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Math TAKS Grade 6th, 7th, and 8th Test Format The 6th. 7th, and 8th grade tests include a test booklet and a separate machine-scorable answer document. Enough room is left around each item in the booklet for students to work each problem. However, student responses must be recorded on the separate answer document. Any item may include application context and extraneous information. Most items will be in a multiple-choice format with four answer choices. Not here or a variation of this phrase may be used as the fourth answer choice when appropriate. Thursday, February 3, 2005 TAKS Math Prep. 2 Test Format There will be a limited number of open-ended griddable items. For these items a seven-column grid (with one column designated as a fixed decimal point) will be provided on the answer document for students to record and bubble in their answers. Digits must be in the correct column(s) with respect to the fixed decimal point. This griddable format is intended to allow students to work a problem and determine the correct answer without being influenced by answer choices. Thursday, February 3, 2005 TAKS Math Prep. 3 Mathematics Chart The Mathematics Chart includes measurement conversions on the front and formulas on the back. A metric ruler and a customary ruler will be provided on the front of the separate Mathematics Chart. Items that require students to measure with a ruler from the Mathematics Chart may be found in any objective as appropriate. Thursday, February 3, 2005 TAKS Math Prep. 4 Thursday, February 3, 2005 TAKS Math Prep. 5 Thursday, February 3, 2005 TAKS Math Prep. 6 Thursday, February 3, 2005 TAKS Math Prep. 7 6th, 7th, and 8th Grade Objectives Objective 1: The student will demonstrate an understanding of numbers, operations, and quantitative reasoning. Objective 2: The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning. Objective 3: The student will demonstrate an understanding of geometry and spatial reasoning. Thursday, February 3, 2005 TAKS Math Prep. 8 6th, 7th, and 8th Grade Objectives Objective 4: The student will demonstrate an understanding of the concepts and uses of measurement. Objective 5: The student will demonstrate an understanding of probability and statistics. Objective 6: The student will demonstrate an understanding of the mathematical processes and tools used in problem solving. Thursday, February 3, 2005 TAKS Math Prep. 9 Objective 6 Problem Solving Plan Understand the problem Organize the information you are given and identify exactly what you must find. You may need information that is not given in the problem, such as a formula. You may be given information that is not needed in order to solve the problem. Make a plan After you have organized the information, decide how to use this information to find an answer. Think about the math concepts that apply to the situation. Identify the order in which you will find new information and the formulas or equations you will use to find it. Carry out the plan After you have chosen a problem-solving strategy, use the strategy to work toward a solution to the problem. Go step-by-step through your plan, writing down important information at each step. Check to see whether your answer is reasonable Check to see whether your answer makes sense. Does it answer the question asked? Is it stated in the correct units? Is it reasonable? You can estimate the solution and then compare the estimate to your answer. They should be approximately equal. Thursday, February 3, 2005 TAKS Math Prep. 10 6th, 7th, and 8th Grade Objective 1 Numbers, Operations, and Quantitive Reasoning 10 test items in all grades At 6th, 7th, and 8th grade, students should be able to: sequence numbers or the words associated with numbers; work with problems that include information expressed as numbers or ranges of numbers; and round numbers before performing any computations when estimating. The use of compatible numbers (numbers that are easy to compute mentally) may be helpful. Thursday, February 3, 2005 TAKS Math Prep. 11 6th Grade Objective 1 Example Frank and Joe each bought a small pizza and ate only part of their pizza. The pictures below show how much of the pizzas were left. What portion of the pizza did Frank and Joe eat altogether? A 3 B 1 3 8 4 C 7 D 1 5 8 8 Thursday, February 3, 2005 TAKS Math Prep. 12 7th Grade Objective 1 Example Identify the group that does NOT contain equivalent fractions, decimals, and percents. A 1, 0.05, 5% B 7, 0.7, 70% 20 10 C 1, 0.125, 