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Milwood Magnet School Curriculum Sequencing Map 8th Grade Math Timeline Big Idea (Overarching Topic or Concept) Enduring Understandin gs Marking Period 1 Week 1-6 Technological Innovations “E3: Making life Easy, Effective and Efficient” Everything has a price Essential Questions What is a good business decision? Scaffolding Questions What effect do fixed and variable costs have on profitability? Which linear representation is most useful? How do income and expense affect profitability? GLCEs MEAP Review - linear (2 weeks) Solutions, Equations, and Linear Inequalities A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values Marking Period 2 Week 7-12 Marking Period 3 Week 13-18 Marking Period 4 Week 19-24 Marking Period 5 Week 25-30 Global Food Chain Alternative Energies “Sustaining and improving food production regionally and globally” “Sustainable power for human benefit” Medical Biotechnology Environmental Biotechnology “Improving our Quality of Life” “Preserving and Restoring our environment” “Adopting a sustainable quality lifestyle for ourselves and our posterity” Prior knowledge helps to solve new problems All choices have consequences How do our actions effect the environment? Does size matter? Making choices always involves compromise What’s good for you may not be good for others What factors need to be considered when making a business decision? How do outside factors impact business operations? How do you determine profitability? What do you need to consider in managing your resources? How is profit represented graphically? Solve Problems Under what circumstances do you need to consider adjusting how you operate? How do you use a graph to justify the choices you make? Non-Linear Functions A.RP.08.01 Identify and N.FL.08.11 Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile.* Solutions, Equations, and Linear Inequalities A.FO.08.10 Understand that to solve the equation represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax3); roots (y = √x ); and exponentials (y = ax , Examining current patterns allows discovery of future applications How do we analyze relationships in a system? How does the pattern of cell growth impact the advances in medicine? How does triangulation of points help to determine distances? Marking Period 6 Week 30-36 Sustainable Systems How can you use knowledge about 3 dimensional shapes to create a sustainable “green” building? Do all cells grow at the same rate? What is the relationship between side lengths and areas? Numbers & Operations Numbers & Operations Volume & Surface Area N.ME.08.02 Understand N.ME.08.01 Understand G.SR.08.06 Know the meanings for zero and negative integer exponents. the meaning of a square root of a number and its connection to the square whose area is the number; understand the meaning of a cube root and its connection to the volume of a cube. N.ME.08.03 Understand that in decimal form, rational numbers either volume formulas for generalized cylinders, generalized cones and pyramids, and apply them to solve problems. G.SR.08.07 Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and Solve Problems N.MR.08.07 Understand percent increase and percent decrease in both sum and product form, e.g., 3% increase of a quantity x is x + .03x = What is the relationship between surface area and volume? Milwood Magnet School Curriculum Sequencing Map 8th Grade Math from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution). A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities. f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution). Text: Say It With Symbols A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions. A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets. Text: Shapes of Algebra a > 0); using tables, graphs, and equations.* A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others. A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable. Quadratic Functions A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in particular, note that solutions of a quadratic equation are the xintercepts of the corresponding quadratic function. A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y 1.03x. N.FL.08.08 Solve problems involving percent increases and decreases. N.MR.08.09 Solve problems involving compounded interest or multiple discounts. Text: Growing, Growing, Growing terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals N.ME.08.04 Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, e.g., √2, √3, π, on the number line. N.FL.08.05 Estimate and solve problems with square roots and cube roots using calculators. N.FL.08.06 Find square roots of perfect squares and approximate the square roots of non-perfect squares by locating between consecutive integers, e.g., √130 is between 11 and 12. Pythagorean Theorem G.GS.08.01 Understand at least one proof of the Pythagorean Theorem; use the Pythagorean cylinders. Visualize Solids G.SR.08.08 Sketch a variety of twodimensional representations of threedimensional solids including orthogonal views (top, front, and side), picture views (projective or isometric), and nets; use such two-dimensional representations to help solve problems. Transformation & Symmetry G.TR.08.09 Understand the definition of a dilation from a point in the plane, and relate it to the definition of similar polygons. G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes and relate them to transformations to solve problems. Text: Kaleidoscopes, Hubcaps, and Mirrors, Filling and Wrapping Milwood Magnet School Curriculum Sequencing Map 8th Grade Math = – (x – 3)2. Theorem and its converse to solve applied problems including perimeter, area, and volume problems. G.LO.08.02 Find the distance between two points on the coordinate plane using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem. Common Formulas