  # Algebra in the Real World

Question: Why is Algebra important? How can Algebra be applied to ‘real life?’ When will I ever
use Algebra in Real Life?

Findings: See ideas below

Observations/Questions: I had endless questions about connecting Algebra to real life. The most
important question was how I could apply this new information to teaching in my classroom.

After doing the batting average activity, students learn how to find game batting averages,
but it left me wondering how seasonal batting averages are found.

I also wonder how I can use more real-life Algebraic applications that relate to sports.

I noticed that there are an endless supply of how Algebra is connected with real life. Many
of the lessons got a bit complicated, but there are plenty of accessible ideas for middle school.

Why did I pick this question? I picked this question because I believe it is a crucial part of
teaching Algebra. In brain research, it has been shown that students remember concepts much
more effectively if they have something to attach it to in their memory. By finding real world
connections to Algebra, students will be able to find more meaning in what they’re learning.

FINDINGS

Quadratics
Windsail Design

 Activity: Find the equations that match the parabolic curves being considered in building windsail masts. Given three points, determine the quadratic function . Investigate how a family of curves can be produced by changing one parameter in the equation.
Relate changes in coefficients of a quadratic
function to their influence on the shape and position
of the parabola on the graph .

Use y = ax(x-h) h = height of mast

Resource – Futures Channel Video “Windsails”

Quadratics
Building Telescope Mirrors Activity:
Find an equation for a new telescope mirror
with a given light-gathering power and focal length.
Graph a quadratic function, then relate the
coefficients of a quadratic function to their influence on
the shape and position of the parabola on the graph.
Use this equation for the parabola:
(y – 0) = .03125(x – 2.12)² - simplifies to :
Y - .03125x² - 0.1325x = .14045
Vertex = (2.12, 0)

Resources – Futures Channel “Looking Into Time”

EQUATIONS
Batting Averages Activity: Find the batting averages of several
baseball players.
Solve an expression by substituting values for
variables .

If a batter has a seasonal batting average of
“S” after a total of “T” times at bat and gets “K” hits
in the game for “N” times at bat, his new batting
average is determined by this expression . **This leaves the question “How do they get the
seasonal average in the first place?

Resource: The Futures Channel – “Ballpark”

Exponential Equations
Population Growth Activity: Determine if the populations of several endangered species are flourishing. Look at the

relationship between the “number of young produced”
(Y) and “time” (t) to model an exponential function
based on population data for several endangered
species. Compare this data with data representing
actual populations.
Use the equation Y = A · 10kt

Resource: The Futures Channel – “The Black Footed Ferret”

LINEAR EQUATIONS
Bungee Barbie Activity: Record data to determine how many rubber
bands will adequately help Barbie to Bungee Jump
safely.

Create a scatterplot and create a line of best
fit.

Predict how many rubber bands will be needed
for Barbie to safely jump from a given height.

Algebra in the Real World Laura Thompson-Beato
How I would use these ideas in my classroom?

“What does Algebra have to do with the Real World?”

The connections to the ‘real world’ that I found for Algebra lend themselves perfectly for use in the
classroom
. The six ideas I talked about are using Algebra for batting averages, finding curvatures for telescope
mirrors, designing windsail sails, studying exponential population growth, using polynomials as applied to the shapes
of roller coasters, and using a Barbie doll to graph a bungee experiment.

The “Batting Average” lesson on The Futures Channel includes the following information for a lesson about
45 minutes long:

If a batter goes into a game with a seasonal batting average of S after a total of T times at bat, and gets K
hits in that game for N times at bat, his new batting average is determined by this equation: 1.

 Batter Jackie Willie Roger Mickey Ila Alta Carita Irma

2. Find the missing number for each batter.

 Batter Jackie Willie Roger Mickey Ila Alta Carita Irma
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