measurement (it rules!)

This week started with me preparing for my presentation on measurement! We had no in class session this week, so I had to adapt my presentation to fit a smaller group. It was interesting to see how being adaptable is still one of the skills I am learning. I naturally like to plan ahead, so when my plans change, I sometimes don't know how to accommodate those changes. I am still learning!

         In my presentation I had students draw out their hands on 1 and 2 square centimetre paper, and count how many centimetres their hand was on each paper. From this, I hoped they would gain an understanding of measuring in square centimetres, what square centimetres are, and how to compare two measurements.
         It went pretty well though. It is also very interesting video taping yourself and being able to look back on what you said and did. I think I would edit some things if I did present this lesson again, but I am happy with the activity,  it is always interesting to get students to understand how they can use the world around them mathematically.
         One of the things we learned online this week was investigation is one of the key aspects of measurement. Our professor discussed how students may not have the basic skills of measurement, and I think that is where my presentation would come in! It is a starting point for measurement.
The topic of measurement has many different features, because one can measure a variety of things. This features include measuring temperature, time, area, perimeter, circumference, and volume. One of the resources I looked through while planning my presentation was the Measurements grade 4-6: a Guide to Effective Instruction in Mathematics, Kindergarten to 6. This guide features really good examples for educators. It is laid out with similar sections as a lesson plan, making it super accessible and easy to read. One section that stood out to me is that it provides specific examples on how to scaffold the problems. There are several examples of "scaffolding suggestion" boxes featured in the document that seem really useful. On Page 49, the document suggests ways to connect a linear representation of time to life events that students will understand, in the scaffolding suggestion box. I think these little ideas and suggestions to educators makes it easier for pre-service teachers to understand, and have ideas to reference. I love documents like this because they take away the fear of trying to implement complex topics scaffolded in effective ways.
         I also sat in on Kursten's presentation, and assisted her in filming it! It was a great experience to see her activity. She also did hers on area, but focused on estimating area. Her activity is also a good introduction or refresher for students. In her presentation, the students cut out pictures and estimated their size based on the other pictures they cut out. This was an excellent example of estimating area! I definitely saw how hard gaining a conceptual understand of measurement can be for students.

snakes on a plane (week 8)

This week was about geometry and spatial sense. I actually do not mind this unit. I like thinking of how things can work together spatially. While reading through the "guide to effective instruction: geometry and spatial sense grades 4-6" teaching guide, I found a lot of information that I could see being very useful when it comes time to implement a lesson. One of the concepts that stood out to me was the inclusion of teaching strategies that are effective for this particular math lesson. They included several examples of instructions on what methods to use to teach geometry and spatial sense such as, "carefully planned activities will enable students to build on these [personal] connections and identify relationships between and among the various areas of geometry and spatial sense" (25). The document contained ample information on how to teach, the basis of why students need to know this information, where the information came from, and most important of all, how to connect it back to our students in a way they will remember. I will definitely be using this guide in my practicum. 

"Geometry Pun" (2016). Retrieved from tumblr.com

Geometry and spatial sense are so essential because they are skills that can translate to everyday. We use shapes in our everyday life, and need a sense of where things fit in the world. There are many real life examples and connections to be made on a unit like this. 
One of the things discussed was the misconceptions regarding comparing different units. For example, students need to be made aware to be careful of comparing shapes with different units. In my presentation, I introduced students to measuring perimeter with 2 inch grid paper, and 1 inch grid paper, an example like this would help students to see the difference measuring with different square centimetres can make. (featured in next weeks blog)

I will work to make sure my students have a conceptual understanding of geometry and spatial sense by providing them with a variety of demonstrated examples, and scaffolding the work to make it easier for them to understand. With a unit like this, which has foundations all the way in ELKP, if a student has missed a concept or doesn't quite understand something, they will struggle to build up any understanding. I will also focus on the big ideas. As was detailed in the effective instruction document, "These big ideas are conceptually related and interdependent, and instructional experiences will often re ect more than one big idea. For example, when students create or analyse designs made by transforming a shape or shapes (location and movement), they demonstrate an understanding of congruence (geometric relationships), and of how congruence is connected to the properties of a shape (properties of two-dimensional shapes and three- dimensional cues)."  (16). This quote stood out to me because it demonstrates the way every step of a lesson can affect a students conceptual understanding of the whole. 

