I keep trying to find activities for my kinesthetic learners. This activity helped students to actually "DO" the math. There were some definite ahah moments for some of my students. I took out some pipe cleaners and handed them out to my pre-calculus class. Pipe cleaners are great for teaching transformations of graphs. Students had to physically move the graph up, down, left or right. We predicted shifts and we found multiple answers to graphs. See below. 1. Either have your student make their own scale on a piece of paper or hand out a scale for your students. 2. With the paper scale in hand, ask them to make a certain graph. I asked my students to make a y = sin x graph. They proceeded to bend the pipe cleaner into a sign wave. The graph could be a parabola, or cubic or even a line. 3. Then I asked them to shift the graph up. Explain what the new equation would be. For my class I then had them shift the graph to the left until it turned out to be the same graph as the original. They shifted it over one period. we found our new equation to be y = sin(x-2π) 4. Have them shift it left or right and predict the new equation 5. Have them move the pipe cleaner into a certain location and then ask for an equation. 6. Ask them to reflect the pipe cleaner over an axis or the origin. Here are some of the things we graphed and explored in my pre-calculus class. Find 5 other graphs that are equivalent to y = sin(x+2π)including at least 1 cosine graph. Find 3 other graphs including at least 2 sine graphs equivalent to y = cos(x) Graph y = cos(x-π)+1 Graph y = -sin(x+2π) Give it a try and let me know how it goes. All the Best, Dave