Algebra 1
Fall Semester | |||||
Unit Title | Unit 1: Solving Equations and Inequalities | Unit 2: Introduction to Functions | Unit 3: Graphing and Writing Linear Functions | Unit 4: System of Linear Equations and Inequalities | Unit 5: Exponents and Radicals |
Time | ~3 weeks | ~3 weeks | ~4 weeks | ~3 weeks | ~4 weeks |
Understandings | Solving a multi-step equation in one variable involves using properties of equality and inverse operations to isolate the variable.
Solving equations with variables on both sides involves manipulating the equation so the variable terms are on one side of the equation and constant terms are on the other.
The solution set of a linear equation in one variable can result in one solution, no solution, or infinitely many solutions.
| A function is a relationship between variables that can be represented in various ways, which are useful for predicting values in real-world situations.
The domain of any relation or function is simply the set of all input values (the independent variables), while the range is the set of all corresponding output values (the dependent variables).
In any real-world problem, the domain and range must be reasonable for the situation being modeled. A reasonable domain includes every possible independent value that makes sense in the context of the problem, and a reasonable range includes every possible dependent value that logically fits the situation. | Linear Functions can be represented in multiple ways and analyzed to extract desired information.
linear equations can be written using key elements from different representations.
The slope of a line represents the vertical change over the horizontal change between any two given points on the line (also known as the change in y over the change in x).
Rate of change is the application of the concept of slope in real-world situations.
| Many real-world mathematical problems can be represented algebraically by systems of equations and inequalities, which can then be used to make estimates or predictions about future occurrences.
Solution(s) to systems of two linear equations are all coordinate points, if any, that satisfy both equations simultaneously.
Systems of two linear equations can be solved using a variety of methods.
| Mathematical properties allow any quantity to be represented by different equivalent expressions. Properties of exponents make it easier to simplify expressions with powers, and rational exponents can be used to represent radicals.
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TEKS | A.5 A, B A.12 E | A.2 A A.6 A A.9 A A.12 A, B, C, D | A.2 A ,B, C, D, E, F, G A.3 A, B, C A.4 A, B, C A.12 B, E | A.2 H, I A.3 D, F, G, H A.5 C | A.11 A, B |
Process Standards | A.1 A, B, C, D, E, F, G | ||||
Algebra 1
Spring Semester | ||||
Unit Title | Unit 6: Polynomials and Factoring | Unit 7: Quadratic Functions | Unit 8: Exponential Functions | Unit 9: Functions and Their Representations |
Time | ~5 weeks | ~5 weeks | ~3 weeks | ~4 weeks |
Understandings | Properties of real numbers are used to maintain equivalence when simplifying polynomial expressions.
Polynomials can be divided using a variety of techniques similar to the techniques used for dividing real numbers.
Some trinomials of the form ax2 + bx + c can be factored into equivalent forms that are the product of two binomials.Not all trinomials are factorable.
| Key attributes of quadratic functions can be used to analyze, describe, write, graph, and solve functions representing real-world problems.
Changes made to the algebraic representation of a quadratic parent function result in a transformation of the graph.
There are a variety of methods to solve quadratic equations with real solutions.
| Exponential functions can be used to write, graph, analyze and describe functions related to real-world problems.
The basic shape of an exponential function can be determined by the values of a and b in the exponential function f(x) = abx, a > 0.
The value of “a” represents the initial amount (y-intercept) of an exponential function.The value of “b” represents the growth or decay factor.
| A linear function is the correct choice to model a situation when the quantity is increasing or decreasing by a constant amount over equal intervals of time.
An exponential function is used to model situations involving growth or decay that happens by a constant factor or percent over equal time periods. This growth starts slowly but eventually becomes extremely rapid.
A quadratic function is used to model situations that increase, reach a maximum (peak), and then decrease, or vice versa (a minimum then increase). This pattern is characterized by a non-constant rate of change that accelerates. |
TEKS | A.8 A A.10 A, B, C, D, E, F | A.3 E A.6 A, B, C A.7 A, B, C A.8 A, B A.12 B | A.9 A, B, C, D, E A.12 B | A.2 A ,B, C, D, E, F, G A.3 A, B, C A.6 A, B, C A.7 A, B, C A.8 A, B A.9 A, B, C, D, E |
Process Standards | A.1 A, B, C, D, E, F, G | |||