Grade 9 Applied Lessons

CBR Motion Detector, Scientific Calculator,
Graph Worksheet

        The old saying goes.."You learn something new everyday" well today I learned something new in regards to technology used for math lessons. My colleague taught a lesson created for Grade 9 Applied class and she used a CBR. If you are like me you are thinking what the heck is that! Well it is a motion detector that connects to a scientific calculator which will display your motion in a graph. This was an introductory lesson to Rates of Change and I think it was a perfect activity to form a students understanding exactly what rate of change means. The package provided to each student clearly explained the steps for setting up the CBR and Calculator. Then the students were provided with 6 separate graphs and had to experiment with their motion patterns read by the CBR in order to re-create the graphs. This helped the students understand the difference between direction and speed. The next worksheet solidified their understanding of the same factors of a graph however they had to work in the reverse order. Thistime the motion of each graph was provided in words and students had to draw the graph based on the description. Now that the students comprehend the meaning of the graph, the teacher incorporated the rate of change formula and had the students calculate rise/run from the graph. I really enjoyed this activity and found the teaching order of the concept to be very effective. The CBR was an excellent tool to use and since this is actually an old piece of technology as is the scientific calculator, we had discussed whether they would create a connector that goes from the CBR to an iPad and the students can use the app for TI-83 or if eventually they create an app that records the motion and displays the graph.

         The other lesson of the night I wanted to share was a fun activity helping students solve for a variable x in an equation. To do this simple activity in your class all you need is mini whiteboards and whiteboard markers or if  you don't have mini whiteboards my colleague made a creative substitution by using clear document sleeves. After placing your students in groups of 4, you provide the entire class with an equation to solve and within each group a student will begin solving by writing down the first step. After the first step is done the student will pass on the whiteboard to the next student in the group who will complete the next step. This will continue until the group has isolated for the variable. what is excellent about this activity is that students have the opportunity to learn from their peers. If a mistake is made in one of the steps the next person will hopefully catch it and help the previous person fix it. This activity can be one of those fun math days especially when you make it a competition and the first group to correctly finish the equation will get a prize. I would definitely do this in my class because it achieves the same goal as providing the students with worksheets on worksheets of equations however it adds that element of excitement.

Grade 9& 10 Academic Lessons

Tonight was the night for geometry! Two of the three grade 9 teachers chose to teach a lesson on the sum of interior angles. Both teachers had very similar lessons but different approaches. My first colleague provided a worksheet with multiple figures and we were to to investigate how to find the sum of the interior angles for each figure. This lesson took a very openended approach, I liked how the students were given time to develop their own thoughts and strategize how they can solve the problem. The students had the support of their peers and constant support form the teacher circulating the classroom. In the end, students presented their findings to the class and we found that the class had come up with multiple strategies. I thought having the students explain to the class what they did to be very useful. Maybe the method we came up with in our group is different from another group and by learning the other groups method I better understood the concept. A worksheet was also provided during the lesson which was an excellent consolidation tool however it could have been referenced more frequently by the teacher. I feel I focused more on the problem and did not bother to summarize my findings during investigation. My other colleague's lesson was more of a teacher driven approach. He began by having us draw a triangle on a paper and draw semi-circles in each corner indicating the angles. We were then instructed to cut out our triangle and cut off the angled corners. From the corners we were asked what we notice about the corners put together and it was that they create 180 degree angle thus solidifying the concept that each triangle has a sum of 180 degrees. From here we worked on a sheet the same as the other lesson splitting up polygons into triangles and calculating the sums. Both lessons lead to the creation of the formula --->SUM =180(n-2) however one lesson was a more direct path towards this formula while the other was more of a discovery process. I think both lessons were excellent, I would use them both and when/where I use them would depend on the type of learners I have in my classroom.

