All good things come to an end...

Me at the beginning of this term:

 

Me Now:

FINAAALLYYY

I do not even know where to begin when reflecting on the year's Junior/Intermediate Mathematics course. Not only did I learn and finally and confidently understand many different strands of math but I also learned how to help my students learn the RIGHT way. I am so excited to include all the various methods and approaches to math so my students can feel the way the man in the gif does when they learn math. I want the students to be confident in their math and have a growth mindset when learning and I can confidently say that I will be able to achieve this with my kiddies because of what this class has offered me.

At the beginning of this course I hated math, and I do not throw that word around gently. I truly believed in M.A.T.H being mental abuse to humans and identified with others who felt the same. I laughed on the first day when Pat announced that every person is a math person and we would grow to love math. I thought that would be impossible to achieve but little did I know that it was a growth mindset I was lacking. I didn't know that my struggling with math was actually my process of learning and from every mistake I made I learned.

Let's go back to the first few weeks of this course... if you want you can join me as I look up into the air and imagine a memory bubble appear...

"Let's start at the very beginning, a very good place to start"

YES I did just use lyrics from The Sound Of Music...

I think the most memorable class with an a- haa moment at the beginning of this year was with fractions! We learned that common denominators can be used not just for addition and subtraction but also for division! This is something that as a student we were never taught. Instead we were taught the more complicated and irrational way. Move over old way and hello new methods! I hope to pass along lessons and methods such as these with my munchkins!

Another one of my favourite memories was the week we completed patterns. This past week I actually taught a lesson with my students on number patterns but prior to using numerical patterns I used the example of skittles and shared with them what I had included in my blog. My students quickly understood what I had to share and it was evident they understood my lesson and the new material they were given. 

My class and I made a growth mindset anchor chart together that we have posted proudly for all to see in the classroom. When students get frustrated with getting a problem in math wrong I just point and the chart and they know they are only steps away from understanding the content! 

In addition to these specific weeks and lessons plus more benefitting my current placement I have also been turning to the textbook for additional resources and advice when composing my math lessons. The teacher tips and activities throughout the chapters help me to find one that is age appropriate for my students and in addition to see the student examples provided to know how to assess my students. 

I think the assignment I benefited most from was the lesson plan for mathematics. Able to receive feedback on the lesson plan helped me to further understand how to make a detailed and appropriate lesson plan for my students. This was a great learning experience and I was happy to receive feedback from it. 

 I think growth mindset is the most important thing I have taken away from this course. I have learned that my brain, specifically my math brain, is always working and always one step closer to problem solving. I am no longer afraid of math and intimidated by word problems and equations. I am no longer intimidated by manipulatives, measurement and fractions. Most importantly I am no longer intimidated by group work. It was this course that made me comfortable and open to working with other people in order to get to the end goal - in order to answer the question.

After working with elbow partners, group work, group congresses and after presenting my activity to my fellow teacher candidates I have learned that every person within a group plays a valuable role.

Overall, I have learned more valuable lessons and methods through this class in comparison to my others and I am thrilled to be able to incorporate them into my classroom with my students. 

If you would like, feel free to scroll below to browse the various memes that will make you laugh that are all connected to math!

Thank you so much for staying and catching up with me on my math journey! Hope you have enjoyed the blog and learned many things from what I have shared!!  

Have a wonderful Christmas and a Happy New Year!!

Emily De Melo

Cardio? No Thank You... I Thought You Said Oreo

Estimation

This weeks class was great! Not only was it filled with a variety of open questions surrounding estimation for each table to work with but it was also filled with OREOS!!!!!

The class opened up with an activity that circulated the room for us to guess how many Oreos were in the jar. Although when it reached my table I just wanted to grab them and run I estimated and nicely passed along. This may or may have not been after Pat told us we would all get our share...

As the jar of Oreos was being passed around the class for them to secretly make an estimation and write it on their sticky note the class continued on with this week's lesson. 

What is an Estimate?

