Thinking in Proportions

Welcome back!

This week's math class was about proportional thinking or proportional reasoning. I'll be honest; when Sue asked us to pull out our interactive notebooks and jot down anything we know about proportional thinking, I completely blanked out. I did not know what this term meant until Sue explained its definition as well as provided us with examples. As we started to work on some word problems, I was able to become more accustomed to the concept.

Proportional reasoning is a part of the Number Sense and Numeration strand within the curriculum. It is defined as "the ability to compare two things or quantities using multiplicative thinking, and using this in a new situation". The term "multiplicative thinking" threw me off a little, but I was able to understand the main idea of the concept. It's all about the comparison of two quantities, just like ratios.

We worked on different word problems whereby we compared two quantities, and tried to use different methods to solve for the answer (number line, chart/table, graph, algebra etc). We walked around the class to observe all of our colleagues work. It's so interesting to see how everyone has their own method and technique that they prefer to use to solve the same questions!

One interesting problem we worked on with our groups was figuring out the height of a giant using a picture of the giant's hand. We were also able to use any materials we wanted, such as a ruler or a calculator.

Image by Yasmine Khaizaran

After everyone had time to work on the problem, each group shared their technique on how they found their answer. Everyone's method was quite similar. We all started off by measuring our own heights and lengths of our hands, averaged out our measurements, and then used multiplication to figure out what the giant's height may be. Although everyone used similar techniques to solve, we each had different answers in the end. This is because we all have different heights and measurements which would alter what numbers we are using to calculate for the final response. This is such a fun and challenging activity that I will be sure to use in my classroom! My group's final response was 8"11. That's a tall giant!

One of my favourite parts of class is observing how we can use children's literature to learn and teach a math subject. We looked at a book called "If You Hopped Like A Frog" by David M. Shwartz. I found a picture book called "Centipede's 100 Shoes" by Tony Ross that would be another great book to read to the class before introducing the proportional reasoning unit to students. Using children's literature to introduce and talk about a math lesson is a fun way to engage students about learning the topic!

 Ross, T. (2003). Centipede's 100 Shoes. New York: H. Holt. 

Integrating Integers Into the Classroom

Welcome back!

This week's math class was all about integers. This was a unit that I didn't mind too much when I was in school. The rules of adding integers always stuck in my mind. A negative integer plus a negative integer makes a negative integer. A positive integer plus a positive integer makes a positive integer. A positive integer plus a negative integer equals a negative integer. When it comes to subtracting integers, it can become a little tricky. A rule that Sue taught us for subtracting two integers is called KFC.

KFC – Keep the first. Flip the minus sign. Change the second integer to the opposite.

For example, (-4) – (-7) becomes (-4) + 7 which equals 3.

We explored different types of activities that would be interesting to use in the classroom when covering this unit. For one activity called "Stick-it Together", we were provided with a word problem and we had to solve the answer and write it on a sticky note. Once we had our answer, we shared it with the rest of our group members and had to decide on one final solution that we all thought was correct. We then wrote our final solution and answer on a sticky note and stuck it on our worksheet. A lot of us realized that it was a tricky word problem and that we had solved the answer incorrectly because we did not read the question carefully.

Here is an image of our work:

Image by Yasmine Khaizaran

The question reads as follows: Mt.Everest, the highest elevation in Asia, is 29, 028 feet above sea level. The Dead Sea, the lowest elevation, is 1, 312 feet below the sea level. What is the different between these two elevations?

When I read the question, my initial instinct was to subtract the two numbers in order to solve for the answer. I thought because we were looking for the "difference", this meant that I would need to use subtraction. What I didn't realize was that the question states that The Dead Sea is "below elevation", in other words, it is a negative number. The correct way to solve would be to use the KFC method to subtract integers. This would mean keeping the first number (29, 028), flipping the subtraction sign into an addition sign, and then changing the negative number (-1, 312) into a positive number. From there, you would need to add the two positive integers in order to find the answer. As easy as this question was, many of us did not read the question thoroughly through, which caused us to make the slightest error.

This word problem was definitely challenging! It would be a great problem-solving activity to use in the classroom when teaching the integer unit to students.

Funky Fractions!

Welcome Back Friends!

