November 11, 2016

This is a multi-day instructional unit for middle school science on kinetic and potential energy. Through investigations of waterwheels, roller coasters, bouncing balls, and a pendulum, students get a feel for energy transformation in a mechanical interaction and build accurate concepts about the Law of Conservation of Energy. The unit also introduces static and kinetic friction, drag, elastic/inelastic collision, and students learn to calculate frictional force. Lessons are all aligned to AAAS Benchmarks, and may be conducted separately or in concert. Editor's Note: Understanding mechanical energy is at the root of many engineering applications in our world. This set of lessons provides inquiry-based exploration, while also introducing simple calculations in the context of real-life situations. It is developmentally appropriate for middle school, but will definitely challenge students. TeachEngineering is a Pathway project of the National Science Digital Library. It provides a large collection of teacher-tested, research-based content for K-12 teachers to connect real-world experiences with curricular content.

- Education > General

- Grade 1
- Grade 2
- Grade 3
- Grade 4
- Grade 5
- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10
- Grade 11
- Grade 12

Make sense of problems and persevere in solving them.

Understand ratio concepts and use ratio reasoning to solve problems.

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Solve unit rate problems including those involving unit pricing and constant speed.

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Recognize and represent proportional relationships between quantities.

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write, read, and evaluate expressions in which letters stand for numbers.

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Reason about and solve one-variable equations and inequalities.

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Solve linear equations in one variable.

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Define, evaluate, and compare functions.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Use functions to model relationships between quantities.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.