## BPS District Mathematics Standards Book

### Math Learning Progressions

#### [A] Algebra

**Math Learning Progressions** **HS Math Concepts**

# [A] Algebra

**Students’ prior knowledge includes:**

- Students work with radical and integer exponents (grade 8)
- Students understand the connections between proportional relationships, line, and linear equations (grade 8)
- Students analyze and solve linear equations and pairs of simultaneous linear equations (grade 8)
- Students analyze proportional relationships and use them to solve real-world and mathematical problems (grade 7)
- Students use properties of operations to generate equivalent expressions (grade 7)
- Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
- Students reason about and solve one-variable equations and inequalities (grade 6)

##### Seeing Structure in Expressions

- Interpret the structure of expressions.
- Write expressions in equivalent forms to solve problems.

##### Arithmetic with Polynomials and Rational Functions

- Perform arithmetic operations on polynomials.
- Understand the relationship between zeros and factors of polynomials.
- Use polynomial identities to solve problems.
- Rewrite rational expressions.

##### Creating Equations and inequalities

- Create equations that describe numbers or relationships.

##### Reasoning with Equations and Inequalities

- Understand solving equations as a process of reasoning and explain the reasoning.
- Solve equations and inequalities in one variable. Solve systems of equations.
- Represent and solve equations and inequalities graphically

## MAT-HS.A Overview: [A] Algebra

### MAT-HS.A-SSE Domain: [A-SSE] Seeing Structure in Expressions

**MAT-HS.A-SSE.01**Interpret expressions that represent a quantity in context*SSE.01.a Interpret parts expressions, such as terms, factors, and coefficients**SSE.01.b Interpret expressions by viewing one or more of their parts as a single entity*

**MAT-HS.A-SSE.02**Use the structure of an expression to Identify ways to rewrite it**MAT-HS.A-SSE.03**Choose and produce an equivalent form of an expression*MAT-HS.A-SSE.03.a factor a quadratic expression to reveal the zeros of the function it define**SSE.03.b Complete the square in a quadratic expression to reveal the maximum or mini**SSE.03.c Use the properties of exponents to transform expressions for exponential fu*

**MAT-HS.A-SSE.04**Derive the formula for the sum of a finite geometric series

### MAT-HS.A-APR Domain: [A-APR] Arithmetic with Polynomials and Rational Expressions

**MAT-HS.A-APR.01**Understand that polynomials form a system analogous to the integers**MAT-HS.A-APR.02**Know and apply the Remainder Theorem**MAT-HS.A-APR.03**Identify zeros of polynomials when suitable factorizations are available**MAT-HS.A-APR.04**Prove polynomial identities and use them to describe numerical relationships**MAT-HS.A-APR.05**Know and apply the Binomial Theorem for the expansion of (x + y)^n**MAT-HS.A-APR.06**Rewrite simple rational expressions in different forms**MAT-HS.A-APR.07**Understand rational expressions form a system analogous to rational numbers

### MAT-HS.A-CED Domain: [A-CED] Creating Equations*

**MAT-HS.A-CED.01**Create equations and inequalities in one variable, Use them to Solve problems*MAT-HS.A-CED.01.a Create and solve linear equations in one variable.**MAT-HS.A-CED.01.b Create and solve exponential equations in one variable.**MAT-HS.A-CED.01.c Create and solve linear inequalities in one variable**MAT-HS.A-CED.01.d Create and solve exponential inequalities in one variable**MAT-HS.A-CED.01.e Create quadratic equations**MAT-HS.A-CED.01.f Create simple rational equations**MAT-HS.A-CED.01.g Create exponential equations*

**MAT-HS.A-CED.02**Create and graph equations in two or more variables to represent relationships*MAT-HS.A-CED.02.a Create and graph linear equations in two or more variables.**A-CED.02.b Create and graph exponential equations in two or more variables.*

**MAT-HS.A-CED.03**represent constraints by equations or inequalities and interpret solutions**MAT-HS.A-CED.04**Rearrange formulas to highlight a quantity of interest

### MAT-HS.A-REI Domain: [A-REI] Reasoning with Equations and Inequalities

**MAT-HS.A-REI.01**Explain each step in solving a simple equation**MAT-HS.A-REI.02**Solve simple rational and radical equations in one variable*A-REI.03.a Solve linear equations in one variable**REI.03.b Solve linear inequalities in one variable*

**MAT-HS.A-REI.03**Solve linear equations and inequalities in one variable**MAT-HS.A-REI.04**Solve quadratic equations in one variable*MAT-HS.A-REI.04.a Use the method of completing the square to transform any quadratic equation**A-REI.04.b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square*

**MAT-HS.A-REI.05**Prove a solution set for 2 variable equation A + N times 2 var equation B**MAT-HS.A-REI.06**Solve systems of linear equations in two variables exactly and with graphs**MAT-HS.A-REI.07**Solve and graph a system of a linear and a quadratic equation in 2 variables**MAT-HS.A-REI.08**Represent a system of linear equations as a single matrix equation**MAT-HS.A-REI.09**Find inverse of a matrix and use it to solve systems of linear equations**MAT-HS.A-REI.10**Understand a graph is the set of an equation's solutions**MAT-HS.A-REI.11**Explain why the xcoord. of where y=f(x) and y=g(x) intersect Solve f(x) = g(x)**MAT-HS.A-REI.12**graph the solutions to a linear inequality in two variables as a half plane

### A Sample of HS Math Concept ALGEBRA to Become Ready for College and Career

#### Seeing Structure in Expressions

- Interpret the structure of expressions.
- Write expressions in equivalent forms to solve problems.

#### Creating Equations and inequalities

- Create equations that describe numbers or relationships.

#### Arithmetic with Polynomials and Rational Functions

- Perform arithmetic operations on polynomials.
- Understand the relationship between zeros and factors of polynomials.
- Use polynomial identities to solve problems.
- Rewrite rational expressions

#### Reasoning with Equations and Inequalities

- Understand solving equations as a process of reasoning and explain the reasoning.
- Solve equations and inequalities in one variable.
- Solve systems of equations.
- Represent and solve equations and inequalities graphically.