- a thoughtful guess

- saves time and effort

- can be used the gauge the accuracy of their calculations

- we do estimates when it is not practical/ possible to count and measure the precise amount of something (aka a full jar of cookies)

Now that we are all on the same page about what an estimate is and what it can be used for, take a look at this week's problem with Daniella and Emily:

As a group, Courtney, Daniella and myself all divided the cube blocks equally as each cube represented one movie ticket. The cubes were a great manipulative for the students to be able to visualize the problem and understand what would be fair! 

Thanks for sharing Daniella:)

Our group had fun with this activity working together to demonstrate the fair share with blocks!

Here is Courtney dividing up the blocks in one of our activities!

Although I know you're just thinking about the Oreos we must move on!!

In addition to learning all about estimation we also learned about MEAN, MEDIAN, and MODE. Here is a fun, short and cute little riddle (with the old methods) to practice and or post in your classroom for your students to remember and decipher between the three!

During our lesson on the three Mean, Median and Mode we learned a different alternative way at calculating the Mean. Throughout our education career we were taught to add up all numbers and divide by how many numbers there are. This method works but there is always another way!!! We learned that you can also find the mean by finding the middle number...

Here is a couple examples if you are confused (Do not worry - I was at first too, but now we can all be Math Geniuses!!)

1) Find the mean (the average) of these 3 consecutive numbers:

4, 5, 6.

Old method: 4 + 5 + 6 = 15

15 / 3 (HOW MANY NUMBERS THERE ARE) = 5

New Method:

4, 5, 6.

5 is the middle number, therefore 5 is the mean.

2) Find the mean (the average) of these 4 consecutive numbers:

3, 4, 5, 6.

Old Method: 3+4+5+6= 18

18/4= 4.5

New Method:

3, 4, 5, 6.

4.5 is the middle number, therefore 4.5 is the mean.

So many neat and cool tricks to teach the students when they are learning these new things! Great way to help any student who is having difficulty understanding how to find the Mean and more!

A great week with lots of new ideas relating to estimation, mean, median, and mode to pass along to our students. Towards the end of class we talked as a group about assessment, feedback, promoting higher order thinking and improve student learning. Here is some pictures of the slideshow that we all discussed. 

Feel free to jot some of these down for what you are assessing your students or to share with your students so they know what is expected. If you do not want to record these for your own purposes, grab a glass of milk and some Oreos and enjoy a snack while reading!

What a great week filled with sugar, group work, new methods and new skills that I cannot wait to share with my students - the methods not the Oreos - those are mine! 

Take care and see you next week,

Emily

Group work does not have to be hard anymore..

Collaboration = Frustration

Frustration = Collaboration 

My entire university career, high school and elementary years was filled with collaboration and group work in multiple subjects. Every time someone mentions collaboration and group work I instantly get frustrated and if someone were to ask me what frustrates me, my response would be collaboration. This has all changed since teachers college and learning to work collaboratively with my teacher candidate peers in classes. I always felt that I was left doing all the work by the end of the task but, and this is shown through this weeks class particularly, the teacher candidates are all learning and want the same thing. We all want to work and help each other succeed and in the end we will be working in collaboration with our students to ensure the same thing. This weeks lesson was enjoyable and went by very quickly because of the hands on, on our feet, critical and fast thinking that each task required and that each group had to master. 

"Alone we are smart, together we are BRILLIANT" - Steven Anderson

Below I have attached two different anchor charts as examples of what an educator and their class can create at the beginning of the year. Both are a different approach at the same outcome - ensuring that the students know what group work is and how it works. Anchor charts are a great resource to have in the classroom to redirect the children to it if they fall off task. As long as students are aware of their expectations and understand them, collaboration within the classroom is possible!

                                 

When entering into the classroom the teacher candidates were instructed to choose a popsicle stick. on each stick there was a printed number on it. Each table was to organize themselves into a group containing one of each number (1-6). This is a great tactic and way at organizing group work. All students are mixed with a variety of levels and skills. Everyone has something to bring to the table and people will work hard to ensure not to let down their group partners. This also acts as a great way to keep kids on track instead of pairing them up with all of their friends they can socialize and mingle with other students in the classroom. I have seen a variety of methods when putting students into different groups and this is by far one of my favourite! Try it and let me know how the groups work out!

