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Number Sense: Grade 8

Hook 1 8.NS.A.1

Prompt: What is an irrational number?

It may be helpful, especially for students new to inquiry, to set some expectations. For instance, ask student groups to write down three observations they can make from reviewing the table before they attempt to define an irrational number. By asking students for proof before answers, you will be teaching them how to be a mathematician and modeling the work mathematicians do. This expectation prevents the exercise from becoming a guessing game where students blurt out answers in the hope of being right and avoiding more rigorous thinking. As they discuss their findings, students will grow to value "proof" in their answers and increase their stamina and capabilities in their problem solving skills. It may be helpful to provide calculators to your students for this problem. This will allow them to focus on their observations rather than getting bogged down in calculations. In the end, when students recognize irrational numbers are created by non-repeating decimals (either on their own or in class discussion), they will have an easier time digesting the formal definition of irrational numbers and a strategy to differentiating between rational and irrational numbers.

Video: What Pi sounds like (3:23)

Hook 1 8.NS.A.2

Prompt: What is the side length of the purple square?

In my experience teaching 8th grade, this standard, for many students, is the most difficult concept to grasp. Often, this is, in part, due to their lack of mastery of multiplication facts but I believe it's more than just that. 8th graders really struggle with the concept of a square root. Therefore, constructing this understanding from the base of students' prior knowledge of squares and their areas offers students a solid foundation from which they can build. A number line labeled from 1 to 12 on the bottom, which is also labeled with square root values on top (i.e. square root of 4 above the 2), is a helpful tool to utilize alongside square models.

Video: Square Root Farmers (2:16)