integers, not a negative experience

Class this week had us finishing up with fractions, a brief introduction to integers and class problem presentations on integers. So lets get started.

First, I am really happy we spent a great deal of time on fractions. I feel as if they are some of the hardest problems in elementary math and finding a way to show the simply way to an answer of a difficult question really makes my job as a teacher easy and it makes sure I can benefit my students. Like I have said before differentiated learning is something that needs to be understood by the teacher, there are many different students who learn a different way than you do and it is your job as the teacher to explore all ways to present and solve a problem. After all, you want your students to succeed, but also understand the problem.

I really enjoyed the mini conference activity. Not only did we get to share our ideas from the "Kitty Cat Problem" but we also had examples from other students in a previous session or class. Since our group solved the problem one way we were able to pair with another group in a "conference" and see the way they solved the problem. This helped us understand how other people see the problem, and when they explain their thought process we are able to see another a solution to the same answer. We went around to look at some other examples of the same question solved a completely different way.  It was actually amazing how many different ways were expressed. One way which I will post below was actually so simple and so smart that I completely overlooked that way when completing the question myself. It goes to show when you are tough a certain way, you tend to avoid other ways of doing a question which I myself am really working on in order to show my students all possible solutions.

Below are the solutions that my group did and another groups solution done a completely different way. The point of the question was to find which store sold cat food a cheaper price.

Finally the class ended with the activity presentations on integers. Integers is not the most difficult concept but again it is great to hear and understand different ways to express a topic. What I really enjoyed was how the presenters really gave us great real life examples of integers. Relating math to real life is great way to have your students understand that math can be applied in the real world and your not just learning math in school to forget about it later.

Continuing Fractions

Last week we continued with fractions, continuing to make them less and less complicated for ourselves and later our students. I guess you can say this is the second 1/2 to the lesson (see what I did there).

One of the big topics this week was division of fractions, pretty scary as we approach Halloween. But of course, there is always a simpler way to do things than the way we have been taught. Most of us had been taught that you only find a common denominator for multiplication of fraction right? Well despite being told no you can't do it, you can actually find a common denominator to help divide fractions easier. When I first heard this of course I was thinking, no not possible I haven't been taught that way. Well consider the following problem. I will go through step by step how to solve it.

Maintaining an open mind when coming to class is really important when attempting to understand new concepts. For someone like myself, I find that extremely hard, I guess you could say I am fairly close-minded when it comes to certain things. I am working really hard to fix that because I want to show my students all the ways to solve different problems because teaching them one way will not be enough for some learners. Every student is different and many of them will not learn the same way as the other so its important to understand different ways to find the same answer. It will help you personally become a better teacher.

Continuing with the lesson we also reviewed six steps to creating an open question, a question that allows the learner to make decisions. These six steps are:

1. Begin with answer.
2. Ask for similarities.
3. Leave certain information out of the problem.
4. Provide several numbers and math words. The students will have to create the problem using the numbers and words.
5. Use soft language.
6. Prove that an idea is true or false.

A simple example would be using the number 43 and the word sum, create a work problem that has  fraction as the answer. An answer could be Jimmy has 21 green apples and 22 red apples that add to a sum of 43 apples total, he has 21/43 green and 22/ 43 red which can be expressed as a ratio of 21:22.

Overall the lesson was really great, I learned another new concept which I look forward to applying in my classroom during my placement block.

Another interesting Lesson/ Fractions

The last class was another new experience for me, bringing new topic and teaching methods to my attention, as well as different ways to solve a single problems. the classes focus this week was fractions and all of the different parts and aspects of teaching and learning the topic if fractions in class. What I found important about the lesson on fractions is how easily relatable it is to real-life situations, which is what we want in order to keep the class involved and help them understand the importance of the lesson.

Take the example of 1/4 or 1 quarter. How many ways can you express that?
25%, 12 to 3 on the clock, which relates to people saying "a quarter after 6", 25 cents of the dollar etc.

A simple fraction related to 3 different things easily.

We then went into the addition and subtraction of fractions and how to explain why we don't add the denominators when adding (because it is a part of a whole) and the overall definition of a fraction to explain to our class.

Definition: a part of a whole number
Characteristics: numerator, denominator, division, percentage, ratio
Examples: 1/4, 25%, 0/4, 4/1
Non- Examples: 14

What I liked was the discussion of what us as teachers want our questions to lead to, our question goals. This had me thinking what I want personally out of the questions I ask during class time. Fearless speaking and sharing is something I consider important. I want my students to be able to discuss together as a group and as a class, even with me, aspects of the problem. When in a group and they are sharing their ideas the different types learners will be able to collaborate, which will lead to various answers and inclusion. This also evokes thinking, because having open questions there will be different answers and when the different earners are discussing their answers, they will be able to see the questions the different ways their peers do.

Finally, I really enjoy using physical manipulatives, because I was never given the opportunity to learn this way, I am able to take these ideas and apply them to my class room along with some of the learning styles I have from when I was in school.

The pictures above are simples ways to have students represent fractions using physical manipulatives that can be found almost anywhere. Chocolate also works great!

Overall the lesson on fractions was intriguing, learning different ways to express fractions and represent them in real-life is new to me, because of the way I have been taught, meaning I am both learning as a student (ways to do these myself) and as a teacher (ways to incorporate into the classroom).

Week Sept. 27.

Hey everyone!!!

So today was my learning activity presentation. I had the topic of whole number operations. Honestly I was really nervous going first and all so I'm hoping it went well. Using what I learned in the class previous, and in other classes I am taking; I decided to gamify the topic and activity in order to grasp the attention of my fellow classmates. I related it to a real life situation (even though it was fictional) and based the question I had on that real life situation. I created a batman vs the riddler theme. Here is my problem:

The Riddler has taken over Gotham City and is hiding out in secret location. In order to enter, Batman needs to solve the code to enter the base and find the Riddler. Will you help defeat the Riddler, Batman needs your help!
Using the resources given to you and techniques learned in class, use the clues left by the Riddler to get the code to help Batman enter the secret hide out.
[The resource would be base ten blocks of 100, 10 and 1 to help with grouping and a number line on graph paper to help with a visual. The clues left by the Riddler are: five numbers add to 100 (Clue 1), the difference between the greatest number and the lowest number is 12 (Clue 2), the numbers in the sequence cannot be the same (Clue 3), there are 2 codes (Clue 4). They would be on separate pages and you would explain to the students they cannot show there clues to another group member, they would have to verbally communicate with each other about their individual clues.]

I really hope the class enjoyed the activity and had fun. Also my fellow class mates who presented also did a great job!

Also, this week in class we focused on multiple ways to express and show how to complete an equation. When doing subtraction we used two methods: compensation subtraction and constant difference.

The example of compensation subtraction is as follows:

 547

-296

simply add 4 to each number you get

 551

-300

 251

The example of constant difference is as follows:

 2002

- 467

when you take away 3 from each number you get

 1999

- 464

 1535

Using these methods you can make equations simpler and easier to follow along and understand the key concepts of subtraction.

We also talked about the different ways to express 25 x 28. We can use an array to simplify the parts of the equation. Also shown in the picture below are the many different we can explain to a learner how to solve for 28 x 25.

Finally, students need to see math as sensible (not something they don't need), useful (related to real life), and do-able (for confidence). We talked about what makes a good math problem and these words also fall under that category. Some other things that make a good problem are wide base, variable, engaging and entertaining.

Thanks for stopping by, catch you next week. :)