# Algebra 1

### Parents, please note that these standards are listed in the order, and for the amount of time, that most Beyond Textbooks schools follow. These are guidelines, and your child's school may vary.

#### Benchmark 1:

1. Alg1.M.A.SSE.A.01a: I can identify the parts of a mathematical expression. (Not Assessed on Benchmark) (5 days)
2. Alg1.M.A.REI.B.03: I can create, solve and graph linear equations and inequalities in one variable. (5 days)
3. Alg1.M.F.IF.A.02:  I can use function notation and solve a function given a specified value. (5 days)
4. Alg1.M.F.IF.B.06: I can calculate and describe the rate of change of a graph or table given specific intervals. (5 days)
5. Alg1.M.A.CED.A.02: I can create and graph an equation with 2 variables. (10 days)
6. Alg1.M.F.IF.B.04: I can identify and interpret the key features of graphs and tables from a linear function. (10 days)
7. Alg1.M.A.S.ID.B.06c: I can create and compare linear functions for a scatter plot. (10 days)
8. Alg1.M.A.S.ID.C.08: I can calculate and interpret the correlation coefficient of a set of linear data and determine whether a correlation implies causation. (10 days)

#### Benchmark 2:

1. Alg1.M.F.IF.C.07a: I can graph a linear function. (5 days)
2. Alg1.M.A.REI.C.06: I can solve a system of equations in two variables using a variety methods. (15 days)
3. Alg1.M.A.REI.D.12: I can create and graph up to three inequalities in two variables and find their solution set. (15 days)
4. Alg1.M.F.LE.A.01: I can identify whether a function is linear or exponential based on its rate of change. (5 days)
5. Alg1.M.F.LE.A.02: I can create both linear and exponential functions from graphs, patterns, tables, and description of relationships. (5 days)
6. Alg1.M.A.APR.A.01: I can add, subtract and multiply polynomials. (10 days)

#### Benchmark 3:

1. Alg1.M.A.APR.B.03: I will be able to find the zeros of a quadratic function to sketch a graph and write a quadratic equation. (20 days)
2. Alg1.M.A.REI.B.04: I can solve a quadratic equation using various methods.           (20 days)
3. Alg1.M.F.IF.C.07b: I can graph a quadratic equation and show key features of the graph. (20 days)
4. Alg1.M.F.IF.C.09: I can compare two functions that are represented in different ways. (5 days)
5. Alg1.M.A.S.ID.A.01: I can represent data using dot plots, histograms and box plots. (15 days)
6. Alg1.M.A.S.ID.A.02: I can find the mean, median, interquartile range and standard deviation of a data set and use the appropriate measures to interpret and compare sets of data and graphs. (15 days)

#### Benchmark 4:

1. Alg1.M.F.IF.A.01: I can determine the domain and range of a graph, set of points and table, and determine whether or not the given data represents a function. (5 days)

1. Alg1.M.N.RN.B.03: Explain why the sum or product of two rational numbers are 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. (Month 1)
2. Alg1.M.A.REI.A.01: 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. (Month 1)
3. Alg1.M.A.CED.A.01: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (Month 2)
4. Alg1.M.F.IF.C.09: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (Month 2)
5. Alg1.M.F.IF.A.01: 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, then 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). (Month 2 & 7)
6. Alg1.M.F.IF.B.05: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person‐hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. (Month 2, 7, & 9)
7. Alg1.M.F.IF.A.02: Use function notations, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (Month 2, 7, & 9)
8. Alg1.M.F.BF.A.01: Write a function that describes a relationship between two quantities. (Month 2)
9. Alg1.M.F.IF.C.07: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  a. Graph linear and quadratic functions and show intercepts, maxima, and minima. (Month 2 & 8)
10. Alg1.M.S.ID.C.07: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (Month 3)
11. Alg1.M.S.ID.B.06: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or chooses a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. (Month 3)
12. Alg1.M.S.ID.C.09: Distinguish between correlation and causation. (Month 3)
13. Alg1.M.S.ID.B.05: Summarize categorical data for two categories in two‐way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends. (Month 3)
14. Alg1.M.N.Q.A.02: Define appropriate quantities for the purpose of descriptive modeling. (Month 3, 4, 7, & 8)
15. Alg1.M.N.Q.A.03: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (Month 3)
16. Alg1.M.A.CED.A.03: 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (Month 4)
17. Alg1.M.A.REI.C.05: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. (Month 4)
18. Alg1.M.REI.D.11: Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (Month 4)
19. Alg1.M.A.REI.D.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). (Month 4)
20. Alg1.M.A.SSE.A.02: Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). (Month 5 and 7)
21. Alg1.M.A.CED.A.04: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. (Month 5 & 7)
22. Alg1.M.F.LE.A.03: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (Month 5)
23. Alg1.M.F.LE.B.05: Interpret the parameters in a linear or exponential function in terms of a context. (Month 5)
24. Alg1.M.F.IF.B.04: 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (Month 5, 7, & 9)
25. Alg1.M.F.BF.A.02: Write recursive and explicit formulas for arithmetic and geometric sequences. (Month 5)
26. Alg1.M.F.IF.C.08: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (Month 7)
27. Alg1.M.A.SSE.B.03: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Month 7)
28. Alg1.M.A.SSE.B.04: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. (Month 7)
29. Alg1.M.S.ID.A.03: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (Month 8)

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