The goal of this task is to use the quotient rule of exponents to help explain how to define the expressions c^k for c>0 and k≤0. This important definition is motivated and explained by the law of exponents: adopting the definitions for the expressions c^0 and c^−n given in the task allows us to maintain the intuitive product and quotient rules known for all positive exponents (which this task assumes students are familiar with).

Size, Scales, and Specialization was developed as part of an effort by the Quantitative Biology at Community Colleges group to provide materials that incorporate mathematical concepts into biology courses. The activity uses published estimates of cell type numbers in the human body along with size, density and weight as a lens to have students calculate ratios, explore exponents, and better understand how the various cell types contribute to an average human's total weight and size. The activity is applicable for majors and non-majors biology courses, and maps to Chapter 4 of the OpenStax Biology 2e textbook. This activity could also be used in a mathematics course as a biologically relevant example.

The activity contains a pre-assessment to gauge student understanding of the material and provides an opportunity for students to predict the number of various cell types, as well as the mass of various cell types, in the human body. This prediction activity is followed with a guided approach to calculating these values. After guiding the students in this activity, students will then have a chance to practice the activity on a new set of cell data provided.

After completing this module students should be able to:

- Compare and contrast the structure and function of different cell types.
-- List the largest and the smallest cells in the body based on number.
-- List the largest and the smallest cells in the body based on mass.
- Describe the advantages of specialization in eukaryotic cells.
-- Give examples of how specialization in cell types affects cell size (volume) and shape.
- Perform measurements and conversions using the metric system.
-- Measure the scale of cell size variation in the human body
-- Calculate the relative proportions of cell types in the human body by mass and frequency

This is a summary and example of my experiences and successes "flipping" my Algebra I classroom in the 2012-13 school year. An example of the materials a student would encounter in a given 24 hour period are included.

Laws of Exponents

Product and Quotient Rules
The Power rule for Exponents
Negative and Zero Exponents
Simplify Expressions using the Exponent Rules

This module explores how cell size and shape varies across cell types in the human body by having students calculate relative proportions of numbers in scientific notation. The adaptation has added a review of scientific notation.

In this powerpoint, several of the resources from the published module 'Sizes, Scales and Specialization' are used to create a mini-module that has students examine the size and abundance of different human cell types using scientific notation.

Explore Logarithms in this free video unit. It is comprised of 6 lessons with 4-7 short videos in each lesson. Featuring the reasoning of Grade 8 students, the unit explores exponential and logarithmic properties and their relationship. The videos provide a foundation for the Common Core State Standards about understanding the inverse relationship between exponents and logarithms. Showing these videos may help teachers that want to help students move fluently between exponential and logarithmic expressions.  

This resource introduces the concept of wind chill, the formula used to measure it and relates it to the causes of hypothermia. A simple experiment using a pie pan, sand, fan and a thermometer demonstrates this concept. The resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

In this lesson, students will interact with variables taking the form of limited value exponents and their related functions.

In this activity, learners use basic measurements of the Earth and pieces of rock and iron to estimate the mass of the Earth. Learners will calculate mass, volume, and density, convert units, and employ the water displacement method. To calculate an even more accurate estimate of the mass of the Earth, this resource includes optional instructions on how to measure the iron core mass.