After meeting up with our group the instructions were to go to each station and complete the task with our friends. Each group member is given a clue that they read out and from there they can either, build the figures or find the solutions! The stations were enjoyable because it sets up that every member of it has a valuable part in order to complete the solution. Everyone is given importance in the group and this motivates everyone to work together which results in SUCCESS!

Here are some of the stations our group visited and completed - together!

 

Most successful group work/ collaboration experience that I have had yet! Collaboration is important, for more reasons than just working as a team. It teaches students to be able to provide feedback, receive feedback, work together, orally communicate their thoughts and understandings and overall will benefit them in their future. With any job and career one has collaboration will be a component of it. By students learning these life skills through their education they will not only succeed through the class they are taking but also in their future. Three cheers for group work!!! Cannot wait to try an activity like this within my classroom!

And for a little inspiration as you leave my blog today here is BILL NYE THE SCIENCE GUY!!

Couldn't have said it better Bill,

Emily

Measurement

WILD ABOUT MEASUREMENT

Learning Goal of Todays Lesson: 

- learn vocabulary for geometry and measurement

- use an organized  inquiry to complete an open question for geometry

Starting out, we took part in a math activity that we have done in a prior week called "I Have, Who Has". This game served as a minds on activity but can also be used as a form of consolidation after a lesson, introduction to content or overview/recap. 

Let the games begin.....

The game starts off with one person who has a clue such as "I have an Hexagon, who has...?" and the person who has a hexagon would respond saying what they have and ask who has their next clue. If done correctly the game includes all the students and will go throughout the classroom quickly. Associated with the game is also a lot of giggles, quick thinking and helping out a peer if they're not quick to respond. This game can, not only for math, be used for a variety of subjects. It helps students show their knowledge of the subject, think on their feet and helps with their ability to recognize and work together with their learning. Great game that I will most defiantly implement in my classroom, both during practicums and during my career.

Following this activity the class worked together to find the perimeter and area of a certain problem. Pat introduced the problem to the class:

"I can create 2 rectangular cages that use the same amount of fence but one cage is 6 square metres greater than the other. What could their side lengths be, if the sides are whole number values?"

She then told us (as advice to us as teacher candidates) that we should, during this task, encourage students to try multiple approaches and when they do to keep tack of what they have tried. This will help the students remain organized in their findings. 

After this activity we worked with our elbow partners with multiple manipulatives that helped us to to explore the many different ways we could measure. Children can, after a task such as this one recognize that there are many different ways in measuring and that everyone can start!

Although not discussed in class, I found the resource below and think it would be great and very beneficial to implement into the classroom when teaching students about measurement. I know as a student measurement always confused me or I had difficulty when trying to remember certain rules. This resource is an Area and Perimeter Board Game and is available for teachers for FREE! Can help students to become pros at their area and perimeter skills. Within my practicum classroom right now the students are learning measurement as well. This week's lesson was a great way for me to pick up more methods and tools at approaching measurement to ensure all the children will be able to understand and grasp the new information.  Click the link below to check out the Board Game Freebie!

https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Board-Game-FREEBIE-2868948

There is a variety of resources available to educators to help them provide the best possible resources and tools to their students. I cannot wait to implement the tools used in this weeks class into my classes. 

Take care and we will have a math congress soon!

Emily

Taste the Rainbow - Learn the Patterns

Touch my candy... I dare you

Another week complete, another math class completed and so much more to learn! This week as a class we concentrated on Patterning and Algebra. This week's 3 hour class was filled with hands on work, presentations, a lot of a - ha moments but also included some frustrations and struggles with relearning Patterning and Algebra. 

