There’s no denying the power of the Post-it. Many brilliant minds within the #MTBoS have harnessed its’ power to help students make sense of mathematics and this week was no different.
Only this time we infused them into a Marilyn Burns must have…
To start we had students build animals from pattern blocks and had partners guess the animal.
Some students were not sold on their partner’s creation which lead to some heated discussions. Score a point for SMP3.
I showed my animal and we decided that it looked most like a dog.
I built the dog to show what it looked like on day 2 and 3.
Teacher tip from Mike Wiernicki: if you have foam pattern blocks you can wet them and they’ll stick to your dry erase board…unfortunately these were wood.
Then we asked… What do you notice?
And we followed that up with, “What will the dog look like on day 4 & 5?”
We asked students to organize their thinking in a table and this is what they collectively came up with:
This was a great opportunity to pull out specific vocabulary with students:
- Students said “The body, head, and feet never change. They always have the same number of pieces.” The term CONSTANT was introduced.
- They also noticed that “The dog’s tail grows one rhombus for every day it’s alive.” VARIABLE was introduced.
We had students find the total number of pieces for the 11th and 21st day.
Student: Do we have to build it?!? That will take forever. What if we don’t have enough pieces?
Me: Can you use what information you already have to figure it out?
The table really helped students recognize vertical AND horizontal patterns which are typically harder to find. We were really surprised by how quickly students found shortcuts to complete the table.
What they noticed…
- The head and body column never change so they placed 4s all the way down.
- The number that went in the tail column matched the number of days.
- The total number of pieces goes up by one each day it grows. (recursive rule)
- The total is always 4 more than the day. (explicit rule)
For the most part, students did an excellent job completing the table…when the days were identified. But when we added a Post-it to the day column things went a little sideways.
Students: Hey! That’s not fair. We don’t know what day it is.
Me: I know. It’s my mystery number.
Student: We can’t finish it without knowing the day.
Me: So give up then! I guess there’s no way for you to tell me how many pieces there will be on the mystery day.
The students began talking amongst each other because they knew something was up.
Student: Yes!!! We CAN do it. We know that the feet, body, and head stay the same no matter what day it is. So put a 4 in that column.
Me: Ok. What else do you know?
Student: Well since we know the tail and day always match, can we put another Post-it in the tail column and put a question mark on it just like the day column? I asked the class to check with their table and decide. Each group came back and said that’s what they wanted.
Me: What about the total?
Student: That’s easy…to figure out the total we just add 4 to the mystery number. So we just write 4 + a Post-it with a “?” mark.
Me: Oh that’s awesome. What happens if I ran out of Post-its. What could we use instead?
Student: Well you could always just draw a square and put a “P” in it for Post-it. It doesn’t matter if we have a “P” or a “?” on it because it’s still gonna be the mystery number.
I could have swore I heard math angels at this very moment. It was one of those moments I’ll never forget.
Looking back at the lesson I would definitely say it went “much too whole group” towards the end. I would have liked students to grapple with the idea of the mystery Post-it at their tables before discussing as a class. I think I just got caught up in the excitement of the moment. (note to self)