## Standards

Standard |
Language |

A.CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equation on coordinate axes with label and scales. |

A.CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. |

A.REI.5 | Prove that, given a system of two equations in two variables, replacing on equation by the sum of that equation and a multiple of the other produces a system with the same solutions. |

A.REI.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. |

A.REI.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |

A.REI.11 | Explain why the x-coordinates of the points where the graphs of the equation and intersect are the solutions of the equation ; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where and/or are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. |

A.REI.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. |

F.IF.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. |

## The “Story” of This Unit

Data can be messy, but there are patterns everywhere! When we look at a scatter plot, all we see is a bunch of dots…can we make any conclusions from these things. Sometimes, the answer is clearly YES…we can use data to create equations (sometimes just by drawing a graphical picture) and we can use that information to make claims about what is likely to happen in the future based on this trend. We will extend our understanding of functions by collecting a lot of inputs and noticing they have a common additive growth over time. Looking at patterns, we will find that complicated things can be made more simple by considering the average change that happens over time. Math is incredibly powerful at using patterns to predict the future.

## Resources

- Balance Beam Interactive (1) http://www.learner.org/courses/learningmath/algebra/session6/part_c/index.html (Flash Required)
- Balance Beams Interactive (2) http://www.hoodamath.com/mobile/games/algebrabalanceequations.html
- Balancing Scales Day 1 (used with permission by Nancy Ku)
- Balancing Scales Day 2 (used with permission by Nancy Ku)