8 th Grade Mathematics Curriculum Map School Year

Transcription

1 8 th Grade Mathematics Curriculum Map School Year First Semester Second Semester Unit P Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Outcomes and Likelihoods Transformations, Congruence and Similarity Exponents Geometric Applications of Exponents Functions Linear Functions Linear Models and Tables Solving Systems of Equations Show What We Know (2 weeks) (5 weeks) (7 weeks) (3 weeks) (2 weeks) (3 weeks) (3 weeks) (3 weeks) (6 weeks) Common Core Georgia Performance Standards MCC7.SP.7 MCC7.SP.8 MCC8.G.1 MCC8.G.2 MCC8.G.3 MCC8.G.4 MCC8.G.5 MCC8.EE.1 MCC8.EE.2 (evaluating) MCC8.EE.3 MCC8.EE.4 MCC8.EE.7a MCC8.EE.7b MCC8.NS.1 MCC8.NS.2 MCC8.G.6 MCC8.G.7 MCC8.G.8 MCC8.G.9 MCC8.EE.2 (equations) MCC8.F.1 MCC8.F.2 MCC8.EE.5 MCC8.EE.6 MCC8.F.3 MCC8.F.4 MCC8.F.5 MCC8.SP.1 MCC8.SP.2 MCC8.SP.3 MCC8.SP.4 MCC8.EE.8a MCC8.EE.8b MCC8.EE.8c ALL PLUS High School Prep Review inequalities exponent rules word problems expressions exponential graphs graphing calculators Unit P is a transition unit for the school year. It will be omitted for future school years. 1

2 Unit P Unit 1 First Semester Unit 2 Unit 3 Outcomes and Likelihoods Transformations, Congruence and Similarity Exponents Geometric Applications of Exponents MCC7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. MCC7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. MCC7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. MCC7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. MCC7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. MCC7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. MCC7.SP.8c Design and use a simulation to generate frequencies for compound events. Understand congruence and similarity using physical models, transparencies, or geometry software. MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on twodimensional figures using coordinates. MCC8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. MCC8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. 2 Work with radicals and integer exponents. MCC8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. MCC8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. MCC8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. MCC8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Analyze and solve linear equations and pairs of simultaneous linear equations. MCC8.EE.7 Solve linear equations in one variable. MCC8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers). MCC8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and Understand and apply the Pythagorean Theorem. MCC8.G.6 Explain a proof of the Pythagorean Theorem and its converse. MCC8.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. MCC8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. MCC8.G.9 Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Work with radicals and integer exponents. MCC8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.

3 collecting like terms. Know that there are numbers that are not rational, and approximate them by rational numbers. MCC8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. MCC8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). 3

4 Unit 4 Functions Unit 5 Linear Functions Second Semester Unit 6 Linear Models and Tables Unit 7 Solving Systems of Equations Unit 8 Show What We Know Define, evaluate, and compare functions. MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. a. MCC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Understand the connections between proportional relationships, lines, and linear equations. MCC8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. MCC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Define, evaluate, and compare functions. MCC8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Use functions to model relationships between quantities. MCC8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. MCC8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Investigate patterns of association in bivariate data. MCC8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Analyze and solve linear equations and pairs of simultaneous linear equations. MCC8.EE.8 Analyze and solve pairs of simultaneous linear equations. MCC8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. MCC8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. MCC8.EE.8c Solve real world and mathematical problems leading to two linear equations in two variables. 4

5 MCC8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. MCC8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. MCC8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two way table. Construct and interpret a two way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. 5

