Making Sense Out of Multiplication...

It seems as though the longer I teach, the more it seems that students just really have difficulty using the multiplication algorithm. When I started to see this more often a few years back, I began to implement the "matrix" or "grilled cheese" method of multiplication. Kids still had trouble with this. It seemed as though this was just a skill that the kids just have to learn. Recently, however, I began to think about how this skill could be learned differently. My students seemed to be pros at multiplying various numbers by a one digit number. I am sure someone else has thought of this before, so I am in no way taking credit for multiplying this way... but when I implemented this method into my Math Enrichment class I saw the light bulbs turn on and it was so exciting that I just had to write this blog. So if you have beat the traditional multiplication algorithm into the ground and are still having students struggle with multiplying, you may want to give this a try. (Bonus: this also shows a real use for the Distributive Property!)

I started my lesson off with some really simple problems involving mental math.

This was to help the students to start thinking about instances where it is easy to use mental math. 


Next, I introduced the idea of breaking up a multiplication problem on the following manner.

By breaking up the first part of the product in this way, the student will ultimately have two very easy multiplication problems to evaluate...

What is nice about this method is that once the second number in the multiplication problem is distributed, the student has two problems involving a number multiplied by a single digit number. This eliminates the need to remember the steps that are involved in multiplying by a two digit number and allows students to utilize some mental math, which makes the whole process much quicker.

Finally, the student just has to add both of the products of the two problems that they completed and they have the product of the original problem. My students (even though they tend to struggle with remembering how to multiply) do very well with this method. The ones that were pretty good with the traditional algorithm, find that this way helps them to multiply more quickly, so they also like using it. I hope you will try this with your students! It has done wonders for mine. 


I will be posting more about this in days to come. Thanks for reading and Happy Teaching!

Applying Plotting Ordered Pairs: Mathica Monster Activity

Mathica Monster

I was trying to figure out how to make an engaging lesson to help my students apply their graphing of ordered pairs skills and I think I have made a fun and entertaining lesson! In this activity students work as partners to plot coordinates of various places in "Scarytown" in order to help Mathica Monster find her way around. I like to try to make math fun for the kids because I think this makes both your day and theirs go much faster and helps to limit excessive behavior problems.

This lesson really helped students to understand the concept of distance between points on a coordinate plane and to apply graphing ordered pairs in relationship to other positions. Even though this year has been tough because we are transitioning to a new and more deep curriculum, I have seen some positive strides over the course of the year from when I first started working with my students to now. It takes time to help students learn how to apply math rather than merely complete basic skills. I am excited to see how I can grow as a teacher and how my students in the future will benefit from going deeper into the math concepts. This blog is my way of reflecting and sharing my ideas of what works with my fellow educators. This was definitely a lesson that I felt enriched the students' understanding of this concept. This lesson can be found at my TpT store for FREE please stop by and browse some of my other resources. If you like what you see please FOLLOW ME.

Here is a video preview of the Mathica Monster Lesson. Thanks for stopping by and I hope you come back!



Reflecting Ordered Pairs Across the Axes: A Hands On Activity Using Mirrors

It has been a while since I have written a blog entry. (Snow days and state testing has backed a lot of my lesson planning up). I am very excited to write about a recent lesson that I completed with my students that involved reflecting across the x and y-axis.

In this lesson, students discovered the mathematical patterns behind reflecting ordered pairs and collections of ordered pairs across the x-axis and y-axis. The students used mirrors to help them see what was happening. It was a lot of fun watching them discover this and it was rewarding to even see my lower ability classes coming up with some amazing observations. (View the video to see this lesson in action.)

Students started out with a short video showing them how to use the mirrors to reflect across each axis.

 

 

 

Here are some glimpses of some of the notes sheets that were featured in the above video.

 

A similar lesson to this would not be difficult to create, however if you like what you see on this blog, the lesson is available at my TpT site and can be viewed here. Thank you for taking time to view this lesson, it was very fun to teach and the students got a very good understanding of it.



 

 

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,