Partitioning Squares to create rectangles

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SWBAT divide squares to create equal rectangles.

Big Idea

Students take what they know about equal shapes and explore dividing squares into equal rectangles.


10 minutes

Yesterday we talked about dividing a square into equal triangles.   Today we are going to work on dividing a square into equal rectangles.

I hand out one construction paper square to each student. 

You have thirty seconds to fold this square into equal rectangles.  (Students should feel free to divide their square into as many rectangles as they want/can) 

Now, share your shape with a friend and explain how you know that your square has equal parts.

 I allow students to share. When finished, I have one or two students share their work with the class—I make sure that they explain how they know that their pieces are equal. 

Introduction to New Material

10 minutes

Now, I want you to fold your square into four equal  rectangles (some students may have already folded their shapes into fourths, but allow others to do so quickly).

Turn and Talk:  What strategies did you use to divide your square into four equal parts?

I allow students to share out and I write those strategies on the board or on chart paper. When finished, I have two students who folded their shapes differently share their work with the class. (Some students might make four long rectangles by making three horizontal folds, others might divide it into four rectangles (squares in this case) by making one horizontal fold and one vertical fold). 

NOTE: This lesson does not discuss how the area of a square divided into rectangular fourths or square fourths have the same area--this will be covered in the next lesson. 

Guided Practice

15 minutes

We are going to work on dividing squares into equal rectangles.  You will receive two pieces of paper.  Using your pencil and your scissors, you will cut your colored paper into four EQUAL rectangles.   Then, you will paste your colored rectangles onto the white square.

As students work, I circulate to determine student understanding and support students who are struggling.  I ask the following guiding questions:

1) How do you know that your rectangles are equal?

2) Could you divide this into a different number of equal rectangles? How would you do that?

Independent Practice

10 minutes

During independent practice, students will answer reflection questions about the square that they just partitioned into rectangles.

As students work, I will circulate to check for understanding and push students to explain their thinking clearly.  


5 minutes

During the closing students will share their work from the guided practice and independent practice with a teammate, explaining how they divided their squares and explaining how they know that their shapes are divided equally.  

I give students the following sentence stems before they begin to share:

I divided my shape by...

I know my rectangles are equal because...

My rectangles are similar to yours because________ and different because_________

Another way I could have divided my square is...