How to Think Proportionally!

Hello Everyone!

Today, I will be recapping this week's lesson on Proportional Thinking!

Going into the class, I really had no idea what Proportional Thinking was. After reading the definition for it, I was still confused. However...as we moved into the rest of the lesson, things started to come back...

We started this week's lesson with covering Proportional Thinking in children's literature. The book that was read, "If You Hopped Like a Frog", had to do with Proportional thinking and compared things to each other. Compared....RATIOS! Finally, it started to come back to me. Proportional Thinking is COMPARING things! With hope in my heart, I sat up straight and welcomed the rest of the lesson.

[Online Image]. Retrieved from Amazon.com

Unfortunately, the next part of the lesson was problem solving. For the most part, I've been okay with the concept of problem solving in the past few classes. However, the question that really stumped me was about the distance traveled by a bike and a car, and how they would eventually meet up. I thought I had it. I drew out my number line, and placed the car and bike on it. After a few minutes of struggling to see why these two forms of transportation, I decided I needed help. As it turns out, my number line was almost right, I just forgot to add NEGATIVE INTEGERS into the equation. The problem was, I knew what I wanted to do to get to the correct answer, but I just forgot how to work it out. After about 10 minutes of frustration, I finally solved the problem in two ways. I was happy that I finally understood the question, but I also felt pretty discouraged.

It wasn't until after I solved the problem that I realized I had done an integer problem very similar to this one last week. In fact, I had solved it the same way! For some reason, my brain could not understand the question, simply because I was reading too much into it, and not focusing on the simple aspects. I should have highlighted or underlined the important parts, instead of just staring at the page. There were definitely lessons learned for me this week, both as a student, and as a future teacher. This was the first time that I really thought about how students process questions, and how I as a teacher can help them to understand them and come to the correct conclusion.

After this question, my brain had given up. I had reached the correct answer, but I was confused (not on how I got to the answer, but how I didn't get it in the first place.) We moved onto the final question, which involved measuring a giant's hand with a non-giant's hand. I'm all for open-ended problem solving, but I just could not wrap my head around how to get an answer, any answer!

Dunn, Erin. "Giant Hand."

Overall, though I did enjoy this lesson, I left it frustrated. I wasn't frustrated with the lesson, but with myself. I started to fall back into my old math habits, and it upset me. I know that I have all the necessary tools in my kit to work on the problem, I just need to be patient with myself because they're a bit rusty! I know that I have the ability to solves problems like these, I just need to work a little harder on it.

Hopefully I'll be able to wrap my head around next week's activities. I just need to keep a positive attitude!

Until next week, Happy Math-ing!

Integers!

Hello Everyone!

This week was a pretty fun one in math! I haven't covered the concept of integers in a long time, but somehow, I have managed to retain a bit of knowledge regarding them. It was very exciting for me to be able to quickly figure out the problems and activities, as this rarely happened in any of my high school math classes. So with that, here's a bit of what we covered last week!

The first thing that happened in class was the integer assignment presentation. This presentation was very informative, and a bit of a refresher to those of us who have not worked with integers for a while. This presentation kick started us into our next activity: Integer Football.

Before this class, I had heard about Integer Football, but had never had the chance to play it. In this game, our table groups were split up into teams and given a number line, a die, and a penny. The goal of the game was to make it to the other team's "end zone". When a team rolled the die, that indicated how many spaces they would move. When a team flipped the coin, it told them what direction they would move. (E.g. Heads positive and to the right, Tails negative and to the left). At the beginning of our game, both teams ended up moving in opposite directions, and therefore, scored no points. I think this game is a great introduction to integers, and includes participation from everyone involved! I also liked this game because we learned new things without even realizing it! I believe that in making concepts and ideas relatable, students will learn and remember them so much better than if it were just placed on the whiteboard.

Dunn, Erin. "Integer Football".