6 Key Vocabulary: Chance Process Compound Event Empirical Event Experimental Probability Independent events Probability Probability Model Relative Frequency of Outcomes Sample space Simple Event Simulation Theoretical Probability Tree diagram Essential Questions: Why must the numeric probability of an event be between 0 and 1? What is the likeliness of an event occurring based on the probability near 0, ½, or 1? How can you determine the likelihood that an event will occur? How are the outcomes of given events distinguished as possible? What is the difference between theoretical and experimental probability? What is the significance of a large number of trials? How do I determine a sample space? How can you represent the likelihood of an event occurring? How are theoretical probabilities used to make predictions or decisions? How can you represent the probability of compound events by constructing models? How can I use probability to determine if a game is worth playing or to figure my chances of winning the lottery? What is the process to design and use a simulation to generate frequencies for compound events? Unit P: Outcomes and Likelihoods August 6 August 17, 2012 CCGPS: MCC7.SP.7 MCC7.SP.8 Prerequisite Skills: number sense computation with whole numbers and decimals, including application of order of operations addition and subtraction of common fractions with like denominators measuring length and finding perimeter and area of rectangles and squares characteristics of 2-D and 3-D shapes data usage and representations Suggested Learning Resources: Core/Common%20Core%20Frameworks/CCGPS_Math_7_7thGra de_unit6se.pdf Probability??? Heads Wins! What are Your Chances? Probably Graphing Rolling Dice Number Cube Sums Dice Game Task Is It Fair? Charity Fair Designing Simulations Double Trouble Tasks: Exemplar: 6 Enduring Understandings: Probabilities are fractions derived from modeling real world experiments and simulations of chance. Modeling real world experiments through trials and simulations are used to predict the probability of a given event. Chance has no memory. For repeated trials of a simple experiment, the outcome of prior trials has no impact on the next. The probability of a given event can be represented as a fraction between 0 and 1. Probabilities are similar to percents. They are all between 0 and 1, where a probability of 0 means an outcome has 0% chance of happening and a probability of 1 means that the outcome will happen 100% of the time. A probability of 50% means an even chance of the outcome occurring. If we add the probabilities of every outcome in a sample space, the sum should always equal 1. The experimental probability or relative frequency of outcomes of an event can be used to estimate the exact probability of an event. Experimental probability approaches theoretical probability when the number of trials is large. Sometimes the outcome of one event does not affect the outcome of another event. (This is when the outcomes are called independent.) Tree diagrams are useful for describing relatively small sample spaces and computing probabilities, as well as for visualizing why the number of outcomes can be extremely large. Simulations can be used to collect data and estimate probabilities for real situations that are sufficiently complex that the theoretical probabilities are not obvious. CCGPS Standards Addressed: MCC7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. MCC7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. MCC7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. MCC7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. MCC7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. MCC7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. MCC7.SP.8c Design and use a simulation to generate frequencies for compound events.

7 Grade 8 Unit P Outcomes and Likelihoods Sample Daily Lesson Plan Day 1 Day 2 Day 3 Day 4 Day 5 August 6 August 7 August 8 August 9 August 10 Rules and Procedures Setting Classroom Culture for Collaborative and Structured Learning Environments Diagnostic Testing Task: Choices, Choices, Choices (7SP8b) Task: Choices, Choices, Choices (7SP8b) Probability (Simple/Compound) (7SP8a,b) Day 6 Day 7 Day 8 Day 9 Day 10 August 13 August 14 August 15 August 16 August 17 Task: What are Your Chance? (7SP8) Task: Rolling Dice (7SP8) Exemplar: Double Trouble (7SP8) Unit Review Unit Assessment Grasp Testing Window Aug 13 th 24th 7

