Math 1A Exemplar
Unit 3 Big Ideas
5) Linear functions have a distinct pattern of change (constant rate of change) that can be seen in tables, graphs, rules, and contexts for these functions. This pattern of changes makes linear functions useful in modeling a variety of real-life situations.
6) Linear equations can be written to solve specific questions about real-life situations. Solutions to equations are values that make the equation true, and those solutions can be found using tables, graphs, technology, or algebraic manipulation.
Collected Data
The purpose of this project is to predict the height of my son over time. I wanted to know how tall he would be when he turned 60 and how long it would take for him to be the same height as me.
Graph
In order to figure out the height of my son, I first had to gather some data. I measured his height as time passed and recorded it onto a table. However, I did not find a clear pattern of change, so I constructed a graph from the data on my table. It didn't have a clear linear pattern, so I drew a best fit line through the data.
Table
Using the data on my best fit line, I created a new table of values from the line. I found a linear patterns of change. The height of my son increases by 2.5 inches every year based off the data.
Table and Rule
From the table, I tried to find a clear pattern so I could construct an algebraic rule. Through the rationale in my work, I was able to identify the rule as
h=27.5 + 2.5 t
h represents the height
t represents the time
27.5 represents the height of my son when he was born
2.5 represents the growth of my son every year
Using the Algebraic Rule
In order to figure out how tall my son would be when he turns 60, I used the algebraic rule and inserted 60 years for the time. I calculated the height to be 177.5 inches.
Realistically, this does not make sense because someone that is 177.5 inches tall is over 14 feet tall.
To find how long it would take for him to be as tall as me (68 inches) I used the algebraic rule again but inserted the height to calculate the time. After solving it, I calculated that when my son turns a little over 16, he will be my height.
Relating the Big Ideas
Linear functions have a distinct pattern of change. You can see the change in the graph because the points construct a line. You can see it in the table because the amount the height increased was at a constant rate of 2.5 inches. You can see that in the equation because the 2.5 represents how much the height of my son changes every year. I can use these tools to model the height of my son as he grows up. However, it is not a good model after a certain age because people stop growing at a linear rate when they get older.
I can use linear equations to solve the height of my son without having to manually create a long table or a large graph to find that data. This was demonstrated by the last section using the algebraic rule.
Rating
I rate myself as an expert because I can make connections between the table, graph, algebraic rule and a context and use linear equations to solve for unknowns.