Injustice - Developers Among Us (SciFiDevCon 2024)
1.5 problem solving using algebraic models
1. Today’s objective:
1. I will use a gener al pr oblem
solving plan to solve r eal-life
pr oblems.
2. When solving real-life problems,
it is sometimes helpful to first
write an equation in words
before you write it in
mathematical symbols.
Verbal model: a word equation
that represents a real-life
problem.
Algebraic model: a
mathematical statement that
3. 1. Write a verbal
model.
2. Assign labels.
3. Write an algebraic
model.
4. Solve the algebraic
model.
4. The Bullet Train runs Verbal Model
between Osaka and Distance = Rate x Time
Fukuoka, a distance Labels
of 550 kilometers. Distance = 550km
When it makes no Rate = r
stops, it takes 2 Time = 2.25 hours
hours and 15 Algebraic Model
minutes to make the 550 = r(2.25)
trip. What is the Solve algebraic model
average speed of the r = 550/2.25 ≈ 244
Bullet Train? Answer the question
The Bullet Train’s average
speed is about 244 km/h.
5. A water-saving faucet Verbal Model
has a flow rate of at Volume = Flow rate x Time
most 9.6 cubic inches Labels
per second. To test Volume = 470
whether your faucet Rate = r
meets this standard,
Time = 35 seconds
you time how long it
Algebraic Model
takes the faucet to fill
a 470 cubic inch pot, 470 = r(35)
obtaining a time of 35 Solve algebraic model
seconds. Find your r = 470/35 ≈ 13.4
faucet’s flow rate. Answer the question
Does it meet the The flow rate is about 13.4
standard for water in.3/s, which does not meet
conservation? the standard.