A.FO.08.07 Recognize and apply the common formulas: (a + b) = a + 2 ab + 2 2 b 2 (a – b)2 = a2 – 2 ab + b 2 (a + b) (a – b) = a2 – b2 ; represent geometrically. A.FO.08.08 Factor simple quadratic expressions with integer coefficients, A.FO.08.09 Solve applied problems involving simple quadratic equations. Geometric Figures G.SR.08.04 Find area Text: Frogs, Fleas, and Painted Cubes Shapes of Algebra (9 weeks) Math Hook Your job is to measure, improve and sustain personal security of your home, school, hang-out spot, etc. Two security companies have submitted multiple proposals to have the honor of your business. You must determine which company meets your current need. Investigation 3 (SIWS) Determine what combination of genetically modified and non-genetically modified crops will need to be grown in order to maintain profitability. Create a graphical representation of the solution and interpret its meaning. (Shapes of Algebra) Investigation 2&3 Frog & Fleas (6 weeks) Suppose your company emits 200 metric tons of carbon each year and the following equation models the cap 10x+ y = 500. Determine when your company will be able to trade permits, when will they have to purchase or change the way their company G3 – 3 wks Explore the relationships between the number of cell divisions and the number of resulting cells. Model this pattern using a table, graph, and equation. Interpret your models. (Growing, growing, growing – 3 weeks) and perimeter of complex figures by subdividing them into basic shapes (quadrilaterals, triangles, circles). G.SR.08.05 Solve applied problems involving areas of triangles, quadrilaterals, and circles. Text: Looking for Pythagoras Practical application of Pythagorean Theorem to find an unknown distance (Pythagoras) Investigation 1 Blueprint for green building 3D shapes represented 2 dimensionally (Kaleidoscopes, hubcaps & mirrors, FW) Milwood Magnet School Curriculum Sequencing Map 8th Grade Math functions, when will they meet the cap? (Research & Review) Investigation 4&5 Vocabulary Distributive Property Equivalent Expressions Expanded Form Exponential Relationship Factored Form Function Parabola Patterns of Change Quadratic Relationship Roots Algebraic Expression Commutative Property of Addition Commutative Property of Multiplication Linear Relationship Order of Operations Surface Area Term X-intercept Y-intercept Solution(s) Constant Term Coefficient Term Variable first/second differences Combination method Justify Standard form of a linear equation Strategy Substitution method System of linear equations System of linear inequalities standard form ax+by=c symbolic reasoning simultaneous linear inequality Estimate Inequality y = mx + b slope-intercept form slope Coordinate Cube Root Cubic Direct Variation Expanded Form Exponential Relationship Factored Form Function Indirect Variation Intercept Maximum Value Minimum Value Parabola Quadratic Expressions Quadratic Functions Relationship Root (zero) equivalent Triangular Numbers Vertex Vertex form Vertical line test Square Root Line of Symmetry Base - i.e. (2^5) where 2 is the “base” Compound Growth Compound Interest Decay Factor Decay Rate Exponent Exponential Decay Exponential Growth Exponential Relationship Growth Factor Growth Rate Rate of Decay Standard Form Vertical Line Test Linear Growth scientific notation Complex Figure Conjecture Consecutive Cube Root Distance Formula Hypotenuse nonsquare rectangle Legs Perfect Squares Pythagorean Theorem Quotient theorem Repeating Decimal Sub-Dividing Terminating Decimal Truncate Area Perimeter Quadrilaterals Rational Number Real Number Square Root Volume Irrational Number Vertices parallelogram Angle of rotation Center of rotation Image Line reflection Mirror symmetry Reflection Reflection line Reflection symmetry Rotation Rotation symmetry Transformation Translation Translation symmetry pi radius diameter prism cylinder sphere triangular prism cone pyramid Congruent Congruent figures Line of symmetry Symmetry Tessellation dimensions base Milwood Magnet School Curriculum Sequencing Map 8th Grade Math height edge volume surface area two-dimensional three-dimensional net rectangular prism faces Formative Assessments Linear Sort Linear Sort Reflection Linear Functions Reflection Identifying Linear Functions Graphic Organizer Unit Summative Assessment Methods of Solving Systems Graphic Organizer Graphing Quadratics Mini Project Guidelines and Rubric Partner Activity - Solving Systems by Equality Linear vs Exponential Brace Map Solving Systems Assessment Equation Comparison Table 8th grade, Unit 1 authentic integrated assessment 8th grade Authentic Assessment 8th grade, Unit 2 authentic integrated assessment 8th grade Authentic Assessment 8th grade, Unit 3 authentic integrated assessment Performance Task: Student Worksheet Rubric Performance Task(Rubric Included): Student Worksheet Student Graphic Organizer Performance Task: Student Worksheet Rubric Example Paragraph SOA Check Up 1 Comparing Linear and Exponential Story Problem 8th grade, Unit 4 authentic integrated assessment 8th grade Authentic Assessment Performance Task: Student Worksheet Rubric 8th grade, Unit 5 authentic integrated assessment 8th grade, Unit 6 authentic integrated assessment Milwood Magnet School Curriculum Sequencing Map 8th Grade Math Resources & Materials http://www.math.co m/students/workshe et/algebra_sp.htm Table, Graph, and Equation Graphic Organizer Curriculum Guide (including Authentic Assessment) Additional Information Curriculum Guide (including SOA Check Up 1) Cyber Kids Videos Revision 12, 4/16/10 http://www.math.com /students/worksheet/a lgebra_sp.htm http://www.math.co m/students/workshe et/algebra_sp.htm Table, Graph, and Equation Graphic Organizer Table, Graph, and Equation Graphic Organizer Asian Carp Fence Article: http://www.technov elgy.com/ct/Science -FictionNews.asp?NewsNu m=312