This past Saturday's workshop on helping English Language Learners was different for two simple reasons. First, the presenters were dedicated, hardworking teachers that didn't want to waste our time in the usual manner. Secondly, the participants, especially the member of my department who were there, wanted to get something out of it. Thus when we sat down to devise an engaging lesson for all learners, fortune smiled upon us.
Earlier in the day, I had shared a mini-lesson on a particular math vocabulary word that students always seemed to have trouble spelling properly:
Me: "How would you say this word?"The other teachers found this story hilarious, and now slop is everyone's favorite word. Inevitably our sample lesson focused on slope, which in all seriousness is one of the most difficult topics for our students to grasp. As we started to talk about various possibilities, I watched as my fellow math teacher was folding a paper accordion-style (presumably out of boredom). When she held it up, I saw stairs. More importantly, I saw a simple, hands-on way to demonstrate slope to our students.
[I write "rope" on the board.]
Students: "Rope!"
Me: "Good. What about this one?"
[I write "hope".]
Students: "Hope!"
Me: "Great! So how do you think you'd pronounce this word?"
[I write "slope".]
Students: "Slope!"
Me: "Excellent! Now what about this word?"
[I write "slop".]
Students: "Slop!"
Me: "Perfect. So when we are studying slope and writing about slope, I don't want to read anything on your papers about the slop of a line!"
Building Stairs
Objective: Students will be able to identify the slope of a line given two points; to create a line given slope; to identify positive, negative, zero and undefined slope visually.
Materials: Several sheets of lined paper for each student.
Vocabulary: slope, rise, run, steep
Opening: Start with a simple problem about slope that you've previously taught--for example, identifying positive, negative, zero or undefined slope visually.
Introduction: Provide some quick refresher notes on different ways to find slope. Collect pictures that show sharp edges that could help students visualize and conceptualize slope: ladders, mountains, the roof of a house, and most importantly, stairs.
Tell your students that they're going to make some stairs that have a specific slope. Talk about the stairs they walk up and down to get to class every day. Ask them what happens when one step isn't the same size as the rest (you trip, fall, break your neck and/or die). Ask how many of them have tripped and fell in this situation. Since my uncle owns the family stair building business, I would share a personal anecdote about that as well.
As suggested by my fellow teachers, we would show a model of completed stairs folded out of lined paper. The lines on the paper would serve as our unit of measurement, eliminating the need for rulers. 4 lines up and 6 lines across would be a slope of 4/6 or 2/3. The example would be labeled "rise" and "run" on each part of the steps. They could also be color coded.
Guided Practice: Have students create, in pairs or small groups, stairs with various slopes. Start with something easy like 4/4 or 2/3, then try 1/10 and 10. Ask students to hold up their stairs each time, which will provide plenty of teachable moments. Ask guiding questions like, "Will stairs with a slope of ___ be more or less steep than the last line we made?" "Would it be easy or hard to climb stairs with a slope of...?" Challenge them to show you zero or undefined slope as well.
Independent Practice: Now you could give your students traditional slope problems to practice, perhaps an assignment from earlier in the year that everyone had trouble with. Encourage them to use their paper to model what they see.
Alternately, you could give students a narrow sliver of lined paper to create stairs that would become part of a 3D mini-poster explaining how to find the slope of a line.
Closing: Ask your students to write a short definition for slope in their own words or show an example. Remind them, of course, to avoid writing about slop.