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8th Grade Mathematics Curriculum Course Description: The 8th Grade Mathematics course is aligned with the Mathematics Core Curriculum of MST Standard 3 of the New York State Learning Standards. It focuses on algebra with a continuation of students’ skills in solving linear equations. Course Essential Questions: TBD 8th Grade State Assessment Information: Approximate Percentage of Questions Assessing Each Strand Strand: Percent: Time allotted: Units: Number Sense and Operations: 11% (2 weeks) (Unit 1) Algebra: 44% (9 weeks) (Unit 2, Unit 2A, Unit 5) Geometry: 35% (7 weeks) (Unit 3, Unit 4) Measurement: 10% (2 weeks) (Unit 1) Probability and Statistics: 0% (0 weeks) Additional Information: 8th Grade Formula Sheet 8th Grade Mathematical Language AECSD 8th Grade Mathematics.doc 1 Post-March 7th Grade Performance Indicators The 7th Grade performance indicators below are denoted by the state as post-test. Therefore, students will be responsible for this knowledge of the 8th Grade assessment. Attention should be given to them during the normal course of instruction or during review. 7.A.2 Add and subtract monomials with exponents of one 7.A.3 Identify a polynomial as an algebraic expression containing one or more terms 7.A.4 Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation 7.A.7 Draw the graphic representation of a pattern from an equation or from a table of data 7.A.8 Create algebraic patterns using charts/tables, graphs, equations, and expressions 7.A.9 Build a pattern to develop a rule for determining the sum of the interior angles of polygons 7.A.10 Write an equation to represent a function from a table of values 7.G.5 Identify the right angle, hypotenuse, and legs of a right triangle 7.G.6 Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem 7.G.8 Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle 7.G.9 Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator 7.M.1 Calculate distance using a map scale 7.M.5 Calculate unit price using proportions 7.M.6 Compare unit prices 7.M.7 Convert money between different currencies with the use of an exchange rate table and a calculator AECSD 8th Grade Mathematics.doc 2 8th Grade Local Math Standards Numbering Key: Local.Grade level.Mathematics strand.standard # e.g. L.8.N.5 (L = local; 8 = 8th Grade; N = Number Sense and Operations; 5 = 5th standard) Number and Operations: L.8.N.5 Estimation Estimate a percent of a quantity in context; justify the reasonableness of an answer using estimation L.8.N.12 Percent, Ratio, Read, write, and identify percents less than 1% and greater than 100%; apply Proportion percents (including tax, percent increase and decrease, simple interest, sale prices, commission, interest rates, and gratuities); use proportions to convert measurements between equivalent units within a given system (metric or customary). L.8.N.13 Power and Roots Use calculation rules for powers for multiplication and division; evaluate expressions with integral exponents Algebra: L.8.A.1 Patterns and Represent data relationships in multiple ways (algebraically, graphically, Representations numerically (in a table), and in words) and convert between forms (e.g. graph a linear equation using a table of ordered pairs); translate between two-step verbal and algebraic statements (expressions, equations, and inequalities). L.8.A.2 Solving Solve multi-step inequalities that include parentheses (distributive property), Equations and variables on both sides of the inequality, and multiplication or division by a Inequalities negative number and graph the solution on a number line; solve systems of linear equations graphically (use only equations in slope-intercept form with integral solutions). L.8.A.3 Expressions Evaluate algebraic expressions; multiply and divide monomials; add and subtract polynomials with integer coefficients; multiply a binomial by a monomial or binomial; divide a polynomial by a monomial (with degree less than the numerator); factor a GCF out of a polynomial; factor trinomials (with a = 1 and c having no more than 3 sets of factors). L.8.A.4 Functions Define a function using correct terminology (domain and range); determine if a relation is a function. L.8.A.5 Quadratics Recognize the characteristics of quadratic equations in tables, graphically, algebraically and in words, and distinguish between linear and quadratic equations. Geometry: L.8.G.1 Shapes and Construct the following figures: congruent segment, congruent angle, Figures perpendicular bisector, angle bisector L.8.G.2 Transformations Describe and identify transformations (rotation, reflection, translation, dilation) and Symmetry using proper notation; perform rotations of 90 and 180 degrees, reflections over a line, translations, and dilations of a given figure; identify properties preserved under each transformation L.8.G.4 Points, Lines, Identify