Today was awesome. I spent the day with 25 educators investigating, exploring, discussing, and grappling with ideas that comprise a big idea in elementary mathematics instruction: multiplication.
The day started with a video from The Math Forum of Max sharing a set of gum balls among a number of people. We spent some time thinking about what kinds of questions the video prompted us to want to investigate. Some of the questions that people were thinking about are as follows:
- If each person gets 1/2, do they all get the same amount of gum balls?
- What would each person’s share of the gum balls be, written as a fraction and as a percent?
- How many gum balls does each person get?
- What does 1/2 mean?
- Is there something here with exponents: 1/2 of a 1/2 of a 1/2?
The actual questions we started our exploration with were:
- How many gum balls does Jaysen get?
- How many gum balls does Marinda get?
- How many gum balls does Zack get?
In addition to the notes each person made, the table groups were asked to represent their solutions using Unifix cubes. It was really interesting to hear and see the different connections that were made when ideas and solutions were described using Unifix cubes. When we went back and looked at the questions we had listed after watching the video, we could answer all of them!! The a-ha moment we had was if we had started with some or most of them, we might not have persevered. However, starting with the three question we did allowed us to take on the questions the group had generated. It was for us, a nice fit of a low floor and taller ceiling kind of task.
We then worked our way through a variety of multiplication algorithms, based on the work of Cathy Fosnot. The teachers explored the strategies of doubling, doubling and halving, and partial products, and how the strategies can be represented using arrays and area models. There was lots of great conversation focused around how the strategies and the models are connected.
After lunch, we worked on a number string, again based on the work of Cathy Fosnot.
10 x 13
2 x 13
12 x 13
20 x 13
22 x 13
29 x 13
Some offered to be in the group that participated in the number string. The rest of the group focused on the instructional moves used when facilitating a number string. The strategies and models we worked on in the morning were put to use in the afternoon: doubling, area and array models, and partial products all made an appearance at some point during the number string and the debrief that followed.
The last part of our day was spent engaging in a different tasks, games, and activities involving multiplication. These were set up in math work stations.
Our closing reflection was a 3-2-1: three ideas that resonated with you or you are considering in some way to include in your work with students, two a-ha moments from the day, and one question you are still pondering.
The best comment of the day: What do we have for homework?