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!!!

4 problems, Tiles 0-9 - only use them once AND GO!

Welcome back to my blog! Hope you have all had a fantastic day!


Today I am going to share a lot of new information with you but am going to talk mostly about my presentation. I presented and shared an activity with my fellow teacher candidates surrounding addition and subtraction! The presentation went very well and all students were engaged in the activity. I hope that you as a reader are just as engaged in the material as they are. If you are a fellow teacher candidate or already have a classroom of your own this activity is fantastic for grades 5 and up! The reason I include that the activity can be used in older grades is because elements of it can be altered and changed around to make the task more difficult and challenging for the students. This activity includes targets finding the missing variables, addition, subtracting and in a whole "building number sense".


At the beginning of the activity I presented to the class how I would carry it out if I were teaching it to a group of elementary students. I would first begin with providing the students with a clear learning goal that is to be achieved through the math activity. As a class I would brainstorm with the children all the different ways in which we could use to succeed, this creates their success criteria. Then i presented my fellow teacher candidates with my activity by splitting them up into groups (six table groups in total). After doing this they were instructed to look at the package on their tables. Within the packages consisted:

- four separate addition and subtraction problems ( 2 of each)
- paper tiles numbered from 0 - 9
- scrap/ extra paper (for those students who prefer writing and solving over manipulatives)

What is missing?

After the classmates pulled all the materials out they were instructed to find the missing variables in the problems provided. They could NOT use the tiles more than once. They were given a time limit and sent off to work as a group to solve the problems.


Below is the worksheet that I handed out for those students who wanted to keep it for their future as an educator or to use during the class time to document their answers.

I walked around the room and facilitated conversation with the groups and saw many different levels of math in one room. This is something that I enjoyed seeing because I saw other candidates helping each other and problem solving as a group. We had one very speedy group and they shared with the class how they resolved the problems so quickly. They won rights to brag for the rest of the class!! I saw some students saying it was difficult or it was easy, something that I am sure when I use this activity in the classroom I will hear as well. All students are at different levels and an option I could have had was to provide the quick and winning group with a multiplication question and division one to see if they could problem solve those together as well. Time did not permit it as I needed to make sure I covered the grounds of the Mathematical Process Expectations and the Overall and Specific Content Expectations of the Curriculum.

What did I learn?

I learned a lot from presenting this activity. Not only did I learn how manipulatives and games keep students, even 20 years and older, engaged in math but I also learned and witnessed different levels of math. I was able to take away from this presentation how beneficial group work is, or even working in pairs, when it comes to problem solving. 

Hope you enjoyed today's blog and keep coming back for more!

Please feel free to use this activity in your own classrooms as an educator and know that it is engaging, fun, educational and successful!

Cheers,

Emily

Weekly Report & Reflection 3

So much to learn, so little time

Hello everyone! Thanks for coming back and checking out what I have been learning! I have lots to share with you in today's blog and cannot wait to get started!



This week was all about learning the different methods and manipulatives one could provide to their classroom to use for division problems and to understand division on a deeper level. Visuals and manipulatives have proven to help children better understand and remember concepts within mathematics because it is a hand on activity that can explain the why in a method other than paper and pen.

Manipulatives galore! 

We did multiple activities and were given various manipulatives to work with when solving the open problems. To begin we worked on our own and picked one fraction that we liked. This fraction would have been a proper, improper or mixed fraction. The fraction I chose was 3 1/4 . I had no other reason for picking this fraction other than it was appealing. Other fractions that my classmates picked ranged from 1/4, 5/8, 1/2. After choosing my own fraction we were asked to find different ways to represent our fraction. I began with shading in a fraction circle to represent mine (Image shown below).

Group Work time!

After doing this I used fraction circle pieces, one of the manipulatives our table was given, to represent my fraction. We were then asked to collaborate with out elbow partners and find ways of adding our fractions together using the manipulatives we wanted. As this was my first time ever using the fractions circles my partner and I agreed and enjoyed using those as one of our ways to show our fractions. Below is a picture of Daniella and I's fractions added together. To remind you my fraction was 3 1/4. There are 5 whole circles (whole numbers) and 3/4 of the yellow circle. Any idea of what Daniella's fraction was?

After doing this activity, as a class, we were introduced to the "Big Ideas about Fractions". This slide was very informative and I feel a great thing to share with my students in the future for them to better understand and grasp the concept and meaning behind fractions.