pairs of vertical, supplementary, and complementary angles and use and Angles relationship of pairs to find angle measures (including algebraically); determine the relationship between pairs of angles formed when parallel lines are cut by a transversal and use relationships to find missing angle measures (including algebraically). L.8.G.7 Coordinate Given a line on a graph: determine its slope and explain its meaning as a constant Geometry rate of change, and determine and explain the meaning of the y-intercept; graph a line from a table of values or from an equation in slope-intercept form; determine the equation of a line given its slope and y-intercept Problem Solving: AECSD 8th Grade Mathematics.doc 3 L.8.PS.1 Organization Analyze situations (identify the problem, identify and obtain needed information, and generate possible strategies) and organize work to solve problems (e.g. use Auburn Problem Solving Process). L.8.PS.2 Strategies Solve problems using a variety of strategies and representations (e.g. using proportions, solving a similar or simpler problem, working backwards, and finding a pattern) and recognize that while there may be more than one way to solve a problem, different methods have advantages and disadvantages L.8.PS.3 Reflection Estimate possible solutions; examine solution to ensure it is reasonable in context of problem; compare solution to original estimate. Reasoning and Proof: L.8.RP.1 Observe patterns, make generalizations, and form and evaluate conjectures; support or refute statements with valid arguments including the use of mathematical language and counterexamples (if appropriate). Communication: L.8.CM.1 Decode and comprehend mathematics expressed verbally and in (technical) writing; clearly and coherently communicate mathematical thinking verbally, visually, and in writing using appropriate mathematical vocabulary and symbols; organize and accurately label work. Connections: L.8.CN.1 Recognize and use connections among branches of mathematics and real life (e.g., make and interpret scale drawings of figures or scale models of objects, determine profit from sale of yearbooks, use tables, graphs, and equations to show a pattern underlying a function) Representations: L.8.Rep.1 Represent mathematical ideas in a variety of ways (verbally, in writing, pictorally, numerically, algebraically, or with physical objects); switch among different representations; explain how different representations can express the same relationship but may differ in efficiency. AECSD 8th Grade Mathematics.doc 4 Math 8B Unit Sequence and Timeline: Unit 1 Percents and Proportions (N.12) Length: ~ 3 weeks Timeframe: Early September to end of September Unit 2 Algebra (A.3 + prior knowledge) Length: ~ 3 weeks Timeframe: End of September to mid-October Unit 2A Solving Equations Length: ~ 4 weeks Timeframe: Mid-October to Thanksgiving Unit 3 Special Angle Pairs (G.4) Length: ~ 2 weeks Timeframe: Beginning of December Unit 4 Transformational Geometry (G.2) Length: ~ 3 weeks Timeframe: Middle of December to start of January Unit 5 Polynomials (A.4, N.13) Length: ~ 5 weeks Timeframe: Middle of January to End of February (note that mid-term falls in middle of unit) Mid-term Review and Administration Length: ~ 1 week Timeframe: End of January (24th and 25th ?) State Assessment Review and Administration Length: ~ 2 weeks Timeframe: Early to mid-March (State Assessment: 3/14 and 3/15) Unit 6 Linear Equations Part 2 (A.2, A.1, G.7) Length: ~ 4 weeks Timeframe: Mid-March to mid-April Unit 7 Quadratics (A.2) Length: ~ 1 week Timeframe: End of April Unit 8 Constructions (G.1) Length: ~ 1 week Timeframe: Beginning of May AECSD 8th Grade Mathematics.doc 5 This Page Intentionally Left Blank AECSD 8th Grade Mathematics.doc 6 Unit 1 Percents and Proportions Length: ~ 3 weeks Timeframe: Early September to end of September State Standards (Shaded statements are identified as Post-March Indicators): 8.N.3 Read, write, and identify percents less than 1% and greater than 100% 8.N.4 Apply percents to: Tax, Percent increase/decrease, Simple interest, Sale price, Commission, Interest rates, Gratuities 8.M.1 Solve equations/proportions to convert to equivalent measurements within metric and customary measurement systems Note: Also allow Fahrenheit to Celsius and vice versa Local Standards: L.8.N.12 Read, write, and identify percents less than 1% and greater than 100%; apply percents (including tax, percent increase and decrease, simple interest, sale prices, commission, interest rates, and gratuities); use proportions to convert measurements between equivalent units within a given system (metric or customary). L.8.N.5 Estimate a percent of a quantity in context; justify the reasonableness of an answer using estimation Big Ideas: The fractional or decimal equivalent of a percent may be more efficient for solving a problem. Percents show up every