Grade 11 Math Lesson Ideas

In class we had two demonstrations for teaching content in the grade 11 math curriculum. One concept was from the grade 11 U/C class and the other from the grade 11 college level. I will first talk about the grade 11 U/C activity.

Spaghetti sine is an activity that can be used in a grade 11 U/C or grade 11 university level math course to help students understand the sine function. This activity would be used during the trigonometric functions unit.

Image retrieved from: http://www.cwu.edu/math/sites/cts.cwu.edu.math/files/images/Spaghetti_Sine_lg.jpg

This activity requires students to cut pieces of raw spaghetti based on a radians/degree wheel. As students start cutting the spaghetti they should start to notice a trend once they make it all the way around the circle for cutting spaghetti pieces. This provides students with a visual representation of where the sine function originates from and can be used to explore other topics such as periods, amplitude and transformations of trigonometric functions.

The next activity was for grade 11 college mathematics and was very practically suited towards choosing an appropriate car insurance company to save you money. The goal of the activity was to figure out how much car insurance would cost with driving school, and whether or not participating in driving school will save you money on your car insurance in the long run. I found this activity very interesting because I love to save money (don't we all?!) so I thought this would be an excellent lesson during the financial unit that will grab the attention of students easily.

Streaming in High School

In class we discussed the idea of streaming in high school. Streaming is placing a student in either academic, applied or locally developed based classes. The stream chosen is often based on the students "best" learning style. Academic classes tend to be more abstract whereas applied classes tend to be more "hands-on." Locally developed classes provided the necessary skills students need to be literate in the subject area but often omit abstract concepts.

The issue I have with streaming is that it limits the students options for their future. If a student is great at mathematics they will likely be in academic math classes but if they have a learning disability for reading and writing they may struggle in English classes which would put them in applied English classes. The issue with this is that you need a grade 12 University English credit to apply to Universities and if the student is a great mathematician but not an amazing writer they unfortunately cannot attend university for anything math related due to the stream they were placed in.

Another issue with streaming is that it happens even before the students enter high school. The students grade 8 teacher will often suggest which stream certain students should be placed in when entering high school. This means the students have to decide their academic future when in just grade 8! I find that unacceptable. We should give the students the opportunity to show their potential in grade 9 and 10 and destream the courses so there isn't so much pressure on students and their parents deciding their academic future at such a young age.

For mathematics in grade 9 the two streams can be broken down as follows:

The applied stream is actually very similar to the academic stream in grade 9 with the only big difference being the omission of the analytic geometry unit. The purpose of these streams is to cater to the different learners present in the school. If we create an environment that positively fosters the learning of every student though, whether math is their strength or weakness, I believe that the streaming would not be necessary.

Strategies and Activities for Grade 9 and 10 Academic Math Classes

This week in class we looked at strategies and activities for grade 9 and 10 academic math classes. Daria started the class with a great activity called Battle Slopes which was an interesting way to reinforce the idea of slope in a grade 9 math class.

Battle Slopes had the same goal as the game Battleship, you had to find the location of the other persons markers to win the game. The twist with battle slopes though was that you could only find the other persons markers using equations such as x+1 and graphing said equation on the grid. If the graph of your equation goes through one of your opponents markers you can deduce the location of their "ship."

This game was very fun and had a good combination of strategy and fairness involved. Some strategies would involve doing things such as starting off with a small slope ie. y=x then translating that line either up or down ie. y=x+1 or y = x - 1. The fairness is a result of the randomness with the markers placed by your opponent as both students playing the game will have an equal opportunity to find the location of the markers based solely on the luck of your equation line hitting one of the markers. 

  

Image retrieved from: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbm3uzi3RoJ9EVo9b4W_RWbmoYykoVyshOjxcCoQt64iMvljmsPn2dqHOhtck4Cg9GWb9ZITsV5qU1ASEGYV9DX5edKGVKBolXI_ikopcznVknY-Y1EuTOJ-qd8vnIIXMggUP-xp6xil2v/s1600/DSCN0747.JPG

Overall I believe this activity would be a good reinforcing tool for practicing slope. This activity could also be used if a lesson finishes early and students need work to do or if students finish a task early. It could even be used later in a future unit as a way for students to review for the upcoming exam.