8 Key Vocabulary: Alternate Exterior Angles Alternate Interior Angles Angle of Rotation Congruent Figures Corresponding Sides Corresponding Angles Dilation Linear Pair Reflection Reflection Line Rotation Same-Side Interior Angles Same-Side Exterior Angles Scale Factor Similar Figures Transformation Translation Transversal Essential Questions How can the coordinate plane help me understand properties of reflections, translations, and rotations? What is the relationship between reflections, translations, and rotations? What is a dilation and how does this transformation affect a figure in the coordinate plane? How can I tell if two figures are similar? In what ways can I represent the relationships that exist between similar figures using the scale factors, length ratios, and area ratios? What strategies can I use to determine missing side lengths and areas of similar figures? Under what conditions are similar figures congruent? When I draw a transversal through parallel lines, what are the special angle and segment relationships that occur? What information is necessary before I can conclude two figures are congruent? Unit 1 Transformations, Congruence, and Similarity August 20 September 21, 2012 CCGPS Standards: MCC8.G.1 MCC8.G.2 MCC8.G.3 MCC8.G.4 MCC8.G.5MRC Prerequisite Skills: computation w/ whole numbers and decimals, (order of operations) addition and subtraction of fractions measuring length and finding perimeter and area of rectangles and squares characteristics of 2-D and 3-D shapes data usage and representations Suggested Learning Resources Framework Core/Common%20Core%20Frameworks/CCGPS_Math _8_8thGrade_Unit1SE.pdf Tasks Introduction to Reflections, Translations, & Rotations Dilations in the Coordinate Plane Changing Shapes Coordinating Reflections, Translations, & Rotations Playing with Dilations (optional) Similar Triangles Lunch Lines Window Pain CMP2 G1 CMP: Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1-5) G2 CMP: Kaleidoscopes, Hubcaps, and Mirrors (Inv. 3) G3 CMP: Stretching and Shrinking (Inv. 2) CMP: Kaleidoscopes, Hubcaps, and Mirrors (Inv. 2, 5) G4 CMP: Kaleidoscopes, Hubcaps, and Mirrors (Inv. 2) G5 CMP: Shapes and Designs (Inv. 3) 8 Enduring Understandings: CCGPS Standards Addressed: Coordinate geometry can be a useful tool for understanding geometric shapes and transformations. Reflections, translations, and rotations are actions that produce congruent geometric objects. A dilation is a transformation that changes the size of a figure, but not the shape. The notation used to describe a dilation includes a scale factor and a center of dilation. A dilation of scale factor k with the center of dilation at the origin may be described by the notation (kx, ky). If the scale factor of a dilation is greater than 1, the image resulting from the dilation is an enlargement. If the scale factor is less than 1, the image is a reduction. Two shapes are similar if the lengths of all the corresponding sides are proportional and all the corresponding angles are congruent. Two similar figures are related by a scale factor, which is the ratio of the lengths of the corresponding sides. Congruent figures have the same size and shape. If the scale factor of a dilation is equal to one, the image resulting from the dilation is congruent to the original figure. When parallel lines are cut by a transversal, corresponding, alternate interior and alternate exterior angles are congruent. Understand congruence and similarity using physical models, transparencies, or geometry software. MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. MCC8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. MCC8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

9 Grade 8 Unit 1 Transformations, Congruence, and Similarity Sample Daily Lesson Plan Grasp Testing Window Aug 13 th 24th Day 1 Day 2 Day 3 Day 4 Day 5 August 20 August 21 August 22 August 23 August 24 Task: Dilations in the Task: Dilations in the Task: Changing Shapes Coordinate Plane Coordinate Plane (G2-4) (G2-4) (G2-4) Intro Task: Reflections, Translations, & Rotations (G1-4) Task: Changing Shapes (G2-4) Day 6 Day 7 Day 8 Day 9 Day 10 August 27 August 28 August 29 August 30 August 31 Task: Coordinate Reflection (Packet of Three Tasks) (G1-4) Task: Coordinate Reflection (Packet of Three Tasks) (G1-4) Task: Coordinate Reflection (Packet of Three Tasks) (G1-4) Review (G1-4) Assessment (Quiz) (G1-4) Day 11 Day 12 Day 13 Day 14 September 3 September 4 September 5 September 6 September 7 Transversal Triangles Triangle Practice Assessment (Quiz) Labor Day (foldable) (G5) (G5) (G5) (G5) Day 15 Day 16 Day 17 Day 18 Day 19 September 10 September 11 September 12 September 13 September 14 Task: Lunch Line Angle Measures Angle Measures Task: Lunch Line Assessment (Quiz) (w/ more practice) (G5) (G5) (G5) (G5) (G5) Day 20 Day 21 Day 22 Day 23 Day 24 September 17 September 18 September 19 September 20 September 21 Unit Review (G1-5) Unit Assessment (G1-5) Fall Break: September 24 th 28 th 9

