Students often have difficulty connecting the Cartesian graph of a function to the actual motion of the variables. Their challenge in visualizing and describing covariation (the way y varies as x varies steadily) relates to their understanding of function families: function families are distinguished by the nature of their covariation. A function whose growth rate remains constant … Continue Reading ››
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A Triple Number Line Model for Visualizing Solutions to Equations
In Algebra 1, I was the king of solving for x. Algebraic manipulation was fun and satisfying, and I was good at it. But my confidence was shaken when I encountered a test question of the variety 4x + 5 = 4x – 3. After subtracting 4x from both sides, I was … Continue Reading ››