Connectivity

  I've been teaching math for a fairly long time and the way its presented has changed so much since I received my credentials.  Recently with the change of focus, I've realized that I should be teaching solving multiple step equations just before I teach slope and graphing.  Technically, if you put y = instead of a constant = you'd have a linear equation.

So I think next year, I'm going to teach solving one, two, and multi-step equations first then move to teaching linear equations as they are so closely related.  This year, I'm slowly realizing I need to connect with certain topics with other topics so students begin to see the relationships with in Math.

So the order I"m looking at for teaching this grouping is as follows.
1. Solving one step equations.
2. Introduce the idea of x and y values as coordinates and or points
3. Solving two step equations.
4. Introduce linear form, function, equations and connect with points
5 Solving multi-step equations with variables on each side.
6. Solving multi-step equations that require combining like terms or distributive property.
7. Identify m and b of  the linear equation.
8. Introduce graphing using m and b. 
9.  Show finding slope from graph using triangles and finding the b.
10. Finding the slope mathematically.

This is a big change for me because I'm so used to teaching solving one and two step equations in one unit.  Later on, I teach linear equations as if they are completely different and isolated.  I've been wondering if that is one reason my students have trouble transferring the knowledge.  Do they see these topics as completely unrelated and therefore must be treated as different topics?

I'm looking for ways to teach certain topics so they make more sense to my students.  So far my teaching factoring of quadratics is going well.
1. Factoring GCF out of the trinomial.
2. Teach the Diamond method of finding the factors.
3. Take those results to be used to factor the quadratic with a leading coefficient of 1.
4. Teach the Diamond method to find factors for a quadratic with a leading coefficient of a so a is not equal to 1.
5.  Have students use the factors to rewrite the trinomial into four terms.  They will practice taking it this far.
6. Complete the factoring from # 5.
7. Introduce the quadratic formula for equations that cannot easily be factored.

I'm only up to step 3 but I had a student who looked at what we were doing and said "UnFOILing the equation."  First time, I've ever heard a student make a direct connection.  It was cool.  I'll get back to this when I'm finished with this part of the unit.