12.5% D 3 , 0.3, 3% 8 100 Thursday, February 3, 2005 TAKS Math Prep. 13 8th Grade Objective 1 Example A math club is selling 3 different sizes of book covers as a fund-raiser. Large covers sell for $4.50 each, medium covers sell for $4.00 each, and small covers sell for $3.50 each. Shanna bought 3 large, 1 medium, and 2 small book covers. Which equation can be used to find c, the total cost of Shanna’s book covers? A c = (3 + 1 + 2)(4.50 + 4.00 + 3.50) B c = 3(4.50) + 2(4.00) + 2(3.50) C c = 3(4.50) + 4.00 + 2(3.50) D c = (3 + 1 + 2)(4.50 + 4.00 + 3.50) 3 Thursday, February 3, 2005 TAKS Math Prep. 14 6th Grade Objective 2 Patterns, Relationships, and Algebraic Reasoning 9 test items At sixth grade, students should be able to: match a description of a proportional situation with a ratio, which may or may not be expressed in lowest terms; identify the method for finding any term of a numerical or geometric sequence; match a relationship represented by an equation or written description with the same relationship shown in pairs of numbers; and match an equation with a given context. Thursday, February 3, 2005 TAKS Math Prep. 15 7th Grade Objective 2 Patterns, Relationships, and Algebraic Thinking 10 test items At seventh grade, students should be able to: write an expression to find the nth term where n represents the position of the term in the sequence; identify the expression when given terms in a sequence, and vice versa; and match a relationship represented by an equation or written description with the same relationship shown in pairs of numbers. Thursday, February 3, 2005 TAKS Math Prep. 16 8th Grade Objective 2 Patterns, Relationships, and Algebraic Reasoning 10 test items At eighth grade, students should be able to: identify proportional and non-proportional relationships; write an expression to find the nth term where n represents the position of the term in the sequence; and identify the expression when given terms in a sequence, and vice versa. Thursday, February 3, 2005 TAKS Math Prep. 17 6th Grade Objective 2 Example At Sandra’s school there is 1 teacher for every 15 students. There are 630 students at the school. Which proportion can be used to find x, the number of teachers? A x = 1 B 15 = x 15 630 1 630 C 1 = x D x = 15 15 630 1 615 Thursday, February 3, 2005 TAKS Math Prep. 18 7th Grade Objective 2 Example Which description shows the relationship between a term and n, its position in the sequence? A Add 3 to n B Multiply n by 2 and then subtract 3 C Multiply n by 2 and then add 3 D Multiply n by 3 and then subtract 2 Thursday, February 3, 2005 TAKS Math Prep. 19 8th Grade Objective 2 Example The table shows land-speed records. Whose land- speed record did Green exceed by exactly 368.84 miles per hour? A Elyston B Cobb C Breedlove D Noble Thursday, February 3, 2005 TAKS Math Prep. 20 6th Grade Objective 3 Geometry and Spatial Reasoning 7 test items At sixth grade, students should be able to: use geometric models shown individually or as part of a more complex figure (for example, an obtuse angle may be shown as part of a trapezoid); identify a method for finding the radius, diameter, or circumference of a circle. The method can be written in words or as a mathematical equation or expression; and graph points, including fractions and decimals, on coordinate grids limited to the first quadrant. Thursday, February 3, 2005 TAKS Math Prep. 21 7th Grade Objective 3 Geometry and Spatial Reasoning 7 test items At seventh grade, students should be able to: use geometric models shown individually or as part of a more-complex figure (for example, supplementary angles may be shown as part of a parallelogram); and graph points on coordinate grids using all four quadrants. Thursday, February 3, 2005 TAKS Math Prep. 22 8th Grade Objective 3 Geometry and Spatial Reasoning 7 test items At eighth grade, students should be able to: find and apply scale factors in problem-solving situations; match a two-dimensional representation of a solid with a three-dimension representation of the same solid, using the top, front, and/or side views of the solid; graph points on coordinate grids using all four quadrants; and recognize a picture or model of the Pythagorean Theorem. Thursday, February 3, 2005 TAKS Math Prep. 23 6th Grade Objective 3 Example A circle with center at point O is shown. Which line segment is 2 times the length of radius OK? F Segment LN G Segment LM H Segment LK J Segment ON Thursday, February 3, 2005 TAKS Math Prep. 24 7th Grade Objective 3 Example Use the protractor in the diagram to read the measure of each angle. One pair of complementary angles is — A ∠DXE and ∠BXC B ∠AXC and ∠CXE C ∠DXE and ∠AXB D ∠CXD and ∠AXB Thursday, February 3, 2005 TAKS Math Prep. 25 8th Grade Objective 3 Example Jackie built a fence around her garden to keep animals out. The dimensions of the area enclosed by the fence are shown in the diagram. What is the total area, in square feet, enclosed by the fence? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Thursday, February 3, 2005 TAKS Math Prep. 26 6th Grade Objective 4 Measurement 5 test items At sixth grade, students should be able to: utilize the conversions and formulas on the Mathematics Chart to solve problems; measure with the ruler on the Mathematics Chart only if the item specifically instructs students to use the ruler; use the given dimensions of a figure to solve problems; recognize abbreviations of measurement units; and use a pictorial representation of a protractor to measure angles. Thursday, February 3, 2005 TAKS Math Prep. 27 7th Grade Objective 4 Measurement 5 test items At seventh grade, students should be able to: utilize the conversions and formulas on the Mathematics Chart to solve problems; measure with the ruler on the Mathematics Chart only if the item specifically instructs students to use the ruler; use the given dimensions of a figure to solve problems; and recognize abbreviations of measurement units. Thursday, February 3, 2005 TAKS Math Prep. 28 8th Grade Objective 4 Measurement 5 test items At eighth grade, students should be able to: utilize the conversions and formulas on the Mathematics Chart to solve problems; measure with the ruler on the Mathematics Chart only if the item specifically instructs students to use the ruler; use the given dimensions of a figure to solve problems; recognize abbreviations of measurement units; and describe, in the form of a verbal or algebraic expression or a mathematical solution, the effect on perimeter, area, or volume when the dimensions of a figure are changed (for example, if the sides of a rectangle are doubled in length, then the perimeter is doubled, and the area is four times the original area; if the edges of a cube are doubled in length, then the volume is eight times the original volume). Thursday, February 3, 2005 TAKS Math Prep. 29 6th Grade Objective 4 Example A family put a rectangular patio in their backyard and planted grass in the rest of the yard. The rectangular backyard is 100 feet by 80 feet, and the patio is 13 feet by 8 feet. What is the area of the backyard that is planted with grass? F 402 sq ft G 7,896 sq ft H 8,000 sq ft J 8,104 sq ft Thursday, February 3, 2005 TAKS Math Prep. 30 7th Grade Objective 4 Example Mrs. Jones wants to paint a wall but not the door on the wall. How many square feet of wall does Mrs. Jones need to paint? F 36 ft2 G 171 ft2 H 129 ft2 J 150 ft2 Thursday, February 3, 2005 TAKS Math Prep. 31 8th Grade Objective 4 Example Mrs. Juárez has a cylindrical pincushion with the net shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the net in centimeters. Which is closest to the lateral surface area of the cylindrical pincushion? A 3.0 cm2 B 6.3 cm2 C 9.4 cm2 D 12.6 cm2 Thursday, February 3, 2005 TAKS Math Prep. 32 6th Grade Objective 5 Probability and Statistics 6 test items At sixth grade, students should be able to: match a situation with a sample space that lists all possible combinations or select the missing portion of a given sample space; match the median, mode, and/or range with a given data set, which may be listed in the text of the item or presented in a graphical representation; identify the missing piece of data that will produce a target median, mode, and/or range for a data set; and match a circle graph with a data set listed in table, chart, graph, or sentence form. Thursday, February 3, 2005 TAKS Math Prep. 33 7th Grade Objective 5 Probability and Statistics 7 test items At seventh grade, students should be able to: match a situation with a sample space that lists all possible combinations or select the missing portion of a given sample space; determine whether the graphical representation of the given data is appropriate and/or accurate; distinguish among mean, median, mode, and range to determine which is most appropriate for a particular purpose; match the mean, median, mode, and/or range with a given data set, which may be listed in the text of the item or presented in a graphical representation; and identify the missing piece of data that will produce a target