Day 130: Paper Folding

Algebra explored the expansion of (a + b)² today. Across 100 students, none of them were able to correctly expand (x + 3)² coming into the day. We plugged x = 2 into different expansions. Most students had 13, some had 25. Everyone agreed that 25 was spot on, but couldn’t come up with an explanation as to what  (x + 3)² expands to and gives 25 out.

We first talked about the area of a square with side length z and how the are is z². I asked ’em what area meant, they told me length times width. I asked ’em what area meant without using an equation… it took bit but we got here.

We folded the paper and labeled like so

IMG_0575

We talked about how the new side length is a + b and to find the area of this square take (a + b)²

They found the length of each piece which makes up the area…

IMG_0576This is where they struggled:

The area of the square calculated from the formula is (a + b)²

But the area is also defied by these squares and rectangles added together.

So…

(a + b)² = a² + 2ab + b²

We used this to expand (x + 3)² to x² + 6x + 9, which gave 25 out for x = 2!!

After a couple more examples students had a good hang of things, I saw a good mix of multiplying out and visual representations.

IMG_0574

 

Tomorrow they are exploring (a + b)(a – b)… it should be fun!

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s