The purpose of this activity is to introduce the language of “a half of” and ”a fourth of” a shape. Students begin by applying the language of halves and fourths, or quarters, to partition each shape. Students are asked to describe “how much” of each shape is shaded to elicit a variety of responses that include the terms half and fourth, or “quarter,” along with the phrases “of the square” or “of the circle.” Monitor for a variety of words and phrases to share in the Activity Synthesis including:

• Phrases that reference the pieces only (“one piece”).
• Phrases that reference that some, but not all, of the shape is shaded (“part of it,” “a little bit”).
• Words that name the pieces (“half,” “fourth,” "quarter”).
• Phrases that name the pieces in reference to the whole shape (“a half of the square,” “a fourth of the circle”).

• Invite previously identified students to share for each problem. Sequence the students in the order described in the narrative.
• “One piece of a shape that is split into two equal parts is called a half. One piece of a shape that is split into four equal parts is called a fourth.”
• For each shape, invite students to describe how much is colored. (Half of the square is colored. A fourth of the circle is colored.)

The purpose of this card sort is for students to connect words and phrases to visual representations of partitioned shapes. Students begin by sorting the cards in a way that makes sense to them. They are invited to sort the shapes, based on the language that can be used to describe them. In the Activity Synthesis, the phrases “two halves” and “four fourths” are introduced to describe shapes where all pieces are shaded. This sorting task gives students opportunities to analyze the number and size of pieces closely and make connections (MP7).

Keep Cards D and N available to use during the Lesson Synthesis.

As students sort the shape cards they look for structure, namely the number of pieces making up each shape, whether or not the pieces are equal, and the number of those pieces that are shaded (MP7).

• Display Card J.
• “How can we describe this shape?” (It is a square. It is cut into halves. The whole shape is shaded.)
• “When a shape is split into halves and both halves are shaded, we say the whole shape is shaded or two halves are shaded.”
• Repeat with Card E.
• “When a shape is split into fourths and all fourths are shaded, we say the whole shape is shaded or four fourths are shaded.”

The purpose of this activity is for students to match language to visual representations of rectangles and circles partitioned and shaded in different ways. 

• Display the circle with four fourths shaded. 
• “Let’s list all the ways we could describe this shape.” (It’s split into fourths. It is split into quarters. Four fourths are shaded.)
• Repeat with other shapes as time permits.