The next game that we played was the spinner game. In this game, players had to combine a series of positive and negative integers to create one whole number. To play the game, a player would roll the die, which coincided with how many integers they were able to use to create the whole number, and spin the spinner, which decided what whole number they players would create. I liked this game because it allowed all players to work on and refine their mental math skills together! I think that this is also a great game to use in the classroom, as it promotes teamwork to solve a problem!

Dunn, Erin. "The Spinner Game".

The penultimate activity in this week's lesson was to work on integer word problems, involving Mount Everest, as a group. I'm not going to lie, this made me a bit nervous, as I had to write down my own answer before collaborating as a group. This made me even more nervous as I compared my answer to the other member's answer, and mine was the only one that was different. We all had alternate ways of processing the question, and after much discussion, somehow my answer turned out to be the correct one. I mean, I was hoping it would be, since I was able to explain how I arrived at it, but I was discouraged when I saw the other answers. The lesson learned from this problem is be confident in your answers (and in yourself!), because you may be right! (regardless of what the other answers are).

Dunn, Erin. "Mount Everest Question".

We ended this week's lesson by placing a number line in our interactive notebooks; something that I hope to use in my own future classroom! This is a great visual aid for all students, as it helps them to count and see the integers that they are adding and subtracting.

I enjoyed this lesson immensely, and hope to use these games and activities to spark collaboration, understanding, and confidence in my students!

Until next week, Happy Math-ing!

Fraction Fun!

Hello all!

This week was pretty busy Math-wise (and otherwise!). I completely forgot to respond to a forum post AND a blog post for math class. Thankfully I just updated my agenda, and will not be making that mistake again!

Anyways, moving on.

In this week's class, we worked on the ever elusive, ever frustrating, fractions. To start the class, we had two presentations. The first presentation featured a neat folding trick! Not known for actually being good or accurate with folding, I'm happy to say that we were not marked on how talented we were. However, this folding trick was very easy to understand, and simple to demonstrate. The class folded the paper into halves, then shaded one half. Then, we folded it in quarters, and coloured in two quarters. What do you know!? They were equivalent fractions! (This led nicely into the next presentation) (Also, I will definitely be using this strategy in my own classroom!)

The next presentation included base ten blocks (my favourite manipulative!) and money. As a class, we were asked to see if we had enough money in our class fund for a new iPad! Each group was given their own envelope of base ten blocks, and was asked to count of how much money we had. We were taught about the hundredths and tenths columns, and were asked to correctly place our amount of money into the columns to see which group had "raised" the most, and so that we could count it as a class.  In the end, I think we had enough for our class iPad, so that activity was a success!

As a music student, I feel your pain. I also have no money.  (I'm also wishing stores took base ten blocks as payment.)

After the activities, we panicked a bit about our upcoming curriculum assignments (no longer panicking, all is well!), and continued with our fraction lesson. My favourite part of this lesson was definitely learning how to make fractions with Hershey chocolate bars. (Another thing that I will be stealing to use in my classroom!) By relating pieces of the Hershey's bar to real life situations, our class was intrigued (and hungry!) The book that provided the lesson was a great resource to use, and I hope that I can find something as relatable to teach to my own students in the future.

Favourite word or phrase? ONE WHOLE CANDY BAR!

After suddenly becoming hungry, we moved on to exploring and playing fraction based games. During this part of the lesson, I also learned that flash cards and the laminating machine are my future best friends. I cannot wait to use flash cards, like the ones we used in class, into my own lessons! I hope it will get my students to participate and ask questions when they don't understand a concept.

We also made a chart of what we thought fractions were, or how they could be described. I haven't done anything with fractions in a long time, so my answers were a little...outside of the box. (Do I get points for creativity?)

When explaining fractions, I will always include examples with pizza. (Fractions are also NOT bananas).

By the end of the lesson, I felt hopeful. I wasn't as discombobulated as I thought I would be with my return to fractions, and that made me feel so great! I hope to use many of the concepts we learned with my own students. (Including solving fractions with the use of clocks! So many connections!)

Next week, we will be taking a look at integers. Fingers crossed for that!

Until next week, Happy Math-ing!