10 Key Vocabulary: Addition Property of Equality Additive Inverse Algebraic Expression Addition Property of Equality Cube Root Decimal Expansion Equation Evaluate an Algebraic Expression Exponent Exponential Notation Inverse Operation Irrational Like Terms Linear Equation in One Variable Multiplication Property of Equality Multiplicative Inverses Perfect Square Radical Rational Scientific Notation Significant Digits Solution Solve Square Root Variable Essential Questions: When are exponents used and why are they important? How can I apply the properties of integer exponents to generate equivalent numerical expressions? How can I represent very small and large numbers using integer exponents and scientific notation? How can I perform operations with numbers expressed in scientific notation? How can I interpret scientific notation that has been generated by technology? Why is it useful for me to know the square root of a number? How do I simplify and evaluate numeric expressions involving integer exponents? What is the difference between rational and irrational numbers? When are rational approximations appropriate? Why do we approximate irrational numbers? What strategies can I use to create and solve linear equations with one solution, infinitely many solutions, or no solutions? Unit 2: Exponents : October 1 November 16 CCGPS: MCC8.EE.1 MCC8.EE.2 (evaluating) MCC8.EE.3 MCC8.EE.4 MCC8.EE.7a MCC8.EE.7b MCC8.NS.1 MCC8.NS.2 Prerequisite Skills: computation with whole numbers and decimals (order of operations) solving equations plotting points in coordinate plane Independent and dependent variables Proportional relationships Suggested Learning Resources: Core/Common%20Core%20Frameworks/CCGPS_Math_8_ 8thGrade_Unit2SE.pdf Tasks: Rational or Irrational Reasoning? A Few Folds. Alien Attack Nesting Dolls Exponential Exponents Exploring Powers of 10 E. coli Giantburgers Writing for a Math Website CMP2 EE1 CMP: Growing, Growing, Growing (Inv. 5) EE2 CMP: Looking for Pythagoras (Inv. 2-4) EE3 CMP: Growing, Growing, Growing (Inv. 1-2, 4-5) EE4 CMP: Growing, Growing, Growing (Inv. 5) EE7 CMP: Thinking With Mathematical Models (Inv. 2) CMP: Say It With Symbols (Inv. 1-3) EE7a CMP: Moving Straight Ahead (Inv. 2) CMP: Say It With Symbols (Inv. 5) CMP: The Shapes of Algebra (Inv. 3-4) EE7b CMP: Thinking With Mathematical Models (Inv. 2) CMP: Say It With Symbols (Inv. 1-4) 10 CCGPS Standards Addressed: Work with radicals and integer exponents. MCC8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. MCC8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. MCC8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. MCC8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Analyze and solve linear equations and pairs of simultaneous linear equations. MCC8.EE.7 Solve linear equations in one variable. MCC8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers). MCC8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Know that there are numbers that are not rational, and approximate them by rational numbers. MCC8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. MCC8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). Enduring Understandings Square roots can be rational or irrational. An irrational number is a real number that cannot be written as a ratio of two integers. Every number has a decimal expansion, for rational numbers it repeats eventually, and can be converted into a rational number. All real numbers can be plotted on a number line. Rational approximations of irrational numbers can be used to compare the size or irrational numbers, locate them approximately on a number line, and estimate the value of expressions. 2 is irrational. Exponents are useful for representing very large or very small numbers. Properties of integer exponents can be use to generate equivalent numerical expressions. Scientific notation can be used to estimate very large or very small quantities and to compare quantities. Linear equations in one variable can have one solution, infinitely many solutions, or no solutions.

11 Grade 8 Unit 2 Exponents Sample Daily Lesson Plan DI: Direct Instruction Part A of Unit Equations and Inequalities Part B of Unit Radicals Part C of Unit Exponents Part D of Unit - Scientific Notation DAY 1 DAY 2 DAY 3 DAY 4 DAY 5 October 1 October 2 October 3 October 4 October 5 DI: Equations Review (EE7) DI: Distributive Property, Expressions, and Combining Like Terms (EE7b) DI: Distributive Property and Combining Like Terms with Equations (EE7b) DI: Practice (EE7b) Assessment (EE7b) DAY 6 DAY 7 DAY 8 DAY 9 DAY 10 October 8 October 9 October 10 October 11 October 12 DI: Discovery of One/No/Infinite Solutions (EE7b) DI: Practice identifying one/none/infinite equations (EE7a,b) Task: Writing for a Math Website Task (EE7a,b) Final Practice/Practice (EE7a,b) Assessment (EE7a,b) DAY 11 DAY 12 DAY 13 DAY 14 DAY 15 October 15 October 16 October 17 October 18 October 19 DI: Discover Perfect DI: Approximate Practice Cubes (1-5) using irrational numbers on a manipulatives tie to number line to the volume (EE2) nearest tenth and whole number (NS2) DI: Discover Perfect Squares 1-15) using manipulatives (EE2) NEW STANDARD Assessment of Perfect Squares/Cubes, Estimating Irrational Numbers (EE2, NS2) DAY 16 DAY 17 DAY 18 DAY 19 DAY 20 October 22 October 23 October 24 October 25 October 26 DI: Decimal Expansion (NS1) DI: Rational vs. Irrational Activity (NS1) NEW STANDARD Practice Assessment (NS1) Discovery Task: Alien Attack Task Use worksheet as note sheet through discovery (EE1) 11