day. Essential Questions: What is the difference between 1/2, .5 and 50%? Why would a store offer a 20% off coupon on top of a 10% off sale rather than just a 30% off sale? Prior Knowledge: to understand concept of whole percents from 0% to 100% to solve a proportion Unit Objectives: to read, write, and identify percents less than 1% and greater than 100% to convert among percents, decimals, and fractions to apply percents to solve a variety of problems to use proportions to convert measurements Resources: SFAW 8th Grade Course 3 – Chapter 6.4 – 6.6 Review Template (No Calculators): Adding and subtracting monomials Simplify: 3x + 4x 7x – 5x AECSD 8th Grade Mathematics.doc 7 Simplify: 5x + 3x 5x – x Simplify: 18x – 7x 4x + 2x Solve proportions Solve: 3/2 = x/4 Solve: 18/27 = x/9 Solve: x/6 = 15/18 Convert among %’s, decimals, and fractions. Convert 2/5 to a decimal and a percentage. Convert .45 to a percentage and a fraction. Convert 6% to a decimal and a fraction. The diagram to the right is an approach to help students recall and organize the relationship between parts, wholes, and percents. It represents that a part can be divided by the whole or the % to get the other, while the whole can be Part multiplied by the percent to get the part. For example, for 3/4, the part is 3, the whole is 4 and the percent is 75%. Three divided by 4 is 75%. Three divided by 75% is 4. Whole % Four times 75% is 3. AECSD 8th Grade Mathematics.doc 8 Unit 2 Algebra Length: ~ 3 weeks Timeframe: End of September to mid-October State Standards (Shaded statements are identified as Post-March Indicators): 8.A.1 Translate verbal sentences into algebraic inequalities 8.A.2 Write verbal expressions that match given mathematical expressions 8.A.3 Describe a situation involving relationships that matches a given graph 8.A.4 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship Local Standards (Stricken text is covered in a separate unit): L.8.A.1 Represent data relationships in multiple ways (algebraically, graphically, numerically (in a table), and in words) and convert between forms (e.g. graph a linear equation using a table of ordered pairs); translate between two-step verbal and algebraic statements (expressions, equations, and inequalities). L.8.A.3 Evaluate algebraic expressions; multiply and divide monomials; add and subtract polynomials with integer coefficients; multiply a binomial by a monomial or binomial; divide a polynomial by a monomial (with degree less than the numerator); factor a GCF out of a polynomial; factor trinomials (with a = 1 and c having no more than 3 sets of factors). L.8.N.5 Estimate a percent of a quantity in context; justify the reasonableness of an answer using estimation Big Ideas: A variable represents an amount that can change. Algebraic statements can have real world meaning. Real world situations can be modeled algebraically and graphically. Essential Questions: Why would you want to model a situation algebraically? Prior Knowledge: (may need to be taught ’05-’06) to distinguish between an expression and an equation to know key words and concepts for the four operations to use order of operations using the set of real numbers to add, subtract, multiply and divide integers to plot an ordered pair on the coordinate plane Unit Objectives: to know that a variable represents an amount that can change to use a variable to represent an unknown quantity to translate a verbal statement into an algebraic expression, equation, or inequality to translate an algebraic expression, equation, or inequality into a verbal statement to evaluate an algebraic expression to complete a table of values AECSD 8th Grade Mathematics.doc 9 to write an equation from a table of values to plot a set of ordered pairs from a table and draw a line through them to describe a situation presented in a graph (linear or nonlinear) to graph a relationship described by an equation or verbal context Resources: SFAW 8th Grade Course 3 – Chapter 4.1 – 4.3 Review Template (Calculators): Pythagorean Theorem: Find the hypotenuse given the lengths of the legs. 3 4 Integer operations: a) -3 - -4 -3 – 4 -3 + -4 3–4 b) -7 - -5 -7 – 5 -7 + -5 7–5 Unit price problems: If 4 equally priced CDs cost 54.80, what is the unit price? Which is a better deal, 12 oz. of Coca-Cola for $.75 or 20 oz. for $1.00? If 3 lbs. of hamburger is 9.77, what is price per pound? AECSD 8th Grade Mathematics.doc 10 Unit 2A Solving Equations (necessary for ’05-‘06) Length: ~ 4 weeks Timeframe: Mid-October to Thanksgiving State Standards (Shaded statements are identified as Post-March Indicators): 7.A.4 Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation 7.A.5 Solve one-step inequalities (positive coefficients only) (see 7.G.10) 7.G.10 Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5) Local Standards: L.7.A.2 Solve multi-step equations that include parentheses (distributive property) and