The following section outlines some sample activities that can be used in the classroom in order to facilitate mathematical learning and the use of mathematical modelling to make predictions. This section provides a brief overview of some of the possible activities and some strategies for helping students progress through the content. I have provided a list of student resources for them to reference when researching and collecting data.
Lesson Activity 1: Using Ratios and Unit rates to compare CO2 emissions in different countries. (5-6 days)
This first activity is a set of lessons that should require a few classes for each part, dependent on your students. Proportional reasoning is a long unit packed with different pieces. Students will learn about rates, unit rates, proportions, and more while learning about Global Warming and CO2 emissions. They will collect their own date, and then learn how to apply the math.
Measuring rainfall, and collecting data from previous years. Temperatures over spans of years.
With our focus on SEL and Social Justice, we will discuss if there is a social issue here.
Students will gather data on the carbon dioxide (CO2) emissions from different countries around the world. We will have a discussion on equity, and is it “fair” that countries that don’t emit much still have the same amount in the atmosphere as the top emitting countries. Students will write a ratio of CO2 emissions to area for each country. Students will create a list ranking the countries by CO2 emissions. Students will then find the area of each country in square miles. Students will then write a ratio of CO2 emissions per square mile of each country. Students will then determine each countries unit rate, comparing CO2 emissions to one square mile. Students will then create a list ranking countries CO2 emissions based on the unit rates. (This will also be a review of ordering decimals for students.)
Students will also gather data on the CO2 emissions for each of the same countries on a per capita basis. Students will create a ratio based upon the CO2 emissions per the total population of each country. Students will create a list ranking the countries by CO2 emissions. Students will then determine the unit rate of CO2 emissions per capita. Students will then create a list ranking countries in order of their CO2 emissions per capita.
Students will use proportions to compare ratios that they have written to determine if any countries have the same rate of CO2 emissions per the same factor.
Lesson Activity 2: Using percent to reduce a carbon footprint. (2 days)
Students will determine their personal carbon footprints. They will look at each item on their list, and brainstorm ways to reduce individual items. Students will then find the percentage of CO2 they are saving from being emitted with the changes they make.
Lesson Activity 3: (Linear Equations)
At the conclusion of this lesson students will:
KNOW: The slope intercept form of the linear equation (y = mx+b);
UNDERSTAND: The limitations of using linear equations when modeling real world phenomena; and that continued CO2 emissions at current rates leads to predictable outcomes for atmospheric carbon (AC) levels and average global temperatures (AGT).
BE ABLE TO DO: • Write linear equations from real-world situations and use them to predict future events.
Students will research carbon dioxide emissions and will collect data on carbon dioxide emissions, and atmospheric concentrations for 2 different years. Students will then make predictions of carbon dioxide emissions in future years, using a linear model.
Understanding Linear Equations:
Students will be learning about slope, the y intercept, the relationship between the x and y axis, and an equation written in slope-intercept form. The equation y = mx +b is one of the most important in all of algebra. The graph y = mx + b is a straight line of ordered pair, i.e. solutions in a line.
Students need to learn: x is independent of y, and y is dependent on x; how to find the slope of a line from 2 points (2 ordered pairs); the y intercept is where we start, the y value without any x; the y intercept, b, is always a constant.
Lesson Activity 4: (Scatter Plots)
Students will gather data and plot the points on a graph. We will discuss what the data means. We will look if the data is linear, or not. Does it have a linear trend?, or is it curved? We will discuss scatter plots and how to write an equation of the trend of the data and how to make predictions.
Lesson Activity 5: (Exponential Equations)
At the conclusion of this lesson students will:
KNOW: The general form of the exponential equation (y = bg^x)
UNDERSTAND: The limitations of using exponential equations when modeling real world phenomena. That continued CO2 emissions at current rates leads to predictable outcomes for atmospheric carbon levels and average global temperatures.
BE ABLE TO DO: • Write exponential equations from real-world situations and use them to predict future events
Data Collection: We know that to have Linear Growth we have to be adding the same amount every year. But the amount of carbon dioxide that is being added each year is going up from the previous year. This cannot be modelled as a linear function, but rather is a Linear function. We cannot use a linear equation to predict into the future, but instead we will use an exponential model to make predictions into the future.
The exponential equation looks like this: y = bg^x It works for situations where the rate of change of y is changing.
Lesson Activity 6: Nasa Math
Students will explore global warming and apply mathematics to solve different problems related to global warming using the Nasa Math website: https://spacemath.gsfc.nasa.gov/Warming.html