue the conversation about these puzzles.  Leave a comment here or on Twitter @MarkChubb3

Skyscraper Puzzles – printable package

An area of mathematics I wish more students had opportunities to explore is spatial/visualization. There are many studies that show just how important spatial/visual reasoning is for mathematical success (I discuss in more depth here), but often, we as teachers aren’t sure where to turn to help our students develop spatial reasoning, or now to make the mathematics our students are learning more spatial.

One such activity I’ve suggested before is Skyscraper Puzzles. I’ve shared these puzzles before (Skyscraper Puzzles and Skyscraper Templates – for relational rods). With the help of my own children, I decided to make new templates. The package includes a page dedicated to explain how to solve the puzzles, as well as instructions on each page.

For details about how to solve a Skyscraper Puzzle, please click here

New Puzzles can be accessed here

*The above files are open to view / print. If you experience difficulties accessing, you might need to use a non-educational account as your school board might be restricting your access.

You’ll notice in the package above that some of the puzzles are missing information like the puzzle below:

Puzzles like these might include information within the puzzle. In the puzzle above, the 1 in the middle of the block refers to the height of that tower (a tower with a height of 1 goes where the 1 is placed).

You might also be interested in watching a few students discussing how to play:

A few thoughts about how you might use these:

As always, I’d love to hear from you. Feel free to write a response, or send me a message on Twitter ( @markchubb3 ).

Can you visualize this?

Many mathematicians are good at searching for patterns in numbers, however, an area that I think we all need to continue to explore is Visualizing.

Instead of just looking for procedural rules, or numeric patterns I encourage you to take one of the following and actually VISUALIZE what is going on.

Pick one of the above that interests you. Answer some of these questions:

  • What relationships do you notice here?
  • What are you curious about?
  • What visual might be helpful to represent this/these relationships?
  • Will these relationships work in other instances? When will it work/ when won’t it work?
  • How might a visual help others see the relationships you’ve noticed?

I’d love to hear some answers. You can respond here below, or via Twitter @MarkChubb3