Topic #1 Create linear equations in one variable The standards listed to the right should be used to help develop A.CED.1 Note: The standards listed to the right will be used to help develop many topics. N.Q.1 Use units as a way to understand problems and guide the solution of multi-step problems N.Q.2 Define appropriate for the purpose of descriptive modeling N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities A.CED.3 Represent constraints by equations or inequalities and interpret solutions as viable or non-viable options in a modeling context Major Standard to address Topic #1 A.REI.3 linear equations in one variable including equations with coefficients represented by letters. The standards listed to the right should be used to help develop A.REI.3 Note: The standards listed to the right will be used to help develop many topics. A.REI.1 Explain the in solving equations in one variable A.SSE.1a Use the structure of an expression to analyze equations or inequalities in to develop a plan for solving the problem. A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations Algebra I Unit 1:Relationships Between Quantities and Reasoning with Equations Topic #2
precision with which answers can be reported parameter A.CED.2(ES&K) Ability to determine unknown parameters needed to create an equation that accurately models a given situation A parameter is a constant or variable term in a function that when changed has an effect on the behavior of the graph of the function but not its general nature. For example, in the intercept form of a line, the parameters are m and b. As the m and b take on different values, the function is still linear, but the graph of each function will differ in slope and/or y-intercept. Examples: significant digits N.Q.3 (ES&K) Knowledge of and ability to rules of significant digits Significant digits or significant figures are digits that carry meaning contributing to the precision of the number. Rules for significant digits All non-zero digits are significant Example : 22.3 has three significant digits Zeros appearing between non-zero digits are significant Example: 302 has three significant digits Leading are not significant Example: 0.046 had two significant zeros Trailing zeros have several rules that apply Trailing zeros in a number containing a decimal point are significant Example: 7.90 have significant figures Tailing zeros in a number that does not have a decimal point may or may not be significant depending on the context of the problem.
Solving one-variable linear equations (including infinite solutions and no solutions)-at the high school level this becomes a fluency expectation. Understanding of and ability to work with rational and irrational numbers. Fluency with properties of numbers. Ability to generate equivalent expressions and equations. Fluency with operations with rational numbers is an expectation at the 7th level. Solving many absolute value equations algebraically requires a student to be able to solve linear equations in one variable. Geometry students will need to be fluent in solving linear equations in one variable to apply geometry concepts. Algebra II Solving polynomial, exponential, logarithmic radical, rational and trigonometric equations may require students to solve linear equations in one variable Determining the domain of a rational function may require a student to solve a linear equation in one variable. The following skills/understandings developed in Middle school should support students in learning “Linear Inequalities in One Variable”: From grades K-8 students have built up to a fluency expectation of solving one-variable linear equations (including infinite solutions and no solutions) Linear Inequalities in One Variable In Algebra I Unit 2 students will: Graph linear inequalities in two variables Graph the solution set to a system of linear inequalities in two variables In Algebra II there are no standards that explicitly mention solving inequalities in either one or two variables. However, instruction could include graphing inequalities in two variables based on each function that is introduced.
Students interpret “unit rate” as the slope of the graph of a proportional relationship. Significant groundwork has been laid towards the understanding of a function. The concept of function is first introduced in 8th grade in terms of “input” and “output” values. In 8th grade students define, evaluate, and compare simple functions. In middle school students spend considerable time studying proportional relationships and their connection to linear equations in two variables. Students have solved systems of linear equations graphically and algebraically. . In Algebra II students will expand their study of functions to include: quadratic radical rational polynomial exponential logarithmic trigonometric . The following skills/understandings developed in Middle school should support students in learning “Exponential Equations in One Variable ”: Exponential Equations in One Variable In Algebra I Unit 2 students will study rational exponents for the first time.
When combining like terms in expressions such as students may think that Question students through the process-asking for a mathematical principle that makes each step valid In a problem such as , students may think that because the variable is alone that they have finished solving the problem. Put a “1” in front of the, so they know to divide by -1 thus getting the final answer of . When solving a problem such students who have been taught to rewrite subtraction problems as addition problems might make the following error. And then to solve the problem the student thinks that it is necessary to subtract 5 from both sides to “undo” the addition. (See below) Several strategies could be used in this situation. Depending on the student’s understanding you may: Model this problem using manipulatives. (algebra tiles, chips, balance) A more abstract approach might include something as simple as the following
Sample Assessment Items The included in this component will be aligned to the standards in the unit and will include: Items purchased from vendors PARCC prototype items PARCC public released items Maryland Public release items Resources This section contains links to materials that are intended to support content instruction in this unit. Interventions/Enrichments Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules. Interdisciplinary Connections Interdisciplinary connections fall into a number of related categories: Literacy standards within the Maryland Common Core State Curriculum Science, Technology, Engineering, and Mathematics standards Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others. Components Key Advances from Grades K–8 According to the Partnership for Assessment of Readiness for College and Careers (PARCC), these standards highlight major steps in a progression of increasing knowledge and skill.