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.