Lesson 5

This Number Talk prompts students to rely on properties of operations and the relationship between multiplication and division to divide within 100. The reasoning here helps students develop fluency in division.

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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How did you use facts you know to find facts you didn’t know?” (I used \(70\div7\) and thought about one more group to find \(77\div7\). I used \(70\div7\) and one less group to find \(63\div7\).)

The purpose of this activity is to deepen students’ understanding that a shape can belong to multiple categories because of its attributes. Students analyze shapes and determine all the ways that each one could be named. The names may refer to a broad category such as triangle or quadrilateral, or a narrower subcategory such as rhombus or rectangle. As they name the different categories students need to be precise both about the meaning of the categories and verifying the properties of the different shapes (MP6).

• Groups of 2
• “Look at the quadrilateral in the first problem. Work independently to circle all the names that you could use to describe the quadrilateral. Be prepared to share your reasoning.”
• 1 minute: independent work time
• “Discuss your responses and reasoning with your partner.”
• 2 minutes: partner discussion
• Share responses.

• “Complete the rest of the problems independently. Be prepared to explain your reasoning.”
• 3–5 minutes: independent work time
• “Now, discuss your answers with your partner. Be sure to explain your reasoning for each way you described the shape. Also, be sure to ask your partner if you have any questions about their reasoning.”
• 5–7 minutes: partner discussion
• Monitor for students who notice that some shapes can be described using multiple terms.

If students use only one name for a shape that can be named in multiple ways, consider asking:

• “How did you describe the shape?”
• “Are there any other names that could be used to describe the shape?”

• Select 1–2 students to share the terms they selected for each of the last four quadrilaterals and their reasoning.
• Consider asking:
  • “Who can restate _____’s reasoning in a different way?”
  • “Does anyone want to add on to _____’s reasoning?”
  • “Do you agree or disagree? Why?”
• “The last shape can be described with 4 of the choices. How is it possible that it can be described in so many ways?” (It is a quadrilateral because it has 4 sides. It is a rhombus because it’s a quadrilateral with 4 sides that are the same length. It is a rectangle because it has 4 right angles and 2 pairs of sides that are the same length. It is a square because it has 4 sides that are the same length and 4 right angles. The last three are more specific descriptions of a quadrilateral.)

The purpose of this activity is for students to apply what they know about the defining attributes of rectangles, rhombuses, and squares to draw shapes that are not those quadrilaterals. They use geometric attributes to explain why their drawings meet the criteria.

• Groups of 2
• “Take a minute and think about how you could draw a shape for each one of these descriptions.”
• 1 minute: quiet think time

• “Now, work with your partner to draw a shape for each statement. Be ready to explain how you know each shape matches the description given.”
• 7–10 minutes: partner work time

• Select students to share their drawings and explanations for the first three problems.
• Highlight explanations that include the defining attributes of squares, rectangles, and rhombuses.
• Invite students to share as many different quadrilaterals as they can think of for the last problem. Display as many as possible.