Since reading about the big idea, I've seen more and more ways I can talk about concepts throughout the classes.
I've been able to discuss solving equations with my Algebra II class today. They are solving exponential equations with same bases. Since the exponent were often algebraic equations, students had to use the same steps as they had when solving simple algebraic equations.
We are also discussed the rules for using powers because they applied in this situation. When students rewrote the bases so both sides had the same base, they had to apply the power to a power rule. It was so great being about to show this.
Next week, they will be learning about logs which follow the rules for working with exponents such as when the bases are the same, the exponents are added. Now there is a second area where the rules of exponents apply other than the section on exponents.
In algebra I, it is great talking about using the same steps to rewrite literal equations as are used for finding a numerical answer from an algebraic equation. It is lovely discussing a situation where the same steps apply but you get a variable rather than a numerical answer.
Several of the teachers use the lattice method for multiplying multi digit numbers together. I've taken the same lattice and used it for multiplying binomials and polynomials together. Many of the students learned it in one class period because they were familiar with the basic process. The same can be said for addition and subtraction of polynomials.
I use diagrams showing multiplication of two digit numbers such as 53 times 22 using 10 block and ones to make a square with the tens units squared for hundreds etc. I use the same diagrams to show binomial multiplication so they can see the x^2 is similar to the hundreds or 10^2. It shows multiplication works the same for both.
I am going to spend some time over the summer looking at redoing the order I teach concepts so maybe I can put ones together which share common concepts.
I'd love to hear what you think. Thanks for reading.