12 DAY 21 DAY 22 DAY 23 DAY 24 DAY 25 Only integer bases no variable bases raised to an exponents. October 29 October 30 October 31 November 1 November 2 DI: Practice with Exponents apply rules (EE1) Task: Exponential Exponents Task make example (EE1) DI: Practice Expressions with Exponents (EE1) Additional Practice (EE1) Assessment (EE1) Example: DAY 26 DAY 27 DAY 28 DAY 29 DAY 30 November 5 November 6 November 7 November 8 November 9 DI: Real-world NO SCHOOL applications (EE4) Task: Exploring Powers of 10 with positive and negative exponents (convert into and out of scientific notation) (EE4) 2 3 DI: Comparing scientific notations how many times larger (EE3) DI: Practice- include multiplication and division of scientific notation (EE3,4) DAY 21 DAY 22 DAY 23 DAY 24 DAY 25 November 12 November 13 November 14 November 15 November 16 Continue Practice Assessment (EE3,4) Unit Review Unit Review Unit Assessment If time permits do the following (transition standards) if not teach in second semester as a mini-unit closer to the CRCT DI: Intro to inequalities with one variable and teach graphing (MCC7.EE.4b) DI: Practice (MCC7.EE.4b) DI: Real World Problem with inequalities (MCC7.EE.4b) DI: Practice (MCC7.EE.4b) Assessment (MCC7.EE.4b) 12

13 Prerequisite Skills: properties of similarity, congruence, and right triangles understand the meaning of congruence: that all corresponding angles and sides are congruent two figures are congruent if they have the same shape and size represent radical expressions in radical form (irrational) or approximate these numbers as rational find square roots of perfect squares write a decimal approximation for an irrational number to a given decimal place measuring length and finding perimeter and area of quadrilaterals characteristics of 2-D and 3-D solids evaluating linear and literal equations in one variable with one solution properties of exponents and real numbers (commutative, associative, distributive, inverse and identity) and order of operations express solutions using the real number system Enduring Understandings: algebraically and geometrically to solve problems involving right triangles. There is a relationship between the Pythagorean Theorem and the distance formula. Both the Pythagorean Theorem and distance formula can be used to find missing side lengths in a coordinate plane and real-world situation. How to solve simple and complex linear and literal equations with one solution. Finding the square root of a number is the inverse operation of squaring that number. Finding the cube root of a number is the inverse operation of cubing that number. Right triangles have a special relationship among the side lengths which can be represented by a model and a formula. Pythagorean Triples can be used to construct right triangles. How to simplify radicals and solve quadratic equations. Attributes of geometric figures can be used to identify figures and find their measures. Relationships between change in length of radius or diameter, height, and volume exist for cylinders, cones and spheres. Unit 3: Geometric Applications of Exponents November 26 December Essential Questions: What method is used to determine the missing length of a line segment given two polygons? What is the length of the side of a square of a certain area? What is the relationship among the lengths of the sides of a right triangle? How can the Pythagorean Theorem be used to solve problems? What is the correlation between the Pythagorean Theorem and the distance formula? How can I use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle? How do I use the Pythagorean Theorem to find the length of the legs of a right triangle? How do I know that I have a convincing argument to informally prove Pythagorean Theorem? What is Pythagorean Theorem and when does it apply? How can I determine the length of a diagonal? How can I find the altitude of an equilateral triangle? How could I find the shortest distance from one point to another if there was an obstacle in the way? Where can I find examples of two and three-dimensional objects in the real-world? How does the change in radius affect the volume of a cylinder, cone, or sphere? How does the change in height affect the volume of a cylinder, cone, or sphere? How does the volume of a cylinder, cone, and sphere with the same radius change if it is doubled? How do I simplify and evaluate algebraic equations involving integer exponents, square and cubed root? How do I know when an estimate, approximation, or exact answer is the desired solution? Suggested Learning Resources: Core/Common%20Core%20Frameworks/CCGPS_Math_8_8thGrade_Unit3SE.pdf Acting Out Pythagoras Plus Comparing TVs Angry Bird App Constructing the Irrational Number Line How Full Is Your Glass? Comparing Spheres and Cylinders Tasks: CMP2 G6 CMP: Looking for Pythagoras (Inv. 3) G7 CMP: Looking for Pythagoras (Inv. 3-4) G8 CMP: Looking for Pythagoras (Inv. 2-3) G9 CMP: Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1-3) CMP: Looking for Pythagoras (Inv. 3-4) CMP: Say It With Symbols (Inv. 1, 3-4) EE2 CMP: Looking for Pythagoras (Inv. 2-4) 13 CCGPS MCC8.G.6 MCC8.G.7 MCC8.G.8 MCC8.G.9 MCC8.EE.2 (equations) Key Vocabulary: Altitude of a Triangle Base (of a Polygon) Coordinate Plane Coordinate Point of a Plane Cone Converse of Pythagorean Theorem Cubed Root Cylinder Deductive Reasoning Diameter Distance Formula Geometric Solid Height of Solids Hypotenuse Irrational Leg of a Triangle Literal Equation Perfect Squares Perfect Cubes Pythagorean Theorem Pythagorean Triples Sphere Square Root Radius Radical Rational Number Right Triangle. Volume CCGPS Standards: Understand and apply the Pythagorean Theorem. MCC8.G.6 Explain a proof of the Pythagorean Theorem and its converse. MCC8.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. MCC8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. MCC8.G.9 Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Work with radicals and integer exponents. MCC8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.

