This Warm-up prompts students to compare four shapes split into pieces. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use, such as “halves” and “fourths.”

• Display Shape A.
• “Clare dice que una cuarta parte del rectángulo está sombreada. ¿Están de acuerdo con Clare? ¿Por qué sí o por qué no?“ // “Clare says a fourth of the rectangle is shaded. Do you agree with Clare? Why or why not?” (No because the pieces aren't the same size. The pieces aren't equal.)

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 “cuánto” // “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 “del cuadrado” // “of the square” or “del círculo” // “of the circle.” Monitor for a variety of words and phrases to share in the Activity Synthesis including:

• Phrases that reference the pieces only (“una parte” // “one piece”).
• Phrases that reference that some, but not all, of the shape is shaded (“parte de ella”, “un poco” // “part of it,” “a little bit”).
• Words that name the pieces (“un medio (o una mitad)”, “un cuarto”, “una cuarta parte” // “half,” “fourth,” “quarter”).
• Phrases that name the pieces in reference to the whole shape (“un medio del cuadrado (o una mitad del cuadrado)”, “un cuarto del círculo” // “a half of the square,” “a fourth of the circle”).

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).

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