mean, median, mode, and/or range for a data set. Thursday, February 3, 2005 TAKS Math Prep. 34 8th Grade Objective 5 Probability and Statistics 8 test items At eighth grade, students should be able to: distinguish between theoretical probability and experimental results; distinguish among mean, median, mode, and range to determine which is most appropriate for a particular purpose; identify the missing piece of data that will produce a target mean, median, mode, and/or range for a data set; and determine whether the graphical representation of the given data is appropriate and/or accurate. Thursday, February 3, 2005 TAKS Math Prep. 35 6th Grade Objective 5 Example Nate has a bag containing 3 red, 2 blue, 4 yellow, and 3 green marbles. If he randomly chooses one marble from the bag, what is the probability that the marble will be blue? A 5 B 1 6 3 C 1 D 1 4 6 Thursday, February 3, 2005 TAKS Math Prep. 36 7th Grade Objective 5 Example Which of the following relationships is best represented by the data in the graph? F Conversion of feet to inches G Conversion of miles to feet H Conversion of feet to yards J Conversion of inches to yards Thursday, February 3, 2005 TAKS Math Prep. 37 8th Grade Objective 5 Example Lily surveyed all the members of the middle school band about their favorite class this semester. The results are shown in the table below. From these results, Lily concluded that band was the favorite class among all the students at her school. Which is the best explanation for why her conclusion might not be valid? F The survey should have been done each day for a week. G The sample was not representative of all the students at the school. H The survey should have been done with eighth-grade students only. J The band meets only 3 days a week. Thursday, February 3, 2005 TAKS Math Prep. 38 6th, 7th, and 8th Grade Objective 6 Mathematical Processes and Tools 9 test items in 6th and 7th grade, 10 test items in 8th grade At 6th, 7th, and 8th grade, students should be able to: select the description of a mathematical situation when provided with a written or pictorial prompt; identify the information that is needed to solve a problem; select or describe the next step or a missing step in a problem- solving situation; match informal language to mathematical language or symbols; identify the question that is being asked or answered; draw a conclusion by investigating patterns and/or sets of examples and nonexamples. A nonexample, or counterexample, proves a general statement to be false; understand that nonsensical words may be used to label sets of examples and/or nonexamples; and choose the correct supporting information for a given conclusion. Thursday, February 3, 2005 TAKS Math Prep. 39 6th Grade Objective 6 Example Anita found the measures of the angles of an isosceles triangle. One angle measured 50°, and the other 2 angles were congruent. Which method can be used to find the measure of each of the congruent angles? A Multiply 50 by 2 and then add 180 B Subtract 50 from 180 and then divide by 2 C Add 50 to 180 and then divide by 3 D Divide 50 by 2 and then subtract from 180 Thursday, February 3, 2005 TAKS Math Prep. 40 7th Grade Objective 6 Example ∠KSD and ∠DSM are supplementary angles. If the measure of ∠KSD is 71°, what is the measure of ∠DSM? A 19°, because the sum of the measures of supplementary angles is 90° B 71°, because the measures of supplementary angles are equal C 109°, because the sum of the measures of supplementary angles is 180° D 289°, because the sum of the measures of supplementary angles is 360° Thursday, February 3, 2005 TAKS Math Prep. 41 8th Grade Objective 6 Example A rectangle and a semicircle can be combined to make an irregular figure. The figures form a pattern. Each rectangle is ½ the height of the rectangle immediately to its left. What would be the area of the next smaller figure in the pattern? A 42 mm2 B 207.72 mm2 C 307.72 mm2 D 349.72 mm2 Thursday, February 3, 2005 TAKS Math Prep. 42 Tips for Student Success Remind your child that in order to foster learning, distractions should always be left outside the classroom. Check your child's agenda books daily. Ask to see completed homework. Periodically, ask to see class folders, notebooks, textbooks and go over these materials with your child. Ensure that your child is at school every day. Remind your child to leave distractions at home or in the lockers. Encourage your child to have a positive attitude toward math. Provide opportunities for your child to use math skills in a wide