Now that I have a good idea of what strategies kids are using and how ready they are for this type of problem, I'll start making groups. I'll have a group of kids who don't really get it at all; they'll be working on connecting multiplication to addition and refining their adding-up strategy by adding groups. I'll have a group who mostly got it and need more practice at the strategies they started to develop; I'll put these kids together and direct them towards certain strategies for multiplying groups that I want them to practise, and I'll spend some time showing them the notation for the type of math they're doing. Ideally, this group will comprise at least half the class. The last group is the kids who jumped immediately to a high strategy involving multiplication or division, or the ones who tried two or three different ways of getting the problem and had all of them work.
Now that I've got my groups, I'm going to find two or three problems that are similar but differ in a couple of respects. The lowest group is getting friendly numbers to work with. They won't see anymore nineteens; they'll get twenties and tens and hundreds, numbers I want them to develop skill at working with in their heads. I'll probably work with them first in a guided math lesson, where we go to one space in the room and start tackling the problem together, with lots of manipulatives to model the problem.
Meanwhile, the middle group has been given a similar problem, with less-friendly numbers, and a couple of discussion questions to guide them towards the strategies I want to see them develop. They're working elsewhere in the room, and I'll check in with them once I've got the lowest group well-established at their task and getting help from each other.
The highest group has been given possibly the same problem as the middle group (to facilitate them learning from each other later on, and transfer between groups if someone either gets it really well or doesn't get it as well as I thought.) But their discussion questions are different. I want them to draw connections between different strategies and begin to develop their patterning. When I get to this group - probably the second day of group work - I'm going to be talking about equivalencies and ratios, both of which are beyond grade-five level according to the curriculum, and possibly showing them some simple algebraic equations for the problems they've got in front of them.
Usually, the middle group starts to run into the higher group as the week progresses, and by the time the week is over, fully half the class will have been exposed to a level of algebra more commonly associated with grade seven than grade five. The goal for the lowest group is to develop their understanding that multiplication is a faster way to add groups, and use concrete materials to get to the point where they can use a more advanced strategy to approach the problem.
At the end of the week or the beginning of the next week, I'll give them another problem as a "game time" activity. I may or may not differentiate this problem or give them a choice of problem to tackle; it depends on how the rest of the week has gone. They have to answer this one independently and answer a couple of questions similar to the discussion questions they've been working on, and this activity determines their mark for this part of the unit.
This got long, part 2
Now that I've got my groups, I'm going to find two or three problems that are similar but differ in a couple of respects. The lowest group is getting friendly numbers to work with. They won't see anymore nineteens; they'll get twenties and tens and hundreds, numbers I want them to develop skill at working with in their heads. I'll probably work with them first in a guided math lesson, where we go to one space in the room and start tackling the problem together, with lots of manipulatives to model the problem.
Meanwhile, the middle group has been given a similar problem, with less-friendly numbers, and a couple of discussion questions to guide them towards the strategies I want to see them develop. They're working elsewhere in the room, and I'll check in with them once I've got the lowest group well-established at their task and getting help from each other.
The highest group has been given possibly the same problem as the middle group (to facilitate them learning from each other later on, and transfer between groups if someone either gets it really well or doesn't get it as well as I thought.) But their discussion questions are different. I want them to draw connections between different strategies and begin to develop their patterning. When I get to this group - probably the second day of group work - I'm going to be talking about equivalencies and ratios, both of which are beyond grade-five level according to the curriculum, and possibly showing them some simple algebraic equations for the problems they've got in front of them.
Usually, the middle group starts to run into the higher group as the week progresses, and by the time the week is over, fully half the class will have been exposed to a level of algebra more commonly associated with grade seven than grade five. The goal for the lowest group is to develop their understanding that multiplication is a faster way to add groups, and use concrete materials to get to the point where they can use a more advanced strategy to approach the problem.
At the end of the week or the beginning of the next week, I'll give them another problem as a "game time" activity. I may or may not differentiate this problem or give them a choice of problem to tackle; it depends on how the rest of the week has gone. They have to answer this one independently and answer a couple of questions similar to the discussion questions they've been working on, and this activity determines their mark for this part of the unit.