Half a Pizza!

During yesterday’s presentations there happened to be two presentations that focused on the interior angles of a polygon. The lessons were presented using a variety of techniques and manipulative materials. The first lesson focused on measuring the angles while finding the formula for the sum of interior angles. The second presentation then built on this and provided a tangible method of finding the interior angles.

The differentiation of these two lessons made me realize that there are a variety of ways that the same learning goals can be met. The lessons complimented one another while still accomplishing the same learning. The first lesson’s work sheet provided a visual component of measuring the angles and properly dividing the polygons into multiple triangles. This allowed us to total the sum of the angles within the triangles and derive a formula from this pattern. The second lesson then added to this learning. The instructor provided us with the visual opportunity to explore the reasoning behind the sum of interior angles of a triangle. He focused on the visual kinesthetic learner and instructed us all to cut out a triangle. We then cut the corners off into “slices of pizza” and put them together to see what shape was created. I immediately noticed it was “half a pizza”. This then prompted the teacher to ask well, what could half a pizza also be known as? We all responded with half a circle, and realized that there was a straight line along the bottom, where all the points of the interior angles met. This straight line had a total of 180 degrees and proved that the interior angle sum of any triangle is 180 degrees. We then utilized this knowledge to explore other shapes and find the formula that was derived in the lesson before.

This concept of accomplishing the same learning goals while utilizing different lesson materials and activities exemplifies the notion of the curriculum being flexible. Both teachers allowed us to understand the formula for the sum of interior angles while accommodating a variety of learning styles. I will apply this in my future teaching while trying a variety of lesson activities. Going outside the box will keep students engaged and encourage them to be active members of their learning. Even though we learned the same lesson back to back we were all still engaged in both activities and met the success criteria.

Making Drill Practice Fun!

Last week in class was our first week of peer presentations. These presentations will last for the next few weeks and I will be commenting on presentations that I enjoy or presenting ideas that I think could work well in my classroom in the future. 

          There were a variety of presentations that focused on the intermediate grades 7 and 8. We played the game of life, the game of battleship, and explored real life problems of the movie Holes. It was interesting to see the same grades approached with such a wide variety of teaching styles. All teachers met the curriculum document expectations and taught us something new, while ensuring we were engaged and enjoying the learning experience. 

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The presentation that I am going to explore more deeply focused on the balancing method of solving equations. The teacher gave us a brief but successful lesson on balancing equations and following the proper steps in order to find the value of ‘x’. She then distributed a variety of materials that allowed us to participate in a game of ‘battleship’. The rules stated that if you guessed your opponents ship location you would then have to solve a problem on the worksheet before a ‘hit’ was declared. This is where the drill practice aspect came in. The worksheet was a simple problem set that could have been handed out and completed during the time at the end of the period, or for homework. Instead this game of battleship brought fun to practice. We quickly became competitive in the game and did not even think twice about having to complete the practice problems, as long as we got a ‘hit’ after completing it successfully. If we were not successful we were required to complete another problem until we got it right. This also ensures that the students who need the most practice will be given the chance to get it right. The students that often answer questions incorrectly will be given the most opportunity to practice, without feeling like the center of attention as they are only answering in front of their partner.

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I strive to use games like this in my classroom as it brings out a theory called Flow theory that stresses the importance of providing the right amount of challenge for your students and allowing them to lose track of time. As mentioned above, students who need more of a challenge will work their way to the bottom of the sheet more quickly, while students who are not successful in answering their first question will be provided with another similar question to practice with. This allows students level of difficulty to be met and individualizes the game. Similarly, I lost track of time while playing. I was focused on winning and forgot about the mathematics that I was engaged in.

          Overall, games will allow students to become engaged in education, and as long as the game fosters interest, communication, and enjoyment it will be successful in the classroom.  

Mr. Moore