Coordinate Grid and Description Cards

Another lesson activity I thought was absolutely incredible was "Speed Dating and Equation Making" . The learning goal was for students to determine the equation of a line when given specific characteristics such as the slope and y-intercept. The activity required the class to be grouped in pairs of two and the desks were set up in a horseshoe shape so the students could rotate partners like speed dating. In each starting pair, one student was given a yellow card with information on the slope and their partner was given a purple card with information about the intercept. The objective of the activity was to put together their information, create the equation of a line and draw the line on the provided coordinate grid. Printed on the grid were hearts on specific points, if the equation they created passed through a point with a heart this would be a match. The class will rotate to all partners and in the end the winner is the person with the most matches. I found this to be very fun activity and an easy way to practice forming and drawing equation of lines. I can also see how this could be adapted to the grade 10 curriculum by having the students match quadratic equations and the hearts could possibly be placed at the vertex.

Math Lessons for Intermediate Classes

In this week's class I was reliving my days as a student in grade 7 and grade 8 math classes. My fellow teacher candidates presented some interesting lesson ideas they created from the grade 7/8 math curriculum and the following are a few ideas that really stood out to me.

MTSOfan. (April 28th 2008)."Monopoly Justice"(Online Image).
Retrieved from:[https://goo.gl/images/OVPtRX] 

One of my colleagues presented a lesson on finances and money management which is a crucial concept for real life application. For years Monopoly has been a best selling board game and not just for its addictive nature but also because it is an important educational tool. My fellow teacher candidate created a lesson which was a play on Monopoly and the learning goal for the class was to understand daily expenses and how to properly manage your budget. The teacher had placed all the students in groups of 4-5 and had assigned a profession to each group or now known as each family. With their profession, the families received a monthly income statement and were instructed to collect their money from the bank which was paper monopoly money. The teacher then advised each family that they were to pay various bills (internet, phone, rent, grocery etc.) and one bill at a time the teacher would provide the percentage that each bill would take from their paycheck and the students were to calculate the exact dollar amount. What I truly enjoyed about this activity was that at all times the students were engaged. One student from each group was in charge of distributing money, collecting money, recording transactions and/or calculations. The students were even able to have fun playing the role of their professions such as the internet company collecting money or the banker handing it out. This activity clearly made the connection between earning and spending and although we were adults playing we even forgot about certain required expenses. Thus this would be a great reality check for students and the enforce the importance of budgeting which is a crucial life skill.

The second lesson that had me intrigued had us practicing with coordinate grids and transformations of figures. The teacher created a story called "Steve the Stick Figure" and the goal at the end of the activity was to explain Steve's story based on his movements. For this activity the class was divided in 8 groups. Each group was sent to a station and at each station we were given coordinates of two points; one representing Steve's head the other his body. After plotting the coordinates and drawing the stick figure on the provided coordinate grid we were to read the transformation instructions specific to that station. For example one station said "Steve walked three blocks right and four blocks north" we then had to translate our points three units right and four units up to find the new coordinates. We then searched for the next station with starting points that matched our coordinates after transformations. This process continued through until all 8 stations were visited and the path was completed. I enjoyed this activity especially the fact that the class was moving and it resembled that of a scavenger hunt for the correct coordinates. I also like the worksheets created for the assignment; one to draw out our figures on coordinate grids, one to organize our steps and describe the transformations that happened at each station, and to consolidate the lesson with a few critical thinking questions where we had to draw conclusions from the movements recorded. Overall I found this to be an excellent lesson and although it was noted to use this near the beginning of a unit I would suggest to use this activity near the end perhaps before a test as it encompasses a lot of different concepts.  


 

What Would the Students Think?

This week in my class we took a focus on the student's perspective when planning a lesson. Below is a script we created showing student concerns after receiving instructions for consolidating the lesson. 

Teacher: Now, instead of solving an equation given to you, you are going to create your own equation with a partner and you must come up with a word problem that corresponds with the equation you create.

For example we make an equation, 29 - x= 13. One example of a corresponding word problem would be "Jenny is on the Price is Right and the price she guessed for a new toaster was $29. The difference between Jenny's guess and the actual retail price is $13. What is the actual retail price?"

