One thing that is important to remember when working with mathematics is that it, in fact, does relate to real life. An extremely drastic example would be the show Numbers; an FBI agent’s little brother is a professor of mathematics of a local university and uses his knowledge of probability, statistics, physics, etc. to help catch ‘the bad guys’. Like I said, although this is a very drastic scenario it really does help one see that math can actually be used in everyday life. Another thing to remember, especially when working with middle school and high school students is to remind them that math is really figuring out relationships between elements; how fast you go in a car and the time it takes you to break, the more interest that is charged to a credit card and the minimum payment that you might have to pay, investments, etc. Teenagers and adolescents hardest concept to come by while struggling through their math classes is that they don’t think that math is applied to them directly and they don’t see the relationships within math itself.
One of the Common Core State Standard sections for mathematics is all about modeling. Modeling means to create a picture, or graph, that represents a function, or relationship, to better understand what the overall effect is. We do this with exponential growth and decay, with parabolic functions showing the movement of something being throw into the air, with investments of businesses and companies, even with the world population. This modeling standard is stated, by the CCSS.Math website, “Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (*).” Other CCSS for Math that is included are:
CCSS.MATH.CONTENT.HSF.BF.A.1.B
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
CCSS.MATH.CONTENT.HSF.BF.A.1.C
(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
CCSS.MATH.CONTENT.HSF.LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
An experiment called ‘Making Cents of Math’ will be how we will tie everything together with a pretty mathematical bow. This experiment uses a Vernier sensor called ‘Dual-Range Force Sensor’. This sensor is used to measure pulling and pushing forces. It could be used to help study the impact of car crashes and it could also be used to study trucks and the amount of force that they are able to pull and it could lead to some findings on how to increase the strength of the truck in order to pull more weight. However, today we will be using it to create a relationship between the amount of pennies and how much they weigh. The sensor looks as such:
The cord you see here will plug into a laptop and it will record the data for you. Instead of the metal mass attached to the hook on the picture on the left we are going to hand a paper cup from the hook. This is going to be how we will measure the weight of all of the pennies. Using the Dual-Range Force Sensor and the appropriate software on the laptop we will be able to create an accurate table, which will then give us our coordinate points that we will graph on a graphing sheet of paper.
Starting out, each group of mathematicians will receive 32 pennies (4 sets of 8 pennies). After their paper cup is properly hanging of the sensor’s hook each group will slowly measure the first set of 8 pennies, only recording the weight after the cup has stopped swaying. This will ensure a more accurate weight. Each group will continually add the second, third, and fourth set of pennies and recording the resulting weight. Now, they can’t have the computer record everything for them! They will have to find the slope of the line that these data points created. They’ll have to use two sets of data points and the slope formula, , and write a complete linear function in the form of , where m is the slope and b is the y-intercept. Also, to assist them in their progress throughout this experiment, they will have to work through the handout which can be found here: https://www.vernier.com/files/sample_labs/RWV-02-DQ-making_cents_of_math.pdf. This will allow them to see the relationship between the pennies and the weight (as well as the picture that they’ll have to create) and it will also allow them to pick apart the experiement and each peice of the equation and determine why each part is important.
This is just a very small experiment, however it teaches the students how they might be able to find a relationship between two different elements and how they can apply math directly to a real life scenario. This is especially important for those students who struggle in realizing that math is important in the everyday life and can be used in the everyday life and that it’s not just something that they’re forced to take for a minimum of 2 years in high school.