Notes & FAQs

This unit should be taught holistically and the three topics of Roots, Pythagorean Theorem, and Volume should be interconnected and weaved together so that students are able to see how all three of these things relate to one another and connect to the prior unit of essential learning with exponents & scientific notation. For example, finding the radius of the circle in a cylinder or cone is an application of square roots and finding the radius of a sphere is an application of cube roots while finding the length of the side of a triangle is also an application of square roots; when the radius or side length is irrational, you have the perfect confluence of 8th grade number system, expression & equation, and geometry standards.

Please note this is the students’ first experience with square roots and cube roots under the 2013 state standards.  Help students understand square roots by connecting them to the power of two forming a square with the root being the length of the side.  Likewise, connect cube roots with the power of three forming a cube and the root being the length of the side. 

The team wanted to highlight that within the item specifications the expectation is that students are able to know from memory the formulas listed; however, they believe that it would be in the student’s best interest to assess their ability to calculate using a formula separate from the student's ability to recall from memory the formula, which is why there are two separate learning goals written.  Recalling a formula from memory does not necessarily imply memorization of formulas; care should be taken to have students explore the relationship between the formulas in question and other simpler formulas.  Students may not be able to remember “the formula,” but might be able to produce it if they have learned the relationships conceptually.  For example, if I know a cylinder is simply a “stack of circles”, then I may be able to produce the formula for a cylinder.  See the work of Kyle Pierce from tapintoteenminds.com for more on the relationship between cylinders, cones & spheres. 

These chapters are traditionally at the very end of the Big Ideas textbook; however, this unit covers several targets. This unit covers several of the major essential pieces of learning that should be covered in 8th grade that are used in future grades. The task force thought that this unit would cover enough topics to be a major focus of the first half of the school year.