Proportional Thinking

          This week's activities focused around the concept of proportional thinking. At first, I was unsure of what this concept entailed. I knew that I had probably learned this concept at some point in my education. However, at this point, I was not sure of what this was. After some guessing, proportional thinking  was defined as "the ability to compare two things using multiplicative thinking, then applying this to new situations." Through this definition, the class was then able to apply their proportional thinking skills to solve various problem solving skills. 

          The first question was called "The Giant's Hand" Problem. Without being given any information, other than the print out of the hand size of the "giant", we were asked to figure out the approximate height of the giant. The image of the giant's hand is found below:

Pagliaro, T. © 2016.

I found this problem a bit challenging at first glance. Through my table group's step by step process, we were able to figure out a rough estimate of the giant's height; which is about 10 ft. We used a ruler to measure the length of the whole hand; which measured about 12 inches (a foot). Then, we each measured our own hands to compare to the giants hands, as well as comparing our own heights. Our next step was to make a ratio equation to help us solve for x. The equation could have looked like 12 inches/ x = 7 inches/ 5.8 ft. I used 5.8 ft to sub in my own height and 7 inches for the length of my own hand. These two values can be substituted for any individual who us trying to complete this question. Through this equation, we found the answer to be 9.9 ft (rounded to 10 ft). Overall, a great question to help students learn how to set up a proportional equation and solve for the unknown variable. 

           The second source we used was a video from Daniel Meyers. This video was focused on the method of 3-Act Math. I found this video very interesting since it promoted people to think about various questions one would ask themselves if they watched this video on building a pyramid out of pennies. The main question was "How many pennies are needed to make this pyramid?" The process is divided into three steps: 1) Watch the video and ask yourself a series of questions, 2) what information would one need to solve the problem, and 3) solve the problem. Here is a link displaying the three steps:

http://threeacts.mrmeyer.com/pyramidofpennies/

This method really allows individuals to problem solve and think of innovative ways to complete the problem. I thought this process is very engaging for students, and individuals in general, to think outside the box and use their pre-existing knowledge to come up with an answer to the problem while promoting inquiry skills. Below is the full video of the experience:

          Lastly for this week, the resource I chose to explore is called "Dirt Bike Proportions." This is a great tool for students to use in the classroom as an extra practicing resource. Through this engaging tool, students are able practice and develop their skills for the concept of proportions. Despite the game being fast paced, students will be able to improve their mental math skills and get faster at solving for "x". In addition, I enjoyed the fact that students have the choice to work independently or work in small groups collaboratively to solve the problems.

          Overall, this week has been very informative. I have learned about new tools and resources to  use in their classroom to help future students become more comfortable in various math concepts. 

Fun with Integers

          For this week, the session focused on learning fun an innovative ways for students to explore and improve their integer skills. 

          The first resource the class explored was through one of our fellow teacher candidates. He chose to use cards in order to help students learn how to subtract and add integers. Red cards signified positive numbers and black cards signified negative numbers. The students had the goal of attaining the answer of 25 through adding or subtracting. The students play two rounds; one round adding the integers to eventually get the answer of 25 and the other subtracting integers to get the answer of 25. I thought this card game was a great way to get students engaged about learning the concept of integers. It gets the students to think on their feet and improve their mental math skills. I believe I would definitely use this in the classroom with my future students. 

Math Hombre. Integer Games. Friday February 4, 2011. Cards [Online Image]. Retrieved from http://mathhombre.blogspot.ca/2011/02/integer-games.html

          The next fun activity we completed was playing "Integer Football." I thought this was a great game to use with students to help the improvement of their skills. Students used a sheet with a number line; which was set up like a football field. One side had a negative end-zone and the other with a positive end-zone. The students are given a coin, in this case we were given a penny, and a die. In order to see how many places he or she moves, the student rolls the die. In order to determine whether he or she moves to the positive or negative end-zone, the students flips the coin; heads for the positive end-zone and tales for the negative end-zone. I thought this was a great game to use with students. It is a fun way that one can practice their skills, but using a concept that is relatable to many students. The game keeps students engaged and interested, while developing their skills.

Pagliaro, T. © 2016.

          Lastly for this week's forum, we had a choice of two resources to explore. I chose to explore the game "Orbit Integers." This is a great game for students to practice their integer adding and subtracting skills either independently or in a collaborative work group. The game allows students to bring out their competitive side and work to develop mental math skills. The more answers the student gets right the more the team space ship moves closer to the finish line. For the future, I believe that I will definitely use this resource for students in my class. 

          Overall, I have learned some great resources to use to help teach students integers. Learning these new methods has put me at ease and feel a bit more comfortable teaching and helping students learn the basic concepts of mathematics. 

Fractions and Decimals

          During this week's session, we touched upon some innovative ways in which we as educators can help students understand the concepts of fractions and decimals. 

Mme. Deminion Weekly. (2015). Fraction and Decimal [Online Image]. Retrieved from http://mmedeminion.weebly.com/number-sense-and-numeration.html

          To begin the class, two groups, one of which being my own group, demonstrated a small activity that teachers would be able to use in the classroom. The first group made an activity focused around fractions 

          My partner and I went first and focused on equivalent fractions. This was geared for a grade 4 class first learning about the concept of equivalent fractions. We used a "Folding Paper" method in order to develop a foundation of the concept for the students. Students simply need two pieces of paper. The students fold one piece of paper into the appropriate parts based on looking at the denominator of the first fraction. The students then shade in the appropriate amount of parts based on looking at the numerator. The students then use the other piece of paper to do the same folding action for the other fraction given. Since the pieces of paper represent the same whole piece (a.k.a the same denominator), we shall look to see if the amount of parts shaded are the same. If they are, then the fractions are considered equivalent. Below is an image of our activity.

