Learning Activities: Week 5

Prior to taking this course on Teaching Mathematics in the Intermediate/Senior Classroom, I thought that it would be a lot harder to incorporate fun and engaging activities within the senior grades as opposed to the younger grades.  However, some of the activities that were explored this week in class proved that even in grade 12 there are plenty of exciting things you can do with your students to keep them engaged in their learning.

Logarithm Dominoes

One of my colleagues made use of personalized dominoes to help solidify students’ understanding of logarithms.  Students played a classic game of dominoes; the only difference was that instead of a certain number of dots on each domino, there were different logarithms.  Throughout this entire game, students were able to practice their skills at solving logarithms.  Each student took turns solving the logarithms and playing one of their dominoes (if possible).  Students were told that each turn should last no longer than 45 seconds.  If a student could not play any of their dominoes, played an incorrect domino, or they took longer than 45 seconds, that student would need to pick up an extra tile.  The person to play all their tiles first wins.

I think that this is a very clever activity to do with your math class.  One thing I like about this activity is that it can be used for many different topics in almost any grade.  For example, this game could be used to help students practice understanding equivalent fractions.  In addition, I thought that this activity was a very engaging way to practice a mathematical concept.  Often, teachers simply assign textbook questions or worksheets with many practice questions on it.  Having students engage in this alternate version of dominoes allows students to practice the same skills that they would if they answered textbook questions but in a more fun and exciting way.  When students are engaged in their learning, students are more likely to better remember and understand different concepts.

If I were to use this in my classroom, one of the things I might eliminate is the timer.  Although I understand that this is so students do not take forever on their turn, I believe that it discourages students who may not be as fast at solving problems.  Students should be told that they should take a “reasonable amount of time” on their turn (encouraging them not to take too long), however, I would not restrict them to a specific amount of time.  Another thing I might do if I were to use this activity in my classroom is create the groups myself.  I believe that creating the groups for this activity could help students learn and practice better.  There are a couple different ways that I would like to try splitting up the groups.  The first way would be to split students up into groups with similar abilities (i.e. students with high skills in one group, students with lower skills in another, etc.).  Splitting the groups up this way would make the game fair because everyone would be on the same level.  In addition, students could help each other throughout the game.  The other way that I would maybe split up the groups would be with a range of abilities in each group (i.e. low, average, and high level students in each group).  I believe that splitting the groups up in this way would allow students to help each other more efficiently.  Higher level students could practice their skills and understanding by assisting the lower level students; whereas lower level students would receive this assistance and therefore better their own understanding.  How I would split up the class would be completely dependent on my specific class and the students within it.

I hope to find ways to use this activity within my classroom, as it is a fun and engaging way for students to solidify their learning. 

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Learning Activities: Week 4

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“When are we ever going to use this in life?”: One of the most common questions students like to throw at their math teachers.  It is very important to not just teach students math concepts, but to show them how it is applicable in their everyday life.  Show them that math is everywhere.  When students are able to see how a mathematic concept can be applied to the real world, it not only helps them better understand the concept, but it also makes math more interesting and fun.

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One of the lessons that we had this week in Teaching Mathematics I/S was very application based.  With the use of three application problems, students were introduced to the concept of exponential functions.  Each student received a handout that had sections for each of the three stations.  The sheet had empty tables of values and graphs on it to lead students through the activities, as well as extension and reflection questions.  At each of the three stations, there was an application problem and some type of manipulative to help students with the problem.  An example of one of the stations was the “Ice Bucket Challenge” station.  Students were given counters to help them visualize how many people were nominated to do the ice bucket challenge each day (assuming that each person nominates three people after they complete the challenge).  Students could fill out the table of values through the help of the counters, and then create a graph representing the day number versus the number of nominations on that day.  Students could try to find a pattern because they were then asked how many people were nominated on the eleventh day (that would be a lot of counters!).

