Equal Parts

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Objective

SWBAT break a square into equal parts.

Big Idea

Students explore how to break a square into equal parts. This is the first lesson in a series of lessons that preview fractions for 3rd grade.

Introduction to New Material

15 minutes

 I start class by giving my students a worksheet inside a sheet protector and a white board marker. The worksheet has two squares printed on it. 

I want you to divide square A into four equal squares using your marker.  I want you to divide square B into four equal triangles using your marker.

I allow students about 1 minute to work.  As students work, I draw two large squares on the board.  After students have finished working, I ask two students to come up and neatly divide the squares on the board into four equal triangles and four equal squares. 

These squares were just divided into EQUAL parts.  What does it mean to have EQUAL parts?

Students will likely respond that being equal sized means that the pieces are all the same size.

Now, I want you to shade in one equal part of the square divided into rectangles and one equal part of the square divided into triangles.

As students shade, I shade in one piece of each of the squares on the board.  

Now, I have a question: does this triangle take up the same amount of space as this rectangle?   Turn to your partner and discuss this question.

Students will likely say that the two shapes do not take up the same amount of space since the shapes are different sizes.  When students respond like this,  I push my students to think further about this question:  

Are the squares the same size?

Are the rectangles all the same size?  Are the triangles all the same size?

What fraction of each of these squares is shaded? 

Now that we know that each of these squares is the same size, and that each piece is equal sized, let's think about the question again: 

Does this triangle take up the same amount of space as this rectangle?   Turn to your partner and discuss this question.

Students should be able to recognize that the shaded rectangle is one fourth of this square and the shaded triangle is one fourth of this square.  Even though the shapes are different sized, they take up the same amount of space since they represent one fourth of the square. To really understand this concretely, you could take the triangular fourth, cut in in half, and put it back together as a square that would exactly match the square fourth

Guided Practice

10 minutes

During the guided practice, students will cut out two squares and divide them into equal triangles and squares. This will allow them to compare the sizes and dig into how the shapes are equal sizes even if they are not the same shape.  hey will then place those cutouts on a square and answer reflection questions that are similar to the discussion questions from the introduction to the new material. (See: student work sample)

Independent Practice

15 minutes

During the independent practice students will work on a problem where they divide a shape into equal parts and then answer questions about whether the halves are equal.  

As students work, I circulate and ask guiding questions:

1) How do you know that the shapes are equal sized?

2) How do these shapes take up the same amount of space if one is a triangle and one is a rectangle?

3)  What fraction did you divide the shape into? 

Closing Discussion

10 minutes

When students are finished with the worksheet, I bring my class back together and we have a class discussion about the worksheets:

1) How do you know that the shapes are equal sized?   

2) How do these shapes take up the same amount of space if one is a triangle and one is a rectangle?