I want to begin with first concentrating on the frustrations and the struggles my group and I all experienced in this week's class. In the picture above shows sixteen slips of cards. The instructions were to group them with their "teammates" in a way. There were equations, graphs, tables and the original model. Now, reading this one might say thats easy or let me try... 4 of the cards were blank. We had to appropriately match them together with their group of 4 and it had to all make sense! After thinking we completed it correctly we were then disappointed to hear that we indeed did not complete the task correctly- they did not match. Although we show signs of frustration, myself included, Pat reminded us that it was okay to make mistakes and that through the mistakes or struggles is how we actually learn. I was able to, through this task, identify with a student that may have a harder time understanding math until they are given further guidance and or motivation to identify where I went wrong and what I needed to do to fix it. This activity quickly showed me how much truth is behind the line that Pat has said consistently along the lines of behind struggle is growth. After struggling with this task and feeling silly about it our group fixed our mistakes and were successful. In addition to being successful we were also confident that although we may not get something at first, with patience and perseverance we will get there. Lesson well learned!

This week we had a variety of students presented and included candy in their presentations...

The below picture shows one of the teacher candidate's presentation on completing the patterns. An easy task and a delicious one as well! We were also given instruction to complete our own pattern. In addition to the skittles we also had a warm-up activity with making number patterns, writing next terms, and finding the rules for each of the number patterns provided. This is just one presenter out of the few that shared their activities with us but the skittles helped to make this one a memorable and tasty one!

Making Math Meaningful - Making Patterning and Algebra Fun!

Within this week's readings there were a variety of teaching tips and ways that an educator can encourage students through their learning of patterning and algebra. I think the idea that the book gave of students being "encouraged to create patterns as soon as they have an understanding of what patterns are" (Making Math Meaningful to Canadian Students, K-8, p. 364) is crucial for a teacher candidate to take away. Once a student can understand what a pattern is and they are able to create their own and learn the different types in addition then this specific strand to them will be successful and easy to achieve. If students are encouraged to create their own they can understand what goes into a pattern and how to recognize it in others. I would, as a teacher, let students make their own and share them with their fellow classmates to complete. This would create a diversity in the patterns the students are creating and completing!

When it is all said and done..

Although this week's class was stressful because I found myself struggling, I can now look on it as a learning experience that I have gained. 

Hope to see you back here again and thanks for reading!

Emily

What is an Integer?

Positive, Negative and All In Between

This week in Mathematics we revisited Integers. I use the term revisited because it, to me, feels like too many years have passed since I have studied or worked with Integers within a classroom setting. Although it is clear that we use integers everyday in our lives without even realizing it having them placed infant of me caused me to be a bit nervous in Tuesday's class. 

Before jumping into integers we had the chance to meet up with our groups from last week and share our solutions and study one other solution on Mr. Joel's kitten math problem we were assigned the previous week. After listening to another group share their findings - which was done in a different method than ours - we shared ours. We were able to have a professional learning conversation with the group and give advice and our likes and dislikes about ours, and their problem solving answers. Below is a picture of (in black and red) our group's solutions and in blue another table that joined to share us. This exercise showed us that although it is one problem and there is one answer we were all able to reach the answers in a different way - we were all able to start which means this was a GOOD word problem. A good word problem should be the goal behind every problem that a teacher provides their students. We, as a class, brainstormed multiple different things that make a good word problem, in addition to being able to get started. Manipulatives, soft language, wide base and challenging are some of the many that the class knew would lead to a good work problem.

Following sharing our findings with one group we got to walk around the class to see each table's methods on finding who's store would be the cheapest to purchase the kitten food from. This is called a class congress and although, unlike a gallery walk where we would leave behind comments for the groups' work we instead compared it back to ours. This work created a lot of ah -ha moments for both my group and myself when seeing all the possible ways of approaching the word problem!

We learned and got to play around with an online game as a class prior to the presentations at the end of the class. The game showed how engaging, even as an adult, a math game can be for students when learning new things.

The multiple presenters all applied math and integers to different parts of our lives - which further proved that we do use integers everyday... even if we do not realize it. 

