This week I am participating in a Blog Hop hosted by Scaffolded Math and Science. We’re tackling math misconceptions by sharing some ideas for how to combat common mistakes.
I’m currently reviewing angle
relationships with a group of eighth grade students. They were very comfortable with the
vocabulary and relationships formed from parallel lines cut by a
transversal. So week two I added to the
challenge by combining angle relationships with linear equation writing and
solving.
Big
Misconception:
When
to combine like terms
versus
When
to add or subtract to move terms
Case
1: Combine Like Terms
In some cases, students were given
supplementary angles. So they needed to
add them together to equal 180 degrees.
For example, students were given same-side interior angles or the
interior angles of a triangle. The x
values all ended up on the same side of the equation.
Case 2: Add or Subtract to
Move Terms
In other cases, students were given
congruent angles. They set each
expression equal to one another. For
example, students were given alternate exterior angles. The x values ended up on opposite sides of
the equation.
Case
3: 2 in 1!
I included some cases that required
students to combine like terms then add or subtract to move terms. For example, students were given an exterior
angle and the two remote interior angles.
What a challenge!
How
we addressed this topic in 3 steps:
FIRST
We talked about when we would see
each case.
Supplementary angles get added to
equal 180. Since the x values will be on
the same side, to solve combine like terms.
Congruent angles are set equal to
one another. Since the x values are on
opposite sides, to solve add or subtract the terms to move them to the other
side.
THEN
I shared with students these key
phrases to help them remember the difference:
Same Side Slide
“Slide the terms together” when they
are on the same side.
Opposite Side, Opposite Operation
When terms are on the opposite side
of the equals sign, use the opposite operation to move one to the other.
FINALLY
We practiced, practiced, practiced!
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