# Build It = Deep Conceptual Understanding of Multiplication

Being a math interventionist is one of the hardest jobs I’ve ever had. It’s like a constant cycle of diagnose…teach…teach…teach…light bulb on…light bulb off…diagnose…teach…teach…teach…

I’ve been working with a group of fourth graders that were just struggling BIG TIME with multiplication. They weren’t able to see how a fact like 3×7 could help them solve 6×7 by just doubling. The numbers were too abstract, and they had nothing to connect it to.

Of course as I dug deeper I found that they simply had zero understanding of what 3×7 really means.  So as usual, I tried to find a way to connect it to real life, my favorite thing ever. I was trying to think of a way to help them remember the difference between rows and columns.  And then it occurred to me as I was waiting in line at the theater, no one wants to wait in line to sit in the first COLUMN for a popular movie. We all want the best seats in the house, so we wait to sit in the first ROW.

Enter the Movie Theater Multiplication Project.  I went home over the weekend, turned off all distractions and poured days and days into authoring this project. I needed to really think for myself what 3×7 represented.  I was not taught this way and I know that it doesn’t come easily to me.  I also had to think of a way that would be meaningful and that would STICK, since that seems to be the biggest challenge facing students in intervention. The last thing that I really needed to think about was the Concrete-Representational-Abstract instructional approach. Kids LOVE to build. The second they walk into my math lab, their hands are all over my cubes, blocks, counters, etc.  Starting with building means that they can usually connect a pictorial representation to it, and then connect that to numbers.

So I made a movie theater or two or three as I wrote the project. I made theaters that were 3 rows of 4 seats, making 12 seats total (3 x 4=12). I made tickets placing them in the correct row and seat number. And finally I made some mega theater designs so they could learn to use known facts to solve harder facts.  There is a fourth stage to the project also that involves some open ended challenges to calculate profits and revenue. Say hello to my little friends:

Seemed like it might actually work!

So I brought the idea to school. I got out some tools and some little tiny bears and THAT got their attention.  Tiny bears! Seriously, that is all it took?!

The first three days of the project were brutal.  They were making columns instead of rows, they were making rows of 20 instead of 20 seats total.  With probing questions they started to see what was happening.  And THEN, light bulbs turned on…and for several days now the light bulbs have stayed on! Is it sticking?! I hope so, and we’ll find out when they get to the mega theaters and can break down more difficult multiplication. Wish me luck!

If you want to try this out, in the preview you will find three parts of the four stages of the project that are free.  You could totally continue the project by giving them your own specifications!

# Level Your Games: More Small Steps for Differentiation

Recently, I had two first grade teachers approach me about fact fluency. They were feeling both frustrated and scattered. They weren’t sure how to organize the time, how to organize the many games, or how to reach students at all the different skill levels they were at.

It is the same story we all have where every child that we teach is functioning at a different level. Some students didn’t even know their combinations to 5, many were learning combinations to 10, and even a few of the students could work within 20.  The games that we were using were just not reaching every student with what they needed…they were flat and one dimensional. WAY too difficult for the students who weren’t on level, and WAY too easy for the students that had already reached mastery.

Enter the post-it note.

In “Steal the Cubes” each post it assigns each group to a level that is right for them.

Those sticky things are my savior when it comes to flexible grouping.

After talking it through, we thought that we would choose just FOUR fact fluency games that the students could rotate through daily. Once they get bored with the same four, we might introduce a new one.  Time in the day is precious, so we knew that they had to be “go-to” games that could be setup, played and cleaned up quickly. We also knew that students grow fast as they learn, and that our groups had to be easy to change in and out.

So here is what we did:

1. We taught ONE game to the students each week.  They played them for a week until they understood the ins and outs of them. Then, once the routines of the games and the game playing behaviors/expectations were taught, we were ready to rotate through them.
2. Each day the teacher chose the game by putting the color of the game out first, leveling the game like in the photo. Each game can be easily modified with different numbers, different cubes, etc. by just changing the post it note.
3. We attached a third level of post it notes for the partners/groups that stayed in the same place for each of the games, the teacher can simply change up the post its when students move levels.

So once again, differentiation can truly be a little small step.  While this one takes a little bit to set up, the students aren’t bored which makes that classroom game time so much more productive!

# Oh My! The Progression of Multiplication

Well, I’ve watched this video three times now and I think I need to watch it at least five more times. I love, love, love how this presented to the audience.

My take aways for when I am teaching multiplication:

1. I need to stop stealing the opportunity to let my students use concrete tools! They should be available every SINGLE DAY.
2. Rushing to the traditional algorithm is a huge mistake. I am thinking we need to have some serious conversations about when to introduce this.
3. I need to let the students explore. Let me say that one again, I need to let the students EXPLORE. So many times when they hit a struggling point I feel this need to jump in and tell…I need a muzzle for my mouth!

What did you take away from this?

# An Approach that Works for Struggling Learners EVERY Time

I have been reading about the Concrete-Representational-Abstract Sequence of Instruction for some time now, especially since I began working with our most struggling math students at our school.

I’m hooked and am a firm believer in this approach!

I know you know that moment… where you find students looking at you with the deer in headlights look.  In my intervention groups, I see it several times in 30 minutes! I was desperately searching for more ways to make math meaningful for them when I discovered this approach. And, I will tell you, it works EVERY time. I mean, EVERY SINGLE TIME. There has not been one single concept that I haven’t been able to master with a child when I used this approach.

If you don’t have time to read the article, the approach is summed up quite simply in three steps:

1. When a student is introduced to a new concept or something unfamiliar, you allow the use of tools. (Concrete)
2. When the student can perform the task, they move on to representing the concept with drawings or pictures. (Representational)
3. When the student can master the task with a drawing or a picture they move to using only numbers and symbols. (Abstract)

* Note it is important to keep all three of these ways visible to promote strong connections and deep conceptual understanding.

I realized that this could be even MORE powerful when students could self assess where they are in this approach. I made this poster with them and we refer to it constantly.

They are constantly checking “where their brains are at” when they are struggling through a problem.  When the numbers and symbols don’t make sense, they actually back themselves up to drawings. If that still doesn’t make sense they back up and use concrete tools.

It has been simply amazing, and you must try it!