~My Weekly Report and Reflection 8~

This week we got to observe mini lessons on topics that could be used at the grade nine and ten levels.  Although some of these activities I have used in my classes before, I definitely appreciated the different approaches that my peers took and can definitely think of ways to integrate new methods into my future teaching.

The first two presentations both focused on the concept of the sum of the interior angles of a triangle and how the number of sides a shape has, has a relationship with its sum of interior angles.  The two presenters took two different approaches.  The first one tackled the discovery of this concept like one would in a science lab.  The students would first understand the problem they were trying to solve, create a hypothesis based on what they thought, and use the tools provided to investigate the problem.  In this case, we were given a variety of shapes and protractors and the freedom to explore however we liked.  The second presenter did things a bit differently.  Instead of letting us have complete reign of the learning, he first focused us on triangles.  Students were told to create any sized triangle they’d like; then, cut it out, mark each interior angle, and cut off each corner of the triangle.  When the corners were pieced together, it made a straight line, showing that all interior angles of a triangle added up to 180 degrees.  Knowing that, he told us to explore some other shapes, and try to find how many triangles can be found in each shape.  Since we knew the sum of the interior angles in a triangle, we could calculate the sum of interior angles in other shapes as well.  We were then able to explore the relationship between the number of sides and the number of triangles in a shape.  If I were to teach this in the future, there were some things I would take from both approaches to this concept.  I really enjoyed how the first presenter gave students the freedom to do whatever they thought.  This is a great way to promote student creativity.  However, if I was told to explore in grade nine, I probably would have given up because I wouldn’t have known where to start.  For that reason, I would try to do more of the second presenter’s approach.  First I would focus on the interior angles of a triangle, have students understand that concept, and then let them explore the other triangles for themselves, giving them time to be creative before coming back together again and discussing findings.

Retrieved from: http://www.mathwarehouse.com/geometry/triangles/angles/images/interior-angles-of-triangle-picture.png

The third presenter did a round of speed dating!  This activity went over creating an equation using a slope and y-intercept, and plotting that line.  I thoroughly enjoyed this activity – it was so much fun and didn’t feel like practicing math at all!  Desks were arranged in a “U” shape and students on one side of the desks were given a card with a slope, the other side a card with a y-intercept.  Pairs would be given one minute to share information, create an equation, and plot the line.  If the line went through any hearts on the grid provided, the pair was a match!  This continued until everyone had seen each other once.  I loved this activity sooo much!  It was simply drill and practice math questions, but it was so much fun that it didn’t feel like that.  When I use this in the future (and I say when, because I definitely will) there are only minor tweaks that I would make.  The first being the handout we were provided.  In the chart, I would have three columns instead of two: Partner’s Name, Equation, and add in a column for Is it a Match?  I would do this, just so that students would have somewhere to record their matches.  The other small change would be to provide students with slightly more time with each partner.  We were having so much fun that for the first 20-30 seconds we would talk with our partners about how it was going so far.  As math teachers, we were all able to create an equation and plot it in the next 30 seconds, but even then, we were running out of time.  For students who are learning this for the first time, I would want to give them some more time to properly do the math.

Retrieved from: http://cyamemphis.org/wp-content/uploads/2015/07/Speed-Dating-2.jpg

The final presentation had a great framework, but I was slightly confused on the concept.  After discussing the properties of three right angle triangles, said triangles were cut out and specific interior angles were arranged to form a right angle.  Students were then given geoboards to try to prove how these triangles worked using similar triangles.  So besides the use of right angled and similar triangles, I was confused as to what concept this activity was addressing.  As well, myself, and those seated around me, were unable to prove it ourselves, so I can only imagine the difficulty most grade ten students would have with this activity.  For that reason, I probably wouldn’t use this activity in the future.  However, I really liked the layout of the lesson.  Most of the time, teachers provide students with the proofs to certain ideas or equations without letting the students try to figure it out themselves.  I really appreciated how the presenter let the students try themselves, while using manipulatives that are a lot easier to work with than writing theories on paper.  So the style in which the presenter approached this topic is definitely something I can see myself incorporating in future lessons.

Retrieved from: http://www.educatorsoutlet.com/images//products/10915DD.jpg

Overall, I really enjoyed all of the activities that were shared!  I can definitely see myself using these ideas in the future!

~My Weekly Report and Reflection 7~ *New semester start*

            This week we got to observe mini lessons on topics that could be used at the grade seven and eight level.  Although these are not the grades I wish to teach in the future, I definitely appreciated the different ideas that my peers brought to the class and can definitely think of ways to integrate their ideas into different grade levels.

