VIEWS: 21 PAGES: 22 POSTED ON: 4/25/2012 Public Domain
8.1 Use proportions to solve scale-model problems with fractions and decimals Enabling Objectives: NOTE: Calculations can be done on a four-function calculator except for fractions. SOL 8.1 builds on SOLs 7.7, 7.12, 6.2, and 6.6 TSW use proportions to solve practical problems, including scale drawings that contain whole numbers, fractions, decimals, and percents. TSW determine if geometric figures (quadrilateral and triangles) are similar; write proportions to express the relationships between corresponding parts of similar polygons. TSW describe/compare two sets of data using ratios and use appropriate notations. (a/b, a to b, a:b). Stress a/b. TSW solve problems that involve addition, subtraction, and/or multiplication with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators 12 (answers in simplest form); and find the quotient, given a dividend and divisor expressed as a decimal through thousandths with exactly one non-zero digit. For divisors with more than one non-zero digit, estimation and calculators will be used. a. Understand vocabulary terms: ratio, proportion, extremes (a/b = c/d, ad=bc, ad are the extremes and bc are the means), means, unit rate, cross products, and scale models. b. Express ratios in lowest terms. c. Determine unit rates using proportions. d. Determine if two ratios form a proportion using cross products. e. Solve proportions using cross products. (Hints: Cross-multiply and divide. The means must equal the extremes). f. Solve word problems using proportions so that the ratios are representing the same comparison. (Hint: It might be helpful to set up the proportion using words first. Ex. meters/kilometers or miles/hours) g. Apply ratio and proportions to solve practical problems. Ex. scale models, enlarging photographs, similar figures, and cooking h. Recognize and demonstrate an understanding of the connection between the part-to- whole fraction concept of percents in ratios and proportions. 8.2 Simplify numerical expressions involving exponents, using order of operations. Enabling Objectives: SOL 8.2 builds on SOLs 7.3 and 6.22. TSW simplify expressions by using order of operations, mental mathematics, and appropriate tools. Exponents will be included. TSW investigate and describe concepts of exponents, perfect squares, and square roots, using calculators to develop exponential patterns.. Patterns will include zero and negative exponents. Investigations will include the binary number system as an application of exponents and patterns. a. Understand vocabulary terms: base, exponent, "squared", "cubed", and "raised to a power". b. Understand all symbols: +,-,,, and the use of grouping symbols: (), [], {}. c. Recognize all addition, subtraction, multiplication, and division facts. d. Recognize and use different forms of expressing multiplication: 4 3, 4 3, 4(3), (4)3, (4)(3) and division: 12 3, 12/3 e. Know how to find the value of a base, raised to a given power: 34 = 3 3 3 3 = 81 strategies: 1. Given a base and an exponent, find its value 2. Given a value and a base, find its corresponding exponent. f. Identify and apply the order of operations rule: P E MD AS: parentheses (grouping symbols), exponents, multiplication and division from left to right, addition and subtraction from left to right. strategies: Memory device: Please Excuse My Dear Aunt Sally 8.3 The student will describe orally and in writing the relationship between the subsets of the real number system. Enabling Objectives: SOL 8.3 builds on SOLs 8.6 and 6.5. TSW given a whole number from 0-100, identify it as a perfect square or find the two consecutive whole numbers between which the square root lies. TSW identify and represent integers on a number line. a. Understand vocabulary terms: counting numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. b. Understand the radical symbol. c. Understand the equality of fractions, decimals, and percents. d. Understand that rational numbers can be written as a decimal that can either terminate or repeat. e. Identify irrational numbers. f. Compare rational and irrational numbers. g. Recognize that rational and irrational numbers together make up the set of real numbers. h. Diagram the real number system including the following subsets: irrational numbers, rational numbers, integers, whole numbers, and natural numbers. Strategies: Use Venn Diagrams to show relationships and solve problems. Compare whole numbers, natural numbers, and integers. (Venn Diagram) i. Understand the concept of a perfect square. j. Find the square root of a number by estimating or using a four-function calculator in order to identify the sets of numbers to which it belongs. k. Identify in which subsets of the real number system a given number belongs. Strategies: Explain orally and in writing why a number belongs in a given subset of . the real number system. Explain orally and in writing why some numbers can belong to more than one subset of the real number system. Restate all numbers in simplest form before classifying. 