In this activity we were provided with old egg cartons and counters or shapes. This activity was eye opening to a new way of teaching children what fractions really means. We were given fractions and as a table, which quickly turned into a class conversation, we put in the counters or took out to represent the fraction given. For example, in the photo below, only half of the carton is filled with the yellow shapes therefore the fraction represented through this would be 1 / 2. This proved to get trickier and more difficult as the fractions were switched around but was a great method at learning to grasp and understand fractions. When students are doing this they could also use this method with mixed fractions - they would just have to fill an entire carton up to represent one whole! Fun and engaging way to get the best out of fractions.

The activity following this one we were provided with 3 clocks each. Our job was to divide correctly the clocks into the following:

1/4

1/2

1/3

At the end of the day....

I was able to learn so many different approaches and ways in which an educator can present to their students surrounding fractions. From my own experiences as a student and from witnessing students throughout volunteering I had come to the conclusion that fractions would always be too difficult to understand and grasp but after this weeks activities I am not only certain that these methods will be very useful in my classroom because they can help students reach a level of understanding that was not there before.

I cannot wait to see what happens next week,

Until then,

Emily

Hope all of you have a fantastic and safe Thanksgiving! Happy Turkey Day:)

Weekly Report & Reflection 2

Hello!

Week 2's class was a success!! Class this week concentrated on student algorithms in addition, subtracting, multiplication and division. Seems like a lot to take in for one class? It wasn't.

Something that I did this week that I will absolutely remember and use in my future classroom is the addition and subtraction algorithm introduced in class. In my elementary years I learned to add and subtract in one way and that method was the "correct" one. I am soon learning throughout the math class that it is not about a correct method, there is no correct method. I was taught to add and subtract from the right to left which to me proved to be difficult. Apparently I was not alone with finding this method difficult.

Learning new ways to add...

In the below photo there is an example of adding from left to right. Personally when I witnessed the teacher lay out this method I was shocked. It all made sense to me, adding left to right just as I read and instantly I told myself that this is how I will teach adding to my students. Why not teach them a way as natural to what they are used to as possible? This will not only come easier to them but boost their confidence and enjoyment for math work. This part of our lecture created an 'ah ha' moment for me because I realized that I was not 'horrible' at math but instead I was not given the methods that worked for me to be as successful as I would have liked and I will remember to use these methods within my own classrooms when I am an educator.

This is one of the alternative methods to addition explained above.

In addition to the above algorithm method there are various other ones that were introduced in class that I have never been introduced to or have never been instructed to use during my education. I will be sure to share these successful methods with my students to ensure that my students have the skills and methods they need in order to be successful and love math. Below is a secondary method to adding numbers for students and this method can also be used for subtraction. This algorithm method is skip counting.

I have attached a resource for educators that has multiple different skip counting worksheets for their students that are printable! Enjoy :)

http://www.kiddoshelter.com/skip-count-by-5-worksheet/

Try this song out with your younger grades!

New ways to multiply too! Multiplication made easy...

Not only were these two addition and subtraction algorithms successful and appealing to me when watching them put to the test but multiplication algorithms were also offered in this week's class. This method will be beneficial for all students learning to multiply and for those that learn in a more visual manner. This concept breaks down the different meanings behind multiplication and why we multiply.

Math has been seen by any as the big, scary bad wolf of school work and after only a few hours learning the different ways to teach, this week specifically learning algorithms, is changing that picture for me and I hope for you reading this as well!

Thanks for checking in and following me throughout the beginning of this math journey! Cannot wait to share some more with you next time.


Until next time,
Emily


Cheers!!

Welcome Readers!!

Hello!

Thanks for stopping by my new blog! I am so excited to get started and journal my experiences and ways to teach math! First of all, I am thrilled to starting Math again. I will not lie, when I was in my younger years and well into high school I found Math class one that I would try to avoid. I found it difficult and was one of those students asking "when will I ever need to use this in real life?".

Although I am still not the strongest in Mathematics after just one class I am open to learning all the different ways of learning and teaching math that are different than what I learned growing up. I cannot wait to share with all of you the new things I learn and how I grow in Mathematics.

My goals pertaining to this blog is to have a spot that not only I can access and keep my findings and new learnings but also to provide a spot for you! Readers who may not love math or who might have had similar experiences as I did. A place for us to all gather together and recognize that math is for everyone and everyone can be good at math!

I hope to inspire and have you come back weekly to see what I am up to!

Emily :)