Kelley, for example, used integers in the sense of temperatures. We learned and were able to grasp and understand that if a temperature is negative it is cold and vice versa. We were also given a couple minutes, included with some great background "around the world" music, to complete ordering the integers in the different countries she provided. Not only did we relearn integers and learn to order them but we also had to be able to complete integer formulas. For example if Country A is 45 degrees colder than Country B it is ? We had to remember that when we add positive to a negative we get less negative and negative to a positive we have less.

Adam, another teacher candidate that presented on integers, provided a different view and spin onto integers. He stated that negative integers were our negative experiences in life and positive integers were to represent positive experiences in our lives. This explanation could be good when teaching integers for intermediate students who are having a difficult time in trying to understand or recognize integers in their everyday lives. 

Check out this poster that you can hang in the classroom to remind students of the different rules of adding and subtracting integers if your student needs to remember them! Although we have learned this week to stray away from those riddles and really understand what is happening when you are subtracting or adding this is still an excellent tools for the little kids!

https://www.amazon.com/Integer-Song-Classroom-Math-Poster/dp/B00OHSOIKY/ref=sr_1_323?s=home-garden&ie=UTF8&qid=1469458737&sr=1-323&keywords=classroom+posters

Check out this page for positive and negative number games for your students! A great resource with relatable scenarios for students to comprehend what the negative and positive signs actually represent!

http://www.teachinginroom6.com/2013/02/positive-and-negative-number-game.html

Great integer week and cannot wait to see what the next class has in store! I have been enjoying learning all the new ways to approach math and participating in the activities that the students have been presenting. 

See you next week..

Take care, 

Emily

Fractions Street - Weekly Report Week 4

IT DOES NOT HAVE TO BE LIKE THIS ANYMORE...


Do you have difficulty with fractions? I know, up until this week's math class, that I have experienced great difficulty with ordering fractions, and other operations that involved fractions. This is not the case anymore and I am so excited to share the methods that I have been taught with you so that you do not have this issue either!

Let's get started!

First off I want to discuss how scared I was of the words fractions and divide in the same sentence. Growing up and no understanding math proved to be difficult enough - did teachers really want me to divide parts of something? It is now clear to me, through much simpler methods, of how this can be done.

DID YOU KNOW COMMON DENOMINATORS CAN BE USED NOT JUST FOR ADDITION AND SUBTRACTION BUT ALSO FOR DIVISION??!!

I didn't either... until now!

We learned that you can either just divide straight across the fractions (numerator divided by numerator 2 and denominator 1 by denominator 2) instead of cross multiplying or flipping or doing anything else just plain silly with the fractions. We also learned that for those fractions that might be difficult to divide to create common denominators to help us solve the division equation! Fractions made easy - who would have ever thought!

In addition to the mind-blowing and "my whole life was a lie" feeling in class this past week we also had the chance to be hands on with some manipulatives. After being read a story of "Mr. Tan's square tile story" we, as individuals in a group, were instructed to complete the square tile with the fractions of the tile we had. 

As you can see from the above two photos it took multiple trial and errors before I achieved the final and complete tile and it MAY HAVE taken more fails than posted above.... may have.

Mr. Tan's tile is fixed!

Below I attached a similar activity offered of forming/ constructing a tile or square with different "broken" shapes and triangles! Try it and tell me how you find the activity! Good luck:)

http://handmadekidsart.com/heart-math-puzzle/

 This taught the class many different things but I feel like what I took away from it the most was having a firm understanding of fractions as a whole. I feel like this activity would be so beneficial in a Junior/ Intermediate classroom for many reasons. First and I feel most importantly, it creates an overall understanding of what fractions are. Fractions are a part of a whole and there could be many smaller or larger fractions - like in the tile example - that add up to a whole number.

I have included a resource that provides access and where to find certain apps for teachers/educators to use in their classrooms in relations to FRACTIONS!!!! Fraction games and apps to keep the kids loving math and learning.

http://imaginationsoup.net/best-fraction-apps-kids/


Overall fantastic class and I am so happy to no longer be afraid of fractions but instead love teaching it and teach my students of the future to love it too!

Next stop INTEGER TRAIN!!!