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In Algebra 1, students demonstrate fluency by creating, comparing, analyzing, solving, providing multiple representations, and identifying the structures of exponential & quadratic functions building on the understanding of linear functions from grade 8 to apply linear, quadratic and exponential models to data and unfamiliar problems.
Essential Standards
F-LE.1 Claim 4 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.1 Claim 4 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
A-CED.A.1 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.
There are no substandards for this standard.
A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
There are no substandards for this standard.
F-IF.C.9 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.
Embed with F-IF.C.9, F-IF.C.7 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 show intercepts...
A−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...
There are no substandards for this standard.
Embed with A-REI.D.11, 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).
There are no substandards for this standard
F-BF.A.1 Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
There are no substandards for this standard
A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t is approximately equal to 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
N-RN.2 (N-RN.1 embedded) Rewrite expressions involving radicals and rational exponents using the properties of exponents.
There are no substandards for this standard.
Embed with N-RN.2, N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3] = 5^[(1/3)3] to hold, so [5^(1/3)]^3] must equal 5.
There are no substandards for this standard.
F-LE.1 1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Achievement Level Descriptors & Evidence
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Achievement Level Descriptors
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Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Achievement Level Descriptors
Evidence
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Achievement Level Descriptors
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Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Achievement Level Descriptors
Evidence
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Achievement Level Descriptors
Evidence
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Achievement Level Descriptors
Evidence
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Achievement Level Descriptors
Evidence
Evidence
Supporting Standards
Embed with F-IF.C.9, F-IF.C.7 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 show intercepts...
Embed with A-REI.D.11, 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).
There are no substandards for this standard
Embed with N-RN.2, N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3] = 5^[(1/3)3] to hold, so [5^(1/3)]^3] must equal 5.
There are no substandards for this standard.
A-SSE.A.1 Interpret parts of an expression, such as terms, factors, and coefficients.
There are no substandards for this standard
A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
There are no substandards for this standard
F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as as y=(1.02)^t, y=(.97)^t, y=(1.01)^12t, and y=(1.2)^(t/10), and classify them as representing exponential growth or decay.
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 non-zero rational number and an irrational number is irrational.
There are no substandards for this standard
F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
There are no substandards for this standard
F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context. [Linear and exponential of form f(x) = b^x + k]
There are no substandards for this standard
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