Lesson 6

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.

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

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

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).

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

• 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.

• “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

• “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.

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.

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

• 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.”

• 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.

• 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.)