I enjoyed the presentations this week because I loved playing with the shapes and seeing how that worked. I particularly enjoyed Ashley's presentation because I felt it was a good lesson for junior learners. I liked the use of manipulatives. Our table actually thought making the shapes and putting them into the bigger diamond was going to be very easy, but it was actually harder as she gave us parameters to follow. 

I also enjoyed learning from James. I liked his trick with flipping the paper to be able to see how shapes are translated and flipped and can move. I tried out the method of doing the exact opposite coordinates, and am happy to have learned that because I feel like I can really use that in my practicum. I do sometimes get lost when it comes to translating shapes and moving them across the grid. While working with students, I often try and get them to cut out a paper or have a physical resource so we can actually work with it, like Jacob did. Overall, I really enjoyed the presentations this week. I have been learning a lot from them. 

This week I am working on my own math presentation on measurement so stay tuned for updates on that! 

let's taco 'bout it ! (and by it I mean patterning and algebra) (week 7)

     

"Let's Taco Bout It" (2016). Pinterest via Hollister Co. Retrieved from https://www.pinterest.com/pin/56154326576907607/

       This week surrounded patterning and algebra. When it comes to algebra, I am automatically lost! I feel like I lack the foundational knowledge to build up my current skills, so I am trying to re-learn and teach myself a lot of these concepts. It has been a challenge.
          We started our learning with a Speed Dating Multiplication number sequence. This activity required us to each start with a number, then pair up repeatedly to have two numbers to multiply together each time. I enjoyed this activity, while I did find it challenging. We were multiplying pretty high numbers, so it our answers were in the thousands. I did like this activity as a "minds on" portion. It got us thinking about multiplication and the relationships between numbers. It is a good example because it can be applied to any grade level. Even grade 3-4's could do this worksheet, the teacher would just give the students smaller numbers to work with.
        While discussing patterning and algebra, one of the things I found was a lot of great activities. The textbook provides a variety of image examples to show patterning. The misconceptions students often had was related to the changes in orientation of a shape. I think this is extremely common, as students often think the way a shape is oriented defines part of it, but this is not the case. Two shapes can be exactly the same but mirrored, or translated. Using manipulative shapes would be a very good way to avoid this.

          One of the things that stood out to me this week was Mohamed's presentation. He was very funny and engaging and I liked the way he presented the equations. I felt like I understood and followed his presentation. One of the main things I was happy he went over was the difference between an equation and an expression. As a student, I struggled with this concept. I often could not identify what the question was asking, which would leave me lost. I liked his distinctions because I think comparing them made them stand out better in my mind. Students would take a lot out of his presentation. I also loved the GOAT! Greatest Of All Time would be a really funny title to introduce to students and let them compete for the title. I also loved that he took the time to relate his examples to real life experiences. I always remember things better when I form the memory around something I already know and understand, so Mohamed's presentation stood out to me after he made the concepts relatable to us as students and educators.
        I also enjoyed Nicole's presentation. She related the Fibonacci equation to the real life Parthenon. This task was challenging and hard to understand, but created a great learning environment. She explained the equation in a very understandable way, and I think if I am teaching that concept I will think back and use some of her ideas. Real life examples stick out in any students memory much more than memorizing an equation will.

