Weekly Report & Reflection #6:

Weekly Reflection:

          This weeks class was focused on the big ideas such as; rate, ratio, and proportions. The main themes of this week were the big ideas for ratios, and proportional thinking. I understood a lot of the lecture, but had trouble understanding the ratios being expanded from a reduced form to a expanded form, and visually representing this. Matt did an excellent job of explaining ratios this week with visually representing the ratios while drawing a picture. I had a problem converting 7/8 to 14/16 and

Heartwell, 2015

drawing the border, trying to enlarge the original photo. Matt's first example of ratios was how many eyes a person has, having two eyes to one body being represented as 2:1.

        This example is an extremely effective tool when using this for elementary school students, getting an overall grasp of what ratios are. The picture to the left represents the problem that Matt gave us as a class to figure out. This problem was answered in many ways by the class, with some students free handing the drawing, to some drawing a border around what they needed to draw, and transferring the image.
           I did a mixture of both, originally free handing it, and then drawing a border to see where I went wrong. In the end I was only a couple boxes off the original image. Matt then had the class think about proportional thinking, more specifically how two ratios can equal the same thing, when expanded. A specific example Matt gave us was when he said represent 1/3 in 7th's which was 7/21.



Things that I learned this Lesson:

1. How to expand ratios
2. Proportional ratios
3. Equivalent ratios

Points I would Like to Make:

• Visually representing the image while drawing a picture on a grid was a very effective teaching strategy
• Group discussions about the final product and how the students got there was extremely effective

Weekly Report:

What I learned this week within the text was proportional reasoning, ratios, number lines, and solving ratio problems. The area that I related to the most to within this chapter was the common errors and misconceptions area. More specifically relating percent to multiplication inappropriately. I had trouble recognizing 4= _ % of 8 when in reality for is 1/2 or 0.5 of 8. The method that was suggested to use to fix this problem was recognizing that 4 was 1/2 of 8. This was a lot easier to visually represent this problem on paper, than mentally representing this.  

Weekly Report & Reflection #5:

Weekly Report & Reflection #5:

Reflection:

        During this week, I learned addition and subtraction using like and unlike signs. The continuing theme of this week was number sense and numeration, more specifically integers and exponents, and procedural fluency for integers. I understood most of the lesson regarding integers, however some of the procedural fluency tasks, I had trouble understanding. More specifically, I had trouble mentally representing the difference between two numbers when being prompted on the board to do so. For example; the number 50 and 22 would be displayed on the board, and we would have to quickly calculate the difference between these numbers as -28 from the number 50 or + 28 starting from the 22. Mentally representing these numbers was extremely hard for myself to do. I understood how to

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complete this question on paper, however mentally representing these numbers and their differences within my mind took some time. We were then asked to figure out the difference between two integers while using a number line.
            Both Kevon, Zach, and Julia did an excellent job describing integers using many different strategies. The most effective strategy that stood out to me was when Julia organized the integers using a number line. This visual representation of using cards and seeing were we would end up within the cards, when asked to add or subtract a certain number. It was extremely interesting to visually see this process being done, and was also very effective in showing where we end up on a number line (deck of cards).

Things that I learned in this lesson:

1. How to add and subtract integers
2. Use a number line to add and subtract numbers
3. Visually represent integers with manipulative's using groups

Points that I would like to make:

• Visually representing a number line with cards was an extremely effective teaching strategy
• Having a group discussion with the class about problems within the lesson was more effective than asking fellow group members

Overall I learned a lot from this lesson, coming away with  stronger idea of how to effectively add and subtract integers. After the class I found a resource that was really effective with reinforcing what we just learned in class, IXL, Grade 7, Add and subtract integers, https://ca.ixl.com/math/grade-7/add-and-subtract-integers. This website can be used as a quick way to test what the student has learned in class with randomized integer questions.

Weekly Report:
What I learned in the text book just was reinforced by my fellow colleagues within their presentations. Where the text book dominated was explaining where common errors and misconceptions are made. One of the errors that I related with was quickly saying that -9 > -4, viewing that 9 is greater than 4 and not recognizing the (-) sign in front of both numbers. The strategy to overcome this error was to review a number line before making your final statement. Viewing a number line helped me out a lot, recognizing that -9,-8,-7.....-4,-3,-2,-1,0 that -4 is in fact > -9. 

Weekly Report & Reflection #4:

Reflection:
During this week, I learned about how to manipulate math problems using objects, in order to understand how to do problems with fractions and multiplication. This photo to the left represents the manipulations we had to do, in order to understand fractions. I manipulated these shapes to represent 1/2,1/3,1/4 , and how these fractions relate to the shapes. These manipulations were guided by a student teacher, having us go through a fractions lesson regarding these shapes. A student teacher also went over how to colour a grid while using decimals, representing that 1.0 represents 100% of the picture, and that 0.5 reflect 1/2 of the picture. We then had to draw a picture based on the decimal number she gave us. For instance if she gave us a number of 0.5 with 20 boxes, we would need to fill in 10 boxes.

Three things that I learned:

1. How to represent fractions with shapes
2. How to represent fractions with decimals
3. How to add fractions with a common denominator

Three Points that I would like to make:

1. Have the class understand the knowledge through instruction from the teacher first, rather than students teaching students 
2. Excellent student instruction however

Questions:

• How do I add large decimals without converting to fractions, using shapes?
• What is the best way to explain to students how to add/subtract fractions when dealing with very unlike numbers, resulting in a large denominator?

Weekly Report:

What I learned from the book this week was how to deal with fractions using the number blocks. The book revealed how to represent fractions out of whole numbers. the text book did a really good job of breaking down the steps when it comes to adding, subtracting and multiplying fractions. 

  

                           

Jeff Heartwell, 2015

Jeff Heartwell, 2015