variables on both sides of the equation; write an equation that represents the pattern from a table of data; solve one-step equations and inequalities and graph the solution set. Big Ideas: Algebra is a tool to model and interpret real situations. Essential Questions: Why is it important to be able to solve equations? How do algebraic properties aid in solving equations? Prior Knowledge: to use distributive property to use order of operations using the set of real numbers to add, subtract, multiply and divide integers to translate a verbal statement into an equation Unit Objectives: to solve and check multi-step equations with parentheses and variables on both sides to write an equation that models a real-world situation and solve it Resources: Review Template (Calculators): Distribute and simplify: Simplify: 4(7 + 3x) + 8x Simplify: -3(8x – 10) – 2x Pythagorean Theorem: Find the length of a leg (include non-perfect squares) 5 3 3 4 AECSD 8th Grade Mathematics.doc 11 Order of Operations: Calculate showing each step: 3 – 5 + 4^2 * 3 5–8/2*4 5 + 7 – (3 + 4) (4 + 7 * 3)/5 1 + 3/3 – 1 + 2^3 AECSD 8th Grade Mathematics.doc 12 Unit 3 Special Angle Pairs Length: ~ 2 weeks Timeframe: Beginning of December State Standards (Shaded statements are identified as Post-March Indicators): 8.A.12 Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines 8.G.1 Identify pairs of vertical angles as congruent 8.G.2 Identify pairs of supplementary and complementary angles 8.G.3 Calculate the missing angle in a supplementary or complementary pair 8.G.4 Determine angle pair relationships when given two parallel lines cut by a transversal 8.G.5 Calculate the missing angle measurements when given two parallel lines cut by a transversal 8.G.6 Calculate the missing angle measurements when given two intersecting lines and an angle Local Standards: L.8.G.4 Identify pairs of vertical, supplementary, and complementary angles and use relationship of pairs to find angle measures (including algebraically); determine the relationship between pairs of angles formed when parallel lines are cut by a transversal and use relationships to find missing angle measures (including algebraically). Big Ideas: Essential Questions: Prior Knowledge: to solve an equation to define and draw an angle Unit Objectives: to define and identify vertical, supplementary, and complementary angles to determine the measure of the other angle (including algebraically) in a vertical, supplementary, or complementary pair; given one angle measure to identify alternate interior, alternate exterior, and corresponding angles on parallel lines cut by a transversal to know and use the fact that alternate interior, alternate exterior, and corresponding angles on parallel lines cut by a transversal are congruent to know and use the fact that interior angles on the same side of the transversal of parallel lines are supplementary to determine the measure of missing angles (including algebraically) formed by parallel lines cut by a transversal AECSD 8th Grade Mathematics.doc 13 Resources: Memory device for students to recall complementary angles. To compliment (complement) someone is the right (angle) thing to do. Review Template (No Calculators): Solve equations: 3(x+2) = 5x Common Percents: 1/5, 1/4, 1/3’s Set up proportions If $1.00 is equivalent to 16 euros, how many euros would you get if you exchanged $27? On a map, if 1 inch = 16 miles and two cities are 4.5 inches apart of the map, how far apart are the actual cities? AECSD 8th Grade Mathematics.doc 14 Unit 4 Transformational Geometry (G.2) Length: ~ 3 weeks Timeframe: Middle of December to start of January State Standards (Shaded statements are identified as Post-March Indicators): 8.G.7 Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations) 8.G.8 Draw the image of a figure under rotations of 90 and 180 degrees 8.G.9 Draw the image of a figure under a reflection over a given line 8.G.10 Draw the image of a figure under a translation 8.G.11 Draw the image of a figure under a dilation 8.G.12 Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation Local Standards: L.8.G.2 Describe and identify transformations (rotation, reflection, translation, dilation) using proper notation; perform rotations of 90 and 180 degrees, reflections over a line, translations, and dilations of a given figure; identify properties preserved under each transformation. Big Ideas: Transformations can be found all around us. Essential Questions: Why are designs more pleasing to the eye when they involve transformations? Prior Knowledge: to graph an ordered pair to measure angles and distances to identify lines of symmetry Unit Objectives: to describe and identify transformations (rotation, reflection, translation, dilation) using proper notation to perform rotations of 90 and 180 degrees of a given figure to perform reflections over a line of a given figure to perform