Then you would solve for x and show all your steps.

Student 1: Miss, can we use any numbers?

Teacher: Yes, in your equation any numbers can be used and you must have one variable "x" to solve for.

Student 2: So do you have to show all the steps when you solve or can you just write "x = ..."

Teacher: When you solve your equation, I want to see all the steps you took to isolate or solve for x, and end by clearly stating statement "x = value".

Student 3: Can we do this in pairs?

Teacher: Yes groups of two only. Each group of two will hand in one paper with one word problem, equation and solution steps.

  

When planning any type of lesson or assignment, it is important to remember that explanations or instructions you hope to provide to the students may not be as clear and concise to them as they are to you. 

Always Time For Technology

            In today's classrooms one question teachers ask themselves when lesson planning is "How can I incorporate technology into my lesson?" There are numerous apps and websites available which can be used to enhance a lesson or for student aid. The challenge for teachers is to explore these methods of technology and decide if they are purposeful towards student learning.

            

       One purpose technology should serve in the classroom is to foster math talk. During our class this week we were working with the website Desmos, more specifically we used the feature Polygraphs. In this feature teachers create a class account and students use their own electronic device to login to the class game. This game is just like an electronic version of the board game Guess Who where students are provided with a grid of different representations and need to guess which picture their classmate has picked. In our case we were working on the quadratics section and were provided with multiple images of parabolas. In order to make an educated guess the students must ask questions (through the app) in order to eliminate the incorrect pictures. This process forced us to practice our math language and knowledge relating to quadratics and translations of parabolas. For example the first question a student may ask "is the parabola concave up?" If the response is yes then the student can eliminate all parabolas facing down. I found the game to be fun, interactive and it tested my math knowledge not only when I was the question person but also as the person answering. 

Class having fun with Headbanz

To compare to a more traditional lesson without the use of technology, we also did an activity called Headbanz. In this activity the teacher presented each of us with an equation written on a card which was attached to a headband. Without looking at our equation we were suppose to wear our headband and ask yes or no questions to our classmates in order to identify our equation. This activity was also excellent for fostering math talk as students needed to clearly explain their thinking in order to describe their equation. Both these games are great for the "Minds On" portion of a lesson as they get the students into the math mindset and prepare them to think critically. I'm sure positives and negatives can be described for both methods however I would not designate one activity to be better than the other since they both accomplish the same goal.  

            Another purpose for technology in the classroom is to make it easier for students to apply their knowledge to real life scenarios. Using Geogebra we were able to overlay a parabola on top of a freeze frame video of a man shooting a basketball towards the net. From the students perspective we were able to see what would happen to our graph as we manipulated different parts of the equation in order to match up with the path of the ball. I enjoyed this activity so much that for my next lesson plan I will have my students find their our picture or video of something that resembles a parabolic curve and have them come up with the equation of the curve using the tools in Geogebra.

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Closing the Gap

         Without question teachers should be prepared to teach to a class that has a range of learning levels however a classroom such as this is a constant challenge for teachers. In regards to math teachers, this challenge arises most often in grades 6-9 where each new concept heavily relies on the use of prior knowledge. Imagine teaching area and surface area formulas in a grade 8 class where a group of your students do not know the proper order of operations (BEDMAS) or do not know how to perform basic operations without the use of a calculator. This would be very difficult to teach to the entire class when a large learning gap exists between these students and students who can apply the new formulas to problems involving critical thinking. The goal of the teacher is narrow the gap and one method of differentiated instruction used is available through EduGains called "Gap Closing Resources". These resources include topic specific diagnostic tests which can help teachers pinpoint what concepts students are stuck on. Once a problem area is identified there are extra work sheets for the student to practice. I have personally worked with these resource sheets in a grade 7 math class. In a class of 26 students there were 5 students who were using Gap closing worksheets. After the teacher had taught the lesson the 5 students would work on problems in their Gap Closing booklet which were related to the lesson. They were required by the teacher to finish those questions before attempting the questions from the textbook or work book assigned that were assigned to the entire class. I believe these booklets do help, most of the students I worked with were making the same mistakes and after practicing questions in the booklet they were able to understand where they were going wrong and as a result they caught up to the rest of the class.             

