Make Math Moments Academy › Forums › MiniCourse Reflections › 4 Strategies To Help Students Start Problems & Stick With Them › Strategy #3: Be More Prince – Discussion

What was your big take away from this particular lesson?
What is something you are still wondering?
Share your thinking below.

I hadn’t thought of this before, but I think I can use those interlocking blocks to teach multivariable algebra. Hmm. HMMM!
I am guilty of rushing my students into an algorithm. Then again, it is not always easy to judge who is ready to make that transition and who is still leagues behind. I have a grade 8 student who has made it this far with (seemingly) no conceptual understanding of multiplication or division. She can do it with a calculator or table, but she has a hard time understanding that multiplication and division are effectively opposites. I wonder how I can support students like this in the same room as students who are roaring ahead at lightning pace.

Ohhhh I KNOW you can! There is so much that can be done when we ask ourselves “how” or “why does this REALLY work?”
I’m excited to hear what you come up with!


The Prince reference really hit the nail on the head for me regarding the amount of time it takes for concepts to build and progress through concrete to visual to abstract. I also appreciated the separation within concrete of using the actual objects and then manipulatives as well as using symbolic prior to operations and numbers within abstract.
The math department at my school really dug into using algebra tiles in all three grade levels this year. Prior to us working at home, sixth grade was able to see how they could be used when working with the distributive property, seventh and eighth grade was able to use them when solving equations. Now that we are all working at home and not able to access these manipulative that are in our classrooms, how can we continue this exploration and discovery through manipulatives with our students virtually?

I think in high school math I have trouble seeing how to make some of these ideas concrete so they can be modeled with blocks or tiles. I know putting in the time and effort to do so will really help students understand.
There’s a scene in the movie stand and deliver where Mr. Escalante announces that they are going to start learning about fractions, and he puts on an apron, pulls out an apple and a big knife. That would be a memorable moment that he started with a concrete example. I need to do likewise for my math kids.

It is definitely more challenging as we move through the grades. Keep in mind that “concrete” doesn’t always mean math manipulatives.
A great start is algebra tiles, in my opinion. Have you used them for like terms? Solving equations? Expanding? Factoring? All great ways to help kids experience math!

I tried Algebra tiles and the didn’t get how to use them! Guess I didn’t do it right.

It is definitely a progression. If students haven’t used base 10 blocks for multiplication and division, then they will try to proceduralize the use of the algebra tiles which isn’t helpful. Ensuring there is a clear understanding for multiplication of whole numbers to expanding with algebraic terms is so important.



The power of manipulatives, it is so easy to go straight to abstract.

So true! We always have to remind ourselves to slow down!


I am guilty of guiding my students to the abstract too early. I see the value in focusing on the concrete first (manipulatives), which leads to the visual representations in drawings and diagrams to the abstract (symbolic).

Awesome to hear. Something else I’ve come to realize is that all three should be used interchangeably throughout the process so connections can be made. I often thought that after some time, we’d move on to the abstract and not go back to the visual or concrete.