I really enjoyed this activity and will use it in my future classroom.  There are multiple different aspects of this lesson that I believe were very beneficial.  First of all, like mentioned in the introduction of this blog post, it is very important to relate mathematics to the real world.  All three of the stations in this activity involved some sort of application problem for students to solve.  Including application problems allows students to better understand the material, rather than just memorize the information and erase it from their brain the second it is no longer needed.  Relating to something that students understand and enjoy, such as the ice bucket challenge, increases students conceptual understanding as opposed to just their procedural understanding.  Another thing I think was very beneficial about this lesson was the use of manipulatives.  Two of the three stations had counters for students to visualize the exponential growth of the application.  This helps students who are visual learners.  The third station involved how many sections are created when folding a piece of paper multiple times.  This station had a stack of paper for students to use while solving the problem.  Again, this is beneficial for visual and tactile learners to help with their understanding.  A final thing I liked about this activity was the kinesthetic aspect of it.  Each station was set up at a different table in the room and students had to move to each of the stations in order to solve the problem.  I think this was an excellent idea, as opposed to simply giving students the tools to solve all three problems at their own desk.  Allowing students to get up and move around during the lesson not only makes the activity more fun and exciting, it also can be very beneficial for kinesthetic learners.

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The only thing I would slightly alter about this activity is some of the wording on the worksheet.  For example, when I first started at Zombie Apocalypse station, I thought that the numbers we were suppose to fill out were the total number of zombies, as opposed to the number of zombies that were infected that day.  Although this is specified on the main sheet at the station, the wording in the table of values on our individual worksheets had me slightly confused at first, until it was clarified by the teacher.  However, this was a very small thing that, once clarified, did not at all impact the great outcome of the activity.  I would definitely use this lesson activity to introduce exponential functions to my future math class.

Learning Activities: Week 3

Different students learn in different ways.  Some students learn best through writing out notes; others learn best through getting up on their feet; some learn best through using tactile objects; other students learn best through simply listening.  There are so many different types of learners that need to be accommodated for in the classroom.  This is why it is important to provide a large variety of instructional activities that are beneficial to many different types of learners.  The learning activities done this week in my course on Teaching Mathematics at the Intermediate/Senior Level were great examples of how to incorporate different types of learning into an instructional activity.

Introduction to Rates of Change Activity

One of the activities this week focused on the math concept rates of change.  Each group of students received a CBR (calculator-based ranger) which can be used to collect data on motion (including distance and speed).  For the first part of the activity, students were given six different distance-time graphs.  The groups had to try to create each graph using the CBR.  Then students were given blank graphs with specific descriptions (example: “walking away from an object slowly”), and students were required to draw what the line would look like.  After this group activity, the class came back together as a whole to do some specific examples on calculating the rate of change of a line.

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I really enjoyed this activity and would definitely use it in my future classroom.  When learning rate of change, distance-time graphs are often used.  In addition, these graphs are often related to real world scenarios (example: “describe a scenario that would produce this distance-time graph”).  However, students rarely get to create distance-time graphs themselves.  What I like about this activity is that students are actually able to get up on their feet and explore with and create distance-time graphs.  By bringing CBRs into the classroom for an activity like this, students get to see their own ideas play out in real life.  It also allows students to discover their own learning.  For example, a student may have thought the graph of someone walking slowly towards the sensor would look one way; however, after testing it using the CBR, perhaps the student discovers that he/she forgot that the slope should be negative.  This activity is a good example of tailoring to different styles of learning.  Clearly from what I previously mentioned, this activity is excellent for kinesthetic/tactile learners.  It can also help students visualize the different types of lines created when comparing distance and time.  I also believe that it is good for students who learn best through discovery.  Students are able to make mistakes and try again.  This activity helps visual learners because students will likely think of this activity when trying to solve future problems.  In addition, I believe it was very beneficial that this activity started with the more application based part of the lesson and then went into the next more mathematical part (i.e. mathematically calculating the slope of a line).  I believe that this made the activity much more engaging.  I look forward to hopefully trying this activity with my future math class.

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If I were to use this activity, I would likely also add a part of the activity where students can create their own distance-time graphs.  For example, students could draw a random graph, predict how they will need to move in order to create that graph, and then test it out using the CBR.