Today while researching information on teaching algebraic fractions, I stumbled across this cool lesson plan
from Open Learn Works on introducing algebraic expressions with a real
life context. This is one of the first lesson plans I've seen that
invokes a situation that does not sound contrived to explain algebraic
expressions.

Too often the only time I see algebraic
expressions is associated with verbal expressions without any
mathematical context but this lesson plans puts the expressions in
context and the questions tend to be open so there is no single correct
answer.

The first activity in the first section has
students look at a picture and a situation to determine which items are
constant or variables. Some things like parking are constant because
the number of spaces available never change but the number of people
using the car parks vary every day. I like this because it shows how
real life items can be classified as variables or constants. Although
the situation is in India, it would be quite easy to change it to a
local shopping mall.

The second activity in the same
section requires students to choose four variables to create algebraic
expressions with. The process chosen uses mind maps, selecting
quantifiers, and putting it all together into expressions that could be
used to model a facet of the situation. These two activities tie the
pieces together.

The second section focuses on real
life applications of substitution and keeps in mind alternatives and
possibilities while keeping limitations and restrictions in mind.
Activity three has students make up stories to go with algebraic
expressions such as 2x + 4 might represent that you bought four more
twice the number of pastries than Sally bought the day before for work.
Or the double decker bus can carry twice more than a regular bus and
still has room for four more people. Students choose the context of the
expression. The fourth section has students take the expression and
generalize it.

The lesson is actually a unit that
could take a week to do, exposes students to real life thinking for a
mathematical situation that they have experience with. This activity
for me requires some serious thought because the town only has a
population of about 1000 people and its extremely isolated. Most
students have been to Anchorage but there are a few who have never left
the village. So I might have to choose a mall in Anchorage.

I
like the lesson because provides specific details of a nice open ended
situation which will encourage higher order thinking to complete the
activity. Check it out and enjoy.