In the Making Number Talks Matter chapter on Division, one of the strategies described was “Make a Tower.”
This strategy immediately reminded me of the 4th grade lesson in Investigations called just that, Multiple Towers. To make the timing even better, I am planning and teaching that lesson with a 4th grade teacher this week. The goal of this lesson is not necessarily eliciting a division strategy, but there is so much possibility for so many things in this lesson. Because of that, however, I am struggling with how we can leave it open enough for the many ideas to emerge, but focused enough to have a purpose in our planning.
The structure of the lesson, as it is the book, looks roughly like this:
Students count around the classroom by 3’s to 72 and it is recorded on the board. They then count by 30’s to 720 and it is recorded on the other side of the board, so both lists are visible. Asking students what they notice and what relationships they see. We record these noticings and leave this because the investigation of multiplying by a multiple of 10 continues to emerge throughout the unit.
Next, as a class, we introduce multiple towers through a context of stacking boxes of 30 oranges. Using post-its on the wall, students place the post-its one above the other, labeling the amount of oranges as the tower grows until it reaches the shoulder height of one student. We then ask if there is anything in the tower that would help us figure out how many oranges are there without counting each one? They estimate how many to the top of the student’s head, ask how many multiples are there, and record equations for it.
Choosing from the list below, students work with a partner to create their own multiple towers as tall as one of them on a strip of paper:
After creating their tower, they answer questions in their activity book about the number of multiples, how they could find the 20th multiple without counting, and writing equations for some pieces of their work. They will continue to reference these towers in the following lessons in which they multiply 2-digit numbers and discuss various strategies and representations for multiplication.
I love this lesson, but as always, I like to play around with different ideas when I am lesson planning and these are some things I cannot wait to chat with Malorie, the 4th grade teacher, about on Monday:
- Instead of a number talk do we open with the count around the classroom to save time for the multiple towers?
- How do we record the multiples? Will different recordings draw out different noticings?
- Do we start with estimation of how many cases of oranges will it be before we just start the tower? Could that draw out their use of multiplication combinations they know?
- Do narrow the list of starting numbers to choose from so there are some really great relationships that emerge, like one factor that is 1/2 of another so the towers have a relationship? or a factor that is 1/3? or do we let them choose their own off of that list within a range?
- Do we put the towers up, walk around and do a notice/wonder before they jump into the activity book pages?
- Do we want to end with a journal prompt? The answer is obviously yes, but what do we want it to be?
- How will this leave her for the next day’s lesson?
Feel free to chime in with thoughts/suggestions and I will post the plan we decide upon after our planning on Monday!