The idea underlying math enrichment is to deepen the understanding of math concepts that advanced students have already mastered. I began meeting with the top math students from each grade level (K-5) a few weeks ago, and I started off my introductions with this definition of enrichment. I didn’t want them to expect to go farther in their math skills, surpassing their peers. I also didn’t want them thinking that they were “above” their classmates who did not join me for this enrichment time. Rather than looking down from the mountain tops, we would dig in; We are in search of the riches (from en-rich-ment) that can only be found by looking beyond the ordinary teaching of math skills.
The challenge to myself is to find novel ways to show the use of math skills. I want the students to see that what they learn in the classroom is very necessary. Even if you never, ever have to use Pathagoream’s theorem, being able to use a formula correctly and understanding why is extremely valuable.
An example of this is my lesson on multiplication for 3rd graders. Having completed an “Understanding Multiplication” lesson weeks earlier, and learning facts for multiplying zero through ten, I wanted to have students use these ideas creatively. I came up with a lesson that shows a way adults use multiplication all of the time without even realizing it!
There are four 3rd grade classes. Each one is very close to 25 students. How many students are in 3rd grade? Adults immediately know that there are about 100 kids in the 3rd grade. How? We instantly know that 4 X 25 = 100. Easy-peezy. But, there are a few things going on behind the scenes. We, grownups, are already rich in the knowledge of four 25s equaling 100, due to decades of dollars and quarters! Also, we know to use the compatible number 25 when numbers are close to it. Third graders have been taught how to round, but they don’t know that it is okay to completely change numbers into “easy to use integers” (compatible) for simplifying computations!
As always, I wasn’t going to just come out and tell them all of this. My math enrichment students had to dig for it, en-rich-ing themselves. I gave them this math problem.
It has to do with them, which is fun. The numbers are accurate. I looked them up on the school’s database. These are the names of the actual third grade teachers.
I read the problem to the enrichment students. Then, I asked them, “What is this problem about?” After the students identified the topic of third-grade population, we discussed what the goal was. You have to provide the total number of students, but there’s a catch; “You have to use multiplication to do it!”
When I walked the students through the Important Information; the data that will be used to solve the problem; I paused to point out some key elements. The students noticed the multiple 26s. I showed them that there was something else they all had in common; They were all in the twenties. There were multiple numbers with a two in the tens.
Finally, it was time for the students to do their work. “Dig in!” I had put the word problem into a Google Jamboard, so I could make a copy for each student in the Google classroom that I’d shared with the enrichment students. They were able to write on the Jamboard, using their iPads. I walked around and witnessed the digging. It was awesome to see the variety of computations. When students told me that they were done, I showed them how to duplicate the Jamboard slide, erase their math, leaving the word problem, so that they had a new work space to solve the problem in a new way.
After letting the students wrestle with the word problem for several minutes, I had students share their calculations. One student multiplied the totals of class sizes by 1 before adding them all together. “Does this meet the parameters of the problem?” I asked the class. Yes. “Is this useful, though?” No. The student had only done this after I told them to come up with multiple ways to solve the problem. I was glad they had, because it was an opportunity to point out making math work for you. “Multiplication is a way to simplify math, believe it or not,” I told them. “Can you multiply 20 times 4 in your head?” Yes; see? I reviewed with the group that multiplying anything times 1 is the identification principle. It simply tells you what you are working with; “One times Dominic, means you have one Dominic” 😉
I had students share their Jamboards on the classroom Googlel Jamboard, so we could witness the different ways to use multiplication. I was impressed by a few students breaking apart bigger numbers before multiplying. Only a couple of students recognized the closeness of the class sizes to the number 25. This presented a teachable moment, and I shared the vocabulary/math concept of compatible numbers.
After this, our time was up. I mentioned that time, like money, presents some compatible numbers. “What is 4 times 15?” I asked the class. When no one answered immediately, I asked, “How many fifteens are in an hour?” They knew this to be four. “So… four 15s makes up one hour… ?”
Sighs and “ah has” could be heard. “If you have a few numbers that are near fifteen, could you use fifteen as a compatible number for multiplication?” Hmmm…
The Captain of Class 