Activity Description Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs.

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Positive Linear Function Machine

Place in mathematics curriculum:

This activity can be used to:

• practice students' pattern finding skills
• introduce basic notions from algebra
• motivate the idea of a function of one variable
• practice students' arithmetic skills

This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. The function is always a simple line of the following form:



where m, the slope, and b, the y-intercept, can be any integer between 0 and 10. This activity would work well in same ability groups of two to three for about forty-five minutes if you use the exploration questions and ten to fifteen minutes otherwise.

Preparations for this activity:

• answer the question "How do I figure out what the numbers are supposed to be? I don't know how to figure it out."
• discuss pattern recognition, input, output, etc...