translations of a given figure to perform dilations of a given figure to perform rotations of 90 and 180 degrees of a given figure on a coordinate plane to perform reflections over a line of a given figure on a coordinate plane to perform translations of a given figure on a coordinate plane to perform dilations of a given figure on a coordinate plane to identify properties preserved under each transformation Resources: Connected Mathematics – Kaleidoscopes, Hubcaps, and Mirrors AECSD 8th Grade Mathematics.doc 15 Investigation 2 – transformations Investigation 3 – transformation on the coordinate plane Review Template (Calculators): Translate words to algebra: Mary is 4 more than 3 times Julie’s age. If Julie’s age is x, represent Mary’s age? Translate algebra to words: Write a sentence for the following situation: 2x + 4 = 18 Evaluate: Find the area of a circle whose diameter is 7. AECSD 8th Grade Mathematics.doc 16 Unit 5 Polynomials (A.4, N.13) Length: ~ 5 weeks Timeframe: Middle of January to End of February (note that mid-term falls in middle of unit) State Standards (Shaded statements are identified as Post-March Indicators): 8.N.1 Develop and apply the laws of exponents for multiplication and division 8.N.2 Evaluate expressions with integral exponents 8.A.6 Multiply and divide monomials 8.A.7 Add and subtract polynomials (integer coefficients) 8.A.8 Multiply a binomial by a monomial or a binomial (integer coefficients) 8.A.9 Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables. 8.A.10 Factor algebraic expressions using the GCF 8.A.11 Factor a trinomial in the form ax2 + bx + c; a=1 and c having no more than three sets of factors Local Standards: L.8.N.13 Use calculation rules for powers for multiplication and division; evaluate expressions with integral exponents L.8.A.3 Evaluate algebraic expressions; multiply and divide monomials; add and subtract polynomials with integer coefficients; multiply a binomial by a monomial or binomial; divide a polynomial by a monomial (with degree less than the numerator); factor a GCF out of a polynomial; factor trinomials (with a = 1 and c having no more than 3 sets of factors). Big Ideas: The subtraction of polynomials involves distributing an unwritten negative one. You must have like terms to add or subtract polynomials. When operating on polynomials, deal with the coefficients and then with the variables. The rules for operating with whole numbers hold true for variables. Essential Questions: What do you do when you have a subtraction symbol directly in front of parentheses? What is the difference between 2x and x2? How do operations on polynomials differ from operating on numbers? Prior Knowledge: to define a polynomial (must be taught in ’05-‘06) to add and subtract monomials (must be taught in ’05-‘06) to add, subtract, multiply, and divide integers to use the distributive property Unit Objectives: to multiply powers to divide powers AECSD 8th Grade Mathematics.doc 17 to evaluate expressions with integral exponents to multiply monomials to divide monomials to divide a polynomial by a monomial (with degree less than the numerator) to add polynomials with integer coefficients to subtract polynomials with integer coefficients to multiply a binomial by a monomial to multiply a binomial by a binomial to factor a trinomial (with a = 1 and c having no more than 3 sets of factors) to factor a GCF out of a polynomial Resources: Review Template (No Calculators): Find the sum of the interior angles of a: Hexagon octagon Solve equations Pythagorean triples Determine if a triangle with sides of 3, 4, and 5 is a right triangle. AECSD 8th Grade Mathematics.doc 18 Unit 6 Linear Equations Part 2 (A.2, A.1, G.7) Length: ~ 4 weeks Timeframe: Mid-March to mid-April State Standards (Shaded statements are identified as Post-March Indicators): 8.A.13 Solve multi-step inequalities and graph the solution set on a number line 8.A.14 Solve linear inequalities by combining like terms, using the distributive property, or moving variables to one side of the inequality (include multiplication or division of inequalities by a negative number) 8.G.18 Solve systems of equations graphically (only linear, integral solutions, y = mx + b format, no vertical/horizontal lines) 8.G.19 Graph the solution set of an inequality on a number line 8.A.17 Define and use correct terminology when referring to function (domain and range) 8.A.18 Determine if a relation is a function 8.A.19 Interpret multiple representations using equation, table of values, and graph 8.G.13 Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change 8.G.14 Determine the y-intercept of a line from a graph and be able to explain the y-intercept 8.G.15 Graph a line using a table of values 8.G.16 Determine the equation of a line given the slope and the y-intercept 8.G.17 Graph a line from an equation in slope-intercept form (y = mx + b) Local Standards: L.8.A.2 Solve multi-step inequalities that include parentheses (distributive property), variables on both sides of the inequality, and multiplication or division by a negative number and graph the solution on a number line; solve systems of linear equations graphically (use only equations in slope-intercept form with integral solutions. L.8.A.4 Define a function using correct terminology (domain and range); determine if a relation is a function. L.8.G.7 Given a line on a graph: determine its slope and explain its meaning as a constant rate of change, and determine and explain the meaning of the y-intercept; graph a line from a table of values or from an equation in slope-intercept form; determine the equation of a line given its slope and y-intercept. Big Ideas: The line represents the infinite set of ordered pairs that make the corresponding linear equation true. There are an infinite number of solutions to an inequality. Essential Questions: Why do you flip the inequality when you multiply or divide the inequality by a negative number? How do you represent the infinite number of solutions to an inequality? Prior Knowledge: (may need to be taught ’05-’06) to solve multi-step equations including parentheses and variable on both sides AECSD 8th Grade Mathematics.doc 19 to solve and graph one-step inequalities to graph points on the coordinate plane Unit Objectives: to solve and check multi-step inequalities with parentheses and variables on both sides to solve and check multi-step inequalities that include negative coefficients to graph the solution of an inequality on a number line to define a function to determine if a relation is a function to identify the domain and range of a function to determine the slope and y-intercept of a line from a graph to explain the meaning of (a) slope as a constant rate of change to explain the meaning of the y-intercept to graph a line from a table of values to graph a line from an equation in slope-intercept form to write the equation of a line given its slope and y-intercept to solve a system of linear equations graphically (equations in slope-intercept form with integral solutions) Resources: Review Template (No Calculators): Square roots: Sqrt 25 + sqrt 49 = Sqrt of 78 is between which two consecutive whole numbers Scientific Notation: Binomial times binomial: AECSD 8th Grade Mathematics.doc 20 Unit 7 Quadratics (A.2) Length: ~ 1 week Timeframe: End of April State Standards (Shaded statements are identified as Post-March Indicators): 8.G.20 Distinguish between linear and nonlinear equations ax2 + bx + c; a=1 (only graphically) 8.G.21 Recognize the characteristics of quadratics in tables, graphs, equations, and situations Local Standards: L.8.A.5 Recognize the characteristics of quadratic equations in tables, graphically, algebraically and in words, and distinguish between linear and quadratic equations. Big Ideas: The graph of a quadratic equation is symmetric. If x2 is the highest power in the equation, then the equation is quadratic and its graph is a parabola. Essential Questions: How can you tell if a relationship is linear or quadratic? Prior Knowledge: (may need to be taught ’05-’06) to graph linear equations to use order of operations with real numbers to factor a quadratic equation (with a = 1) Unit Objectives: to identify a quadratic relationship from a table, a graph, an equation or from context to distinguish between linear and quadratic equations to graph a quadratic equation (with a = 1 and domain given) – (if time allows) to find the roots of a quadratic equation graphically and by factoring – (if time allows) Resources: SFAW 8th Grade Course 3 – Chapter ? Review Template (No Calculators): Factor trinomial: Multiply fractions: Add/subtract fractions: AECSD 8th Grade Mathematics.doc 21 This Page Intentionally Left Blank AECSD 8th Grade Mathematics.doc 22 Unit 8 Constructions Length: ~ 1 week Timeframe: Beginning of May State Standards (Shaded statements are identified as Post-March Indicators): 8.G.0 Construct the following using a straight edge and compass: Segment congruent to a segment, Angle congruent to an angle, Perpendicular bisector, Angle bisector Local Standards: L.8.G.1 Construct the following figures: congruent segment, congruent angle, perpendicular bisector, angle bisector Big Ideas: A compass and straightedge are the only tools allowed for constructions. Essential Questions: Why do we still practice constructions? Prior Knowledge: (may need to be taught ’05-’06) to define congruent segments, congruent angles, perpendicular, bisector Unit Objectives: to construct congruent segments to construct congruent angles to construct a perpendicular bisector of a segment to construct an angle bisector of an angle Resources: Discovering Geometry? Review Template (No Calculators): Factor GCF: Division of fractions: Special pairs of angles AECSD 8th Grade Mathematics.doc 23