Warm-up: Which One Doesn’t Belong: More Attributes (10 minutes)
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 one doesn’t belong?
- “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.”
Activity 1: What Makes These Shapes So? (35 minutes)
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.
Advances: Conversing, Representing
Supports accessibility for: Social-Emotional Functioning, Attention
- 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
These are right triangles.
These are not right triangles.
- Which of the following are right triangles? Circle them.
- What makes a shape a right triangle?
These are rectangles.
These are not rectangles.
- Which of the following are rectangles? Circle them.
- What makes a shape a rectangle?
These are rhombuses.
These are not rhombuses.
- Which of the following are rhombuses? Circle them.
- What makes a shape a rhombus?
These are squares.
These are not squares.
- Which of the following are squares? Circle them.
- What makes a shape a square?
- 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.
Display a poster with a labeled rhombus, rectangle, and square.
“Today we learned about the attributes of each one of these quadrilaterals.”
“What are the important attributes of each quadrilateral?” (Rhombuses have sides that are all the same length. Rectangles have sides across from each other that are equal and all the angles are right angles. All the sides are equal and all the angles are right angles in a square.)
Record responses on the poster.
“How are these quadrilaterals alike? How are they different?” (All three of them have 4 sides. The square and the rhombus both have sides that are all the same length. The square and the rectangle both have right angles.)