There are other resources and technologies that can be used to help reinforce other topics in grade 9 and 10 academic classes such as:

Desmos
Manipulatives
Graphing Calculators

It should be noted though that technology should only be used during a lesson if it helps reinforce the learning of the new material, not just as a gimmick tool. 

Expanding Your Curriculum Knowledge Beyond High School

Secondary school teachers are often well versed in understanding the components of the grade 9-12 mathematics curriculum's and how to develop lessons that address each of the curriculum requirements. One component that is often overlooked by high school teachers, especially those teaching grade 9 mathematics classes, is delving into the elementary mathematics curriculum. This gives teachers an understanding of where our students are coming from and an idea of the knowledge that they have likely already obtained.

It is important for teachers to understand the knowledge basis from which our students are coming from. This allows us to develop effective lessons that will scaffold on the previous knowledge that the students have already obtained in elementary level mathematics.

During assessment it could also be noted that students may be struggling with a certain concept. This could be due to the lack of prerequisite knowledge in a certain topic from elementary which is hindering students progress in learning new material. Although not part of the high school curriculum it is your role as a teacher to ensure each student is achieving their individual successes, which may require you giving a brief lesson on elementary level topics to refresh student's minds on certain topics.

In our class this week we were given curriculum expectations for grades 7-9 and tried to develop continuum's that would link concept ideas across each grade. This proved to be a challenging task as not all of the topics made direct correlations, especially when going from grade 8 to 9. This showed how big the gap was between content in grade 9 and and elementary, which is why it is important that teachers teaching that grade should become familiar with the elementary level content.

Continnum chart linking curriculum expectations from grades 7-9.

There is also a variety of resources available on Edugains that link curriculum expectations across the grades.

First Teaching Block

For my first teaching block I was teaching the light and geometric optics unit of a grade 10 academic science class. During the practicum I learned many new skills and strategies that could be applied to any type of classroom. In this post I will talk about some of the experiences I had while on my teaching block as well as some of the challenges and difficulties that I had to overcome.

This practicum was the first time I had taught in a classroom setting. I had some tutoring and coaching experience but had never run a classroom before. One of the first challenges I encountered while teaching was pacing. Due to being in a university style setting for the past 4 years, my pacing was a little bit too fast at the beginning of block but as I gained more experience the pacing became much better and was definitely one of my biggest improvements.

Being organized was extremely important during the first block. I learned many strategies that I would use in a future classroom to help keep everything organized within the classroom. One of the key organizational strategies that my teacher used was a binder that was always within the classroom that contained extra notes/worksheets. It was the students responsibility if they missed a lesson or multiple lessons to pick-up the notes/worksheets they are missing from the binder which was organized by date of the notes and divided by each class as well. This made it much easier for putting student's who had missed days back on track.

Having an academic class, classroom management and behaviour was not a huge issue for me. Some students would be a little rowdy at times but I found that proximity during lessons and changing pace often would quiet them down.

Although I wasn't teaching a mathematics course there was still some math involved in the optics unit. The mirror equation shown above was one of the equations we would use in the class to find the distance of an image produced in a mirror. It was interesting to see how all of the students had different math capabilities within the class. I broke down each question step by step and included the class when solving problems to help cater to all of the different leveled math learners within the class. We also did a lab which had a component that applied the equation which the students found useful!

Image retrieved from: http://previews.123rf.com/images/alexraths/alexraths1209/alexraths120900001/15134543-Teacher-with-a-group-of-high-school-students-in-classroom-Stock-Photo.jpg

Overall I found my first block to be very successful. I learned many useful skills that I could use in any future classroom and gained the valuable experience of teaching in a real classroom. Can't wait until my next practicum!

Online Session Reflections

Online Session 1

In the first part of the online session we looked at Five Practices for facilitating mathematical discussions around cognitively demanding tasks within the classroom. As a beginning teacher I found that some of these tasks may be a bit challenging for me such as anticipating likely student responses. Because we are all different learners there are students in my class that will likely think of different ways to solve mathematical problems I present that I did not think about. This is perfectly acceptable but as a beginning teacher I may find it more difficult to anticipate all of the student responses to questions due to my lack of experience as a teacher. With more experience though and getting to know my students better it will make it easier to anticipate individual student's responses to questions.

