Week 11 Reflection

This weeks mathematics blog focuses on the Measurement strand and will be based on the three tremendous presentations from this week. These presentations used hands on methods of teaching to get students and engaged and excited about what they are learning.

The first presenter, myself, taught a lesson that targets grade 8 and focuses on the measurement of the volume of a cylinder. I started by having the groups brainstorm and familiarize themselves with the area formulas for triangles, rectangles and circles. Once each group had done this, i explained to them that a 2D shape becomes a 3D shape when you add a height component to it. In terms of formulas, simply multiply the area formula by h to find its volume formula.
                                                                                                                                                         

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The students then took a package of Oreos and calculated the volume of the numbers of Oreos that each question asked. By using Oreos, students could identify that there are different ways to determine the volume of several objects of the same size. 

The next presenter used small square manipulatives to help each group understand the relationship between side length and area. We were told that we could only use 36 cubes and must make as many rectangles as we could with those 36 squares. 

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Knowing that the cubes had to equal 36, our group began to think of all the multiples of 36. After making rectangles of 1x36, 2x18, 3x12, 4x9, 6x6, 9x4, 12x3, 18x2 and 36x1, we recorded the area of each and found that it was the same each time. 

The last presentation used objects to help students approximate length. By using objects to approximate height, it helped us get an idea of using appropriate units when measuring things. 

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As one would guess, it is much easier to determine how many popsicle sticks tall a classmate is rather than how many paper clips. The same is true when measuring in actual units. I can look at someone and approximate that they are 1.5 meters tall. I would be much more difficult however to guess how many centimetres or millimetres tall the person is. This lesson did a great job of explaining and showing this. I will definitely use a variation of these lessons in my own class one day since they are very engaging and help students visualize difficult measurement concepts. 

Week 9 Reflection

The presenters last week focused on Patterns and Algebra and how we could teach these units in oure classrooms. One of the presenters gave each group a massive grid that had numbers 1 through 10 on each axis and in the middle was the product of the numbers on each axis. For example, if you go across the top axis until 6, and then you drop down 4 squares, you will then be in the quadrant that represents 6 x 4. Since we know that 6 X 4 = 24, it evidently showed 24 in that box. Because each side is numbered from 1 through 10, the numbers on the grid therefore range from 1 x 1 to 10 x 10 or 1 to 100.

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The presenter then had us use counters and highlighters to represent patterns on the grid. As the picture shows, my group chose a non-linear pattern of 1 4 9 16 25 36... Given this increase, we determined that the rule for this pattern was T squared. This means that the output value is equal to the input number multiplied by itself. To verify that this rule works, we can examine the 5th term in the sequence. Since the term number is 5, we simply compute 5 x 5 to find that the value for the 5th term is 25. This technique for learning patterns in algebra is wonderful for the classroom as it teaches students about the relationships between numbers while providing a hands on experience that will keep them engaged.

Another presenter cut out pattern squares to help each group visually understand the patterns and how they are changing from one term to the next. This method was a great as it allowed each group to see first hand how each patter was changing and therefore, come up with an appropriate rule to fit the pattern. Students certainly appreciate visuals and hands on aids so i believe this method will be very beneficial to students and how they learn.

Overall, each of the presents last week did a great job explaining their lessons and guiding each group through the action portion of the lesson. I really enjoyed coming up with pattern rules with my group members and this is the best way to make learning happen with students as well.

Week 7 Reflection

This weeks class explored the topics of integers and exponents. Though these two subjects were scheduled to be learned, the presentations for this week only focused on exponents. Two presentations stood out to me as they both approached integers in two different ways, both of which kept students busy and engaged.

The first presentation that stood out to me gave each group 2 question. The answer to each questions was a series of 4 integers that would be determined using the 4 clues provided. Some examples of clues that were provided are as follows:

1. The first integer and the last integer have a sum of 28.
2. When arranged from least to greatest, the 4th integer minus the 2nd integer equals 8.
3. The first two integers when multiplied together will equal 12.
4. All four numbers are even.

Knowing these clues, students must arrange different possible answers that fulfill these requirements, while of course knowing that there is only one sequence of 4 numbers that can be correct. This lesson was great as it required each group to work together and think critically about the possible solutions for the question. The only problem that i had with this was when the presenter explained that there should have been 8 clues instead of 4. Considering how every single group struggle to get an answer with only 4 clues, i believe that having 4 more would have made a noticeable difference.

