Teaching the Concept of Dividing Fractions to Middle Schoolers Can Be Done Successfully!

At the end of a few beautiful and restful snow days, I am getting ready to go back to work today. (It has always been a well known fact that teachers enjoy getting those calls more than the kids do!) Having a little extra time off has given me time to spruce up my dividing fractions unit and take what I did (which worked really well with my 6th graders) and share some of my thoughts with you about what I think is the best way to develop this concept in the classroom.

Common Core Does NOT Mean that the Algorithm Has to Be Thrown Out the Window...

I have listened to various professional opinions in regard to this misconception about the Common Core Curriculum. The goal of this approach to math is that the students become better at mathematical reasoning. When teaching this concept, I took the approach that I wanted the students to discover as much as they possibly could on their own in the most visual way possible. I wanted them to truly understand each step of the algorithm before they even began using it. Why do algorithms even exist? This is the question I want my kids to understand, not just tell them to "Do these steps and you will get the correct answer." Algorithms are a result of looking at numerous problems visually to see if you notice any patterns. If something is noticed over and over again about a certain type of math problem, this pattern can be used to create a set of rule (algorithms) that work no matter what. I tell my students that usually the algorithm is a short cut that is a result of much research.

Here was the sequence of discovery lessons that I wrote to help guide my students to this conclusion.

Sequence of Lessons:
Pre-requisite Skill: Multiplying Fractions Students will learn what is really happening when two values are being multiplied together. This will help them to understand why you multiply the numerators together to get the new numerator and why you multiply the two denominators together to get the new denominator.

Lesson Includes:
•Fully typed out UBD lesson plan and Teacher Notes
•Power Point and all Instructional Videos
•Accompanying Student Notes Sheet
•Practice Worksheets

Lesson 1: Introduction to Dividing Students will first manipulate counter chips to better understand what they are doing when they are dividing. Students will then manipulate fraction bars either by using a fraction bar manipulative website (or by using the attached templates that students can cut out if access to computers is not possible) to also discover what happens when you divide a whole number by a fraction. Students will begin to discover a pattern when they divide a whole number by a fraction.

Lesson Includes:
•Fully typed out UBD lesson plan and Teacher Notes
•Power Point and all Instructional Videos
•Accompanying Student Notes Sheet
•Practice Worksheets

Lesson 2: What is a reciprocal? Students will once again use the fraction bar manipulative website to understand what a reciprocal is. They will discover that a reciprocal is what you can multiply a fraction by in order to make a MAGIC ONE©.

Lesson Includes:
•Fully typed out UBD lesson plan and Teacher Notes
•Power Point and all Instructional Videos
•Accompanying Student Notes Sheet
•Practice Worksheets

Lesson 3: Learning Why the Dividing Fractions Algorithm Works.
In this lesson students will use what they discovered in the previous lessons to recognize patterns. Through this understanding they will work through a template that they will be able to describe in detail to better ultimately better understand the algorithm.

Lesson Includes:
•Fully typed out UBD lesson plan and Teacher Notes
•Power Point and all Instructional Videos
•Accompanying Student Notes Sheet
•Practice Worksheets

If this looks like something you may be interested in using in your class, you can find this lesson on my TpT website: http://www.teacherspayteachers.com/Product/Betta-Maths-Survival-Guide-to-Multiplying-and-Dividing-Fractions-1076050.

This lesson has really helped my students to truly understand how to divide fractions and they can also explain why the algorithm works.

Some of my students were able to then progress from the template shown above to merely multiplying the first fraction in the division problem by the reciprocal. (I allow them to do this if they discover this on their own.)

Thank you for visiting my blog. I should be writing some more soon!

Sincerely,

 

A Common Core Conceptual Approach to Explaining the Distributive Property

Hello. It has been a while since I have blogged, but I had to inform you about a great way for students to discover the distributive property. This property is a vital part of algebra and students need it as a bulding block to understand such topics as "FOIL" and finding common factors.

In this lesson, students must manipulate rectangles (representing variable terms) and squares (representing constant terms) to show that the distributive property is basically stating that the number on the outside of the parenthesis determines how many groups of the value on the inside of the parenthesis are needed to simplify the expression.

This lesson worked very nicely to help my students discover the DISTRIBUTIVE PROPERTY on their own and really helped them to make sense of how to apply the property. I love it when discovery lessons work like they are intended to!!! The students retain so much more if they can make sense of it on their own. If you are interested in obtaining this lesson please visit my TpT store!

Students begin by exploring what it means to have a certain number of groups of
an expression within a parenthesis.

Fully typed out UBD lesson plan is included with purchase. Merely print out the document
and have on hand for those surprise evaluations.

All answers for Warm-up, Practice problems and assessment question are included.

Today I Attended an Inspirational Teacher's Workshop with Dan Meyer

I know, a workshop on a Saturday that I did not even get paid for... crazy right? In my 10 years of teaching this was probably one of the best sessions that I attended. I urge you if you have not read about Dan Meyer and his educational message, that you take some time to do so!

I have so many ideas about how to better my lessons. The three questions that I came away with that I plan to ask myself from now on to help bring meaning to my lessons are:

Questions I have learned to ask effectively. From Dan Meyer's workshop.

There are also a great deal of FREE resources that he shared with us. These resources can be used at teh teacher's discretion and really motivated me that concepts can be introduced effectively without laboring for hours on creating videos or scenarios up out of thin air. You can use what is already available as a "jumping board" to help you introduce the concepts you are beginning to teach students. Amazing!

I cannot wait to start using some of the following resources in my classroom. The following was one resource I really appreciated having access to and wanted to pass onto my readers.