8.4 Solve practical problems involving whole numbers, integers, and rational numbers, including percents. Problems will be of varying complexities, involving real-life data. Enabling Objectives: SOL 8.4 builds on SOLs 7.6, 7.5, 6.8, 6.7, and 6.6. TSW solve practical problems involving basic operations with integers by formulating rules for operating with integers and using a number line to compute; and explain the need for integers, using examples from real life situations. TSW solve consumer application problems involving tips, discounts, sales tax, and simple interest, using whole numbers, fractions, decimals, and percents. TSW solve multi-step consumer application problems involving fractions and decimals and present data and conclusions in paragraphs, table, or graphs. TSW use estimation strategies to solve multi-step practical problems involving whole numbers, decimals, and fractions. TSW solve problems that involve addition, subtraction, and/or multiplication with fractions and mixed numbers. a. Understand consumer terms, such as: tips, discounts, sales tax, and simple interest as well as percent. b. Add, subtract, multiply, and divide whole numbers, integers, decimals and fractions. c. Convert between fractions, decimals, and percents. d. Solve percent problems using proportions, equations, and triangle method. e. To find the percent of increase or decrease. f. Use problem-solving strategies. g. Identify information necessary to solve the problem. (mark out information that is extra.) h. Translate verbal phrases into algebraic or numerical expressions to solve practical problems. (Look for keywords.) i. Estimate before solving the problem using various strategies. (Rounding, front-end clustering, comparison to known benchmarks [ones, tens, hundreds], and compatible numbers.] j. Analyze results to see if they are reasonable. 8.5 Apply the order of operations to evaluate algebraic expressions for given replacement values of specified variables. Enabling Objectives: SOL 8.5 builds on SOLs 8.2 and 7.3. TSW simplify numerical expressions involving exponents, using order of operation. TSW simplify expressions by using order of operations, mental mathematics, and appropriate tools. Exponents will be included. a. Understand vocabulary terms: variable, replacement values, expressions, equations, algebraic/numerical expression, inequalities, and numerical coefficient, like and unlike terms. (Hint: Students should understand the difference between expressions and equations.) b. Be able to compute and use all types of rational numbers as replacement values. c. Know that when they are given a replacement value for a variable, that replacement is used every time that variable is used in the expression. Different variables represent different replacement values. d. Understand that 2a means 2 times a. e. Understand that they may simplify the expression first and then substitute in the replacement value OR substitutive first and then simplify. Ex: 3a + [a - (a - 2)] when a = 6 Simplify, then substitute: 3a + a - a + 2 3a + 2 3(6) + 2 18 + 2 20 8.6 Given a whole number from 0-100, identify it as a perfect square or find the two consecutive whole numbers between which the square root lies. Enabling Objectives: SOL 8.6 builds on SOLs 8.2 and 6.22. TSW simplify numerical expressions involving exponents, using order of operations. TSW investigate and describe concepts of exponents, perfect squares, and square roots, using calculators to develop exponential patterns. Patterns will include zero and negative exponents. Investigations will include the binary number system as an application of exponents and patters. a. Understand vocabulary terms: square root, perfect square, consecutive, and between. b. Generate the list of perfect squares from 1 to 100 and become very familiar with them. c. Know and understand that the inverse of squaring is taking the square root. d. Know what a radical sign is and not confuse it with a division sign. Strategy: Given a square root of a perfect square, give its value in whole number form: sqrt(49) = 7 and vice versa: 10 = sqrt(100) e. Given a square root of a number, which is not a perfect square, find the two consecutive whole numbers between which the square root lies by looking at their generated list of perfect squares. f. Know how to find the square root on a calculator: press the number first, then the square root key, not vice versa. g. Recognize that positive rational numbers have 2 square roots: one is positive and the other is negative. 