WEEK 61X *insert Drake's voice*

Hey friends!

Long time no see! I was on a small, but well deserved break because it was my reading week! Over the past few weeks, I've been thinking and reflecting on my experienced with math. I have been thinking about what I've been learning so far and how I've been using math in my daily life.

Quick! 
Solve this part 1 problem to proceed.. how many minutes have I been away, since my last blog post?

I have been away since September 29th, 2017. Today is September 27th, 2017.
How many weeks is that? It has been exactly 4 weeks in total.

So let's break that down. How many days are in a week? Yes, 7 days. So 7 x 4 = 28.

I have been away for 28 days! Now, how many hours in a day? 24! Keep going...you are so close... how many minutes in a hour? 60!

So.. let's work our way back up. 60 minutes in an hour multiplied by 24 hours= 1440 minutes in one day! Wow! Now,  1440 minutes multiplied by 28 days...

= 40, 320 minutes!

Now, those are a lot of minutes! I hope that you make every minute meaningful in your life, because as you see, time flies! Now that I've got your attention, I want to talk about what we focused on this week in math. This week, we discussed ratios and proportions. I've had quite extensive work with tutoring math and I've noticed that my students between Grades 4 and 10 really struggle with the concept. They usually need a lot of coaching and repetition to really cement ratio rules in math. I've also noticed that when students receive an application question, where they need to make connections, they can't organize their ratios properly. In this case, teachers might use the aid of manipulatives to try and cement the mathematical concepts and processes involved.

Manipulatives Activity for Ratios and Links with our Course

No attribution required.

The Ontario Curriculum for mathematics states that, "using manipulatives to construct representations helps students to: see patterns and relationships; make connections between the concrete and the abstract; test, revise, and confirm their reasoning; remember how they solved a problem; communicate their reasoning to others". Tying that into our class textbook, a quote from Small (2016) states that, "it is believed that manipulatives help students by providing • models the student can refer to (i.e., visualize) even when the manipulatives are no longer present • a reason for students to work cooperatively to solve problems • a reason for students to discuss mathematical ideas and verbalize their thinking • a level of autonomy since students could work with the materials without teacher guidance". It is clear that manipulatives play an important role in helping students visualize and make math thinking meaningful.

This week, my colleague had our class group do an Oreos activity to show how ratios work. She gave us each a plate and we had to divide the Oreo cookies with each other based on the ratio she called out. We were able to see how the Oreos were distributed and we had a chance to visually understand the magnitude of the numbers as they were made into ratios. The best part was eating them at the end!

Links With The Curriculum
Last question before you go, part 2! How much time did I spend studying if I spent my time 3 times as much time studying than relaxing? So in terms of ratio, that would look like, 3:1. Follow along... 

3:1 = 40, 320 minutes                        

Total 4 = 40, 320 minutes
40, 320 minutes/4= 10, 080 minutes
10, 080 minutes multiplied by 3= 30, 240 minutes
10, 080 minutes multiplied by 1= 10, 080 minutes

So, I spent 30, 240 minutes studying and 10, 080 minutes relaxing! I prefer a flipped ratio for this, but what can you do as a student, right?

This problem would probably be introduced to a Grade 6 classroom as a proportion strand through number sense and numeration. The Ontario Curriculum states that, "by the end of Grade 6, students will: – represent ratios found in real-life contexts, using concrete materials, drawings,and standard fractional notation (Sample problem: In a classroom of 28 students, 12 are female.What is the ratio of male students to female students?)". You can see how the sample problem is very similar to ours!

Make your minutes count and your days meaningful, friends! Have a SP00KTACULAR HALLOWEEN!

Nathan Shields. (2013, September 26). Halloween Math Pumpkin [Photo]. Retrieved from https://www.flickr.com/photos/maaorg/9955531593

Teddy