During the warm up of this lesson, I create groups, each with dots inside, to model multiplication. This is a review of the process that was used for the lesson Multiplication Models and Structure, where I taught students to draw sets of equal groups to model multiplication.
During the previous lesson, I demonstrated using circles with dots on the inside to show equal groups, and I modeled the format to write number sentences in the format of groups x objects in a group = whole amount. Students also wrote the repeated addition sentence for the number of objects inside of each group.
For example, if there are three groups, each with four dots inside, the number sentences are written as:
3 x 4 = 12 and 4 + 4 + 4 = 12
Today I am not using repeated addition because the focus is on multiplication.
First, I draw a few examples for products less than 36 including 3 x 6, 7 x 5, and 4 x 8. I remind students about the importance of using dice patterns (as this allows students to subitize). Additional exposure to subitizing not only assists students in being more accurate in their computations, it develops pattern recognition. For students still struggling with developing their number sense, subitizing helps to develop strategies such as compensation and counting on, because it gives students structure for composing and decomposing numbers. In my class, using dot patterns is is an expectation aligned with MP6 - attend to precision. When children draw the dots randomly, I remind them that this is not a mathematical representation. I also know it interferes with the development of the equal groups concept.
Then, I have students draw equal groups on their individual whiteboards and write the matching multiplication sentence on their board. I provided number sentences for the students to draw including:
2 x 3, 5 x 6, and 2 x 9.
After students put away their whiteboards, I call them back to the carpet and describe the scenario of having a container of pencils that need to be passed out and shared by the students. Since there are six teams in our class, we need to figure out how many pencils each team receives. We don't have much time, and we need to distribute them quickly.
I show students a group of pencils. I ask them to help me come up with a quick plan to solve sharing them out fairly. I have the students share their thinking with a partner sitting next to them. At this point in the lesson, I chose not to have a share out and demonstration of their plans and solutions because I want them to try different ideas in the next section of the lesson. In circulating, I record their plans on a sheet of paper and these plans will be tried in the wrap up of the lesson.
Students get to chose their partner to work with in this section of the lesson. I give each set of partners an even number of linking cubes to put into equal groups.
Prior to the lesson, I separated groups of cubes into even quantities. Students were given either 36 or 48 counters each. These numbers are specifically chosen because many different models of equal groups can be derived using the same number of counters.
I provide white copy paper for the students to draw their equal groups. As students display one equal grouping, I instruct them to continue on to find other ways to group the counters equally.
Using some of the suggestions from the students earlier in the lesson, I demonstrate some of their strategies. One is to draw two groups and check to see if the number of counters was even. Another suggestion is to pick 25 groups because that is the number of students we had in the classroom. We discuss how easy or difficult it would it be to draw 25 groups and agree that choosing two groups is easier than 25, but they couldn't come up with another option.
Next, I ask the students to draw two equal groups on their whiteboards. Two students ask for help with their number of cubes, and I model four equal groups for them. The number of cubes this show how they had sort the groups into two groups of eighteen.
When I ask for their thinking, this group says they just guessed and tried four groups and explained it worked. The boy that had asked for two more counters explains he used skip counting to help him set up equal groups. Many students still want to put their counters into benchmark groups of five and ten, but cannot come up with a strategy to create equal groups unless it was groups of two.