# Thinking with Mathematical Models

### Topics

Represent data using multiple representations, recognize and use linear and non linear (inverse variation) models, use residual analysis, use scatter plots, two way tables, correlation coefficients, and standard deviation

### Overview of Changes

*Significant changes* The CCSS standards for statistics are addressed in this unit.

### Description of Changes

The first three investigations of this unit have changed very little from the preceding edition. A few changes involve problem context and giving more attention to residual analysis as a technique for measuring the goodness-of-fit of a function model to given data. There is some additional coverage of slope, connecting with ideas from seventh grade units. The fourth and fifth investigations present new material that addresses the Common Core State Standards requirements regarding correlation and 2-way table analysis

#### Investigation 4 (NEW) - Variability and Association in Numeric Data

The problems of this investigation review and enhance student understanding and skill in data analysis by focusing on two key statistical concepts—correlation and standard deviation. Students explore positive and negative correlations shown in scatter plots of bivariate data, use of the correlation coefficient as a measure of linearity for scatter plots, and the standard deviation as a measure of spread in single variable distributions.

#### Investigation 5 (NEW) - Variability and Association in Categorical Data

The problems in this investigation review and enhance student understanding and skill in data analysis by focusing on use of 2-way tables to test the strength of association between categorical variables.

New Investigation | Changes in CMP2 Investigation |
---|---|

Investigation 1 Exploring Data Patterns |
Investigation 1 similar to Investigation 1 in CMP2 |

Investigation 2 Linear Models and Equations |
Investigation 1 similar to Investigation 1 in CMP2 |

Investigation 3 Inverse Variation |
Investigation 1 similar to Investigation 1 in CMP2 |

Investigation 4 Variability and Associations in Numerical Data |
Investigation 4 is new. See description above. |

Investigation 5 Variability and Associations in Categorical Data |
Investigation 5 is new. See description above. |