"The Parthenon and Phi: The Golden Rule" (2016). Retrieved from Google Images. http://www.goldennumber.net/parthenon-phi-golden-ratio/

      One of the other concepts we discussed was teaching students who are learning or have learned English as a second language. This was very useful and can be applied to any subject area. I love when we discuss problems like this because it feels like very relatable information that I can see myself using out in the classroom. We discussed the challenges that come with teaching ESL students, but also were provided with strategies to consider. I have worked with a few students while volunteering that are ESL learners. I found that cues and gestures worked best for me, as I am already one of those people who talks with their hands. One of the things that stood out to me most of all was the idea of a language directory/ personal language dictionary. I loved loved loved this idea! I cannot wait to try it out. I may even apply it to an English class and make them all do it, regardless of their first language. The idea of students keeping a book that they write words they do not understand, may have heard in a different context, do not really know what it means, feel like they need to engage with it more is so exciting. I think it would be really beneficial to do.

"Lesson Plan ClipArt" 

      So far, I have found the hardest part of planning a lesson to be getting started. I feel like I do not know where to start. I have seen these great ideas, and understand the curriculum documents, and have started to become familiar with the process as a whole, but I still feel unsure about where to begin. It is a very intimidating process, because it comes with a lot of responsibility, and I want to do right by my students. The terminology in lesson plans has also been challenging to distinguish. We have gone over it once in our practicum class, but I still do not feel like I have a clear understanding of the terminology. I am also struggling through picking out curriculum specific and overall expectations, but am learning that and feel like I have clear expectations on that part.
        To make lessons learner-centered I plan on considering my students first when planning a lesson. I will make sure to be critical of ideas and think about my students when deciding whether they will work or not. At its core, lesson planning should first and foremost consider the effectiveness of teaching to these particular students. One cannot just take a generalized lesson plan and apply it to all students because not all students learn the same way. I hope to take each student into consideration when planning lessons.
   

6:12 (ratios and proportions) (week 6)

     This week we discussed ratios and proportion. To ensure my students develop a full understanding of these concepts, I plan to use the strategies we discussed in class. One of the things we did was use real life example, such as baking to understand how we need to proportion things out. Guliana used this example to demonstrate how chefs and bakers need to know their proportions and ratios because they are constantly asked to very quickly alter recipes in order to feed less or more people. This means having a complete understanding of the numbers and how they are balanced in order to make sure there is just enough ingredients. An example of that is if one adds to much salt to a batch of cookies they will not taste good. If we are doubling the batch, we have to know how much to add to each individual ingredient so it does not negatively affect the whole. The same works for ratios. Ratios are a good base for comparing things. They allow students to have an understanding of how two numbers can be contrasted against each other, or compared. This will allow the students to have a better understanding of how numbers work. The relationship of 4 blue squares :2 green squares can also be thought of as 2 green squares: 4 blue squares. This could also be expressed as a fraction, 2/6 or a percentage, 33.33%. 

6 Squares. (October 2016). Casey Made with Pages. 

   

    We also looked at percentages, because the topics are so closely related and interchangeable.With percentages, I always find the visuals a very good representation of determining and understanding percentages. I find this unit to be very important because it is extremely useful in everyday life. Even to this day, students are given marks out of 100%. This means that if they have an understanding of what a percentages is, they can take the mark of 25/40 and know that they got 62.5% on their test. Practical skills like that are always useful and can be applied in various situations. In the textbook, it does state that one of the common misconceptions is students who do not have an understanding of percents that are above 100%. Explaining this as equivalent to a mixed fraction would be a very good strategy. I think I would also try and draw a visual, like one of the grid visuals used throughout the textbook, to demonstrate what it means to have more than enough, and to show how that works as a mixed fraction. With these, pie graphs are also a great visual, for another class I made a pie graph about students who wanted to join a book club: 

    This was a silly joke, because I obviously did not actually ask 90 people to join a book club. But the percentage needed to be out of 100%, and I wanted it to be obvious that it was many more people that did not want to join, so I took the numbers of 60 people who did not want to join, 3 people who wanted to hang out, and 2 people who wanted to join and multiplied them all by 2 so that my ratio could be out of 100%. The initial ratio would have been 60: 3: 2. This pie graph is a good visual because it provides students with a representation of parts out of a whole. If they can see that the numbers represent something, they will have an easier time developing a conceptual understanding of these concepts. 
    In Chapter 16 of the textbook, a section was dedicated to Appropriate Manipulatives. From this, I found my understanding of teaching this subject was greatly increased. It listed counters, cubes, tiles, or balancing scales and paper bags. I think the activity with balancing scales would be really fun for students to do. It would provide a real life example they can understand. The algebra tiles would also be a very good manipulative for this topic. They can be used to show how the formulaic expression is equal. I think using these manipulatives to show ratio and proportion would be great. 