I find the Five Practices beneficial for the classroom because they provide a student-centered approach to learning that creates a more dynamic and engaging classroom. For example, one of the practices is selecting students to present their mathematical responses. This can be beneficial because it shows student's how their peers solve mathematical problems and in an ideal classroom where there is no judging other students you can also occasionally select students with a common error in their formulation of their solution to the problem which can generate discussion as well as enlighten other students who had made the same mistake.

The second part of the first online module challenged us to think outside the box by solving problems using different approaches that students may use. This exercise was useful because it challenged me to use different approaches to solving a problem then what I would normally be used to which is good preparation for when I will have to anticipate student's responses to math problems while teaching.

Online Session 2

Formative assessment is important tool used to determine the level of understanding students have on certain topics/concepts/ideas. There are different ways that you can approach using formative assessment but there are five key universal steps that can be used to help achieve effective formative assessment. One of these steps is sharing learning goals with the students. This allows the students to have an idea of what they should learn at the end of a lesson so that they can asked themselves "did I achieve the learning goal today?" Another very important step is providing feedback that moves learning forward. Feedback can be provided in written, oral or through a demonstration and should force students to engage cognitively about their own work.

Written feedback to a student should provide a question to the student rather than just a "correct" or "incorrect." You should provide the student with a reasoning for why their answer was good or incorrect that allows them to think about other options or methods. For example in a substitution/elimination problem that a student solves using substitution only you may write down as feedback "great answer! can you think of another method that you can use to solve the problem?"

The teacher should also guide student's using feedback rather than providing them with the correct answer right away. This allows students to think back to the problem rather than just seeing the correct answer and moving on.


Another important thing with feedback that I believe is very important is providing enough time for students to read and think about their feedback. You can provide students with feedback on an assignment or test and tell them to read the feedback and they may or may not do so. Providing time in class to look at the feedback makes it more likely that student's will look at their feedback and cognitively engage in it.

Overall I believe feedback is important tool for all students whether they are struggling or excelling at a topic it can be beneficial for both those types of students if used effectively and this module was a great way of thinking about feedback and how it can be used in a math classroom effectively.

Using Appropriate Contexts to Teach Mathematics

Have you ever been in a math classroom where a student asks the teacher, "why do we need to learn this?" or "How is this going to help us in real life?" Often times these questions is asked by students when an abstract topic is being taught. Crafting questions and presenting difficult/abstract topics with contexts that connect the material to real life events could help engage students who are questioning why they should learn certain topics.

A great example was done in our class this week where we had to figure out how many classrooms a billion empty shopping bags would fit into. To help solve the problem we were given measuring tape, about 20 shopping bags and a container. Our group decided that we would fill the container given with as many shopping bags possible, then measure the dimensions (length, width and height) of both the container and the classroom. Once we found how many bags could fit within the small container we compared the volume of the container containing the bags to the volume of the classroom. A ratio was then done to show how many bags would fit in 1 classroom. Since 1 billion bags would not fit into just one classroom we found how many more classrooms would be required. It was found that about 225 classrooms would be required to fit 1 billion shopping bags. 

This question was interesting because it addressed a variety of topics such as:

• Measurement
• Calculation of Volume
• Environmental implications
• Ratios

Figure retrieved from: http://images.teamsugar.com/files/users/6/61259/33_2007/Carrier_bags.jpg

Students are able to use what they have learned within the classroom to solve problems such as these that provide a real-world context.

With that being said, the development of these types of questions may not always be easy. A question such as the one shown above requires the students within your class to be quite familiar with a variety of topics. Some classrooms may struggle with the complexity of problems such as the one above and need more guidance. Because every classroom is different, it is important to develop questions with context that can be solved by the students within your classroom based on the knowledge of your students assessed by the teacher. If you are looking for more real-world type math problems an excellent website to check out is http://www.realworldmath.org/ which has a variety of lessons for teachers to help teach certain topics with questions that give real-world contexts.

Figure retrieved from: http://www.realworldmath.org

Not all context questions require an activity to be performed though. There are many other ways in which teachers can accommodate context into their classroom. The first way is through a "hook" at the beginning of a lesson, A hook is used to generate student interest on a certain topic and can be done in different ways such as an activity, a video, a discussion, etc. Providing a context within that hook allows students to see why it is important to learn the topic that they are about to cover and also may increase classroom engagement.

Overall, providing a meaningful context to mathematical problems can help improve student engagement within the classroom but the way that context is taught should be based on the needs of your students.

What do you think about the importance of context within our classrooms?