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## Derive the Equation of a Circle using Pythagorean Theorem

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Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

## Solving Equations with Unknown Numbers (addends)

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Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = □ – 3, 6 + 6 = ∆.

## Equation Word Problems

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Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, including reasoning strategies such as using visual fraction models and equations to represent the problem.
For example:
• How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?
• How many 3/4-cup servings are in 2/3 of a cup of yogurt?
• How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

## Equation of Ellipse

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Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

## True or False Equations

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Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

## Equation of a Hyperbola

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Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

## Equations

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Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Solve real-world and mathematical problems by writing and solving equations .

## Graphing Linear Equations on a Graphing Calculator

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Graphing Calculator Lesson (TI-84)

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3.

## Solving Trigonometric Equations

Graphing Calculator Lesson (TI-84)

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

## Graphing Polar Equations

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Graphing Calculator Lesson (TI-84)

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.