Make Math Moments Academy › Forums › Full Workshop Reflections › Module 4: Teaching Through Problem Solving to Build Understanding › Lesson 46: How can you be more Prince? › Lesson 46: Question

Lesson 46: Question

How will you be more Prince this week in your math lessons?

I can be more Prince this week by giving my students actual probability tools such as bag with coloured tiles, dice, coins and spinners to determine theoretical and experimental probability. Students will be given opportunities to use arrays and tree diagrams to represent all possible outcomes. Students will then write the probability of different outcomes as a fraction, decimal or percent.

While I love using virtual manipulatives, I can’t wait to be back in a functional inperson classroom where my kids can have tiles and base 10 blocks and other manipulatives on demand. I teach mostly 6th grade, and those concrete representations are still SOOOOO important! The virtual manipulatives work, but not nearly as well for a starting place!!!

I need to explore this idea with factoring!!! That was amazing to see, I wonder how negatives work into that model?

Ok, just spent about an hour on this idea. I cannot see a pattern for how to set things up correctly on the first try. It seems pretty guess and check. Is there a way to know how many rows there will be? If not, I assume this is used for an introduction only (concrete) and then leading to abstract ways which will be used the rest of the time?

Hey @Bob Have you seen my video on Sneaking in Factoring? https://youtu.be/6B99vE7RnU0 There’s a follow up with completing the square.



Since Covid, I have been using tables in Google sheets to make arrays and strips (as number lines) a lot. The great thing is that my students are really used to them and can do it a lot. I need to do a better job of using more of the pictures of donuts before I so quickly move to the more abstract tools like coloured chips and arrays.

Remote learning has made this more challenging for sure, however it seems like you’ve found some ways to keep things as concrete as possible. Also reminder that you can grab your brainingcamp license to use!


The great thing about concrete to visual then to abstract is that is a guidance to remediate for students who missed this knowledge at their grade level. By stepping back to concrete, students who need it, get it and students who don’t need it, step to their level of comfort whether its visual or abstract. It can also “wow” the students who do the procedure without understanding and earn us a little credibility.

So true. I love how concrete and visuals can help all learners “see” the math. Often our students using symbolic notation are unaware or forget why what they are doing almost automatically actually works. This is a great way to keep that connection.


Your Prince analogy is fantastic. I have to think back to when he started to use his symbol and went by “The Artist Formerly known as Prince” I had to roll my eyes. (I was young and did not listen to his music. But hearing his performance at a halftime show, I began to understand his music and accepted his music.
But your concreteness fading model is a very logical connection to this idea. It is not until students can appreciate the math can they understand the abstract symbolic method. I do something similar to the concept of completing the square with quadratics. I always start by going through what a square is and have students construct squares with toothpicks. Asking the question, “How do you know it is a square?” gaining a typical response of all sides are the same. Then pulling out the algebra tiles to have the students do the same as above but with tiles and the square is filled in. Then I ask the question, “How do you know it is a square?” A typical response of all sides is the same. But at this point, have them write the expression for the sides. Then I give them a set of algebra tiles to completely create a square, where they may need to add some tiles to complete the square—obviously asking the same question as above but asking for justification. Eventually (not typically on the same day), I will give them an expression like y = x2 + 8x and ask them to create a perfect square trinomial.

@scott.mcnutt I echo your exact feeling toward Prince! I also would roll my eyes about the symbol haha!
Love your lesson here for completing the square. Have you checkout our video on using algebra tiles for completing the square yet? We have two: https://youtu.be/f8wuG0xIC8w
