Partitioning squares to create triangles

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Objective

SWBAT partition squares into same-size triangles.

Big Idea

Students learn about equal shapes and then explore dividing squares to make equal triangles.

Hook

10 minutes

I start class by handing every student a paper square.  I ask them to fold it to make triangles.  I then allow students a minute to experiment with dividing their squares into triangles.

Turn and talk: Share how you folded your shape with your partner.  How is your partners shape similar or different from yours?

Before students share, I introduce the following sentence stems:

I folded my square into triangles by…

My shape is similar to yours because___________  My shape is different from yours because___________.

I allow students to share their shapes.  When finished, I ask one or two students to share out how they and their partner made their square into triangles AND how their triangles are similar and/or different.   

Introduction to New Material

10 minutes

Today we are going to learn how to divide a shape into EQUAL triangles.  Equal means that each triangle is the same size.

Turn and talk: are the triangles in your shape EQUAL?  How do you know?

I have one student with an equally divided shape (2, 4, or 8 triangles) share out and one student who does not have equally divided shapes share out, explaining WHY their shapes are equal/unequal.

I draw a square on the board and divide it into unequal triangles (i.e: I draw three triangles)

Turn and talk:  Are these equal or not equal?  How do you know?

Students should be able to identify the unequally divided shapes as not equal because not every triangle is the same size.

I draw another square on the board.

I need someone to come up and divide this shape into EQUAL triangles (student could divide the shape into 2, 4, 8, or 16 triangles)

After student has divided the shape into triangles,  I ask:

Turn and talk: Are the triangles in this square equal sized?  How do you know?

(Depending on student attention and ability, this might be a good time to start discussing fractions). 

Are there any other ways that we can divide this square into triangles? 

Turn and talk: are the triangles in this square equal sized?  How do you know?

Guided Practice

10 minutes

We are going to work on dividing shapes into equal triangles.  You will receive two pieces of paper.  Using your pencil and your scissors, you will cut your colored paper into four EQUAL triangles.  Then, you will paste your colored triangles 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 triangles are equal?

2) Could you divide this into a different number of equal triangles? 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 triangles.  

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

Closing

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 triangles are equal because...

My triangles are similar to yours because________ and different because_________