Holes

            The first presentation was a real-world problem that approached the concepts of conversion and volume in an interesting way.   Students were to use the story from the novel and movie “Holes” to determine how many of X-Ray’s holes Stanley could fill in a year if X-Ray’s shovel was an inch shorter than Stanley’s.  I thought this was such a cool idea because it had a practical purpose to it and if one was invested in the plot (like most of our class was growing up), it was definitely motivating to try and answer.  If I were to use this idea in the future, however, I would make some changes.  I would definitely pick a real world application that had more significance to my students.  This story was a great pick for our class, but for today’s generation, they may not have even heard of it.  Also, the amount of conversion from metric to imperial units was a bit problematic for me.  Either I would decide to completely leave those conversions out, or instead, make this idea more of a paired performance task where students have to work with things that are foreign to them and try to solve the problem.  Lastly, the presenter brought in measuring cups to visually represent what the holes looked like and the difference between X-Ray and Stanley’s holes.  However, he didn’t go into much detail about it.  I would have loved to see what he could have done with those manipulatives to help students understand better.

Retrieved from: https://www.walden.com/wp-content/uploads/2003/04/holes-hero.jpg

The Adventure of Steve the Stick Figure

Retrieved from: http://images.clipartpanda
.com/sad-girl-stick-figure-image.png

            The second presentation followed Steve the Stick figure and his adventure around the classroom to teach transformations.  Students would start at one station and would have to determine what the transformation at the station was asking for, and where Steve (the coordinates) would end up.  After travelling around the room, students would answer some questions on their sheets using words instead of numbers and transformations.  I really enjoyed this activity as well!  I think it’s a great idea to get students up and moving around the classroom.  However, if I were to use this idea in the future I would make some changes.  I might consider doing this activity in a larger room, so that students would have more room when at the same station.  As well, depending on the behaviour of the students, I would even consider doing this activity around the school – I think students would have a lot of fun travelling to different locations in the building.  I would also be wary on what the symbol was that we are transforming.  In this case it was Steve the stick figure where there was a “head” and a “butt.”  Sometimes this was confusing to keep track of when drawing.  I would maybe consider changing the shape for next time.

The Game of Life

            The third presentation was the game of life!  This activity taught idea of percents, ratios, and rates in a practical real world situation.  I thoroughly enjoyed this activity.  Each table (or family) was given a career and a monthly salary.  Each “month,” the families would have to pay their rent and internet charges.  After that, they would have to buy clothes and food for their family; however, there were flyers with coupons for certain percentages off as well as sales.  Lastly, families would have to save some money in the bank each month for future uses.  At the end of the game, it was shared what families had what incomes and who was struggling to pay their bills.  I thought this was a fantastic activity that I will definitely use again in the future.  A lot of the time, students don’t understand why they learn the things they do because they don’t feel like they will ever use it again in the future.  This is such a practical day to day application that students will actually learn from and use in their future!  If I were to use this in the future, I would make some small tweaks.  I would definitely make the groups a bit smaller than we had them.  I think groups are good for discussion and debate on how money should be spent but more than 3 per group is too many voices in my opinion.  As well, I would have everything pre-arranged in folders and each group would be given a folder with their details as well as flyers and sales for the following months and students would instead have to budget their pay for the next year.  This may become more of a performance task type activity, but I think that the general discussion they would have, and the experience of budgeting for a longer period of time would be a great experience for students to have.

Retrieved from: http://cdn.edgecast.steamstatic.com/steam/apps/403120/header.jpg?t=1465471547

Battleship

            The final presentation was also a great one!  This presentation provided a fun way to approach practice drills of solving single variable equations.  Everyone was given a 7x8 grid and basically played the game Battleship in pairs.  The catch was, if you hit your opponent’s ship, you had to correctly solve an equation for x in order for your hit to count.  I really enjoyed this game!  I thought it was a lot of fun and as a very competitive person, I was very motivated to keep playing.  However, if I were to use this idea in the future, I would definitely make some changes to the handout.  The activity itself was wonderful, however, as time went on, our battleship sheet began to get very confusing, and our equation sheet was forgotten.  Instead of having the two on separate sheets I would have combined the equations with the grid so that in each box there was an equation to be solved.  This way, instead of switching back and forth, the questions would be present in each box if that box was selected.  I would also make a much smaller grid in the corner of the page for students to put their own ship’s placement.  Having to share where you had guess AND where your opponent had guessed on the same grid got confusing fast.  By separating the two, it would be much easier for students to keep track of what was happening.

Retrieved from: http://static.kidspot.com.au/cm_assets/32032/battleship-game-main-jpg-20151022131744.jpg~q75,dx720y-u0r1g0,c--.jpg

Overall, I really enjoyed all of the activities that were shared!  I can definitely see myself using all of these ideas in the future!