A Number Talk encourages students to look for structure and relationships that can help them reason about expressions. This activity puts students in the mindset of a Number Talk writer. It prompts them to anticipate some ways that others might decompose, rearrange, and compose numbers, or to otherwise make use of structure to find the value of an expression. The work here will be helpful as students consider the numbers and numerical relationships to use as they write their own expressions later.

• Invite students to share their mental computation strategies. Collect and record as many strategies as time permits.
• If no students mentioned making use of one or more preceding expressions in their mental computation, ask them how it could be done. (See Student Responses for examples.)
• Select a couple of students to share their new expressions. Ask the class to find the value of each expression mentally.

In this activity, students use their understanding of place value and knowledge of operations on numbers to write new multiplication and division expressions. Students study the given expressions and their relationships, and consider how they could find the value of each expression mentally. Next, they propose new expressions to complete each Number Talk.

• Select students, who reasoned differently, to share their expressions. Record each set.
• Ask the class to determine the reasoning behind the new expression(s), and ask the writers to respond to the feedback.
• “How might the second expression help someone find the value of the third expression?”
• “How might the third expression help someone find the value of the fourth?”

In this optional activity, students are given four expressions—three expressions involve operations of two whole numbers and one involves multiplication of a whole number and a fraction. Students choose one expression and write three new ones to create a Number Talk activity.

Students have considerably more freedom to decide the direction of subsequent expressions, but should be just as prepared to explain the rationale behind their expressions. Expect the increased openness to be a greater cognitive lift for students.

For the Activity Synthesis, ask each group of 2 students to test their set by presenting it to another group and attending to how others reason about their expressions.

• “Work with another group and take turns presenting your Number Talk.”
• “Show one expression at a time. Move on only after an answer and an explanation are given. Record their reasoning.”
• After students have a chance to test their Number Talk, discuss questions such as:
  • “Did others reason in a way you anticipated?”
  • “Were there expressions that you’d revise?”