Algebra 1 – Common Core – NYS Common Core Standard Assessments
F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Typically in these lessons we work on small-scale problems where students collect data from sample questions or they may be given data to create a chart. Next, we plot a graph and discuss the domain and range. Students make a connection to the “Function Machine” an input (x) goes in and you get an output (y). However, a modification ties in the global piece to further discuss the importance of education for women. We will compare crude birth rate against mean years of women’s education.
Students will be working on collecting data themselves from Gapminder.com. They will individually graph five countries between each interval of crude birth rate (10-20, 21-35 and 36-55) totaling 15 data points. Students will be comparing crude birth rate against mean years of women’s education. Through this assignment, students will be using math skills to learn more about the relationship between education and population growth. This will give them a new approach for applying their math skills to a real world problem, and might allow them to value the education they are privileged to. The ability to access resources such as Gapminder.com where you can visualize and easily understand complicated relationships such as the examples here will give students exposure to sophisticated views, and will hopefully foster empathy towards others that are not able to receive the same education.
Informal outcome assessment – Students will complete a graph (in Excel) with 15 data points and answer (7-10) questions. There will be a peer-to-peer share out discussing the hypothesis that can be made from the data points, strong or weak correlation, and positive or negative.
F.IF.1 - Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
When graphing and relating x and y values to domain and range, it is imperative for students to realize each element of the domain is paired with exactly one element of the range. Additionally, we will discuss the meaning behind f(x) and y = f(x), and the process for finding f(x) based on a set of data points (linear regression). A modification was made for students to complete a Global Temperature Lab by finding the mean average temperature for 12 months of any city and year. Students will answer questions based on the function graphed.
Students will be working on researching data and answering questions that connect Earth Science to Math. They will recognize and express their own perspectives and understanding of the world. Students will also be able to create an equation based on their graphed points to make decisions concerning globally significant questions.
Informal outcome assessment – I will pair students for this activity, and allow them to discuss their findings. This will be especially worthwhile during the short answers on hemispheres, temperatures and what similarities exists between the graphs. The lab will consist of an Excel spreadsheet and (10-15) questions.
More on globalizing this standard can be found in my Global Education Unit Plan.