##
* *Reflection: Modeling
Find The Array - Section 4: Closure

Because it is a new skill for students to write equations using the distributive property, it was important for me to provide a model of these equations for the students to use. The students had different sizes of arrays, and their equations were based on their own array. This required the students to compare their array with mine, match the number for rows to be used as the distributive factor, and then break the factor for the columns into separate addends.

The use of this equation will require additional practice and activities for students to fully understand. This lesson is an introduction and illustration of the distributive property.

*Modeling*

*Modeling: Modeling*

# Find The Array

Lesson 1 of 13

## Objective: SWBAT create arrays and determine the area using square tiles.

## Big Idea: Students create arrays with two different colors of tiles and they will begin to use the distributive property of multiplication for their array.

*65 minutes*

#### Warm-Up

*5 min*

During the warm-up for this lesson, the students built arrays with items in their desks. Most students choose to use crayons for the activity because they have the most of this item in their desks. Other students use linking cubes to build an array. The purpose of this activity is to review the concept that arrays have equal rows and equal columns. The students describe the differences between rows and columns. They also determine the rows and the columns all need the same quantity of items for it to be an array.

*expand content*

#### Model For The Group

*5 min*

To begin the lesson, I show students that we will be constructing an array using square tiles that have been placed into bags. The bags all contain different numbers of tiles, and there are somewhere between 20-90 tiles in each bag.

I explain to the students each of us will need to create an array to find out how many tiles are in each bag. Adding to the complexity of the problem, the bags contain two different colors of tiles. I ask the students to keep the colors separated when creating arrays. I want their focus to be on arrays and area, rather than on patterns.

I ask the students to discuss with a partner their ideas and plan a strategy for this task. Some of of the information I overhear is, *"I'm going to start with a row of five to make it easier to count." *Another student discusses building a frame and then filling in tiles. This statement is an example of when I'll step into the discussion, and using questions and reminders discuss again that arrays are an arrangement of rows and columns not a frame.

The students are sent to their desks to begin working on building their arrays.

*expand content*

#### Try It On Your Own

*40 min*

Students build arrays with tiles, and determine separate arrays using distributive property.

As students concentrate and focus on building arrays, the students use many different strategies. Some students build two separate arrays at the same time based on color. Some students work on one color at a time, and other students are randomly mixing colors to find equal rows and columns. Other students are counting their tiles to see if they can make a connection to the number for use with skip counting.

After the students build their arrays, they record it on sheet of graph paper. The array is to match with colors their group of tiles.

*expand content*

#### Closure

*15 min*

To close this lesson, the students write equations together to describe arrays they have built in their journals. I model for the students writing multiplication sentences to describe a sample array. I want my students to be comfortable writing number sentences for simple arrays. Once they have this skill, they can begin transferring this skill to apply to writing number sentences with an understanding of how the distributive property applies. This requires specific, explicit, step-by-step modeling to help the students combine the two number sentences into one number sentence.

#### Resources

*expand content*

- LESSON 1: Find The Array
- LESSON 2: Combinations Using Multiplication Trees
- LESSON 3: Arrays Focusing On Rows and Columns
- LESSON 4: Understanding Multiplication With Equal Groups
- LESSON 5: Equal Groups: How Many Stars In The Sky?
- LESSON 6: Multiplication Facts With Arrays
- LESSON 7: Solving Multi-Step Word Problems
- LESSON 8: Write A Different Fact Game
- LESSON 9: Multiplication Using The Commutative Property
- LESSON 10: Three Fish Limit Multiplication Word Problem
- LESSON 11: Word Problems With Order of Operations (Day 1 & 2)
- LESSON 12: Target Number Game
- LESSON 13: Patterns In Multiplication (Days 1 - 5)