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!

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!