# What have we been up to

In the bleak mid-winter, we have been studding echinoderms and math more than anything.  In addition to the Montessori geometry lessons, we have been working on bi, tri, and larger nomials.

Brooks wanted to shade his squares.

The boys have reviewed the process of creating binomials and trinomials.  We began with a review of the products of a monomial (one number) and a binomial (two numbers added together).  For example:  3 x (5 + 4).  I am really figuring out 9 x 3.  But sometimes in math it is easier to break apart a number.  So away we go.

We then moved to squares of binomial.  Using a hundereds square, we discussed how many beads total in a one hundred square (100 – it is not a trick question) then we discussed how many rows across and down (10 by 10).  We knew the answer and knew the problem 10 x 10 = 100. But we thought we could find another way to find the product.  Lets divide the 10 into 7 + 3.

We took a rubber band and placed it around the bead square three in from the side and another and placed it seven down from the top.  Then we wrote out our new problem (7 + 3)squared.  Then we looked at the shapes formed.  Two perfect squares and two rectangles.

the problems reads (7 + 3)sq = 7sq + 3sq + (7×3) + (3×7)  or 49+9+21+21                 and wow it equals 100.

We then applied what we knew to trinomials using a box of flat pieces of plastic sized to each possible factor – ie: 1 square wide by 9 squares long. We transfered that to the papers.

More on xnomials later.