Over the duration of six weeks, we worked in a math unit called "Shadows." During the unit, we worked to solve the unit problem, which was to find a formula for how long a shadow was. When first given the unit problem, I considered it a simple task but soon after I realized there were many steps and ideas that needed to be learned before the unit goal could be reached. Throughout these six weeks, we learned about trigonometry, similarity, patterns, congruency, and using angles to solve problems. These new math ideas were just things we needed to know to find out our bigger goal for the unit.
One of the first activities we did using manipulatives was physically measuring a shadow or Shadow Data Gathering. When measuring a shadow you need to use four variables, L for the height of the light source, D for the distance from the object to the light source, H for the height of the object and S for the shadow length. These four variables would be the ones you use in the formula for how long a shadow is, our unit goal. This activity helped develop my understanding throughout the unit because it was a hands on experience of measuring a shadow, which relates you back to the unit goal. This also helped because instead of just seeing it in pictures or solving it in homework's such as the sun problem and the lamp problem we got a visual, hands on interpretation,
After measuring shadows and finding out what variables were needed to solve the unit problem the next thing we learned was how to create formulas using an In-Out table. In POW 17 making an In-Out table and identifying patterns was key to finding the formula needed and it is the same situation for solving our unit problem. Although formulas do not relate to shadows, they relate to what our unit goal is, which is finding a formula.
After using In-Out tables, finding formulas and measuring shadows we took a turn in our studies to a more geometric side of this problem. The next concept we studied was similarity....
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