14 Grade 8 Unit 3 Geometric Applications of Exponents Sample Daily Lesson Plan Day 1 Day 2 Day 3 Day 4 Day 5 November 26 November 27 November 28 November 29 November 30 Pythagoras Plus Task Continued (G6-8) Pythagoras Plus Task Notes on Pythagorean Theorem (G6-8) Pythagorean Practice Problems (G6-8) Direct Instruction: Practice w/ Converse, Straight line on graph, right angles not set on graph, real world problems (tv diagonal, pool), Pythag triples (G6-8) > (G6-8) Day 6 Day 7 Day 8 Day 9 Day 10 December 3 December 4 December 5 December 6 December 7 Continued Continued Continued (G6-8) (G6-8) (G9) > Assessment (Quiz) Pythagorean Theorem (G6-8) Notes/Intro/Review (Geo Solids to visualize) (G9) Cylinder, Cone, Pyramid, Sphere > Day 11 Day 12 Day 13 Day 14 Day 15 December 10 December 11 December 12 December 13 December 14 Continued Assessment (Quiz) Unit Review Unit Assessment Unit Assessment (G9) (G9) (G6-9) (G6-9) (G6-9) > Day 16 Day 17 Day 18 Day 19 Day 20 December 17 December 18 December 19 December 20 December 21 Prepare and take the Semester 1 Exam 14

15 Prerequisite Skills: computation with whole numbers and decimals, including application of order of operations plotting points in a four quadrant coordinate plan understanding of independent and dependent variables characteristics of a proportional relationship Key Vocabulary: Domain Function Graph of a Function Range of a Function Enduring Understandings: A function is a specific type of relationship in which each input has a unique output. A function can be represented in an input-output table. A function can be represented graphically using ordered pairs that consist of the input and the output of the function in the form (input, output). A function can be represented with an algebraic rule. Unit 4: Functions November 14 December 16, 2011 CCGPS Standards: MCC8.F.1 MCC8.F.2 Suggested Learning Resources: Core/Common%20Core%20Frameworks/CCGPS_M ath_8_8thgrade_unit4se.pdf Task Secret Codes and Number Rules Vending Machines Order Matters Which is which? Culminating Task: Function Mess CMP F1 CMP: Moving Straight Ahead (Inv. 1-5) F2 CMP: Thinking With Mathematical Models (Inv. 1) CMP: Growing, Growing, Growing (Inv. 1) CMP: Frogs, Fleas, and Painted Cubes (Inv. 2-4) CMP: Say It With Symbols (Inv. 2) GPS Standards Addressed: Essential Question: Define, evaluate, and compare functions. MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. MCC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions What is a function? What are the characteristics of a function? How do you determine if relations are functions? How is a function different from a relation? Why is it important to know which variable is the independent variable? How can a function be recognized in any form? What is the best way to represent a function? How do you represent relations and functions using tables, graphs, words, and algebraic equations? What strategies can I use to identify patterns? How does looking at patterns relate to functions? How are sets of numbers related to each other? How can you use functions to model realworld situations? How can graphs and equations of functions help us to interpret real-world problems? 15

