Subject: Algebra 1



|Subject: 8th/CC Math I |Timeframe Needed for Completion: 9 weeks |

|Grade Level: 8th | |

|Unit Title: Quadratic Functions, Pythagorean Theorem, Geometry |Grading Period: 4th nine weeks |

|Big Idea/Theme: Understandings: |

|Understand and apply the Pythagorean Theorem |

|Explain a proof of the Pythagorean Theorem and its converse |

|Find distance between two points using the Pythagorean Theorem |

|Interpret functions that arise in applications in terms of a context |

|Analyze functions using different representations |

|Build a function that models a relationship between two quantities |

|Build new functions from existing functions |

|Construct and compare linear, quadratic, and exponential models and solve problems |

|Write expressions in equivalent forms to solve problems |

|Solve equations and inequalities in one variable |

|Represent and solve equations and inequalities graphically |

|Experiment with transformations in the plane |

|Use coordinates to prove simple geometric theorems algebraically |

|Explain volume formulas and use them to solve problems |

|Essential Questions: |Curriculum Goals/Objectives |

|What are some real world applications which would use quadratic equations? | |

|Why is it important to understand different rates of increasing values ? |F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a |

|Does the intersection of two functions have any practical value in real world situations. Explain why |quantity increasing linearly, quadratically, or (more generally) as a polynomial function |

|or why not. |A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the |

|Why is it important to know the precise definitions for geometric terms? |quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the |

|How caould you determine how tall a person is from a picture without a measuring device? |function it defines Complete the square in a quadratic expression to reveal the maximum or minimum |

|How do we use the Pythagorean Theorem in everyday life? |value of the function it defines. Use the properties of exponents to transform expressions for |

|Given a diagonal line segment, how can we use the Pythagorean Theorem to determine its’ length? |exponential functions. For example the expression 1.15t can be rewritten as (1.151/12 )12t = 1.01212t |

|Why is it important to know if lines are parallel or perpendicular? |to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. |

|Why is it important to know the perimeter or area of geometric figures in our everyday life? |G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line and line segment, |

|Why is it important to know the volume of a container? |based on the undefined notions of a point, line, distance along a line, and distance around a circular |

| |arc. |

| |8.G.6 Explain a proof of the Pythagorean Theorem and its converse. |

| |8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world |

| |and mathematical problems in two and three dimensions. |

| |8.G.8 Apply the Pythagorean theorem to find the distance between two points in a coordinate system. |

| |G.CPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or |

| |disprove that a figure defined by 4 given points in the coordinate plane is a rectangle; prove or |

| |disprove that the point |

| |( 1,square root 3) lies on the circle centered at the origin and containing the point (0, 2). |

| |G.CPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric |

| |problems (e.g. find the equation of a line parallel or perpendicular to a given line that passes through|

| |a given point). |

| |G.CPE.6 Find the point on a directed line segment between two given points that partitions the segment |

| |into a given ratio.. |

| |G.CPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g> |

| |using the distance formula |

| |G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, volume of a |

| |cylinder, pyramid and cone. Use dissection arguments, Cavalieri’s principle, and informal limit |

| |arguments. |

| |G.GMD.3 Use volume formulas for cylinders, pyramids, cones and spheres to solve problems. |

|Essential Skills/Vocabulary: | |

|Vocabulary: | |

|completing the square | |

|minimum value | |

|maximum value | |

|vertex form | |

|square root | |

|successive approximations | |

|angle | |

|circle | |

|perpendicular lines | |

|parallel lines | |

|line segment | |

|point | |

|arc | |

|length of an arc | |

|right triangle | |

|hypotenuse | |

|legs | |

|Pythagorean Theorem | |

|Pythagorean Triple | |

|slope | |

|ratio | |

|rectangles | |

|triangles | |

|perimeter | |

|area | |

|volume | |

|cylinder | |

|pyramid | |

|cone | |

|sphere | |

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|Essential skills: | |

|Understand through graphs and tables how quantities increase | |

|Factoring quadratic expressions | |

|Completing the square for quadratic functions | |

|Using properties of exponents | |

|Derive the quadratic formula by completing the square | |

|Understand why taking the square root of both sides of an equation yields two solutions | |

|Understand the intersection of two functions, of any type, is the solution of the equations | |

|Graph equations using the graphing calculator | |

|Explain a proof of the Pythagorean Theorem | |

|Determine the unknown lengths of a right triangle using the Pythagorean Theorem | |

|Apply the Pythagorean Theorem to determine distance in the coordinate plane | |

|Use coordinates to prove simple geometric theorems algebraically | |

|Use the slope formula to solve geometric problems | |

|Find the point on a line segment that divides the segment into a given ratio | |

|Use coordinates to compute perimeter and area | |

|Explain circumference and area formulas for a circle by determining the meaning of each term | |

|Explain volume formulas for a cylinder, pyramid and cone by determining the meaning of each term | |

|Using formulas solve problems for cylinders, pyramids, cones and spheres | |

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|Guiding Questions: | |

|Which functions increase at a constant rate? | |

|Which functions increase at varied rates? | |

|Explain the meaning of the zeros in a quadratic function. | |

|Explain what the vertex represents, and how to determine minimum or maximum values. | |

|How do you determine growth or decay using properties of exponents? | |

|How do you use properties of exponents to rewrite exponential functions? | |

|What are the steps for completing the square? | |

|Can different type equations (linear, quadratic, exponential, etc.) have a common solution? Where is | |

|the solution? | |

|What is an angle? | |

|What is a circle? | |

|What are parallel lines? | |

|What are perpendicular lines? | |

|How can we tell if lines are parallel or perpendicular from their slopes? | |

|How do we determine the length of an arc on a circle? | |

|Given three lengths, how do you determine if they form a right triangle? | |

|Given points A and B on the coordinate plane, how do you determine the length of segment AB? | |

|Prove or disprove that a given point lies on a geometric figure | |

|Find equations parallel or perpendicular to a given line | |

|Using coordinate geometry and the distance formula how can you find the perimeters of polygons and the | |

|areas of rectangles and triangles | |

|How do you determine the circumference and area of a circle? | |

|Explain how the formulas for volume of a cylinder, pyramid and cone are developed. | |

|What is the volume relationship between a cylinder and a cone. | |

|What is the exponential term for perimeter, area and volume? Why is this exponent used in each case? | |

|Explain using units of measure. (ft, cm, etc.) | |

|Materials Suggestions: |

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|NCDPI Resources: |

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|National Library of Manipulatives |

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|NCTM Illuminations |

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|Lesson Plan sites and Activities: |

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|Math Graphic Organizers |

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|Problem Solving/Problem Websites |

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|Currituck County Schools – Common Core Resources |

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|AVID Library/Mathematics Write Path I and II |

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