**SAT****® Preparation Course**

**Unit 1: Heart of Algebra**

**Unit 1: Heart of Algebra**

The
redesigned SAT® focuses strongly on algebra and the key concepts that are most essential for success in college and career. Heart of Algebra will assess students’ ability to analyze, fluently solve, and create linear equations and inequalities. Students will also be expected to analyze and fluently solve equations and systems of equations using multiple techniques.

To assess full command of the material, these problems will vary significantly in form and appearance. Problems may be straightforward fluency exercises or may pose challenges of strategy or understanding, such as interpreting the interplay between graphical and algebraic representations or solving as a process of reasoning. Students will be required to demonstrate both procedural skill and a deeper understanding of the concepts that undergird linear equations and functions to successfully exhibit a command of the Heart of Algebra.

By the end of the previous course, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.

To assess full command of the material, these problems will vary significantly in form and appearance. Problems may be straightforward fluency exercises or may pose challenges of strategy or understanding, such as interpreting the interplay between graphical and algebraic representations or solving as a process of reasoning. Students will be required to demonstrate both procedural skill and a deeper understanding of the concepts that undergird linear equations and functions to successfully exhibit a command of the Heart of Algebra.

By the end of the previous course, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.

**What will my child learn?**

Students will:

SAT.HOA.01

**Create, solve, or interpret a linear expression or equation in one variable**that represents a context. The expression or equation will have rational coefficients, and multiple steps may be required to simplify the expression, simplify the equation, or solve for the variable in the equation.

**Alignment to HCPSS Math Course(s) & Course Standard(s):**Mathematics 8 (Unit 3 - 8.EE.C.7) | Algebra 1 (Unit 2 - A.REI.B.3 | Overarching Standards - A.CED.A.1 | Unit 1 - A.CED.A.2)

College Board - item 6 | Ivy Global - item 1 | Ivy Global - item 6 | Ivy Global - section 3, item 1 | Ivy Global - section 4, item 31 | Learnerator - Solve variable linear equations in context**Check for Understanding:**

**Create, solve, or interpret linear inequalities in one variable**that represent a context. The inequality will have rational coefficients, and multiple steps may be required to simplify or solve for the variable.

Algebra 1 (Unit 2 - A.REI.B.3)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 9 | College Board - item 12 | Ivy Global - item 2 | Ivy Global - section 3, items 4 & 16 | Ivy Global - section 4, item 14 | Learnerator - Single variable linear inequalities in context

SAT.HOA.03

**Algebraically solve linear equations (or inequalities) in one variable.**The equation (or inequality) will have rational coefficients and may require multiple steps to solve for the variable; the equation may yield no solution, one solution, or infinitely many solutions. The student may also be asked to determine the value of a constant or coefficient for an equation with no solution or infinitely many solutions.

Mathematics 8 (Unit 3 - 8.EE.C.7)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - section 3, items 9 & 18 | Learnerator - Solving single variable linear equations

SAT.HOA.04

**Interpret the variables and constants in expressions for linear functions within the context presented.**The student will make connections between a context and the linear equation that models the context and will identify or describe the real-life meaning of a constant term, a variable, or a feature of the given equation.

Mathematics 8 (Unit 3 - 8.F.B.4) | Algebra 1 (Overarching Standards - A.SSE.A.1) | (Unit 2 [Part 2] S.ID.C.7)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 8 | Learnerator - Interpreting variables and constants

SAT.HOA.05

**Build a linear function that models a linear relationship between two quantities.**The student will describe a linear relationship that models a context using either an equation in two variables or function notation. The equation or function will have rational coefficients, and multiple steps may be required to build and simplify the equation or function.

Algebra 1 (Unit 1 - A.CED.A.2)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 17 | College Board item 19 | Ivy Global - item 4 | Ivy Global - section 4, item 8 | Learnerator - Modeling linear relationships

SAT.HOA.06

**Understand connections between algebraic and graphical representations.**The student will select a graph described by a given linear equation, select a linear equation that describes a given graph, determine the equation of a line given a verbal description of its graph, determine key features of the graph of a linear function from its equation, or determine how a graph may be affected by a change in its equation.

Mathematics 8 (Unit 3 - 8.F.B.4) | Algebra 1 (Unit 2 [Part 1] - F.IF.C.9, F.BF.B.3, & F.IF.B.4)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 4 | College Board - item 27 | Ivy Global - section 3, items 2 & 10 | Ivy Global - section 4, items 7, 9, & 19 | Learnerator - Algebraic & graphical relationships

SAT.HOA.07

**Algebraically solve systems of two linear equations in two variables.**The equations will have rational coefficients, and the system may yield no solution, one solution, or infinitely many solutions. The student may also be asked to determine the value of a constant or coefficient of an equation in which the system has no solution, one solution, or infinitely many solutions.

Mathematics 8 (Unit 3 - 8.EE.C.8, 8.EE.C.8a, 8.EE.C.8b) | Algebra 1 (Unit 2 [Part 3] - A.REI.C.6)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - items 5 & 7 | Ivy Global - section 4, item 27 | Learnerator - Systems of linear equations

SAT.HOA.08

**Create, solve, and interpret systems of two linear equations in two variables.**The student will analyze one or more constraints that exist between two variables by creating, solving, or analyzing a system of linear equations to represent a context. The equations will have rational coefficients, and multiple steps may be required to simplify or solve the system.

Mathematics 8 (Unit 3 - 8.EE.C.8, 8.EE.C.8a, 8.EE.C.8b) | Algebra 1 (Unit 2 [Part 3] - A.REI.C.5, A.REI.C.6, A.REI.D.11)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 18 | Learnerator - Solving systems of equations in context

SAT.HOA.09

**Create, solve, and interpret systems of linear inequalities in two variables.**The student will analyze one or more constraints that exist between two variables by creating, solving, or interpreting an inequality in two variables or a system of inequalities in two variables to represent a context. Multiple steps may be required to create the inequality or system of inequalities or to determine whether a given point is in the solution set.

Algebra 1 (Unit 2 [Part 3] - A.REI.D.11, A.REI.D.12)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**College Board - item 1 | Ivy Global - item 3 | Learnerator - Solving systems of linear equations

Tools and TechnologyDesmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! |
More 4 UThe Khan Academy has produced videos of worked examples of concepts found in the Heart of Algebra portion of the new SAT®. Khan Academy also has four official practice exams from College Board. |