8.7 Verify by measuring and describe the relationships between vertical angles and angles that are supplementary and complementary. Enabling objectives: SOL 8.7 builds on SOL 6.13. TSW estimate angle measures using 45, 90, and 180 as referents and use the appropriate tools to measure the given angles. a. Understand vocabulary terms: complementary angels, supplementary angles, adjacent angles, vertical angles, and corresponding angles. b. Be able to measure angles using a protractor and classify the angles as acute, obtuse, right, or straight angles. c. Realize that a straight-line measures 180 and a right angle measure 90. d. Use an alphabetical memory device to remember the difference between complementary and supplementary angles: C comes before S in the alphabet, and 90 comes before 180 when counting. Strategies using enabling objectives a-d: 1. Using manipulative triangles, find the 60 and 30 angles respectively. Place them adjacent to each other. What do they form together? A right angle (90). These two angles are complementary and adjacent. Now separate them again. These two angles are complementary, but not adjacent. 2. Using manipulative triangles, find the 60 and 120 angles respectively. Place them adjacent to each other. What do they form? A straight-line (180). These two angles are supplementary and adjacent. Now separate them again. These two angles are supplementary and not adjacent. 3. Using the figure, measure all three angles: ABC, CBD, and ABD. Realize that mABD = mABC + mCBD A C B D 1. Explore meaning of complementary, supplementary, and adjacent angles using student drawings: Draw two intersecting lines, measure all four angles, noting which angles have equal measures and which pairs are supplementary. Draw a line with a point on it. Draw a ray from that point. What is the result? Supplementary adjacent angles. Extend the ray into a line. What is the result? Vertical angles. e. Describe real life situations using vertical angles: scissors, pliers, and hedgers. (Landscape of Geometry Video) 8.8 Investigate and solve problems involving volume and surface area of cones and pyramids, using concrete materials and practical situations. Enabling Objectives: SOL 8.8 builds on SOLs 8.10, 7.9, and 7.13 TSW describe, classify and construct plane figures and solid figures, including prisms, pyramids, cylinders, and cones. TSW investigate and solve problems involving volume and surface area of rectangular prisms and cylinders, using concrete materials and practical situations to develop formulas. TSW construct a three-dimensional model using cubes, given the top, side, and/or bottom views, and determine the volume and surface area of the model. a. Define volume and surface area and understand when, in a given situation, you would need to find the volume or the surface area (be able to give an example of each). b. Know that multiply by 1/3 means dividing by 3. c. Know that r2 means r r. d. Know that numbers and variables placed next to each other in a formula imply multiplication. e. Understand that B represents the area of the base. f. Know how to find the area and perimeter of a rectangle. g. Understand vocabulary terms: radius, diameter, height, and lateral height. h. Know that the length of a diameter equals twice the length of a radius. i. The student will be able to, using a model of a cone and pyramid, point out the following: radius, height, slants height, and base. j. The student will be able to, using a drawing of a cone and pyramid, label out the following: radius, height, slants height, and base. k. Understand why surface area is measured in square units but volume is measure in cubic units. l. The student will be able to, given the surface area formula, tell which part of the formula represents the area of which plane figure. Surface area of cone = rl + r2 Curved Circle Surface (base) Surface area of pyramid = ½lp + B 4 Triangles + rectangle (base) m. The student will be able to, given the formula and appropriate measurements, find the surface area and volume of a cone and pyramid in real life situations. For example, how much ice cream would it take to fill and ice cream cone or how much paint would it take to cover a pyramid? 8.9 The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations such as tiling, fabric design, art, and scaling. Enabling Objectives: SOL 8.9 builds on SOLs 7.26, 6.21, and 6.13 TSW identify and graph ordered pairs in the 4 quadrants of a coordinate plane. TSW recognize/describe/extend a variety of numerical and geometric patterns. TSW estimate angle measures 45, 90, and 180 a. Define the various transformations (rotation, reflection, translation, and dilation). Hint: Dilation is enlarging and reducing proportionally as in similar figures. b. Correlate a rotation to a turn, a refection to a flip, a translation to a slide, and a dilation to a scale. c. Demonstrate reflection on graph paper over the x-axis, y-axis, and the line x=y. d. Identify symmetry in objects. Ex. Alphabet, pictures, geometric figures, nature, etc. e. Identify different transformations in tiling, fabrics, patterns, art (Escher’s work), etc. f. Demonstrate rotations of geometric shapes. g. Rotate shapes when given the number of degrees of rotation. h. Apply formula to a geometric figure to create a transformation (x,y) = (x + a, y + b) i. Apply formula to a geometric figure to create a dilation (x,y) = (nx, my) j. Explore to see what shapes can be tessellated. k. Create designs using rotations, reflections, and translation or patterns. 