Fractions and Decimals, Week 4

Hi Everyone,

This week was dedicated to exploring and discussing fractions and decimals. This particular topic I find extremely interesting because it has real-world application. This is not to say that other areas of math do not, however, I personally find myself using fractions and decimals very frequently throughout the day, and because I find it so applicable, it is easy for me to understand and communicate to others.

Small, M. (2013). 277

Within the math curriculum, it states that students must have a deep and thorough understanding of number sense and numeration, which is the category that fractions and decimals fall into. Understandably, with each increasing grade the complexity of the problems increase, and the textbook that we utilize in class is a great example of how this occurs. Additionally, the textbook demonstrates many useful student assessment examples to try to demonstrate where the student is in understanding the mathematical processes and what needs to be improved upon. To the right I have included an example straight out of the textbook within Chapter 11: Fractions. We are to determine where the student understands the question and the areas that need improvement. It is great that this student is trying to use visual representations to demonstrate their knowledge of fractions, however, the future focus for this student needs to be understanding equivalent fractions, and one strategy that can be utilized is by using manipulatives. Through the use of manipulatives, this student will be able to get a more thorough understanding of equivalent fractions, and the next step would be to try to use mental, conceptual math for understanding equivalent fractions. If this student had manipulatives available, they may more clearly understand that 6/9 is equivalent to 2/3 (see below for manipulative examples)

Katic, K©. 2015. Math Manipulatives, Polygons.

Katic, K©. 2015. Math Manipulatives, Circles.

Through this discussion, I have discovered that these manipulatives will be extremely useful within my own educational activities. I find that through personal experiences and conversations I have had with a variety of individuals (as well as textbook examples) that visual representations of mathematical problems make the question and solution more tangible. For example, a student once told me that by having manipulatives readily available in class, it makes math more fun because they understand the problem better! Isn't that what we want as educators, for math to be more fun for students through active engagement? When I was taking the two photos to the side, I forgot how much fun and useful manipulatives are to try to figure out fraction and decimal problems. This methodology for solving problems is going to be readily available to my students, along with helpful instruction and applicable, real world math questions. They allow students to explore their understanding of math deeper, which will be extremely beneficial to them in their adult lives. As an educator, that is the ultimate goal, for my students to be able to take their math skills they learn in the classroom with them into their adult lives.

My next steps will be to further discover resources that my students can access in order to gain a more holistic, deeper understanding of math, as well as gaining insightful feedback from experienced teachers and what they believe are successful strategies for teaching math effectively.

References 
Ontario. (2005). The Ontario Curriculum, Grades 1-8. (6th Ed). Toronto: Ontario, Ministry of Education. 
Small, M. (2013). Chapter 11: Fractions and Chapter 12: Decimals. In Making Math Meaningful to Canadian Students, K-8. (2nd Ed.) Nelson Education. Toronto: Canada.