    To ensure my students misconceptions are addressed correctly I will listen closely as they explain things. I plan to develop resources in the classroom that ensure that each student who is misunderstanding something, or feels they do not have the right tool to address the problem, will receive extra guidance and further explanations. Being able to understand their misconceptions is the first place I would start, and as someone who will have had the same misconceptions as a math struggler, I think I will be able to see the thought process behind some of these students. I always found I applied the wrong concepts to math units. I will attempt to learn from the student and see how they thought out the problem so that I can then address it. Group work is another great resource so that the students can then help each other out. Hands on projects and real life examples are my favourite ideas to developing students complete understanding of concepts. Ensuring the students understand will come from practice and continuous learning. 

positives and negatives (5)

       This week was all about integers! We talked extensively about how hard it can be for everyone (students, teachers) to understand the concept of negative and positive numbers. They can get lost if we just show an equation with a mixture of integers and don't have a background explanation for what is going on.

     It is always hard to find real life examples that make sense to students but also teach them something they will remember. For this subject, I loved all the cool ways we learned how to keep track of the positive, negative relationships and their outcomes. One of my favourite graphics is this one: 

"Integers"" Don Steward. (2016). Retrieved From http://donsteward.blogspot.ca  

    Finding unique yet relatable ways to describe and explain things will be the most effective way to reach the students. I find that real life examples with a combination of pictures and words help me, so I will try and access my students through those means. I want to appeal to all learners while providing them with challenging material. I think the above image is a nice place to start, with that image I would then include temperature and think of all the ways I could demonstrate how integers actually visually work. One of the other ideas that was suggested is a sideways number line. I personally love number lines and how they provide a nice clear visual of what the numbers are doing, how they are moving or jumping around, so I think that could be very useful.
   One of the things discussed in the textbook was around the misconception of "two positives makes a negative" (351). Sometimes boxing students into rules makes them forget the other aspects of the question. In this situation, the students can forget that the rule applies for multiplication and division instead of addition and subtraction. This is an example of students not thinking about the real world applications and what the question actually means. 

"Printable Number Line- Vertical" (2016). Retrieved from https://www.printablepaper.net/preview/Numberline-Vertical

    Another one of the activities I really enjoyed was a game that was a cross between Jeopardy and Battleship. We had math equations that we had to quickly figure out that featured both positive and negative numbers, and then had a sheet with the answers that acted as our Battleship board. It was a fun way to get students to really quickly do several math problems. I found it was very helpful at reminding me what adding and subtracting positives and negatives entails. I definitely would consider thinking of a similar game to play with my students.

     We also talked about exponents this week. I do not mind exponents, because it seems to be a very straightforward topic to me. It is a set of rules that are to be followed, and because of that we have to ensure that students remember what the exponent represents. 

"Exponents". Sixth Grade Math Blog. (2016). Retrieved From http://hemsmath6.weebly.com/exponents.html

    

    

       I think like most topics, this is one that just needs to be broken down into smaller steps for students to understand. It is easy to do once we have the base of remembering the rules and knowing the terminology. For a topic like this, I think it is really important to spend time on the base work such as fully understanding the terminology used to describe these numbers. From there, I would try and explain why we simplify by making it an exponent, like the above example demonstrates. If students first have the basis of when and why to use exponents, they will then know what to do and how to do it to solve the problem. 

