So today I gave them this slide and said I want you to solve a puzzle!

They broke out their iPads and used the Algebra Tile app to put together the rectangle. The kids worked away and you could see them trying to put tiles in a way to make the rectangle
….and they soon found out that they had to fit a certain way!!
On take up we made sure everyone had either my rectangle or a rotated version.

Then we did this one…..

After we were done I asked the class: “If the combination of squares and rectangles makes up the area, what are the dimensions of the rectangle?” They had a little bit of a hard time here, but finally could see the x + 4 and the x + 2 as the length and the width. I then wrote …

And then I heard some “aaah”s. We had previously seen both versions of the quadratic expressions and discussed why the factored form helped us out quite a bit if we wanted to find the x-intercepts.

We stopped there….It only took us 15 minutes. Tomorrow we will do a few more…..always writing the factored form after. I will also try to get students to notice efficient strategies to make the rectangles.

Why did you put 4 x terms along the width and 2 x terms along the length?

How does that relate to the number of singles?

Where I hope to go with these warm ups is to factor all types of trinomials:

Perfect Squares

This time…..make a square

… and get this…

Trinomials of the Type ax^2 +bx + c

Completing the square too!!!!

This time…make a square

We’ll be definitely working our way out of the app and onto paper with area diagrams…

Factoring

Completing the square

Completing the square

I think working with these puzzles for the next few weeks first will give us a strong base when it’s time to factor to help solve equations and then complete the square. I think I’ll track all the warm ups we do like this and I’ll post them all!