Halves

I start this lesson by reading aloud, “Give Me Half” (the YouTube version can be found here: Give Me Half).  I like to begin this lesson with this read aloud because it not only introduces the concept of halves and wholes, but it is based around the concept of sharing a pizza.  Sharing is something that all students can relate to and can easily understand.

After reading the story, I demonstrate how to fold a shape to show one whole and two halves using the student cut outs.  I then have them cut out the shapes from the Halves_student cutouts.docx and have them practice folding the shapes in half.

For children to understand halves (1.G.A.3), they must understand that a shape in itself is a whole. When a whole has two equal parts, these equal parts are called halves.  Folding a two-dimensional shape helps children see one whole and two halves. Without measuring and counting, children can tell if the parts made by folding are fair shares or not.  I like to encourage children to use words such as fair shares, one whole or one, and the name halves. Using the language of fractions with geometric models helps children establish their understanding of fractional parts (MP6).

I then draw two large rectangles on the board. I call on two children to divide one rectangle into two equal parts and the other rectangle into two unequal parts. Discuss each pair of drawings.

• Which drawing shows equal parts? How do you know? 
• How do you know that the other drawing shows unequal parts? 

I then display the first slide of the Halves.ppt and read the following problem aloud:

Two friends share the sandwich on the left. How can they cut the sandwich so each gets an equal share?

• How many equal shares do you need?  (2)

I have a volunteer draw a line to divide the sandwich into two equal shares.

• Now look at the whole sandwich. How can you describe its shares? (The whole sandwich is made up of two equal shares.)

I continue by reading the following problem:

Two other friends share the sandwich on the right. How could this sandwich be cut a different way so each friend gets an equal share?

If children drew a vertical line in the first sandwich, I would encourage them to draw a horizontal line or a diagonal line to show equal shares in the second sandwich.

• When you cut a shape into equal shares, is each share bigger or smaller than the whole. Explain. (Each share is smaller than the whole because you are cutting it up to share.)

Next I display the second slide of the Halves.ppt and work through the model with children.

• How many equal shares are shown? 2
• How many halves are shown? 2
• How many halves make 1 whole? 2

I emphasize that when a shape has two equal shares, the equal shares are called halves, and each individual share is called a half (MP6).

I then display the third slide of the PPT, which also corresponds with the first few problems of the Halves_worksheet.docx.  I have children notice that the same shape is shown in questions 1 and 2, and the same shape is shown in questions 3 and 4. I encourage children to show halves for the same shape in a different way. Once children complete questions 1–4, I ask the following question.

• Is there more than one way to show halves on a shape? Explain.  (Yes. As long as the two parts are equal, the line can go in different places.)

Next, once students have understood the concept of equal shares, I release them to complete the worksheet independently. 

In this picture, you can see a student who has successfully mastered the concept of what is half of a circle or rectangle: