2nd Quarter

We are now in the second quarter. Today was the first day. Here is a summary of where we are and what I think has been accomplished (I will also mark above what I think has been done and still needs to be done):

So far they:
  • "know" how to:
    • find output from input when given a recipe
    • graph from a recipe and a table
    • read points off graphs
    • find easy equations from tables
    • locate "slope" in the graph
  • "understand" rate of change in story problems.
We need to:
  • establish:
    1. that lines have constant rate of change and other functions do not
    2. slope as rate of change
    3. where in the equation we find slope
    4. where in the equation we find y-intercept
  • learn
    • how to write an equation from table or graph
    • find input from output (read off graphs, solve equations)
    • find equation of a line through two points (no formula given - ever)
  • understand
    • slope (fractional slope, too)
I propose that tomorrow we do hq4, talk about last homework, work on linear relationships 2 which will address 1, then have them make tables and graph following:

y=-3x+1
y=4-x^2
y=x^3-1
y=3x-4

which will further work on 1, but also start addressing 3. and 4. After that we would work on

http://standards.nctm.org/ document/eexamples/chap5/5.2/ standalone.htm

followed by the second (melting snow problem).

In the meantime, we have worked on the activity, but have not gone back to the snow melt yet. Here are some homeworks that have been assigned.

Linear_Relationships_HW4.docx
Linear_Relationships_HW4.pdf

Algebra_Tables_from_Graphs.pdf

Linear_Relationships_HW6.docx
Linear_Relationships_HW6.pdf

RunnerActivityHandout.docx
RunnerActivityHandout.pdf

Linear_Relationships_HW7.pdf

Diane Crim suggested we play a game "read my mind" where they give me inputs, and I give them back the outputs, until someone is able to guess the rule which I use to generate the outputs. Brian added a twist where they're not supposed to just tell us a rule, but rather give both input and output instead. This allows more kids to come up with a rule instead of always having the same student do it. This is becoming a part of the class. I am soon going to modify it first by allowing only two inputs, then by not allowing 0 as an input.

I think I have done the students disservice by not being better prepared, more organized and with greater vision. We have had some awesome lessons, but I don't think I have followed through enough. In other words, seems that things are left unsaid, and sometimes disconnected. The hope is that eventually we will tie up all the lose ends. I'll try to start tomorrow.




Describing linear patterns with...

  • writing
  • pictures
  • numbers
  • graphs
  • equations


Infuse with statistics (scatterplot, + and - correlation, estimate values by linear extrapolation)
Equivalent expressions (different procedures yield same results therefore they are equivalent)

  • clearing fractions
  • distributive property
  • combining like terms
  • dealing with variables on both sides
  • inverse operations
Solving equations: start backwards! give x=1 and have them come up with a complicated equation that’s equivalent to this one.