Real World Application of Algebraic Expressions

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.