Beyond the Classroom

Math night! Today was math night at my former school. An event where parents and students worked together and completed math problems. This is a new initiative. I was not there, but my former students decided to leave such a warm voicemail that I could not resist posting on this blog.

Teaching can be very difficult and stressful without much or any positive feedback, and if you are enthusiastic about teaching, sometimes we always wonder and ask ourselves "is what I'm doing really meaningful? "Am I really making a difference?"

I am grateful, and thankful that despite only being with them for 4 months, the bond that I have with my students has clearly transcended my classroom. My students call, text, and email just to say hello and to talk, and/or to ask me questions and help them with their homework. I love them too.

Division of Fractions by Whole Numbers and Fractions by Fractions

Before the Christmas break we were learning how to divide fractions by whole numbers (and by extension, divide fractions by fractions). I've always found that is much easier to teach this using models so that the kids understand the concepts before applying any rules or algorithms. Students and even teachers (some anyway) are familiar with using "Keep Change Flip" as a procedural method used to solve division with fractions, but don't truly understand why it works. As follows:

Given the following problem: Mr. E has ½ a bar of hersheys chocolate. He wants to split it equally between his three friends. How much chocolate will each friend get?

Chocolate bar before dividing equally between 3 friends (½)

 

Chocolate bar after dividing it equally between 3 friends (⅙)

Therefore:

From there, students develop the understanding that dividing is the same thing as multiplying by the reciprocal (For example: ½ ÷ 3 = ⅙, and can also be written as ½ × ⅓  which also equals ⅙).

Knowing that division is the same as multiplying by the reciprocal, you can easily divide fractions by fractions.

Example:  ½ ÷ ⅙ can be written as ½ ×  6/1 which = 6/2 which = 3.

Lastly, this also applies to whole numbers. Example:  
12 ÷ 4 = 3 
12 × 1/4 = 12/4 = 3


Wait!
If you have time, watch the video below of a student that has difficulty with the model (mainly due to a lack of conceptual knowledge of division) and my attempt (which I don't think was that great) at helping her solve the problem!

P.S. - Division of fractions by fractions can be modeled using fraction strips. I made a post prior to this where students were using them to solve word problems. It can be found here: Dividing Fractions by Fractions - Fraction Strips

A New Adventure~

Recently, I was accepted to the University of Delaware! I received notification that I was granted admission to the University of Delaware's graduate program of Education (PhD). I will obtain a PhD in Education with a specialization in Mathematics. This has some similarities to what I did in grad school for the M.S. in Ed. The main focus (or at least one of them) of the program is to examine critical issues of mathematics teaching and learning across K-12.

Continuing my studies was always lingering on my mind, and the opportunity to do is finally here. I still remember being 17 and getting accepted to Penn State, only to not be able to attend due to the cost of tuition. The University of Delaware offered to pay the entire tuition, in addition to offering a stipend, contingent upon teaching and doing research throughout my enrollment! Channeling my excitement and inner blue hen! 😊

Farewell~

December 23rd was my last day of teaching 6th grade math! I have resigned from the DOE as of last month. I love all of my students and wish each and every last one of them the best in their educational careers, and with whomever their next math teacher will be. As I mentioned last post, and also evidenced by the insane amount of students who bum-rushed me (this includes 7th graders) on the last day, I've made a humongous impact on their learning as well as their lives. When the bell rang, over 30+ students came out of nowhere and were in my room yelling and shouting, each for a hug. I gave every last one of them a hug.

When I saw students literally cry and hug me, it made me realize just how much of an important part I was in their daily life. An entire year can pass, and they will never forget the experiences they shared with you! As a teacher, you realize that some students do not have any element of consistency in their life other than you. Just one moment with them can change their entire future, and it's almost like students need someone they can believe in. Perhaps they are level 1's, or level 2's, or 3's or 4's. But, a love for respecting oneself and each other, an inspiration to succeed in school, and a newfound love and appreciation for math...What number does that equate to? How can you quantify that? And I love each and every one of them.

I will continue to update this blog with math topics and any other videos/explanations that we covered in class before the year. Below are some of the well-wishes and farewells my students gave me along with some hilarious videos of my students trolling me!

The Impact of a Teacher

Readers! I can't get rid of them! And that's fine. Clearly they don't plan on getting rid of me anytime soon and it looks like we've found a place in each other's hearts. That lasts forever. It's amazing to see the impact I made on this cohort whom never stop short of entering my room (it's like a party!) to chat and kick it!

GCF Word Problems

It has been such a while since I've made a post! My nephews were victims of a major car accident days ago and are currently recovering.  I am also sick with the flu and wasn't able to teach yesterday.

We've been going over GCF word problems in class! Today I had students look at the following task from Illustrative Mathematics: Bake Sale Task


The idea is for students to gain the understanding that the cookies can be arranged into different numbers of bags based on the factors of the total number of cookies. Example:

48 Chocolate Chip Cookies can be arranged in the following ways:

 

Later students develop an understanding that if they are to arrange the vanilla wafers and the chocolate chip cookies into bags with the same amount of cookies in each bag and none left over, that the only way to do so would be by using common factors of 48 and 64.

Influencing a Generation

Every year kids who love you will return to see how you are doing. My former students always return each year and make a comment (or a complaint) about something new!

2014: Tokens
2015: Jumbo Tokens
2016: Rug Area, scent, laminated posters/word wall

It feels good to hear "I miss you" and "can you be my 7th grade math teacher?" It makes me happy that I was a pillar of support and love for these kids. Some of them may have no role models and no support outside of school, but they have a home in my classroom.

I may have been strict, but I held them to fair and high expectations to play their part in the creation of a productive classroom. They passed by my room today during my prep time and pretended to be in 6th grade again! With no hesitation I snapped a picture of last years cohort:

Next post will be about the latest topics we've covered in math class.

Homework - Tape Diagrams and Equivalent Ratios - 10/5/2016

We've been using tape diagrams to visualize equivalent ratios. The homework for October 5th has us demonstrate how we can use tape diagrams to show that two ratios are equivalent as well as solve ratio word problems.

The video below should help with the problem set for tonight's homework. As usual, if you have any questions leave a comment and I will get back to you as soon as possible!

Homework/Classwork - Equivalent Ratios and Tape Diagrams

Last week we used tape diagrams to learn about equivalent ratios and solve word problems. Tape diagrams are a great way to visualize ratio relationships. Last week's classwork is an example of how we can use a tape diagram to represent and solve a problem.

The videos below should help with what we've been covering in class recently!  If you have any questions please feel free to leave a comment and I'll get back as soon as possible!

Classwork - Tape Diagrams and Equivalent Ratios

Last week we used tape diagrams to learn about equivalent ratios and solve word problems. Tape diagrams are a great way to visualize ratio relationships. Below is an example of how we can use a tape diagram to represent and solve a problem.

Example: The ratio of the number of shoes Mr. E has to the number of sneakers Mr. E has is 5:2

If Mr. E has 25 shoes, how many sneakers does he have?

The five tapes represent the number of shoes Mr. E has. If we divide (25 ÷ 5)  then we know that each tape represents 5 shoes.

Now we can find out the number of sneakers Mr. E has, which is 10. Mr. E has 10 sneakers.