Category Archives: Teaching and Learning

Partial Products

Every year I spend too long reviewing basic algorithms. This year I’m going to jump in feet first and begin by doing partial products to develop both the multiplication algorithm, and then the division algorithm. I know the majority of my students know the multiplication algorithm but only a handful of them can explain why it works.

Last year I spent some time doing partial products with base ten blocks and students really seemed to expand their knowledge of these basic algorithms. I found a great activity to expand on what I did here.

Once students understand this activity they can then begin to draw generalized rectangle models to lead into the distributive property.


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It seems like a really good idea. I just hope I can keep up with it. I have an idea of how I would like this to go. Here’s the plan: I will post pencasts to Edmodo, students will watch the pencasts for homework and then fill out a summary sheet. Kind of like this one.

Here’s an example of a pencast I did using the Livescribe pens last year:


I’m not sure if the pencast is the best way to record the information, but this is the technology I have now, so I’m going to give it a try.



When students enter middle school, we hope they have mastered numbers. By mastering numbers, I mean, having strong numeracy skills and knowing the general processes for the operations.

Unfortunately, most students in the sixth grade are still struggling with numeracy. This is going to be a strong focus for the beginning of my year. (Yes, I know it’s awful to drill multiplication facts, but it has to be done.) I didn’t focus on these skills as much as I should have last year, and when we reached fractions some students just couldn’t keep up. They didn’t have the automaticity that was necessary to work with fractions.

I recently came across a book by Pamela Weber Harris, Building Powerful Numeracy for Middle and High School Students. This seems to be the answer to my problem. In it she outlines basic strategies and models, beginning with addition that students should know, and the number strings to teach them.For example:

39 + 41

23 + 31

Well, you get the idea. The question becomes how to fit it into 45 minute periods? Hmmm…

Some ideas I’ve been thinking of for drilling multiplication (it doesn’t look as bad in italics) :

A Friendly Game of Nubble

Multiplication War

Missing Number Problems

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