# Problem Solving in Algebra 1

In my Algebra 1 class problem solving is a main emphasis. Each week the students have a special problem to complete on Fridays. It normally involves several steps and some creative thinking. Here is one from last week:

This problem was taken from Drexel University’s problems of the week.

When students respond their written explanation is just as important as the mathematical methods they used. Here is an excellent response I received last week:

First I made t = time in hours that has passed by since 8:15 { so at 8:15, t=0}
then I have
(0,50) and (1.5, 62)

for (time, temperature in Fahrenheit). Forming a linear equation here. I first had to determine the slope. That will be
m = (62 – 50) / (1.5 – 0)
m = 8

Since the y-intercept (50), then I wrote the linear equation through slope-intercept form. I came up with
y = mx + b

I replaced y with F for temperature in Fahrenheit, and x with t for time and ended up with

F = 8t + 50

in order to answer the second question I did this

104 = 8t + 50
54 = 8t
t = 6.75 hrs

6.75 hrs after 8:15AM is 3PM.

At 5PM, t=8.75. Thus

F = 8(8.75) + 50
F = 70 + 50
F = 120

So by 5PM, the water in the tub will have a temperature of 120 degrees F.

The water in the tub won’t be heated in a linear fashion. It will be heated in a logarithmic fashion. Because the wood-burning stove has a maximum temperature, then eventually the water can only be heated until that temperature. If  i assumed that the water follows a linear trend, then it can go beyond the wood-burning stove’s maximum temperature. Another reason why it cannot follow a linear trend is that the particles would begin to heat faster during the first few moments, but eventually slowdown in heating up.

Look all the excellent vocabulary that was included and how clearly you can follow each step. Being able to explain a problem like that in writing means a student fully understands the concepts.

# Coffee Shop Conundrum

A coffee shop posts the prices of different combinations of muffins, breakfast sandwiches, and coffees in the sign above. Can you use the sign to determine the individual price of each item?