Below are the math topics that will be integrated into the Environmental Science (Climate Change) curriculum for Saturday Academy 2011-2012.  Also below are the district (middle and high school) standards that align with each topic.

NOTE:  Please use this information as a foundation to the integration of the math into the curriculum.  As we venture into the curriculum and potentially discover other areas of interests, then we can make modifications.

## STATISTICS

(middle/high school)Determine and explain the measures of central tendency (mode, median, mean), interpret differences in shape, center, and spread in the context of the data sets, and explain effects of extreme data points (outliers). (▲M8.4.2.K3, 10408, CC.S.ID.3, ACT)

(middle/high school)Understand and explain the difference between and identify situations with independent and dependent events in an experiment, simulation, or situation. (CC.7.SP.8)

## GRAPHING

(middle/high school)Understand that the graph of a line on the coordinate plane is an infinite collection of points that satisfy an equation in two variables. Use that understanding to find points on a line when given an equation or test whether given points are a solution for an equation, both by hand and by using a calculator. (▲M8.3.4.K1b, CC.A.REI.10, ACT)

(middle/high school)Know and explain the use m and b as parameters in y = mx + b. Identify how constants and coefficients affect a linear graph and interpret the meaning of the intercepts and slope in a real-world situation. (rMHS.2.3.A2, rMHS.2.3.K6, 10210/10304)

(middle/high school)Translate between written, numeric, algebraic, geometric, tabular, and symbolic representations of linear relationships of real-world problems. (▲M8.2.3.A3)

(middle/high school)Determine if a given graphical, algebraic, or geometric model is an accurate representation of a given real-world situation. (▲M8.2.4.A2)

(NC) Create, represent, and solve linear equations from real-world problems; graph equations on coordinate axes with labels and scales. (▲MHS.2.2.A2, 20201/20301, CC.A.CED.2, CC.A.REI.10, ACT)

## DATA INTERPRETATION

(middle/high school)Identify independent and dependent variables within a given situation. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (CC.6.EE.9)

Perform computations in data from tables and graphs. (CC.S.ID.5, ACT)

Understand and explain why a certain measure of central tendency is more appropriate based on the shape of data distribution.  Be able to calculate mean, median, inter-quartile range and standard deviation and explain their meaningfulness in the context of real-world data sets. Explain the effect of outliers on measures of central tendency. (▲MHS.4.2.K4, 20406/20409, CC.S.ID.2, CC.SID.3, ACT)

Read, create, analyze, and represent two sets of quantitative data. (▲MHS.4.2.A1, ▲MHS.4.2.K5, 20401/20402/20403/20404/20405, ACT)

1. charts, tables, and frequency tables
2. bar, line, and circle graphs
3. Venn diagrams
4. stem-and-leaf plots
5. scatter plots (line of best fit and predictions)
6. box-and-whisker plot

Explain how bias, measurement error, and misleading graphs can affect the interpretation of data.

(CC.S.IC.1, ACT)

Identify domain, range, independent variable, and dependent variable of linear, constant and quadratic relationships given a graph, table or equation. (20209, CC.F.IF.1)

## PROBABILITY

(middle/high school)Find and represent probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (▲M8.4.1.K3, ▲M8.4.1.A4, 10403/10404, CC.7.SP.8a-c, ACT)

(middle/high school)Find the conditional and joint probability of two dependent events in an experiment, simulation, or situation. (CC.7.SP.8, ACT)

Interpret differences in center and spread of the data sets, looking at the range and the shape of the distribution including symmetrical, skewed, and uniform distribution, accounting for possible effects of extreme data points (outliers). (20411, CC.S.ID.3, ACT)

## SOLVING EQUATIONS

Generate and solve multi-step real-world problems in applications such as business, chemistry, and physics with real numbers and algebraic expressions using computational procedures including roots, powers and scientific notation. (▲MHS.1.4.A1a, 20109, CC.8.EE.4, ACT)

(middle/high school) Solve equations by constructing a viable argument to justify the solution; explain each step as following from the previous step including using the names of mathematical properties. (▲M8.1.2.A1a,d, ▲M8.1.2.A1b,d, rMHS.1.2.K3a, rMHS.1.2.K3b,e, 10111/10112, CC.A.REI.1)

(middle/high school)Performs addition, subtraction, multiplication, and division of integers. (▲M8.1.4.K2a, ACT)

(middle/high school)Evaluate expressions that require using order of operations at specific values.  Include: absolute value, exponents up to third degree, expressions with at most four operations, and formulas used in real world problems.  Explain order of operations in conventional order when there are no parentheses to specify a particular order. (▲M8.1.4.K2b, 10104, CC.6.EE.2c, ACT)

(middle/high school)Generate and/or solve one- and two-step real-world problems using computational procedures and mathematical concepts with rational numbers, the irrational number pi as an approximation, and applications of percents. (▲M8.1.4.A1a-c, 10105)

## CONVERSIONS

NOT SPECIFICALLY FOUND AS A MATH STANDARD, WHICH COULD MEAN THAT IT’S PROBABLY FOUND IN THE DISTRICT SCIENCE STANDARDS.  DEFINITELY NEEDS TO BE INTEGRATED.

## GEOMETRY

(middle/high school)Solve real-world problems using the properties of corresponding parts of similar and congruent figures.  Include: scale drawings, map reading, proportions, or indirect measurements. (▲M8.3.1.A1a, 10312)

Use proportional relationships to solve multi-step percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent of a number, number when a percent of a number is given, percent increase and decrease, percent error. (▲MHS.1.4.A1d, 20105/20110, CC.7.RP.3, ACT)