Lesson 4

This warm-up prompts students to compare four shapes. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about the characteristics of the items in comparison to one another. During the synthesis, emphasize that three of the shapes are quadrilaterals, even though they look very different.

• Groups of 2
• Display the images.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “Which shapes are quadrilaterals? How do you know?” (A, B, and D. They all have four sides.)
• “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to identify the attributes that make a quadrilateral a rectangle, a rhombus, or a square. They do so by studying examples and non-examples, looking for features that each set has in common and drawing conclusions accordingly (MP7). The goal is not to craft the most precise definition for each, but to develop an understanding of the defining geometric attributes.

• Create a chart with labels showing a rectangle, rhombus, and square for the lesson synthesis.

• Groups of 2–3
• Display the examples and non-examples of right triangles.
• “The triangles on the left are right triangles. The ones on the right are not. Take a minute to think about their differences.”
• “Then, choose all the shapes that are right triangles from the set labeled A–H. Write down what you think makes a shape a right triangle.”
• 1–2 minutes: quiet think time
• 1–2 minutes: partner discussion
• Share responses.
• “All triangles on the left and triangle E in the set are right angles. A triangle with a right angle is a right triangle.”

• “Work with your group to analyze what makes a shape a rectangle, a rhombus, or a square. Each group will look at one type of quadrilateral.”
• Assign each group one quadrilateral to analyze.
• 3–5 minutes: small-group work time
• “Now, share your work with another group that worked on the same quadrilateral. Be sure to ask any questions you have about each other’s work.”
• 3–5 minutes: small-group discussion

• Invite 1–2 groups who analyzed rectangles to share their responses. Record their responses.
• Ask the class:
  • “Do you agree with the shapes that are marked as rectangles (or rhombuses or squares)?”
  • “Do you agree with the descriptions?”
  • “Is there any part of the descriptions you’d say differently?”
  • “Is there anything you'd add to the description?”
• When students have finished describing rectangles, highlight that: “A shape is a rectangle only if it is a quadrilateral with only right angles, and the sides that are across from each other are the same length.”
• Repeat the discussion with rhombuses and squares.