In January, I spent some time in the two grades 4 & 5 classrooms at Hamilton Elementary. Coverage was provided to teachers so that they could observe and take part in math lessons in another teacher’s classroom. Teacher were then able to teach this lesson to their own classes, having seen and heard how another class responded and thus, anticipating and planning for their own students. This form of “adapted lesson study” is a common structure we use in professional learning in our district, with time to plan together, observe and discuss and then enact and debrief. The teachers at Hamilton had requested a focus on teaching through the big ideas in the curriculum.
For both classes we focused our planning around these big ideas:
Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.
Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.
To focus the students’ thinking, connection-making and our discussions, the question we posed for the students to investigate was: What is the relationship between multiplication and division?
For each class we began with a game, to activate students’ thinking, get them talking about mathematics and to practice computing multiplication facts. In one class we played Product Gameboard and in the other, the card game Salute.
After discussing the strategies the students used in each game, a problem was introduced to each class. Both of the problems were taken from the book: Good Uestions for Math Teaching. Using different strategies, I facilities meaning-making of the problems with the students and then the students began to engage in problem-solving. They had an opportunity to “turn and talk” and share their strategies and were encouraged to approach the problem in different ways.
The students all began with the same problem but could adjust the number of students in the school (in the problem context) they were working with. They used whiteboard to show their different approaches to solving the problem.
As students shared their solutions and strategies, we asked the students to listen to each other and build on or connecting to each others’ thinking as part of the discourse.
In the second class, a related problem was presented.
What was interesting to notice as students engaged with this problem is that none of the students paid attention to the “four grades”- it was not required information to work through the problem but would have added an extra layer of complexity and context. We did pause near the end of our time together and this was pointed out, and if I had been with the class the next day, I might have had them re-visit this problem, being mindful of the “four grades” context.
What students did pay attention to in terms of sense-making for this problem was the types of sports students might be playing and the number of students that would make sense for each team. The students found a context (tennis) that made sense of having one person per team and two per team (doubles). The students shared their different solutions on the large whiteboard which we used as a starting point to compare and contrast their different solutions and strategies and have the students make connections to how both multiplication and division are related and could be used to engage with both of the problems posed to the classes.
Teaching through the big ideas was also a topic of conversation during an afternoon of Hamilton’s professional development day in January. We will be continuing our conversation at Hamilton’s pro-d day in May and continue to think about ways to nurture ways for students to make connections between mathematical concepts and strategies.