Pagliaro, T. © 2016.

          For the second demonstration, the group chose to focus their activity on decimals; more specifically place value for a grade 5 class. They used an interactive worksheet in order to make the concept of place value relatable to students. They made use of a piggy bank analogy and saving money in order to get students engaged in the activity. The group also made use of manipulatives, the counting blocks, to give a visual representation for the money being saved. Overall, I believe this was a great interactive activity that a teacher could use in their classroom for this concept. Below is an image of the worksheet the group used.

Pagliaro, T. © 2016.

          Another activity we learned focused around fractions once again. Our instructor demonstrated a great innovative way to make equivalent fractions relatable to students. 

          Instead of using the traditional terminology of finding the lowest common denominator, LCM, she used clocks and time in order to help students understand this concept. In this case, the LCM would be time; 60 to represent the 60 minutes in one hour. The various clocks were then divided into 3 different fractions: 1/4 = 15 minutes, 1/2 = 30 minutes, and 1/3 = 20 minutes. Students will then be able to use these clocks as a foundation to help them understand adding and subtracting using equivalent fractions. In addition, the class also received a different method for teaching the values of different fractions through the use of a folding number line. Every student is given a rectangular piece of paper and then folds the paper into the various parts based on the denominator given; whether it be 4 (into 4 parts), 3 (into 3 parts), etc. These two activities are then put in our interactive notebooks for future reference.  Here are some pictures to help visualize the activities. 

 

Pagliaro, T. © 2016.

Pagliaro, T. © 2016.

           Overall, I believe this week's activities were very educational. I learned a variety of new innovative activities to use in the classroom. Learning fractions and decimals can sometimes be difficult. Therefore, I hope to use these activities in the classroom with future students in order to make these concepts engaging and interactive. 

Learning New Ways!!!

          In this week's session, we learned new methods of solving the four basic operations in math: addition, subtraction, multiplication and division. We were all able to see 4 different methods of completing questions of each mathematical concept. After completing the various sample questions, I discovered that I use traditional methods for completing questions in all four concepts. However by the end of this session, I was very intrigued by some new methods I had never seen before.

          The first method I found interesting was solving subtraction problems. This method is called the Singapore Method. Instead of using the traditional method of regrouping, this method allows students to subtract the tens place of a number first in order to get the bottom number that is being subtracted to zero. I believe this method will help students a great deal if they are unable to grasp the concept of regrouping. In the image below, the four types of methods are demonstrated; with the Singapore method being visualized in the bottom left corner.  Since the first number to being the subtraction is 0, an individual using the traditional method would borrow from the number on the left. However, with this method, one subtracts the bottom number, in this case 6, from both numbers. This will ensure the bottom number to end in a 0; making it easier for the student to complete the subtraction.

Pagliaro, Teressa-Marie. Instructor's Photo. Image of instructor's slide. Retrieved from Teresa-Marie Pagliaro's photos. 

          The second method that struck my interest was solving multiplication problems using the Multiplying Lines method. Instead of using the traditional multiplication methods, using one's basic times tables skills, students draw a series of lines to obtain the same answers. I found this method extremely interesting due to the fact that it is a new perspective of looking at multiplication. The following link will give a demonstration of how this method is done.

https://www.youtube.com/watch?v=_AJvshZmYPs

          Overall, I believe teachers should always keep an open mind to different teaching methods. Each student learns in a different way. Therefore, we should all as educators keep an open mind to new ideas in order to create a comfortable learning environment for students.

Welcome to Math!

Hello fellow classmates,

       My name is Teresa-Marie Pagliaro and I am a recent graduate of McMaster University with a Honours BA in French. One of my great admirations is learning new languages and helping students become acquainted with the French language. Due to this admiration, I also took many courses in linguistics. My studies in linguistics allowed me to gain a different perceptive of the general makeup of languages; from the basis of learning sounds to the use of words in forming well structured sentences for communication and writing purposes. This same sort of learning process can be applied to learning math as well. For math, we must learn the basic foundation operations, such as addition, subtraction, multiplication and division, before we go on into learning new and more complex problems.

       Since high school, I have not taken any math courses. However, I do believe that I have developed a great foundation of mathematical knowledge through my elementary and high school education in the subject. Math was never one of my favourite subjects, but I managed to obtain a general understanding of its concepts. One way I have tried to re-familiarize myself with J/I concepts is working as a tutor at the Hamilton Oxford Learning Centre.  Primarily, I help students, from grades 1 to 8, with their English or French homework; but I occasionally work with math students. Working at an Oxford has helped me enhance my pre-attained math knowledge and allow it to grow as I review the various math concepts with students.
    
      By the end of this course, I hope to gain a better understanding of techniques that I will be able to use in the classroom. Many students find math difficult; as did I. As an educator, I believe it is important to make the students feel less anxious about learning and completing math concepts. Math concepts should not be feared. In order to promote the retention of information, teachers should make the concepts relatable to the students on some level. Whether it is through using sports, food, movies, etc. teachers can try to use any material to help the students remember the material they have just learned  Therefore, I would like to learn different strategies that will help engage students and create a fun learning environment in order to build confident math skills.

Clipart. 2016. Math Symbols Clipart [Online Image]. Retrieved from http://cliparts.co/clipart/7428.

Looking forward to the rest of the semester and future posts,

Teresa-Marie Pagliaro