Math Telephone

I used Sarah Carter’s Representations of a Relation Telephone activity last year.  You can read all about the activity in her blog post.  In short, it works just like the game of “telephone”.  A student starts by writing six ordered pairs on the bottom, passes the paper to the next person who creates the graph, who passes it on the the next person who creates the table from looking at just the graph.  This continues until you get to the top of the paper with the ordered pairs again.  If done correctly, the ordered pairs should be the same.

I really liked it, but I knew there were some tweaks I wanted to make the second time around, and it went much better this time.  Part of it could have been that I had already explained the activity once, so I did a better job of explaining it and anticipating where students would struggle.  The first year I did this I actually had one group start whispering ordered pairs into each other’s ears.  I don’t know if they just weren’t listening or if my directions were that bad…probably a combination of both.  Thankfully that didn’t happen this year!

Sarah also shared an updated version of her activity here which also helped as she’s included more instructions on the sheet itself.

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The first time I did this I made the mistake of having one piece of paper per group of 4-5 students.  What was I thinking?!  That meant for 10+ minutes about 6 students in my class were working while the others were supposed to wait patiently?!  Not my brightest move ever.  This year all students had their own paper so everyone was doing something at all times.  This went MUCH better.


As I watched the activity with my first class of the day, I noticed that it was taking students FOREVER to just fold the paper, and one student commented, “Folding the paper was the hardest part of this!”  I found that rather than folding it in an accordion at first it worked better for my students if each person just folded the bottom representation under before passing their paper on to the next person -these instructions are also on Sarah’s updated version.


Overall it was a big success.  I loved watching students look at where the mistakes were made when they were done, and the second time they did it several students were thinking ahead when they created their ordered pairs to try to make it “easier” or linear -which will lead perfectly into what we’re getting to later in this unit.  I even had a student who doesn’t usually get too excited about much of anything say, “This is actually fun.”

I was thinking today what other concepts this could be used for and remembered one I made last year for my 6th graders on exponents.  Since last year, I lost the editable version of the document I made, so I recreated it and added some of Sarah’s instructions to it.  You can download the file here.

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What other concepts could this idea be used for?


6th Grade Unit 2: Intro to Algebra (Part 1 -Exponents, Prime Factorization, Properties, and Order of Operations)

Unit 2 in 6th grade is an introduction to algebra.  This is one of my favorite units.  I love order of operations, and I love introducing students to solving equations.  I break the unit up into multiple parts.  Here is part 1.


We start the unit talking about exponents so that students can use exponents when we get to prime factorization and order of operations.  I typically spend about a day on this and use Kahoot for practice.  I also incorporate this throughout the unit in brain breaks.  “Ok everyone stand up!  2 to the 3rd power.  (Then I give them time to think about what the answer is.)  Do 2 to the 3rd power jumping jacks.”

Prime Factorization

Then we review prime and composite numbers before getting into prime factorization.

(I incorporate prime/composite into brain breaks as well.  “Think of a prime number.  Do that many sit-ups or push ups.”)

I also incorporate a brain break called Factor Hop into this part of the unit as well.  I put four numbers in the corners of my room.  Students go stand next to a number.  I pick a number and if that number is a factor of the number students are standing by they have to move to a different corner, but they are not allowed to walk.  Some students really get into it and have a lot of fun with coming up with other ways to move to a different number.

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Which one doesn’t belong? works great as a warm-up a few days after going over prime and composite numbers to review this vocab.  Students will also usually bring up factors in our conversation.


Since students typically have already learned how to do prime factorization using the factor tree method, I do a couple examples of that before introducing them a method similar to the birthday cake method I found on Sarah’s blog.


I’ve started using this method because for a couple reasons.  In my opinion it’s more organized than the factor tree method, and I like that it can be applied to other concepts such as greatest common factor as well as with variables.  The high school teachers in my district also use it.


Then we get into properties of numbers.  We start with the associative property, identity property, and commutative property.  I co-taught with a teacher a couple years ago who was a huge help when it came to teaching properties.  She did a great job of helping students see the connection between what the word actually means and what is happening in the property.

Commutative Property:  You see the word “commute” so the numbers “commute” or change places.

Associative Property:  You see the word “associate”.  For example, you may associate with certain people at basketball practice, and you associate with other people at church.  In the associative property we see numbers “associating” with different numbers.

Identity Property:  Identity is who you are, so in the identity property the number wants to keep it’s identity.  It wants to stay the same.  After we talk about that, I introduce this property by saying, “I’m a 5.  We’re adding.  I want to stay the same.  I want to keep my identity.  What do I need to do?”  Then, “Ok, now we’re multiplying.  I’m a 5, and I want to keep my identity.  What do I need to do this time?”

