# Lesson 6

Rectangles and Squares

## Warm-up: Number Talk: Some Sums (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding 2 two-digit numbers within 100. Students continue to develop their understanding of place value and how it can be used when adding numbers. This warm-up encourages students to choose methods that they can use to add larger numbers mentally, such as adding by place value.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$57 + 10$$
• $$57 + 11$$
• $$57 + 21$$
• $$57 + 42$$

### Activity Synthesis

• “Did anyone approach the problem in a different way?”
• “How can you use the problem before to help you solve this one?”

## Activity 1: Rectangles and Squares (20 minutes)

### Narrative

The purpose of this activity is for students to identify defining and non-defining attributes of rectangles and squares. Students begin by noticing what is the same about four rectangles (one being a square). As they notice, they identify some defining attributes (four sides, four square corners, pairs of sides that are the same length). Then given non-examples of rectangles, students notice what makes the non-examples different from examples. Some, but not all, of the attributes students mention will be defining attributes. For example, students may notice that a rectangle has two long sides and two short sides, but this isn't a defining attribute.

In the synthesis, students identify squares and rectangles from their card set and the teacher supports students in developing statements about the defining attributes of these shapes. This gives students an opportunity to use language precisely to distinguish squares and rectangles (MP6).

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs a set of Flat Shape Cards from a previous lesson.

### Launch

• Groups of 2
• Display the first question.
• “These are rectangles. What do you notice about them?“ (I notice a square. I notice that one is colored in. They all have four sides and four corners. Sometimes there are two pairs of sides with the same length.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Why do you think a square is with these rectangles?“ (It has four straight sides, four square corners, and it's closed, so it is a rectangle.)
• Display the next question, keeping the first question visible.
• “These are ‘not rectangles.’ What makes the ‘not rectangles’ different from the rectangles?” (One has a flat corner instead of pointy. One has a line that sticks out. One doesn't have square corners.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “We saw that a square is a type of rectangle. Now you are going think about ‘squares’ and ‘not squares.’ Write your thinking in your book. Think about each question on your own, then share your thinking with your partner.”
• 5 minutes: partner work time

### Student Facing

1. These are rectangles.

What is the same about all these rectangles?

2. These are not rectangles.

What makes these shapes different from the rectangles?

3. These are squares.

What is the same about all these squares?

4. These are not squares.

What makes these shapes different from the squares?

### Activity Synthesis

• “What did you notice about the squares? What is the same about them?”
• “What makes the ‘not squares’ different from squares?”
• Give each group a set of shape cards from previous lessons.
• “Work with your partner to sort your shape cards into the categories of ‘rectangles,’ and ‘not rectangles.’”
• Share responses.

## Activity 2: Draw Rectangles and Squares (15 minutes)

### Narrative

The purpose of this activity is for students to draw squares and rectangles. Students use dot paper to draw the shapes. As they draw, they attend to the attributes of squares and rectangles. Students also draw shapes that are not rectangles or squares. They may use the shape cards to visualize and draw shapes.

MLR7 Compare and Connect. Synthesis: After all the student-drawn shapes have been presented, lead a discussion comparing, contrasting, and connecting the different shapes. Ask, “What do the shapes have in common?” and “How are they different?”
Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing on paper: students can share their learning orally or using pictures.
Supports accessibility for: Language, Conceptual Understanding

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Dot Paper - Standard

### Required Preparation

• Each group of 2 needs a set of Flat Shape Cards from the previous activity.

### Launch

• Groups of 2
• Give each group a set of flat shape cards and two pieces of dot paper.
• “Now, we’ll practice drawing. You will draw examples and non-examples of rectangles then squares. As you draw the shapes, think about how you know they are examples or non-examples. You may use the shape cards to help you.”

### Activity

• 8 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for examples and non-examples of rectangles. Have students record shapes on a chart to display during the synthesis. Be sure to include a square.

### Student Facing

1. Draw 5 rectangles.

How do you know these are rectangles?

2. Draw 3 shapes that are not rectangles.

How do you know these are not rectangles?

3. Draw 5 squares.

How do you know these are squares?

4. Draw 3 shapes that are not squares.

How do you know these are not squares?

### Activity Synthesis

• Display the chart of student-drawn shapes.
• “Which of these shapes are rectangles and which are not rectangles? How do you know?” (Rectangles have four sides and four square corners.)
• Circle each rectangle students identify.
• When students identify the square, ask:
• “How many sides does it have?” (4)
• “How many corners does it have?” (4)
• “Is a square an example of a rectangle?” (Yes, because it has four straight sides and four square corners.)

## Lesson Synthesis

### Lesson Synthesis

“Today we learned about squares and rectangles.”

”What is true about all rectangles?” (Rectangles have four straight sides, four square corners, all sides touch, and opposite sides are the same length.)

“What is true about some rectangles, but not all rectangles?” (They can be colored in. They can have two sides that are really long and two sides that are short. They can have sides that are all the same size, like squares.)