Last week's math class was all about fractions, which happened to be one of my least favourite units unfortunately. Whenever we were to start this unit in school, I definitely was not the happiest. I would always try to make the situation a little more pleasant by thinking of these mathematical expressions as delicious pizza. Although this wasn't my favourite unit growing up, I genuinely enjoyed the activities we completed in that week's class. I started to see a more interactive and fun side to this unit that I will be sure to pass along to my students as a teacher.

That week, my partner Teresa and I had our learning activity presentation. Our theme was based around the title "Equivalent Fractions" where we planned out a lesson and activity to teach the concept of equivalent fractions to a Grade 4 class. The overall objective was for students to demonstrate an understanding of counting by fractional amounts (in terms of identifying equivalent fractions). Our activity involved using a folding paper technique that would serve as a guiding tool when working with counting and equalizing fractions.

Here is a picture of the folding paper we demonstrated in front of the class, and had each student prepare:

Photo taken by Yasmine Khaizaran

The activity works by having each student pull out a blank sheet of paper. We numbered each student as either group 1 or 2. Group 1 was to take the sheet of paper and fold it right in half. We then asked the group how many parts were in the sheet of paper (or visualize as a pizza), and then how many parts would we need to shade in with a pencil/pen if we wanted to make the sheet even. They would have had to shade in 1 part out of 2. Group 2 was to do the same with their sheet of paper, except fold it twice so that there are 4 equal parts. They were also to shade in 2 parts in order to make both folding papers equal. We demonstrated on the board that Group 1's sheet was expressed as 1/2 and Group 2's sheet was expressed as 2/4. Both sets of fractions are equivalent, or the same.

Teresa and I found that this technique would work well as a visual for the students in order for them to get a better understanding of how whole numbers are divided into fractions. It was also a great technique to use for a group of grade 4's who need a refresher on fractions, and advance them further by expressing what equivalent fractions look like. The final task required for our activity was for the students to work in pairs or groups and complete a worksheet on equivalent fractions using the folding paper method as a guiding tool.

One interesting learning technique we looked at in class was using children's literature to teach math. We read one storybook called "The Hershey's Milk Chocolate Fractions Book" by Jerry Pallotta and Rob Bolster. This was really enjoyable as well as educational!

Pallotta, J., & Bolster, R. (1999, December 1). [Digital image]. Retrieved October 12, 2016, from http://www.scholastic.com/content5/media/products/92/0439135192_xlg.jpg 

Evolving From Conventional Math

Good evening and welcome back!

This week's math class was all about embracing different ways of problem solving. We began with an activity where we were split into pairs and provided with two sets of coloured blocks. We had to come up with a value for each coloured block. Afterwards, we were asked to work together with our table and collaborate our ideas and values of the block. We could either use the same value that we came up with, or drop our idea and use the rest of the table's values of the blocks. Once more, we merged with another table and were to do the same thing. Finally, we had to come together as one class and decide on what we wanted each coloured blocks values to be. This became a little difficult as some groups preferred what they had come up with, and other groups liked their own ideas. We eventually had to conform and take a vote to decide what our final block values would be. This shows how change is not an easy thing to adapt to, but it also shows the variety in thinking and learning. We each had our own method that we were comfortable with; they were all different however they were still correct.

Here is a picture I took in class of our activity (featuring James!)

On a similar subject, Sue had gone over the different methods of problem solving and algorithms for operations (addition, subtraction, multiplication and division). One technique that really caught my attention was an algorithm used to solve a multiplication question called "multiplying by drawing lines". I have never seen anything like this! This is definitely an interesting technique that promoted the idea of embracing the diversity in learning math. It is important to realize that there isn't just the one traditional method of problem solving.

Below is a video demonstrating the method of drawing lines to solve a multiplication question:

 M. (2014). Multiply Numbers And Algebra Equations By Drawing Lines. Retrieved October 02, 2016, from https://www.youtube.com/watch?v=0SZw8jpfAk0

 

This week's class was right up my alley as I always felt that I was forced to learn one way in math. I was only taught one method in solving problems, which I either was never able to grasp or understand, or was not appealing to me. I know that if I was provided with more of a choice in my years of learning math, I would have enjoyed it much more. Since I was only taught 'black or white', I had a hard time boosting my confidence in my work, as a lot of the time I was told that my answers were incorrect. This goes to show that we cannot force or provide one method of teaching. As educators, we should encourage different methods of learning, as we all learn and think differently!