8.10 Describe, classify and construct plane figures and solid figures, including prisms, pyramids, cylinders, and cones. Enabling Objectives: SOL 8.10 builds on SOLs 7.10, 7.11, 6.14, and 6.17. TSW compare and contract the following quadrilaterals: a parallelogram, rectangle, square, rhombus, and trapezoid. Use deductive reasoning and inference to make classifications of polygons. TSW identify and draw the following polygons: pentagon, hexagon, heptagon, octagon, nonagon, and decagon. TSW identify, classify, and describe the characteristics of plane figures, including similarities and differences. TSW sketch, construct models, and classify rectangular prisms, cones, cylinders, and pyramids. a. List which solid figures have 2 bases (prism, cylinder) and which solid figures have 1 base (cone, pyramid). b. List which solid figures come to a point (cone, pyramid) and make the connection that they come to a point BECAUSE they only have one base. c. List which solid figures have circular bases (cylinder, cone) and which have rectangular bases (rectangular prism, rectangular pyramid). Strategies 1. Given the name or drawing of a solid figure, list the plane figures that form the sides: rectangular pyramid: 1 rectangle & 4 triangles (2 pairs of triangles) cone: 1 circle & 1 curved surface cylinder: 2 circles & 1 rectangle rectangular prism: 6 rectangles (3 pairs of rectangles: top & bottom, front & back, left & right) 2. Given a “net” or flat drawing of the sides of a solid figure, determine which solid figure it would form, first by actually constructing them from paper, and second, without construction but just by recognition. 8.11 Verify the Pythagorean Theorem by measuring; apply the Pythagorean Theorem to find the missing length of a side of a right triennial when the length of the other two sides is given. Enabling Objectives: SOL 8.11 builds on SOLs 8.2, 8.6, 7.25, 6.22, and 6.23 TSW simplify numerical expressions involving exponents, using order of operations. TSW given a whole number from 0-100, identify it as a perfect square or find the two consecutive whole numbers between which the square root lies. TSW solve practical problems requiring the solution of a two-step linear equation and inequalities in one variable, using strategies involving inverse operations and integers. TSW investigate and describe concepts of exponents, perfect square, and square roots, using calculators to develop exponential patterns. Patterns will include zero and negative exponents. Investigations will include the binary number system as an application of exponents and patterns. TSW model/solve algebraic equations, using concrete materials, and solve one- step linear equations in one variable, involving whole number coefficients and positive rational solutions. a. Understand vocabulary terms: right angle, right triangle, legs and hypotenuse of a right triangle, and diagonal of a rectangle. b. Understand that the hypotenuse is the longest side of a right triangle and that it is across from the right angle. Understand that the “legs” are the shorter 2 sides and that they form the right angle. Strategy: Give various pictures of right triangles with the right angle in different locations, be able to identify the legs and hypotenuse. c. Discover the Pythagorean Theorem by using one or more of the following strategies: 1. Use tile manipulative to verify the Pythagorean Theorem, as in the drawings of 32 + 42 = 52 2. Given a right triangle manipulative, the student will: A. identify the legs and hypotenuse B. use a ruler to measure the 3 sides of the triangle C. use a calculator to square the lengths of the sides or the triangle D. add the squares of the legs to verify that it equals the square of the hypotenuse 3. Given a ruler and protractor, the student will draw a right triangle (steps 1-4 are the same as in strategy #2) Video: The Pythagorean Theorem By Allied Video Corporation P.O. Box 702618 Tulsa, Oklahoma 74170 (800) 926=5892 d. Using the Pythagorean Theorem: Find the hypotenuse when both legs are known Find one of the legs when the hypotenuse and the other leg are know. e. Solve real life application problems with the Pythagorean Theorem, such as: “John takes a shortcut to school by walking diagonally across an empty lot. The rectangular lot is 15 yards wide and 25 yards long. How much shorter is the shortcut that a route on the sides of the lot?” 8.12 Analyze problem situations, such as games of chance, board games, or grading scales, and make predictions, using knowledge of probability. Enabling Objectives: SOL 8.12 builds on SOLs 7.18, 7.17, 7.16, 7.15, and 6.20 TSW identify and describe the number of possible arrangements of several objects, using a tree diagram or the Basic