        To assess just how wide the learning gap is in the classroom, teachers can incorporate a variety of websites and apps into a pre-lesson or pre-unit "warm up" as opposed to a traditional test of existing knowledge. In my class this week we explored a website called "Which One Doesn't Belong" where four pictures within a similar category are shown together and students must describe how and why one picture is unlike the rest. The website organizes the pictures into the sections; Shapes, Numbers and Graphs and each section has pictures that range in grade level. I think a great idea for teachers would be to combine the concept of this website with a Kahoot presentation. Not only can teachers use the pictures from wodb, they can create many similar questions focusing on the same specific mathematical concept. By using this anonymous forum, students may feel more relaxed and inclined to answer honestly instead of guessing or not answering on regular tests. Also by customizing their own Kahoot, teachers should be able to get a general idea of the knowledge gap in their classroom. In the end this teaching strategy would not be a loss because for students who are struggling this exercise could possibly help them better understand a concept and for students who are excelling this is a great way to review and strengthen their skills before moving on to a new unit.

References:

Gap Closing. (2016). Edugains.ca. Retrieved 11 October 2016, from http://www.edugains.ca/newsite/math/gap_closing.html

Which One Doesn't Belong. (2016). Wodb.ca. Retrieved 11 October 2016, from http://wodb.ca/shapes.html

Kahoot!. (2016). Kahoot.it. Retrieved 11 October 2016, from https://kahoot.it/#/

Image:

Learning Gap. (2016). Retrieved from https://www.quora.com/I-always-hear-people-advising-JEE-aspirants-to-get-their-concepts-cleared-But-how-do-we-get-clear-concepts

Open Question, Open Mind

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The one thing about math I have always taken solace in is the fact that there is one answer. That one answer poses a challenge that I feel I have to meet. It is just like reading a book, doing a puzzle or even watching a movie I need to see it all come to one concrete end. Conversely to these thoughts, I have also learned that math is not always straight forward, it can be messy and complicated with multiple answers or there are those questions that remain unanswered. Of course I still love the straight forward questions but as I continue my work in mathematics, now through a teaching lens, I realize that the real learning took place while working on the "messy" questions. In order for students to work on these types of questions teachers need to develop confident, independent and critical thinking in their students. One way to gradually develop these skills is to implement open ended questions in a lesson plan. I can tell you that at first trying to use open ended questions in math is not as easy as english for example, but with practice it becomes second nature. In my teaching mathematics class this week we discussed some common and effective examples of open questions. Questions that leave a lot of room for student interpretation are comparison questions; asking students how a figure or an equation compares to another. Another key point we discussed was how teachers should provide enough information to form a problem but not too much information to completely restrict the question. Using words such as "approximately", "minimum" or "maximum" can open the question to multiple solutions. Below are two examples of open questions where the approach was providing the answer and having the students work backward to formulate the questions. 

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               In one of my placements during my undergrad, I taught the unit on area and perimeter to the grade 7 class. One assignment I gave to the class was similar to one of the unit problems from the textbook however I tweaked it making it more of an open ended problem. The students were required to create a patio design under some restrictions including using only the five specific shapes. (Prior to completing the problem I had marked out the five shapes on the floor using tape and the students calculated the area by measuring the floor tiles.) In the end each student had submitted a completely unique patio design. As long as the design included the five shapes and met the minimum area requirements then each of the designs were 100% correct. I think this assignment was a good balance between open ended and closed questions. After asking the students to formulate their own solutions to the design, I then asked all of them the same closed questions which they had to answer in relation to their own individual design area. I believe problems such as these are beneficial to all students because at the very least everyone can make an attempt and as I mentioned before this is a step towards building their confidence when dealing with math. 

Patio Problem

Resources

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