# Introducing Subtraction

What if you built a rule that would enable you to count backwards? How would it be the opposite of addition? What would happen if it goes past zero?

# Graphing

Graphs as we know them were first invented by Galileo. They are powerful images of functions. I will introduce you to graphs by letting you graph different functions represented by a table. Fill in each table visualize its graph.

# Motion Problems

George is in New York and Martha is in Washington. They leave at the same time and follow the same road to meet each other on the way. The distance between New York and Washington is 229 miles. George has a fast horse and averages 16 miles/hr. Martha has a slow carriage and averages 7 miles/hr. How far will George have gone when they meet?

# Make a Hundreds Table

This is the graduation exercise for the basic use of spreadsheets. We combine rules and addressing to have students build their own hundreds table in the fewest steps. There are many ways of doing this and students can be as creative and exploratory as they want. Nor should they feel limited to tables that start at 1 and go to 100. These rules, these patterns should enable them to start anywhere and build any size table they can imagine. We strongly encourage students to stretch their minds here and to think outside of this box.

# Build a Times Table

Students are tasked to build a times table in just two steps. They have to learn to use absolute as well as relative addressing to do, and the Lab takes them through using them. We encourage students to work with just a row or a column rather than with the table as a whole because doing so makes it easier to see what is wrong or what does not follow the pattern. We believe students should learn to struggle to solve problems and that persistence, patience, and grit are important for all of us to have. We therefore do not want to tell students how to do something but rather to let them explore and try and keep at it until they get it. Spreadsheets with their openness and feedback provide a great opportunity for doing this in Labs like this. It is one of our favorites.