Counting Principle. TSW determine the probability of a given simple event and express that probability as a ratio, decimal, or a percents as appropriate for the given situation. TSW make a sample space for experiments and represent it in the form of a list, chart, picture, or tree diagram. TSW investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event. TSW determine and interpret the probability of an even occurring from a given sample space. a. Understand vocabulary terms: probability, sample space, equally likely, permutation, outcome, simulation, theoretical probability, factorial, counting principle, dependent event, independent event, fair game, and unfair game. b. Investigate theoretical probability of an event by determining its sample space using a tree diagram, model, list, etc. c. Simulate and event and compare the results with the theoretical probability. d. Describe the difference between the probability of an even found through simulations versus the theoretical probability of the same event. e. Determine the probability of a simple even by comparing the number of ways an event can occur as compared to the sample space. Write as a ratio, fraction, decimal, and percent. f. Predict the outcome of an event. g. Conduct an experiment to test the results of the prediction. h. Convert fractions to decimals to percents. i. Reduce fractions. j. Gather and organize data. k. Identify bias in the sampling procedures. (surveys, spreadsheets, interviews) l. Use data to make prediction to solve problems (tree diagrams, cause and effect, and simulations). m. Calculate probability using permutations and combinations. n. Investigate probability with and without replacement. o. Determine if a game is fair or unfair. p. Design a statistical experiment to study a problem. Conduct the experiment. Interpret the results. Make predictions. Justify the predictions q. Predict the probability of winning the lottery and how the lottery could be changed so the player would have a better chance to win. r. Solve real life problem situations using probability. (Make predictions, draw conclusions, and find solutions.) 8.13 Use information displayed in line, bar, circle, and picture graphs and histograms to make comparisons, predictions, and inferences. Enabling Objectives: NOTE: The use of a spreadsheet program will enhance the comprehension of this SOL. SOL 8.13 builds on SOLs 7.19, 7.21, 7.20, 6.18, and 6.19. TSW create and solve problems involving the mean, median, mode, and range of a set of data. TSW make inferences and predictions based on the analysis of a set of data that the student(s) collect. TSW display data, using frequency distributions, line plots, stem-and-leaf plots, box-and-whiskey plots, and scattergrams. TSW given a problem situation, collect/analyze/display/interpret data in line, bar, and circle graphs and stem-and-leaf and box-and-whisker plats. TSW describe the man, median, and mode as measures of central tendency and determine their meaning for a set of data. a. Recognize the difference between line, bar, circle, picture graphs, as well as a histogram. b. Interpret data in a specific graph. Strategy: Find graphs on the Internet and have students answer related questions. c. Explore the uses of a computer-graphing program. Strategy: Have students collect data on a certain topic, enter results on a spreadsheet, and have the computer develop graphs. d. Design a circle graph from a set of data. Strategy: Draw circles, measure angles, change decimals to percents, and compute percentages. e. Interpret how statistical data is displayed in a histogram. 8.14 Use a matrix to organize and describe data. Enabling Objectives: NOTE: Calculations can be done on a four-function calculator. Optional: Use of a graphic calculator will extend this SOL into algebra. a. Define and develop a working knowledge of a matrix. b. Describe the dimensions of a matrix by its rows and columns. c. Explain the components of a entry code and how it is used. erow, column Ex. E2,3 = entry at row 2, column 3 d. Locate information in a matrix by its entry code as well as identify the entry code of a given item. e. Collect data on various concepts such as wages, baseball stats, stock markets, and display the data in a matrix. f. Construct a matrix. g. Optional: Add and subtract matrices. (Hint: Matrices must have the same dimensions.) 