Introduction to Intercepts – Mini-lesson with Scaffolded Section for Computing

Here is a link to the document, with images showing the notes. This is a mini-lesson with the following components.

  • A fill in the blank for writing the lesson objective.
  • A Do now which serves as an initiation to the lesson. The y-intercept can be discussed in the context of buying 0 slices of pizza and paying $1.
  • A notes section on what an intercept is.
  • Practice session on identifying intercepts in graphs and tables.
  • A scaffolded steps section on computing the ordered pair of the intercepts.

Interpreting Slope Intercept

Slope is one of the most important topics covered in high school algebra yet it is one of the least understood concepts. I have two observations about this. First, slope is often introduced with the formula and not as a rate of change. Second, students intuitively understand slope as rate of change conceptually when presented in a relevant, real life context. The challenge is compounded when slope is presented with the y-intercept.slope intercept scaffolding

In the photo I present slope and y-intercept in a context students can understand (money is their most intuitive prior knowledge). The highlighting makes it easier for them to see the context, specifically the variables. I have the students work on this handout and I circulate and ask questions.

Here’s a typical exchange – working through problems 11, 12:

  • Me: “Look at the table, what’s changing?”
  • Student: “the cost”
  • Me: “How much is it changing?”
  • Student: “20”
  • Me: “20 what?”
  • Student: “20 cost”
  • Me: “What are you counting when you talk about cost?”
  • Student: “money…dollars”
  • Me: “So the price is going up 20 what?”
  • Student: “Dollars”
  • Me: Show me this on the yellow” (student knows from before ┬áto write +$20)
  • Me: “What else is changing?”
  • Student: “People”
  • Me: “By how much”
  • Student: “1 people…person”
  • Me: “write that on the green”
  • Me: “Now do this same thing on the graph. Where do you start?” (they put their pencil on the y-intercept
  • Me: “What do you do next?” (they typically know to move over and up)
  • Me: “Use green to highlight the over” (they highlight)
  • Me: “How much did you go over?”
  • Student: “1…1 person”
  • Me: “Now what?” (Student goes up.)
  • Me: “Highlight that in yellow.” (They highlight.)
  • Me: “How much did it go up?”
  • Student: “2…20…20 dollars”
  • Me: “What is a rate?” (I make them look at their notes until they say something about divide or fraction or point to a rate)
  • Me: “So what is the rate of change?”
  • Student: “$20 and 1 person”
  • Me: “Look at the problem at the top. What is the 20?”
  • Student: “$20 per person.”

I point out that you can find this rate or slope in the equation, the table and in the graph.