   

    One of the other topics we discussed was manipulatives. I know how hard it can be to decide when to introduce manipulatives into a topic. When assisting grade three's in learning multiplication, I had chosen to introduce manipulatives far too early in the conversation, and found my students did not have a good enough base to work with the manipulatives on. It was a hard lesson to learn but I definitely noticed right away that they did not have that foundation, and then the manipulatives because useless instead of being a good tool to use. I think teaching the lesson with demonstrations and visuals is always a good thing, but the students need to have that clear outlined lesson first, where they are taught how to do it, before giving them the tools to explore how it works on their own. The manipulatives are an amazing tool for kinaesthetic and visual learners, but I think mathematic lessons need to be fully explained and detailed out to students before they get to that point. 

   Overall, another great week with various advances in mathematics. I am thrilled to be learning more ways to teach and hope to continue having fun and inventive examples to present to the students. 

My Math Forum Question

Due to the upcoming Thanksgiving vacation, I am planning a road trip to Kitchener- Waterloo, Ontario to visit friends and family. My starting point is Fort Erie, Ontario. 

Delicious lasagna that is awaiting my arrival

1. Please draw the route that I should take on this map 

B) Now that we have the route planned out, we need to figure out how long it is going to take me to get there. The trip is 165 kilometres one-way. I have to be there in time for dinner at 5:30pm. What time should I leave home at if I am driving 100km/hour constantly throughout the trip?

C) What if I decided to take the back roads, and would have to alter my speed and travel at 80 kilometres for the trip? What time would I have to leave home at then? 

D) The next step is to figure out how much money I will need for gas. I have a small car that holds 76 litres of gas in the tank at one time. I plan to fill the gas tank to full before I leave, gas is priced at $0.94 per litre. How much will it cost me to fill up my tank?

Fractions and Decimals! (week 4)

I will ensure that my students have a conceptual understanding of fractions and decimals by displaying to them the basic concept of both terms before elaborating on those concepts. I think that most confusion can stem from not having an understanding of why those numbers are in the place value they are, as well as what it means to switch fraction to a decimal and vice versa.

The most basic part of understanding fractions is realizing what the numbers mean and what they actually represent. I will work to show my students that through interactive conversations and examples. The textbook provided some great activities involving games and creativity that I would consider using. The pizza game we played in class, where we all started with a number and that number had a portion of the pizza such as 3/4ths of a pizza, and that had to be compared to everyone else’s number even though they had different denominators, showed us the importance of having the same denominator to compare fractions. I would definitely want to try to do something like that to start off my students, to make sure that they fully grasped the concept of fractions. 

As far as decimals, I find the place value charts to be the most effective for me so far, so I would first try that with my students. Placing the decimal into a chart and demonstrating the movement of the number while having the title of “tenth” or “ones” columns was very helpful to my understanding. I think that creating a place value chart would be the first place to start with students. I have done this with the grade three students I work with, and they use a thing called a “place value house” and act as though the columns are neighbours and when they have to borrow it is the neighbour knocking on the door asking to borrow some eggs. This was a good technique because it reminded the kids of the values in the columns. 

I also really enjoyed Nicolina's example of having to match the fraction to the decimal. It was very similar to this online game, that I found when I was looking up fractions and decimals.  The matching game of having a mixture of fractions and decimals and having to match the equivalent fraction to its decimal was a quick, fun way to practice conversion skills.

Fraction Pizza. Clipart Kids. (2016). Accessed through : http://www.clipartkid.com/pizza-fraction-cliparts/

In my placement, I have yet to see the students work on fractions. They were working on scatter plot graphs when I went in last time, and it was really interesting to see them work through the problems. I started with some questions that were actually kind of hard to answer, luckily after talking it through, my memory was jogged to remember how to create the algebraic expression and keep the y axis the same while changing the steepness of the slope. I cannot wait to find out some more techniques that I can use in the classroom. I have tried to implement a few so far, such as encouraging students to work through the problem in pairs. I have found that this math course is really helping me in my placement since they do math the first two periods I am there.