##
* *Reflection: Developing a Conceptual Understanding
Partition & Measurement Models - Section 1: Warm Up

A clear and specific focus on the structure of the division sentence is critical for developing students' understanding of this concept. Understanding that the dividend represents the whole amount, the divisor represents the items in a group, and the quotient represents the number of groups should not be skipped over. Understanding this structure will help students determine the type of model that can be used to solve.

It is also important to discuss what "remainders" represent. When students encounter remainders, they need to understand that the remainder represents less than a whole group rather than less of an item.

For example 7 ÷ 2 = 3 remainder 1. If the context is houses, there is one house that is not part of a whole group of two. It is not possible to share the house equally among the three groups. Understanding this concept is crucial to understanding division.

*Conceptual Understanding*

*Developing a Conceptual Understanding: Conceptual Understanding*

# Partition & Measurement Models

Lesson 1 of 5

## Objective: SWBAT explain the difference between a division models of partition and measurement.

## Big Idea: Understanding the structure of a division sentence results in different type of models. Students practice using groups and number lines to solve divisions.

*45 minutes*

#### Warm Up

*5 min*

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.

*expand content*

#### Flip Book

*15 min*

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.

*expand content*

#### Hands On With Tiles Partners

*20 min*

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.

*expand content*

#### Wrap Up

*5 min*

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.

*expand content*

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