Algebra

Understand and add, subtract, and multiply simple polynomials
Lesson SetsAAPR.1
1. Classify polynomialsAAPR.1

2. Subtract polynomials by changing subtraction to additionAAPR.1

3. Understand standard form through operations on polynomials with unl...AAPR.1

4. Multiply polynomials using an area modelAAPR.1

5. Multiply polynomials using distributive propertyAAPR.1

6. Determine which operations are closed for polynomialsAAPR.1


Know and apply the Remainder Theorem

Identify zeros and construct graphs of 2degree polynomials
Lesson SetsAAPR.3
1. Understand why graphs of second degree polynomials are curvedAAPR.3

2. Find the zeros of first and second degree polynomialsAAPR.3

3. Graph a quadratic function using its zerosAAPR.3

4. Find the hang time of a football using the zeros of the quadratic f...AAPR.3

5. Use the graph of a quadratic function to optimize priceAAPR.3

6. Understand limitations of using zeros to graph a quadratic functionAAPR.3

7. Find a second degree polynomial equation using zerosAAPR.3


Prove polynomial identities and use them to describe numerical relationships
Lesson SetsAAPR.4
1. Prove the pattern in a relationshipAAPR.4

2. Relate changes in the edges of a cube using a polynomial equationAAPR.4

3. Find the near square of a numberAAPR.4

4. Describe the combined area of two squaresAAPR.4

5. Find the dimensions of a figure formed by the difference between tw...AAPR.4

6. Describe the relationship of the difference between two consecutive...AAPR.4


Rewrite simple rational expressions in different forms

Create equations and inequalities in one variable and use them to solve problems.

Create and graph equations in two or more variables to represent relationships between quantities
Lesson SetsACED.2
1. Write and graph a linear function by examining a tableACED.2

2. Write and graph a linear function by examining a reallife scenarioACED.2

3. Write and graph a quadratic function by examining a tableACED.2

4. Write and graph a quadratic function by examining a reallife scenarioACED.2

5. Write and graph an exponential function by examining a tableACED.2

6. Write and graph an exponential function by examining a reallife sc...ACED.2


Represent constraints by linear equations, inequalities and systems
Lesson SetsACED.3
1. Represent constraints on solutions using linear equationsACED.3

2. Represent constraints on solutions using linear inequalitiesACED.3

3. Represent constraints on solutions using systems of linear equationsACED.3

4. Represent constraints on solutions using systems of linear inequali...ACED.3


Rearrange formulas to highlight a quantity of interest
Lesson Sets

Explain each step in solving a simple equation and justify solution methods
Lesson SetsAREI.1
1. Solve an equation using a balance scaleAREI.1

2. Solve an equation using a balance scale and check answerAREI.1

3. Solve an equation using the distributive propertyAREI.1

4. Justify each step in solving an equation using properties of equati...AREI.1

5. Justify each step in solving an equation using properties of equati...AREI.1

6. Solve an equation by working backwardsAREI.1


Solve simple rational and radical equations in one variable
Lesson SetsAREI.2
1. Solve rational equations using the least common denominatorAREI.2

2. Solve rational equations by eliminating denominatorsAREI.2

3. Solve fraction problems by writing and solving equationsAREI.2

4. Solve realworld problems using rational equationsAREI.2

5. Solve perimeter and area problems by writing and solving rational e...AREI.2


Solve linear equations and inequalities in one variable
Lesson SetsAREI.3
1. Solve equations in one variableAREI.3

2. Solve equations with variables on both sidesAREI.3

3. Solve word problems by solving equations with one variableAREI.3

4. Solve equations where some coefficients are represented by lettersAREI.3

5. Solve simple inequalities using additive and multiplicative inversesAREI.3

6. Solve inequalities using additive and multiplicative inversesAREI.3

7. Solve compound inequalitiesAREI.3

8. Solve inequality word problemsAREI.3


Transform quadratic equations by completing the square, derive the quadratic formula
Lesson SetsAREI.4a
1. Complete the square with a modelAREI.4a

2. Compare modeling and symbolic methods of completing the squareAREI.4a

3. Complete the square symbolicallyAREI.4a

4. Complete the square with a model when a > 1AREI.4a

5. Complete the square with a model and symbolically when a > 1AREI.4a

6. Complete the square symbolically when a > 1AREI.4a

7. Derive the quadratic formula by completing the squareAREI.4a


Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring
Lesson SetsAREI.4b
1. Solve a quadratic equation by graphingAREI.4b

2. Solve a quadratic equation by inspectionAREI.4b

3. Solve a quadratic equation by taking a square rootAREI.4b

4. Solve a quadratic equation by factoringAREI.4b

5. Solve a quadratic equation by completing the squareAREI.4b

6. Solve a quadratic equation with no real solutions by completing the...AREI.4b

7. Solve a quadratic using the quadratic formulaAREI.4b

8. Solve a quadratic equation with no real solutions using the quadrat...AREI.4b

9. Determine the nature of the solutions of a quadratic using the quad...AREI.4b

10. Determine the best method to solve a quadratic equationAREI.4b


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

Solve systems of linear equations exactly and approximately
Lesson SetsAREI.6
1. Model a reallife situation using a system of linear equationsAREI.6

2. Estimate the solution to a system of equations by graphingAREI.6

3. Solve a system of linear equations using substitutionAREI.6

4. Solve a system of linear equations using eliminationAREI.6

5. Choose a method for solving a system of equationsAREI.6


Solve a simple system consisting of a linear equation and a quadratic equation in two variables

Understand graphs of equations in two variables

Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions, find the solutions approximately
Lesson SetsAREI.11
1. Approximate the xcoordinate of an intersection of two linesAREI.11

2. Find the xcoordinate of an intersection by making a tableAREI.11

3. Find the xcoordinate of an intersection by graphing the equationsAREI.11

4. Find the xcoordinate of an intersection by setting the equations e...AREI.11


Graph the solutions to linear inequalities in two variables and systems of linear inequalities in two variables
Lesson SetsAREI.12
1. Graph a linear inequality with a < or ≤ symbolAREI.12

2. Graphing linear inequalities with a > or ≥ symbolAREI.12

3. Check the halfplane for correct shadingAREI.12

4. Graph systems of inequalities by shading their intersectionAREI.12

5. Check graphing of a system of inequalitiesAREI.12

6. Find solutions to linear inequalities from contextAREI.12


Factor a quadratic expression to reveal the zeros of the function it defines
Lesson SetsASSE.3a
1. Find zeros of quadratic functions using tablesASSE.3a

2. Find zeros of quadratic functions using factored formASSE.3a

3. Find xintercepts of linear functionsASSE.3a

4. Find zeros of quadratic functions by factoringASSE.3a

5. Distinguish between quadratic expressions and equationsASSE.3a


Complete the square in a quadratic expression
Lesson SetsASSE.3b 
Use the properties of exponents to transform expressions