Partitioning Rectangles and Squares

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SWBAT equally divide rectangles and squares into columns and rows.

Big Idea

In this lesson, students use cube manipulatives to equally explore partitioning of shapes.


5 minutes

I start class by putting a picture of a rectangle underneath my document camera (be sure your rectangle is evenly divisible by whatever manipulative you are using to partition it). 

The cafeteria workers made a huge pan of lasagna for lunch.  They need to figure out how many pieces they can make.  Each piece needs to be this big (I hold up a cube, place value ones block, tile, or piece of construction paper cut into a small square). 

Turn and talk: How can I determine how many pieces of lasagna I have using these materials? 

After students share with their partner, ask a few students to share their ideas with the whole class.  

Students may suggest arranging the cubes inside the shape, tracing the cubes or drawing rows and columns. 

Introduction to New Material

10 minutes

After taking student suggestions, I arrange the cubes, place value blocks, or construction paper rectangles into columns and rows.

After arranging the cubes, I ask the following questions: 

How many columns of brownies do I have? 

How many rows of brownies do I have? 

How many total brownies do I have?

We just divided a shape into rows and columns.  Today we  are going to practice dividing a shape into equal parts. Today we will use cubes to divide shapes.  Tomorrow we will use our pencils to divide shapes by making columns and rows. 

Guided Practice

10 minutes

You are going to work in partners to figure out how to divide some shapes.  You and your partner will each receive a worksheet and a bag of place value cubes. It is very important that you are recording the information on your worksheet and checking your work.

I arrange my class in heterogenous pairs and give each group one bag of cubes and one worksheet.  As students work, I circulate to provide support by asking guiding questions. 

1) How many columns do you have?  How do you know?

2) How many rows do you have?  How do you know?

3) How many total cubes or pieces do you have?

4) What have you done to make sure your work is accurate? 



Independent Practice

15 minutes

Independent Practice is tiered based on understanding of this concept.  I determine groups based on understanding and performance during the guided practice and general mathematical understanding. 

Group A: In need of intervention

Students in Group A will work with me to divide shapes into columns and rows using cubes or place value ones blocks.  Students will notate the number of  columns, rows, and total number of cubes in each shape. 

Group B: Right on track!

Students in Group B will work in partners or alone to divide shapes into columns and rows. Students in this group will have the option to use cubes to divide their shape, but will also be required to draw columns and rows using their pencil (i.e: they can use cubes to set up the problem but then should trace the cubes to show columns and rows). 

Group C: Extension 

Students in group C will work in partners or alone to divide rectangles into columns and rows using only their pencils.  This group will not work with cubes and will be pushed to divide their rectangles using only their knowledge of columns and rows. 



5 minutes

Now that we have worked to divide shapes into columns and rows, I want you to share your first two problems with a partner in your group. 

When students are finished sharing, I ask one person from each group (A/B/C) to share their work with the class using the following sentence stems:

 I divided this shape into______ columns and _____ rows by....

I used this strategy...

I checked my work by...