Factor (and Fashion) Fun

This week we've been investigating, How can we use models to represent multiplication?

In third grade, most students learned to model multiplication using arrays, or arrangements in equal rows and columns that form rectangles.  On Monday, students were assigned a (related) pair of numbers and used this strategy to build all of the possible arrays for their numbers with tiles.  We connected the dimensions of an array to factors in a multiplication equation.

After this, students drew their arrays on graph paper.

They made posters showing an organized a list of factors and factor pairs used to model the total number the array showed, which is the product in multiplication.

Before working on their second number, we paused for a brief discussion of things we noticed.

Since then, students have thought up more helpful strategies for making sure they've found all the factors of a number:

• 2 is a factor of all even numbers.
• Test factors less than half way in order from least to greatest (or greatest to least).
• Use skip counting to see if you can "land" on a number.  If you can, then it's a factor of the number.
• If the number has a 0 or 5 in the ones place, then you know 5 will be a factor.
• If the number has a 0 in the ones place, then you know 10 will be a factor.
• When finding factors of numbers that are more than 10 groups of a number, use a x10 fact, so you don't have to do so much counting.  For example, if you're trying to figure out if 3 is a factor of 45, start at 3x10=30, then count on by 3's:  33, 36, 39, 42, 45.
• You can also use facts you know to help you count faster.

Today we looked at our array posters and answered the following questions:

• Which numbers have only one array?
• Which numbers have a square array?
• Which numbers have the most arrays?

This lead to a discussion about prime, square, and composite numbers:

In their Interactive Math Journals, students identified examples of these numbers on a hundred chart.

Tomorrow we'll discuss how finding factors for one of our numbers helped us find factors of the other (related) number.  The explanation is related to this...

On a fun note, I knew it would be a good day when I noticed this unplanned coincidence in our "cul-de-sac".  :-)

Ms. Kirkham said she almost wore a scarf and was planning on trying out a way to wear it very similar to this!  :-)