As a sixth-grade math teacher (or any math teacher fourth-grade and above), you have probably told students that the value of a digit is ten-times greater as you move each place value to the left. This is true: 5 ones becomes 50 ones (5 tens).  I have said this to my students. But, as I write these posts and think carefully about my students’ difficulty in understanding math, I realize that this simple statement is complex. To conceptualize “ten-times greater as moving from ones to tens” is difficult. Even as I write this, I think, “C’mon Steve, this is silly; 5 ones to 5 tens is ten times more. It is not that hard!”.

Maybe so, but I think that having students go through the process shown in these videos is worthwhile. It builds kids’ knowledge base of mathematics. Shown in the videos is the idea of regrouping using a logical process. To state, “If you construct 10 equal groups of things, then you can regroup those things into groups of 10, which become the place value: tens”. Applying this same process to other simple examples is enlightening. Two examples:

1. The Problem:    3 x 5    three groups of 5 things per group. Since you have 5 units/ones/things in each group, you can take one unit from each group to make groups of 3; in this case, five groups of 3 units, or threes.
2. Draw the same problem (3 x 5) as an array. Make the columns equal the groups, and the rows equal the number of units in each group. So, there are 3 columns and 5 rows. Now, you can take one item from each row and construct 5 columns with 3 rows.

This is difficult for me to think through and to write because I have a long history of math bias/education, i.e., my thinking is not flexible. Kids, on the other hand, do not have a history of math bias. I expect that their thinking will be much more flexible. We will see.

A couple of notes on these videos:

(1)  These are the first videos that I have posted. View these in HD so the text will not be blurry.

(2)  The full screen mode works fine on my Mac in Google Chrome. For reasons I do not understand, the full screen mode is not working on my PC desktop in Google Chrome. However, it does work in Firefox, although the display is always messed up in Firefox. Safari does not give me the option for either HD or full screen.

This is the same video without the text.