Unit 3: Exponents with Scientific Notation

The big idea of this unit is identifying and generating equivalent expressions utilizing exponent rules.  The meaning of exponents can be reengaged first to provide a foundation for students discovering these rules rather than simply telling them what they are and having them memorize them (see note on M8.U3.1a).  This unit introduces the meaning of a zero exponent and a negative exponent for the first time.  A simple paper folding activity with an accompanying T-chart (# of layers dependent on # of folds) proposed by Brad Fulton is an excellent way to introduce these two new ideas using powers of 2.  Simply learning these rules is not enough; the key is to be able to recognize and generate equivalent expressions in all their forms, not just the simplified form.  Scientific notation is a chance to apply learning in a new context to ensure transfer and provide an opportunity for reengagement for those who have not yet learned it.  The design team recommends collaborating with science teachers to decide what & how much work around scientific notation will be covered by each course.  Depth is further explored by comparing the size of numbers to one another and using them to estimate values as well as extending exponent rules to algebraic expressions in preparation for Algebra 1.  Additional depth can be found by extending the Power of a Power rule to Power of a Product and Power of a Quotient rules explicitly as well as engaging in a level 4 understanding of scientific notation, using scientific notation and choosing units of appropriate size for realistic measurements. 

The work on integer exponents here prepares students for the next unit and exponential functions in Algebra 1.  Time should be spent examining visual models of x (length), x^2 (area) & x^3 (volume).  Exponents in base 10 are covered in 5th grade & any base in 6th grade so reengagement may be necessary.  The design team recommends collaborating with science teachers to decide what & how much work around scientific notation will be covered by each course.