16 Grade 8 Unit 4 Functions Sample Daily Lesson Plan DI: Direct Instruction DAY 1 DAY 2 DAY 3 DAY 4 January 7 January 8 January 9 January 10 January 11 NO SCHOOL!!! Task: Secret Codes (F1) DI: Extra Practice (F1) Task: Vending Machine with extra practice (F1) DI: Practice with each representation of functions (equations, mapping, tables, graphs) (F2) DAY 5 DAY 6 DAY 8 DAY 9 January 14 January 15 January 16 January 17 January 18 Task: Order Matters (F1,2) WRITING TEST!!! Task: Which is Which? (F1,2) Assessment over function types See example below: Unit Assessment Task: Function Mess (F1,2) Example: Develop 10 different options of things that are functions and not functions, relations and not relations. Have students to create a 4 block table like below and place the item in correct portion of the graphic organizer. Function Not Function Relation A C Not Relation B A) Y = 3x + 7 B) 25, 50, 75, 100 C) X Y D) Etc 16

17 Key Vocabulary: Intersecting Lines Origin Proportional Relationships Slope Unit Rate Prerequisite Skills: determining unit rate applying proportional relationships recognizing a function in various forms plotting points on a coordinate plane understanding of writing rules for sequences and number patterns differences in graphing of discrete and continuous data attributes of similar figures Enduring Understandings: Patterns and relationships can be represented graphically, numerically, and symbolically. Several ways of reasoning, all grounded in sense making, can be generalized into algorithms for solving proportion problems. Unit 5: Linear Functions January 3 February 17, 2012 CCGPS Standards: MCC8.EE.5 MCC8.EE.6 MCC8.F.3 Suggested Learning Resources: Core/Common%20Core%20Frameworks/CCGPS_Math _8_8thGrade_Unit5SE.pdf Task By the Book What s My Line? Culminating Task: Filling the Tank CMP2 EE5 CMP: Thinking With Mathematical Models (Inv. 2) EE6 CMP: Moving Straight Ahead (Inv. 4) CMP: Thinking with Mathematical Models (Inv. 2) F3 CMP: Thinking With Mathematical Models (Inv. 2-3, 5) CMP: Growing, Growing, Growing (Inv. 3) CMP: The Shapes of Algebra (Inv. 4) CMP: Say It With Symbols (Inv. 4) 17 Essential Questions: How can patterns, relations, and functions be used as tools to best describe and help explain real-life relationships? How can the same mathematical idea be represented in a different way? Why would that be useful? What is the significance of the patterns that exist between the triangles created on the graph of a linear function? When two functions share the same rate of change, what might be different about their tables, graphs and equations? What might be the same? What does the slope of the function line tell me about the unit rate? What does the unit rate tell me about the slope of the function line? CCGPS Standards: Understand the connections between proportional relationships, lines, and linear equations. MCC8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. MCC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Define, evaluate, and compare functions. MCC8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

18 Grade 8 Unit 5 Linear Functions Sample Daily Lesson Plan Day 1 Day 2 Day 3 Day 4 Jan 22 Jan 23 Jan 24 Jan 25 Task: By the Book (EE5) Task: By the Book (EE5) w/ practice Direct Instruction: (EE5,6) - Slope - Find the Rate of Change from pattern Continue (EE5,6) Day 5 Day 6 Day 7 Day 8 Day 9 Jan 28 Jan 29 Jan 30 Jan 31 Feb 1 Warm up: Proportional Relationships with Triangles (to prepare for task) Task: What s My Line? (EE6) Task: What s My Line? (EE6) Direct Instruction: (EE6) y-intercept Direct Instruction: (EE6) y-intercept Assessment (quiz) (EE5,6) Slope and y-intercept Day 10 Day 11 Day 12 Day 13 Day 14 Feb 4 Feb 5 Feb 6 Feb 7 Feb 8 Writing Equations: Assessment (quiz) (EE6, Unit Review (EE5,6, F3) (EE6, F3) F3) - y= mx + b - Standard form - Point-slope form Writing Equations: (EE6, F3) - y= mx + b - Standard form - Point-slope form Writing Equations: - y= mx + b - Standard form - Point-slope form Unit Assessment (EE5,6 and F3) Culminating Task: Filling the Tank and/or M/C test 18