The second presentation worth mentioning also explored integers but did so in a way that had real life practical applications. The presenter compiled several questions that used these real life practical applications and had each group solve them. One question had a starting temperature, then had a series of temperature increases and decreases over a span of a couple days and then asked what the final temperature would be. By using a number line, students in intermediate grades can visualize how the temperature is changing in the question. The same method of questions were used for representing a series of golf scores. By taking positive and negative integers and placing them on a number line, students could see the change that occurred given the numbers provided. I believe that this type of question is great for students because it can be explained in simple, real life terms that they can understand.

I would definitely consider using these lessons in my future classroom. I think that the question with the hints given requires students to work together and use critical thinking and problem solving skills which are essential to develop. The real life practical examples in the questions are also very useful and applying them alongside a number line can produce a great visual for students of all grades and all levels.

Week 5 Reflection

          There were two presentations this week that stood out in my mind as useful ways of teaching fractions. The first involved the use of different geometric shapes such as hexagons, rhombuses, trapezoids and triangles as a way of representing parts of a whole.

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          As the picture above shows, the triangles, trapezoids and rhombuses can be combined to create a whole. This means that these shapes each represent a different fraction of a whole. Assuming that a whole is represented by the hexagon which can also be labeled as 6/6 triangles, then a triangle is 1/6 as it is that much of one whole. Because a rhombus is 2 triangles, it represents 2/6 or 1/3. And lastly, the trapezoid is equivalent to 3 triangles which is represented as a fraction by 3/6 or 1/2.
          This way of representing fractions is an interesting change from using blocks or other conventional methods and i will definitely incorporate it in my classroom one day. Although none of the topics discussed this week were terribly difficult, finding ways to explain fractions to people who have never used them before can certainly be. In my practicum placement today, i taught a lesson on converting decimals with whole numbers into fractions or mixed numbers. It was quite challenging to find a way to effectively portray how 2.75 becomes 2 3/4 when changed and reduced. I later found that simply telling the students to put the tenth and hundredth digits over 100 every time made it easier for them to understand and apply.
          The second lesson that stuck with me this week also dealt with fractions but approached it in a different way. Each group were assigned different fractions which added up to 10/10 to represent all the fingers and thumbs on two hands. These fractions were then assigned a colour. Each group was then supposed to colour in that percentage of nails in the specified colour.

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          As the picture above indicates, our group had 1/10 black, 2/10 blue, 3/10 yellow and 4/10 purple. The order that we coloured the nails did not matter, the point of the exercise was to represent the fraction of fingers and using colours was certainly a great way to do this. This is another great lesson that i think would be a good one to use in the classroom. It really gets students engaged and excited to do something hands on and working in groups with their classmates. Limiting the fractions to n/10 does mean that not all grades will benefit from this lesson. But as an introduction to fractions for a 4/5 class, i do not think there is a better method out there.
          Having seen students in grade 6 struggle to understand how fractions work, i really understand the importance of building a good foundation for this type of learning. Because not all students are visual learners and wont simply learn the practicality of fractions through observation and repetition, it is essential that teachers learn to incorporate more engaging methods of teaching fractions as a way of building a foundation for future learning.

Week 3 Reflection

 A topic discussed in this weeks class that i will incorporate in my classroom is the idea of a fixed mind set versus a growth mind set. A fixed mind set is found in someone who is negative, not confident and thinks that they cannot better themselves through learning and hard work. They believe that their knowledge cannot be changed and they are unable to learn something because they are not smart enough. The opposite to this is a growth mind set.  An individual with a growth mindset will accept that they made a mistake and will do everything they can to fix their problem and correct the work.
This week also consisted of an activity where we analyzed a pattern using blocks and examining how it changed. Generally speaking, i did not find any of the work from this week difficult or particularly useful when it comes to teaching.
I enjoyed getting to know my fellow teachers and developing our groups for our projects. Overall, im not entirely sure what i should be expecting from this course. The first 2 classes weren't overly beneficial and i do not know when they real teaching lessons will begin, Having a background related to math, i was hoping we would dive into the teaching of math more quickly, but that does not seem to be the case. I have high expectations for this week.