Focusing on the relationship between division and multiplication is a critical skill for students. To begin this lesson we begin with a basic review of division to model 12 divided by 4 with a small manipulative such as a round chip or cube. We practice different ways to share and divide the 12 counters equally among different groups. As each new model is built, a corresponding division sentence is written based on the format of whole amount ÷ chips in the group = groups.
12 chips ÷ 4 = 3 groups, 12 ÷ 2 = 6, 12 ÷ 3 = 4
This structure is important for the students to understand when students will be working with remainders and equal groups.
This lesson compares the difference between different types of division including partition models and measurement models. During the warm up the students practiced partition models of division and equal shares to determine the number of items in a group. For example, there are 12 apples. If there are four teachers, how many apples will each teacher receive?
12 ÷ ____ = 4
Measurement models can be related to repeated subtraction and include models on a number line to find the number of groups. For example, there are 12 apples. If each teacher is given 3 apples, how many teachers will receive apples?
12 ÷ 3 = _____
The students' flip books are created with examples each of these types of division models.
Practicing these two types of problems includes students using tiles to solve as they draw models. I find it is important to continue to use a manipulative during to help students understand the structure of the sentences, and the difference between groups and items within a group.
I chose two problems that would be somewhat challenging for the students to solve because they are not known facts by most of the students in my class. The first problem was 54 ÷ _____ = 3.
Students need to create a partition model by drawing three groups to find how many items are in each group.
The second problem is 48 ÷ 12 = _____. The students use a number line to demonstrate repeated subtraction.
Because of the importance of understanding the structure of these types of sentences and the models connected to divisor and quotient, I have the students write the examples we've discussed (12 ÷ 4 = 3 and 12 ÷ 3 = 4) in their math journals.