Alg+1+-+Unit+7


 * ===**Common Core Standard(s)**===

//**A-REI.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 and exponential ONLY.**


 * //A-REI.6.//** Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. **(Solving systems using the inverse matrix is not included but should be STRONGLY considered when teaching this standard.) (No creating systems of equations with context is included in High School Math 1 but must be included in order to do the linear programming standard below A-CED.3)**


 * //A-REI.5//**. 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. **(Substitution method)**


 * //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.


 * //A-CED.3.//** Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. //For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.// || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Mathematical Practice(s)**===
 * 1. Make sense of problems and perseveres in solving them.**
 * 2. Reason abstractly and quantitatively.**
 * 3. Construct viable arguments and critique the reasoning of others.**
 * 4. Model with mathematics**
 * 5. Use appropriately tools strategically**
 * 6. Attend to precision**
 * 7. Look for and make use of structure**
 * 8. Look for and express regularity in repeated reasoning.** ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Information Technology Standard**
|| ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Revised Bloom's Level of thinking**
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===
 * Remembering**
 * Understanding**
 * Applying**
 * Analyzing**
 * Evaluating**
 * Creating** ||

**Learning Target/Task Analysis**

 * Linking prior knowledge: Without context, students should have in eighth grade, solved systems of equations. From prior units, students should be able to use a table of values, should be able to graph linear and exponential functions by hand and with calculator.**

**I can...**
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===
 * A-REI.11 I understand the meaning of a system of equations.**
 * I can explain why the x coordinates of two functions intersect and are solutions to the system of equations.**
 * Ex. Solve the following equations by graphing. Give your answers to the nearest tenth.**
 * 3(2^x) = 6x – 7**
 * 10x + 5 = - x + 8**
 * I can the link the use of tables to understand how the x coordinates are solutions.**
 * A-REI.6 I can use graphing to solve systems of equations.**
 * I can use matrices to solve systems of equations.**
 * A-REI.5 I can solve systems of equations using the substitution method.**
 * A.REI.6 I can use context to create systems of linear equations.**
 * A-REI.12 I can graph systems of linear inequalities in two variables as a half-plane. (By hand and with calculator)**
 * I can graph systems of linear inequalities in two variables as a half-plane. (Include three or more inequalities in two variables/linear programming - by hand and with calculator)**
 * A-CED.3 I can find the constraints within a system of linear inequalities.**
 * I can, from context, set up a system of linear inequalities using the given constraints.**
 * I can interpret solutions as viable and non-viable options from context.**

**Essential Vocabulary**
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===
 * systems of linear equations/inequalities, substitution method, constraints, half-plane, strict inequality(non-inclusive inequality), viable solutions, non-viable solutions, corresponding**

**Enrichment:**
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Instructional Resources**
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===