19 Key Vocabulary: Model Interpret Initial Value Qualitative Variables Linear Non-linear Slope Rate of Change Bivariate Data Quantitative Variables Scatter Plot Line of Best Fit Clustering Outlier Suggested Learning Resources: Core/Common%20Core%20Frameworks/CCGPS_Math_8_8thGrade_Unit6SE.pdf Task Winter Is Over Heartbeats Walk the Graph Forget the Formula Heartbeats Too Mineral Samples Walking Race and Making Money Mini-Problems My Cotton Boll Data Outdoor Theater How Long Should Shoe Laces Really Be? Culminating Task: Is the Data Linear? CMP2 F4 CMP: Thinking With Mathematical Models (Inv. 1-3) CMP: The Shapes of Algebra (Inv. 4) CMP: Say It With Symbols (Inv. 4) F5 CMP: Thinking With Mathematical Models (Inv. 2) CMP: Growing, Growing, Growing (Inv. 1-4) CMP: Frogs, Fleas, and Painted Cubes (Inv. 1-4) CMP: Say It With Symbols (Inv. 4) SP1 CMP: Samples and Populations (Inv. 4) SP2 CMP: Moving Straight Ahead (Inv. 1-4) CMP: Thinking With Mathematical Models (Inv. 2) CMP: Samples and Populations (Inv. 4) SP3 CMP: Moving Straight Ahead (Inv. 1-4) CMP: Thinking with Mathematical Models (Inv. 2-3) CMP: The Shapes of Algebra (Inv. 2-3) SP4 CMP: Data About Us (Inv. 2) Unit 6: Linear Models and Tables February 27 - March 16, 2012 Enduring Understandings: 19 CCGPS Standards: MCC8.F.4 MCC8.F.5 MCC8.SP.1 MCC8.SP.2 MCC8.SP.3 MCC8.SP.4 Collecting and examining data can sometimes help one discover patterns in the way in which two quantities vary. Changes in varying quantities are often related by patterns which, once discovered, can be used to predict outcomes and solve problems. Written descriptions, tables, graphs, and equations are useful in representing and investigating relationships between varying quantities. Different representations (written descriptions, tables, graphs, and equations) of the relationships between varying quantities may have different strengths and weaknesses. Linear functions may be used to represent and generalize real situations. Slope and y-intercept are keys to solving real problems involving linear relationships. CCGPS Standards: Use functions to model relationships between quantities. MCC8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. MCC8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Investigate patterns of association in bivariate data. MCC8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. MCC8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. MCC8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. MCC8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two way table. Construct and interpret a two way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. Essential Question: How can I find the rate of change from a table, graph, equation, or verbal description? How can I find the initial value from a table, graph, equations, or verbal description? How can I write a function to model a linear relationship? How can I sketch a graph given a verbal description? How can I describe a situation given a graph? How can I analyze a scatter plot? How can I create a linear model given a scatter plot? How can I use a linear model to solve problems? How can I use bivariate data to solve problems? What strategies can I use to help me understand and represent real situations involving linear relationships? How can the properties of lines help me to understand graphing linear functions? What can I infer from the data? How can functions be used to model realworld situations? How does a change in one variable affect the other variable in a given situation? Which tells me more about the relationship I am investigating a table, a graph or an equation? Why? Prerequisite Skills: identifying and calculating slope identifying the y-intercept creating graphs using given data analyzing graphs making predictions from a graph

20 Grade 8 Unit 6 Linear Models and Tables Sample Daily Lesson Plan DI: Direct Instruction DAY 1 DAY 2 DAY 3 DAY 4 DAY 5 February 11 February 12 February 13 February 14 February 15 DI: Graphing equations in slope-intercept form (use different values for b, graphing positive, negative, undefined and zero slopes) MCC8F4, 5 Continue MCC8F4, 5 Assess graphing equations in slope-intercept form. MCC8F4, 5 DI: Review area of rectangular prism and volume Task: Winter is Over MCC8F4,5; MCC8SP1 Continue WINTER BREAK WINTER BREAK WINTER BREAK WINTER BREAK WINTER BREAK February 18 February 19 February 20 February 21 February 22 DAY 6 DAY 7 DAY 8 DAY 9 DAY 10 February 25 February 26 February 27 February 28 March 1 Task: Heartbeats Introduce Scatterplots MCC8F4,5; MCC8SP1 Task: Walk the Graph MCC8F4,5; MCC8SP2,3,4 DI: Create scatterplots and draw lines of best fit. MCC8SP1,2,3,4 continue DI: Review Box-and- Whisker Plots Task: Heartbeats Too MCC8F4,5; MCC8SP1,2,4 DAY 11 DAY 12 DAY 13 DAY 14 DAY 15 March 4 March 5 March 6 March 7 March 8 Assessment of line of best fit and scatterplots Culminating Task: Is this Data Linear? Continue Unit Review Unit Test 20