Then for practice, we use this Desmos activity from Cathy Yenca.  I edited her version to not include the Distributive property, since we hadn’t covered that one yet.

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Then I used Sarah Carter’s Two truths and a Lie activity.  My students really enjoyed this. You can download the template from here blog post here.

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I loved this one from one of my students.  I read it too fast the first couple times and missed their mistake.

For a few days leading up to teaching students the distributive property we do math talks, and this has made teaching the distributive property go SO much better for me.  In almost every class, I will have a student who will use the distributive property in the math talk so we can talk about so-and-so’s method of multiplying and then I’ll later introduce the term distributive property.



Then for practice, I came up with this Desmos activity.

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I color coded the cards, and I usually go over this with students before they start the activity so they don’t become overwhelmed when they start.

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Order of Operations

I’ve started introducing order of operations by having the following up on my SMART board along with an example problem on the whiteboard and having students do a stand and talk to talk about which things need to be done before others.

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I’ve liked this change.  I enjoy listening to their conversations as they talk, and it also gives me insight into where they are at in their understanding of order of operations as well as how they were taught this as 5th graders.

In every class a student usually brings up PEMDAS, and then we discuss what I don’t like about that acronym.  I love that students are able to tell me things like the “P” stands for parentheses and there are other grouping symbols besides that, and “it looks like you have to do multiplication before division, but you don’t.  They’re on the same level and you read it like a book going from left to right.”  It was also music to my ears when a student said, “PEMDAS?  What’s that?  I’ve never heard that before.”  To which I replied, “Great!  You don’t need to know what it means!”

This has also become one of my favorite warm-ups of all time.

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Over the years, I’ve built up a quite a collection of order of operations activities, and I’ll pick a few of those for practice.

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  • Espresso Puzzles from Greg Tang Math (scroll through this page to find the Espresso Puzzles)

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Exponent Unit

This was the first time I’ve taught exponents without explicitly telling students the “rules” at some point within the unit.  Many students still said things like, “Oh, so when you divide, you subtract the exponents.”  I have mixed feelings over this.  Yes, I want my students to notice patterns, but not at the expense of understanding the math they are doing.  This is one of the things I struggle ensuring as a teacher -that after my students have noticed patterns, they still understand what is actually happening.

I started the unit with a modified version of Andrew Stadel’s exponent mistakes worksheet.  (I know I found someone else’s version of this worksheet that I modified, but I can’t remember where I got it.)  This was something we came back to periodically throughout the unit.  On one of the last days of the unit, we went over the correct answers as a class for the first time.  After going over the sheet, I asked my students to think back to their reaction when I first gave them the worksheet.  Many sort of freaked out and several others were convinced that some of the problems were actually correct.  It was fun for me to see them realize they had learned something throughout the unit because they could now correctly do all of the problems.

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The rest of the first day we focused on identifying the base and writing things in expanded form.  The next several days I spent at least one full day on the product rule, power rule, and quotient rule.  The link for the worksheets I used is at the end of this post.  Again, I know I modified those worksheets from ones I found somewhere online at one point, but I can’t remember where I found them.

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I used this Which One Doesn’t Belong? as a warm-up one day.  I’ve really been loving using these as warm-ups this year.  I love how much vocab students use while doing these.


About this point in the unit, I was not in my morning class a few days in a row due to state testing with my 6th graders.  I was looking for self-checking practice for students on exponent problems.  The challenge for me was we hadn’t talked about the zero power yet or negative exponents.  Most everything I was finding online included those types of problems.  Here’s what I came up with.

I modified Kate Nowak’s row game to work for where my students were at.

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I don’t know if “Two Truths and a Lie” is the correct name for the next worksheet I created, but I couldn’t think of another name and was running out of time, so I went with it.  Basically, students were to simplify 3 different problems.  Two of the problems would have the same answer (the two truths) and the other problem had a different answer (the lie).

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I also had a sheet of Yohaku puzzles ready which I LOVED, but I didn’t end up using it then.  I did, however, use it later in a few of my classes.  I love that there are so many different solutions to these puzzles.  I definitely want to look at the other puzzles on that site for future use.

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When I was finally back with all classes after state testing, we reviewed using this Desmos activity I created.

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absolutely LOVE this Desmos activity from Mathy Cathy for an introduction to zero and negative exponents.

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We ended the unit with some more practice combining all different types of problems.

Here is the link to download the worksheets from this unit.