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. |

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.

- 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)

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Standard |
Language |

A.CED.1 |
Create equations and inequalities in one variable and use them to solve problems. |

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.CED.4 |
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. |

A.REI.1 |
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. |

A.REI.3 |
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |

Our world has balance, well it should, and we learn about equality through the balance of equal and opposites. Learning to solve an equation or an inequality is understanding balance and equal opposites. We can use equations and inequalities to solve for things we don’t know yet based on the simple premise that the two sides are balanced. We will expand and generalize on some common truths we will learn throughout the unit.

- http://www.learner.org/courses/learningmath/algebra/session6/part_c/index.html (Flash Required)
- Balance Beams Interactive 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)

Standard |
Language |

A.SSE.1 |
Interpret expressions that represent a quantity in terms of its context. |

A.SSE.1.a |
Interpret parts of an expression, such as terms, factors, and coefficients. |

A.SSE.2 |
Use the structure of an expression to identify ways to rewrite it. |

A.APR.1 |
Understand that polynomials form a system analogous to the integers, namely they are closed under the operation of addition, subtraction, and multiplication; Add, subtract, multiply polynomials. |

N.RN.3 |
Explain why the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. |

Numbers tell a story about the world they are placed into. We need a common language to talk about these numbers and symbols. We need to build a common language and understand what basic expectations can be known when a math sentence (expression) is displayed. Expressions and numbers (rational & irrational) interact with one another in specific ways, mathematicians hold specific expectations for how these sets of numbers and symbols interact with one another, and generalizations can be made to simplify how much we need to think about these relationships. While seemingly tricky at first, these numbers and symbols always behave in the same ways…we need to understand those ways of interacting.

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Standard |
Language |

F.IF.1 |
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, the f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). |

F.IF.2 |
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |

F.IF.4 |
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. |

F.IF.5 |
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |

F.IF.7 |
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. |

F.BF.1 |
Combine standard function types using arithmetic operations. |

Functions take an input (we call this the domain)…the function “does something” and we get an output (we call this the range). Anything that has a predictable output is called a function, if it doesn’t the input and output are relational, but NOT a function. Understanding what functions are, how they behave and what is considered possible inputs or possible outputs are essential to mathematical thinking. Essentially, we are generalizing possibilities for what could be…and making formal mathematical statements about these possibilities. To make things more complex, we should be able to consider multiple functions and combine them together…the benefit of this is that similar operations only need to be completed once and matters can be made simple. The purpose of learning information in this unit is to understand that functions can make our life more simple, learn how to use functions, learn the “possibilities” of different functions and combine functions to make very complicated things more simple.

- F.IF.4 – Graphing Stories
- F.IF.4 – Moving Man Graphs
- F.BF.1 – Polynomial Addition and Subtraction:
- Desmos Activity-Domain & Range
- Online Lesson on Algebra Tiles
- Interactive Online Algebra Tiles
- IXL Practice problems

A2U1 Practice Test with Key

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I look forward to an exciting year with you.

-Mr. Germanis

I look forward to an exciting year with you.

-Mr. Germanis

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