Grade 3: Patterns 
5 Coins and the Magic Doubling Pot or 1000 Coins
Students explore the choice between taking 1000 coins or starting with 5 coins and using the Magic Doubling Pot 10 times.

Grade 4: Variable 
Variable Machine Lesson
Using a cylindrical "variable machine" to assign numbers from 0 to 25 to the 26 letters of the alphabet, students explore the value of different words, how to maximize and minimize the value of words and how to "set" the machine to get a specific value for a given word, all as a vehicle for helping develop the concept of variable and the linkage of numbers and letters.

Grade 5: Tiles 
Tiling a Patio
Building from previous work exploring patterns and square numbers, this lesson asks students to explore the number of central(brown) tiles and the number of border (white) tiles needed for increasing larger square patios. A key focus of this lesson is finding and analyzing the two different patterns that emerge.

Grade 6: Paving 
Paving Lesson
Building from previous work exploring patterns and linking ttables, verbal rules and symbolic equations, this lesson asks students to explore the number of paving tiles needed to surround a 20 x 20 pool. A key focus of this lesson is the question of what an equation is good for and why a generalization in the form of an explicit rule is valuable.

Grade 7: Graphs 
Graphs: Connections to Other Representations
This 90minute lesson is designed to strengthen understanding of the connections between graphs, tables, ordered pairs and symbolic rules for linear patterns. Building from writing and sharing stories about graphical relationships, students create tables and graphs from linear functions expressed verbally and then create function rules for numerical patterns.

Grade 8: Bridges 
Breaking the Bridge with Pennies
Building from a previous lesson that varied the thickness of a paper "bridge," this lesson is based on the data that students collect on the relationship between the length of a paper "bridge" and the number of pennies that can be supported by the bridge before it collapses. This exploration entails an inverse, nonlinear relationship and helps students connect graphical and tabular representation and use them to make predictions about the breaking weight of other bridges.


The Reflections Project was created through generous contributions by the Duke Energy Corporation.