How Many Brownies Do I Have? : Partitioning Rectangles into Columns and Rows

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Objective

SWBAT equally divide squares and rectangles using columns and rows.

Big Idea

Students use their knowledge of columns and rows to equally divide squares and rectangles.

Hook

5 minutes

Last night, I had some friends over for dinner.  I made brownies for dessert.  In order for everyone to have enough, I divided my brownies into four columns and three rows. 

I draw a large rectangle on the board or post a picture of a pan of brownies. 

If this rectangle is my pan of brownies, how should I cut it to make four columns and three rows?  Turn and tell your partner how I can divide this pan into four columns and three rows. Each piece needs to be the same size. 

I allow students 30 seconds- 1 minute to discuss the question.  When finished, I have 1-2 partners share out their ideas. 

Introduction to New Material

10 minutes

When students are finished sharing, I have 2-3 students come to the board and draw how they would divide the shape.  I make sure students are checking their work to determine that they drew the correct number of columns/rows and that the shapes are the same size. 

NOTE: Some students might think that they need to draw 3  lines to make 3 rows and 4 lines to make 4 columns.  When students do that, I ask them to check their work and discuss ways to make their work more accurate.

When finished with this discussion, I ask students: How many total brownies do I have? How do you know?

Have students share their strategies for how to determine the total number of pieces (some students  may count by ones, other by groups, while others may multiply, etc.)

When finished, hand out white boards and have students work on another practice problem.  

I have a  rectangular birthday cake.  I need to divide it into three columns and two rows.  How should I divide the cake? 

As students work, I circulate to check for understanding.  When students have finished, I have one or two share their work, pointing out their columns and rows and explaining how many total pieces my birthday cake has. 

Guided Practice

15 minutes

We are going to practice dividing shapes in stations.  At each station, there is a shape that needs to be divided, along with instructions about how many rows and columns you need to create.  You are your partner will work independently to divide the shape and then check your work with your partner.  We will switch stations every five minutes.

Every station should be equipped with dry erase markers for every student and enough of the shape sheets so that every student can be working.  As students work, I circulate to check in on students, especially those who did not show mastery during the introduction to new material. 

(Note: if you don’t want to do this as centers, you can simply hand out the sheets in  a packet and have students do the work as partner work--I chose to have students do this activity in centers to get them moving and allow them to work collaboratively).

 

Independent Practice

15 minutes

During independent practice, students will work alone (or in partners) to solve problems where they partition shapes.  

As students work, I will circulate to check in with students and make sure that they are completing accurate work.  

I will ask the following guiding questions: 

(1) How many lines did you draw to make ______ columns/ rows?

(2) What are you doing to make sure that your work is accurate?/ How did you check your work?

(3) How can you fix this rectangle to make sure that is has the correct number of columns/ rows? 

Closing

5 minutes

Now that you have worked independently to divide shapes using columns and rows, I want two or three students to share out their work.  As you share, I want you to explain what strategies you used to divide your shape.