My students would tell you
that I say this about every lesson, but I really think that teaching students how
to write linear equations is my

*favorite*unit. There’s ample opportunity for exploration and discovery, applications, and extensions!
Explore
the Ideas

The unit that precedes
writing equations is typically centered on slope and rate of change. I get so excited when we start looking at
equations and graphs in terms of slope that I usually start pointing out
patterns or leading students to make connections and draw inferences about the
y-intercept themselves. At this point, we typically spend a little time looking at arithmetic sequences. We use the arithmetic sequence formula, and
then discover patterns to formulate our own formula (which – ahem – is
basically slope-intercept form).

CCSS 8.EE.B.6 mandates that
we “use similar triangles to explain why the slope m is the same between any
two distinct points… [and] derive the equation
y=mx for a line through the origin and the equation y=mx+b for a line
intercepting the vertical axis at b.”
I’ve created a discovery worksheet that facilitates the exploration of
these big ideas. You can scoop it up
here.

Get
the Basics

Organized notes and
repetitive reminders of the steps are super important here. I will typically create an anchor chart that
outlines the steps given each potential set of information. Notice all of the exact language that I use
(also great for your ELLs).

Demonstrate a variety of
examples and allow students ample time to practice their new skills. I teach in a 55-60 minute class period, and I
spend two days on each topic: writing equations given a graph (or slope and
y-intercept), writing equations given the slope and a point, writing equations
given two points. The first day we take
notes and begin to practice the new skill.
Then we continue hands-on practice on the second day. Check out my differentiated notes and practice here. Opportunities for differentiation here!

Make
it Real

I’m not talking about
textbook word problems here…
snore. Cow population, birth defects,
what?? There are so many examples of
linear relationships in our students’ lives.
Use examples about social media, sports, music, etc. I have a set of rate of change and initial value task cards that uses real examples.

Students also love the
analysis and discussion required for this discovery worksheet about planning a
road trip. Ask students to draw
inferences, make predictions using their equation, discuss limitations, and –
most importantly – allow time for debate.
You will turn those adolescent brains right on when they get to argue,
and your colleagues in the humanities will thank you for practicing supporting
arguments with evidence.

Practice
Makes Permanent

Here’s a fun way to
practice a new skill or review at the end of the unit:

~
NOTE ~ Depending on your comfort level with thinking on the fly this lesson
could potentially have ZERO prep.

1) Everyone sits at their desk
with a piece of notebook paper and a pencil.

2) 4-5 students at a time go to
your front whiteboard. (I rotate through
the class to make sure everyone gets up once before repeating volunteers. This means I often end up with a few
“non-volunteers” at the end. I typically
motivate students to volunteer early because they know the rule is that the
practice problems generally get harder as we go.)

3) Announce a slope and a point
(for example). Everyone at their desk
writes down the information on their paper at the same time that the volunteers
on the front board use the whiteboard markers.
Everyone in the class writes the equation given that information. I focus on the students at the front and
provide subtle redirection as needed, scan the class to make sure everyone is
working, and provide assistance to a student or two at their seats if needed.

4) We discuss things that are
great or potential pitfalls to watch for then repeat with a new group at the
front board.

5) Everyone loves it! And seriously… I very rarely prep for this lesson.

And of course I’d be remiss
if I didn’t mention that I have a super popular OMG game for this topic. Haven’t played yet?

O. M. G… you don’t know what you’re
missing! ;)

Extend
the Unit

So many opportunities for
extension here! You could introduce
relationships with parallel or perpendicular lines, scatter plots (and really
collect data), standard form of linear equations, graphing calculator
extensions and more!

Here’s a fun one for your
high flyers:

Write the equation of the
line perpendicular to 2x-y=8 that shares the same x-intercept as the given
line.

(Answer: y=-0.5x+2)

Join in the
conversation! What are your favorite
ways to teach students how to write linear equations?

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