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
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,