THREE ACT LESSONS - also from Dan Meyer.

ACT I - basically the idea is to draw the students in by showing them a video clip or picture that sparks their attention. (Keep the math out of it).

ACT II - Ask them the math question and have them investigate it more. Give them tools or insturction as they need it.

ACT III- Validate the answers they arrived at, let them see the various ways that the asnwer was found.

He also acknowledges that this is the "hook" but that students still need to practice problems in class and at home in order to master the skill.

I am planning on incorporating this with my 6th graders and was very excited to have the oppurtunity to attend this workshop. Have a great weekend!

Interactive Lesson on Relating Ratios to their Proportionate and Equivalent Forms

This lesson worked really well last week for all levels of classes because it scaffolded the thought process needed to find equivalent ratios. Student could manipulate the shapes and were encouraged to use ratio language to make sense this concept.

 

The video above gives a short preview/explanation of the lesson. Our school has access to the promethean board and ActivInspire so this is a flipchart and PDF student notes file and works best when students can utilize a computer individually in a computer lab setting or laptop cart setting. (If you are someone that may want a low tech version of this lesson, please contact me through TpT by finding this product and describing to me what you would like through the "QUESTION" prompt.) You can find this lesson at my store. This lesson is aligned with CCSS 6RP1 and includes answer keys describing how the lesson should progress.

Introducing the Concept of Rate

This week, I finished up working on helping my students to understand basic ratios through a variety of activities. Yesterday, I introduced the idea of rate by posing a challenge  to my students.

Given two tracks, can anyone beat me in a hopping race???

The students were first asked to examine the two tracks and make predictions about who would win this race. (When making your two tracks it is important that the teacher's track is spaced out to cover twice the distance of the student's track.)

It was a lot of fun to hear the different predictions. My most challenging and most active class (also at the end of the day) was really into it. They noticed right away that the race would not be fair and started throwing out phrases such as "You are trying to cheat us!". This really got them to be engaged!

Once the students had a chance to analyze both tracks, I chose a student at random (I use popscicle sticks with their names on them) to race against. I raced against four different students. The rules were that each person on each track would have to hop the distance alloted them by the post-it notes and every post-it note had to be hit. The first person to make it to their last post-it note would win. (To make it even more competitive, I taunted them a bit and kept writing the score on the board each time I beat one of them. Have fun with it!)

After I raced the four lucky students, we began to discuss the activity further. I had a few prompting questions in my mind prior to starting the discussion. (Since I want the kids to discover the idea of rate on their own, I wanted to make sure I did not give away too much information.) Students were partnered up and asked to journal their thoughts in their math notebooks as we discussed with the whole group.

1. Was the race fair, why or why not?
2. Why was I able to win each race?
3. What do you notice about my track compared to your track?

My students did a nice job (all ability levels) of coming to the conclusion that I was able to hop a larger distance each time I hopped than they were able to. My more advanced math class began using frequency tables to analyze the information and were right on the verge of coming up with their own definition of rate when it was time to leave class, so I will have to continue discussion on Monday. It was hard to not tell them the answer, but very rewarding to see them thinking it through and so actively engaged. I will be completing this lesson Monday and will write more about its conclusion at a later date!

I also came across some really good hands-on lessons (already made up for you) that help students work with and use unit rate at ILLUMINATIONS. I plan to use these next week as I continue introducing the concept of unit rate and its uses.

Thanks for stopping by and have a wonderful week!

The First Week Went Great! We Began the Ratios Unit...

We began the Ratios Unit this past week and I am excited to say that it went well. What a great start to the year, I have nice students that gave me a really good effort on the Ratios Pre-Test and I am currently completing their Student Achievement Growth Cards. (These come from my Betta Math Ratios and Proportions Unit.)

Another useful tool that I found online is a ratios worksheet generator. This can be found at MathAids and also generates the key for various topics. I use it a lot for basic skills when I may not have time to create my own worksheets.

In preparing for next week, I am going to focus on getting students to really be able to understand how to write and simplify ratios through a number of activities. I am using an adapted version of the Math Workshop that I purchased from:

The author of the math workshop I will be using and adapting to middle school classroom has been kind enough to allow me to blog about this. I wanted to make sure I awarded her the proper credit because it has helped me organize my thoughts about encorporating math workshop in my 6th grade classroom.

I believe that this is where the curriculum is taking us and gives you the flexibility to hit numerous learning styles in one class period and promote differentiate learning.

I will also be blogging more about student portfolios and my students' interactive math notebook. Since textbooks are becoming more of a secondary reference, student notebooks are even more important to their success. Please stop back here frequently because my intention is to blog on a weekly basis and I would love any feedback any other professionals may offer.

To those of you starting back to work...have a great year!

Exploring the Number Line

 

As I research the Common Core Curriculum, I am realizing more and more that a lot of the curriculum revolves around students being able to understand and manipulate a number line. This is especially true when they are working with fractions. As I began to think about some good activities that I might be able to create to help them start the year with an understanding of the number line, I decided the best way to introduce this would be through a few activities. One activity has students use their estimation skills to decide whether a fraction is less than, equal to or greater than 1/2.

 I also like to introduce concepts to students in a fun and interactive way. I created a game called "Eat the Fly" that students will enjoy and it can also be applied to other concepts by merely using different game cards. Once you have th game set up, you will have the game pieces to use later on for other topics. (I like the old saying "work smarter not harder!)

 If this product looks like something you might be able to use in your classroom, please download it from my TpT store HERE. While you are there, please click the "follow me" link to get updates about new products from my store. Thanks for your interest and please visit my blog to see how I am implementing the Common Core Curriculum into my classroom.