8.15 Investigate and describe functional relationships, including the number of sides of a regular polygon and the maximum number of possible diagonals, expressing the algebraic concept of the number of diagonals of the nth-sided polygon. Enabling Objectives: NOTE: Calculations can be done on a four-function calculator. SOL 8.15 builds on SOLs 8.5, 7.22, 7.14, 7.11, 6.21, and 6.14 TSW apply the order of operations to evaluate algebraic expressions for given replacement values of specified variables. TSW investigate and describe functional relationships, including the number of sides of a regular polygon and the sum of the measures of the interior angles. TSW inscribe equilateral triangles, square, and hexagons in circles using a compass and a straight edge. TSW identify and draw the following polygons: pentagon, hexagon, heptagon, octagon, nonagon, and decagon. TSW recognize/describe/extend a variety of numerical and geometric patterns. TSW identify, classify, and describe the characteristics of plane figures, including similarities and differences. a. Understand vocabulary terms: regular polygon, diagonal, and interior angles. b. Recognize and describe the differences between terms in numerical patterns. (Hint: Does it increase or decrease, is it a multiple, or a combination?) c. Describe the relationship between consecutive terms in numerical patterns using mathematical symbols. d. Develop and apply strategies using a variety of geometric patterns (ex. Flips, slides, turns, symmetry, etc.) e. Extend and create a variety of numerical and geometric patterns using a determined rule/mathematical relationship. f. Construct regular polygons using a compass and protractor. g. Explore to find the sum of the measures of the interior angles of a regular polygon. h. Explore and explain geometric patterns using manipulative (blocks, cubes, grid paper, etc.) i. Explore and explain numerical patterns. (Number lines, tables, etc.) j. Complete a given pattern. Investigate to find other functions such as speed to distance, time to distance, and area of a square. 8.16 Solve multi-step equations in one variable Enabling Objectives: SOL 8.16 builds on SOLs 8.2, 7.23, 7.24, 7.25, and 6.23 TSW simplify numerical expressions involving exponents, using order of operations. TSW write verbal expressions/sentences as algebraic expressions/equations. TSW use algebraic terms appropriately in written and/or oral expression: equation, inequality, variable, expression, term, coefficient, domain, and range. TSW solve practical problems requiring the solution of two-step linear equations and inequalities in one variable, using strategies involving inverse operations and integers. TSW model solve algebraic equations, using concrete materials, and solve one- step linear equations in one variable, involving whole number coefficients and positive rational solutions. a. Compute within the set of rational numbers. HINT: Stress operations with negative numbers b. Understand inverse operations. c. Recognize, understand and use formulas such as perimeter, area, and circumference. Ex. Find width when given area and length. d. Apply the process for solving equations. 1. Simplify both sides of the equation. 2. Use inverse operations to isolate variables. Suggestion: Have students eliminate the variable with the smallest coefficient 3. Eliminate numerical coefficients. 4. Check answers by replacing values of the variables into the equation. e. Discuss how to substitute know variable value in formulas and solve. 8.17 Graph a linear equation in two variables on the coordinate plane using a table of ordered pairs. Enabling Objectives: SOL 8.17 builds on SOLs 8.5, 8.16, 7.24, 7.25, 7.26, and 6.23. TSW apply the order of operations to evaluate algebraic expressions for given replacement values of specified variables. TSW solve multi-step equations in one variable. TSW use algebraic terms appropriately in written and/or oral expression: equation, inequality, variable, expression, term, coefficient, domain, and range. TSW solve practical problems requiring the solution of two-step linear equations and inequalities in one variable, using strategies involving inverse operations and integers. TSW identify and graph ordered pairs in the four quadrants of a coordinate plane. TSW model/solve algebraic equations, using concrete materials, and solve one- step linear equations in one variable, involving whole number coefficients and positive rational solutions. a. Recognize the graph of a linear equation to be the graph of a straight line. b. Given an ordered pair determine by substitution if it is a solution for a linear equation in two variables. c. Make a table of ordered pairs. 1. Discuss independent and dependent variables. 2. Select values for x. (Discuss appropriate choices for values of x in each equation.) (Use one positive x value, zero, and one negative x value.) (You may want to specify a range so the values do not become too large or the computations too confusing.) 3. Substitute chosen x values in order to find y. d. Graph ordered pairs and connect with a straight line. e. Recognize that if the line is not straight, the work is incorrect. 