The purpose of this activity is for students to think about cube roots of numbers in relation to the two integer values they are closest to. Students are encouraged to use the fact that is a solution to the equation . Students can draw a number line if that helps them reason about the magnitude of the given cube roots, but this is not required. 

Monitor for students that multiply non-integers by hand to try and approximate. While this isn’t the preferred strategy, their work could be used to think about which integer the cube root is closest to during the Activity Synthesis.

The purpose of this discussion is for students to share the strategies they used to approximate cube roots by looking at perfect cubes. For each question, ask 1–2 students:

• “What strategy did you use to figure out the two whole numbers?” (I made a list of perfect cubes and then found which two the number was between.)

During the discussion, make a class display of perfect cubes up to at least , or add them to the existing display of perfect squares. This display should be posted in the classroom for the remaining lessons within this unit.

In this activity, students use rational approximations of irrational numbers to place both rational and irrational numbers on a number line. This reinforces the definition of a cube root as a solution to the equation of the form . This is also the first time that students are asked to think about negative cube roots. 

The purpose of this discussion is to make sure students understand how they can use rational numbers to approximate irrational numbers. Display the number line from the Task Statement for all to see. Select 1–2 groups to share their reasoning for each value placement and record their values on the displayed number line. After each placement, ask if any students used different reasoning and invite them to share with the class.