STATS in Algebra 1 By Laura Worrall

STATS & the CCSS We as Algebra 1 teachers need to cover the following statistical concepts: One variable data displays such as dotplots, stem plots, histograms, and boxplots Center, Shape, and Spread (COOL STAT STUDENTS) Mean, median, mode The relationship between the mean and median in symmetric distributions versus skewed distributions IQR and range – stress the importance of variability

The 3 Regression Models: LEQ Linear, Exponential, and Quadratic Regression Models Linear: interpretation of slope and y-intercept in context, scatterplots, correlation coefficient (r), residual Exponential: recognition of this model and construction of this model Quadratic: recognition of this model and construction of this model It’s very important to emphasize that all interpretations must be in context of the situation under study. Time plots are also useful to show trends over time.

Categorical Variables Students need to be able to analyze the relationship between two categorical variables by finding conditional, joint, and marginal probabilities in a two- way table, also called a contingency table. Clearly distinguish between quantitative and categorical variables Determine through relative frequencies if two categorical variables are related (dependent) or not related (independent) Segmented bar graphs are very helpful here.

Assumptions We need to assume that students are familiar with the following basic concepts before we start the stats unit so a day of review may be needed and beneficial. Slope Y-intercept Linear Equation Exponential Equation Quadratic Equation One variable data versus two variable data

Timeline According to the district’s suggested time frame, we need to allow 12 days for the teaching of stats. These are assumed to be twelve minute periods. Breakdown: 6 days – regression models 3 days – CSS 1 day – categorical data 1 day – review 1 day - test

Technology We will use a bit of technology today to explore time plots and regression models. If you don’t have access to a set of TI’s, just the simple display of the scatter plots and models on the TI is a great learning tool for the algebra students.

Interpreting Slope We need to be careful about teaching only the graphical meaning of the slope. The trend seen in the CCSS is to focus on the conceptual understanding. Slope to algebra kids usually means rise/run or looks like a fraction. As algebra teachers, we need to help our students gain a deeper understanding of the slope that allows them to give meaningful interpretations when dealing with linear models. We will look at several examples today by starting with a glance at what we want our higher level students to be able to do.

Let the STATS BEGIN!