8.18 Describe and represent relations using tables, graphs, and rules. Enabling Objectives: SOL 8.18 builds on SOLs 8.13, 8.17, 7.16, 7.20, 7.25, 7.26, 6.8 and 6.18 TSW use information displayed in line, bar, circle, and picture graphs and histograms to make comparisons, predictions, and inferences. TSW graph a linear equation in two variables on the coordinate plane using a table of ordered pairs. TSW make a sample space for experiments and represent it in the form of a list, chart, picture, or tree diagram. TSW display data, using frequency distributions, line plots, stem-and-leaf plots, box-and-whisker plots, and scattergrams. TSW solve practical problems requiring the solution of two-step linear equations and inequalities in one variable, using strategies involving inverse operations and integers. TSW identify and graph ordered pairs in the four quadrants of a coordinate plane. TSW solve multi-step consumer application problems involving fractions and decimals and present data and conclusions in paragraphs, table, or graphs. TSW given a problem situation, collect/analyze/display/interpret data in line, bar, and circle graphs and stem-and-leaf and box-and-whisker plots. a. Understand the vocabulary terms: relation, formula, domain, and range. b. Given a number or geometric pattern or a table of ordered pairs, be able to find the rule that applies: addition, subtraction, multiplication, division or a combination as well as exponential powers. c. Use a rule or equation to create a table of ordered pairs and/or its graph. d. Use a graph to find a rule by listing ordered pairs in a table and finding a pattern. e. Recognize that functions can be presented in 4 ways: as equations, in function tables, on graphs, or word forms. 8.19 Create and solve problems using proportions, formulas, and functions. Enabling Objectives: NOTE: Calculations can be done on a four-function calculator. SOL 8.19 builds on SOLs: 8.1, 8.4, 8.5, 8.11, 8.15, 7.7, 7.8, 7.9, 7.12, 7.22, 7.23, 7.25, 6.2, 6.7, 6.11, 6.12, and 6.23 TSW use proportions to solve scale-model problems with fractions and decimals. TSW solve practical problems involving whole numbers, integers, and rational numbers, including percents. Problems will be of varying complexities, involving real-life data. TSW apply the order of operations to evaluate algebraic expressions for given replacement values of specified variables. TSW verify the Pythagorean Theorem by measuring; apply the Pythagorean Theorem to find the missing length of a side of a right triangle when the lengths of the other two sides are give. TSW investigate and describe functional relationships, including the number of sides of a regular polygon and the maximum number of possible diagonals, expressing the algebraic concept of the number of diagonals of the nth-sided polygon. TSW use proportions to solve practical problems, including scale drawings that contain whole numbers, fractions, decimals, and percents. TSW given appropriate dimensions, estimate and find the area of polygons by subdividing them into rectangles and right triangles. TSW investigate and solve problems involving volume and surface area of rectangular prisms and cylinders, using concrete materials and practical situations to develop formulas. TSW determine if geometric figures (quadrilaterals and triangles) are similar; write proportions to express the relationships between corresponding parts of similar polygons. TSW investigate and describe functional relationships, including the number of sides of a regular polygon and the sum of the measures of the interior angles. TSW write verbal expressions/sentences as algebraic expressions/equations. TSW solve practical problems requiring the solution of two-step linear equations and inequalities in one variable, using strategies involving inverse operations and integers. TSW describe/compare two sets of data using ratios and will use appropriate notations (a/b, a to b, a:b) TSW determine if a problem situation involving polygons of 4 sides represents the application of perimeter or area and apply the appropriate formula. TSW create/solve problems by finding the circumference and/or area of a circle when given diameter or radius. Using concrete materials or computer models, derive approximations for pi from measurements for circumference and diameter. TSW model/solve algebraic equations, using concrete materials, and solve one- step linear equations in one variable, involving whole number coefficients and positive rational solutions. a. Understand the vocabulary terms: proportions, formulas, functions, relations, ratios, ordered pairs, domain, and range. b. Create real life problems involving proportions, formulas, functions that can be solve algebraically. c. Create a function table or chart form the specified data or a given function. d. Solve word problems involving proportions by comparing their cross products (ex. Scale drawings, similar figures, etc.) e. Use algebraic formulas or equations to solve real life problems. Ex. Solve distance/rate and time formula, perimeter, area, circumference, volume, and surface area. f. Solve word problems using problem-solving strategies. (read, choose an appropriate math process, estimate the answer, find the answer, determine if the answer is reasonable) g. Graph a linear function from specified data or given function.