Domino Effect From Mathalicious

In Algebra 1B we just finished our outcome on Writing Linear Equations.  Yawn!  The students were okay with the lessons, which were mostly chalk and talk.  I guess that's what they're used to and don't question it.  I on the other hand know better.  I know there's great things to come, like Barbie Bungee, and cup stacking, and rope tying.  Anyway, the tests proved my point.  The students were okay with the information for any given day, but talk about something different during the next class and they confuse the two types of problems.

Now we're on to the next outcome which is applications of linear equations.  My hope is that tying these numbers to something real will help and we can go back an retest.  My point of entry here is pizza, more specifically Mathalicious' lesson Domino Effect.  It took about two days and the students did really well with it.  When we started the lesson and the students saw that a medium two-topping pizza cost $13.97 and a medium four-topping pizza cost $16.96, they immediately found the price per topping.  I didn't ask them to do that.  I wasn't even finished talking about my favorite pizza toppings.  It was their natural curiosity that took them there.  I can only imagine if I wrote the two ordered pairs on the board (2, 13.97) and (4, 16.95).  They would look at me and wait.  Because there is no obvious question.  Then again without being prompted they were curious about the price of a plain pizza.

We had some great conversations about slope (price per topping) and y-intercept (price of plain pizza), equations, variable, and even domain and range.

Here's the best part.  The students even developed their own way to find the pieces of a linear equation.  I taught them to find slope, then use vertex form y=m(x-h)+k to write the whole equation.  But from Domino Effect this is what they discovered:

Finding slope is still the same.  (y2-y1)/(x2-x1) and it makes sense.

Finding the y-intercept is new:  To find the price of just the pizza with no toppings you can take the total price minus the price of the toppings.
For the two-topping pizza -->   $13.97 - 2($1.49) = $10.99
OR
For the four-topping pizza --> $16.96 - 4($1.49) = $10.99
 AND
with Variables -->  y2 - x2(m) = b   OR   y1 - x1(m) = b

You and I know that it's just the slope-intercept formula rearranged, but they have stumbled on to something amazing here.

When the students and I were in the boring outcome of just writing the equations, and I would give two  ordered pairs and ask for the equation, they were very concerned about which point to plug into the equation.  They would ask me again and again if I was sure they would produce the same answer.  I would show them time and again with both points to help get the point across (pun intended).  Now after this lesson they see that it doesn't matter which pizza you use to find the price of a plain, they will both produce the same answer.  Bingo!!