variety of everyday activities (at the grocery store, reading ads, setting the table, buying gasoline, figuring gas mileage, etc.) Have your child practice making change. Encourage your child to play with numbers. Thursday, February 3, 2005 TAKS Math Prep. 43 More Tips for Student Success Read books that are math related with your child. Help your child notice mathematical patterns in everyday occurrences. Have your child practice sorting and classifying items by common attributes, such as color, size, and number of sides in a shape. Have your child notice geometric shapes in his/her surroundings. Meet with your child's teachers and ask what type of additional help your child needs. Share with your child examples of how you use math in your job or life. Work the online math test produced by TEA with your child (www.tea.state.tx.us). Develop a sense of reasonableness for solutions or for mathematical thinking. Watch HISD's After-School Algebra Show with your child. Help your child learn how to use a graphing calculator. Encourage your child to use mathematical sites on the Internet. Thursday, February 3, 2005 TAKS Math Prep. 44 Useful Web Sites and Q&A TAKS Information Booklets: http://www.tea.state.tx.us/student.assess ment/taks/booklets/index.html Released TAKS Tests: http://www.tea.state.tx.us/student.assess ment/resources/release/taks/index.html TAKS Study Guides: http://www.tea.state.tx.us/student.assess ment/resources/guides/study/index.html Thursday, February 3, 2005 TAKS Math Prep. 45 Objectives and Sub-objectives 6th, 7th, and 8th Grade 6th Grade Objective 1 (6.1) The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (A) compare and order non-negative rational numbers; (B) generate equivalent forms of rational numbers, including whole numbers, fractions, and decimals; (C) use integers to represent real-life situations; (D) write prime factorizations using exponents; and (E) identify factors and multiples, including common factors and common multiples. Thursday, February 3, 2005 TAKS Math Prep. 47 6th Grade Objective 1 (cont.) (6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (A) model addition and subtraction situations involving fractions with [objects,] pictures, words, and numbers; (B) use addition and subtraction to solve problems involving fractions and decimals; (C) use multiplication and division of whole numbers to solve problems, including situations involving equivalent ratios and rates; and (D) estimate and round to approximate reasonable results and to solve problems where exact answers are not required. Thursday, February 3, 2005 TAKS Math Prep. 48 6th Grade Objective 2 (6.3) The student solves problems involving proportional relationships. The student is expected to: (A) use ratios to describe proportional situations; (B) represent ratios and percents with [concrete] models, fractions, and decimals; and (C) use ratios to make predictions in proportional situations. Thursday, February 3, 2005 TAKS Math Prep. 49 6th Grade Objective 2 (cont.) (6.4) The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to: (A) use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, perimeter, area, etc.; and (B) generate formulas to represent relationships involving perimeter, area, volume of a rectangular prism, etc., from a table of data. Thursday, February 3, 2005 TAKS Math Prep. 50 6th Grade Objective 2 (cont.) (6.5) The student uses letters to represent an unknown in an equation. The student is expected to: (A) formulate an equation from a problem situation. Thursday, February 3, 2005 TAKS Math Prep. 51 6th Grade Objective 3 (6.6) The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: (A) use angle measurements to classify angles as acute, obtuse, or right; (B) identify relationships involving angles in triangles and quadrilaterals; and (C) describe the relationship between radius, diameter, and circumference of a circle. Thursday, February 3, 2005 TAKS Math Prep. 52 6th Grade Objective 3 (cont.) (6.7) The student uses coordinate geometry to identify location in two dimensions. The student is expected to: (A) locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. Thursday, February 3, 2005 TAKS Math Prep. 53 6th Grade Objective 4 (6.8) The student solves application problems involving estimation and measurement of length, area, time, temperature, capacity, weight, and angles. The student is expected to: (A) estimate measurements and evaluate reasonableness of results; (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter and circumference), area, time, temperature, capacity, and weight; (C) measure angles; and (D) convert measures within the same measurement system (customary and metric) based on relationships between units. Thursday, February 3, 2005 TAKS Math Prep. 54 6th Grade Objective 5 (6.9) The student uses experimental and theoretical probability to make predictions. The student is expected to: (A) construct sample spaces using lists, tree diagrams, and combinations; and (B) find the probabilities of a simple event and its complement and describe the relationship between the two. Thursday, February 3, 2005 TAKS Math Prep. 55 6th Grade Objective 6 (6.10) The student uses statistical representations to analyze data. The student is expected to: (A) [draw and] compare different graphical representations of the same data; (B) use median, mode, and range to describe data; (C) sketch circle graphs to display data; and (D) solve problems by collecting, organizing, displaying, and interpreting data. Thursday, February 3, 2005 TAKS Math Prep. 56 6th Grade Objective 6 (cont.) (6.11) The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; and (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. Thursday, February 3, 2005 TAKS Math Prep. 57 6th Grade Objective 6 (cont.) (6.12) The student communicates about mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Thursday, February 3, 2005 TAKS Math Prep. 58 6th Grade Objective 6 (cont.) (6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and non-examples; and (B) validate his/her conclusions using mathematical properties and relationships. Thursday, February 3, 2005 TAKS Math Prep. 59 7th Grade Objective 1 (7.1) The student represents and uses numbers in a variety of equivalent forms. The student is expected to: (A) compare and order integers and positive rational numbers; (B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, [or with a calculator]; and (C) represent squares and square roots using geometric models. Thursday, February 3, 2005 TAKS Math Prep. 60 7th Grade Objective 1 (cont.) (7.2) The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to: (A) represent multiplication and division situations involving fractions and decimals with [concrete] models, pictures, words, and numbers; (B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals; (C) use models to add, subtract, multiply, and divide integers and connect the actions to algorithms; (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student- teacher ratio; (E) simplify numerical expressions involving order of operations and exponents; (F) select and use appropriate operations to solve problems and justify the selections; and (G) determine the reasonableness of a solution to a problem. Thursday, February 3, 2005 TAKS Math Prep. 61 7th Grade Objective 2 (7.3) The student solves problems involving proportional relationships. The student is expected to: (A) estimate and find solutions to application problems involving percent; and (B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Thursday, February 3, 2005 TAKS Math Prep. 62 7th Grade Objective 2 (cont.) (7.4) The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling; (B) graph data to demonstrate relationships in familiar concepts, such as conversions, perimeter, area, circumference, volume, and scaling; and (C) describe the relationship between the terms in a sequence and their positions in the sequence. Thursday, February 3, 2005 TAKS Math Prep. 63 7th Grade Objective 2 (cont.) (7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to: (A) use [concrete] models to solve equations and use symbols to record the actions; and (B) formulate a possible problem situation when given a simple equation. Thursday, February 3, 2005 TAKS Math Prep. 64 7th Grade Objective 3 (7.6) The student compares and classifies shapes and solids using geometric vocabulary and properties. The student is expected to: (A) use angle measurements to classify pairs of angles as complementary or supplementary; (B) use properties to classify shapes, including triangles, quadrilaterals, pentagons, and circles; (C) use properties to classify solids, including pyramids, cones, prisms, and cylinders; and (D) use critical attributes to define similarity. Thursday, February 3, 2005 TAKS Math Prep. 65 7th Grade Objective 3 (cont.) (7.7) The student uses coordinate geometry to describe location on a plane. The student is expected to: (A) locate and name points on a coordinate plane using ordered pairs of integers; and (B) graph translations on a coordinate plane. Thursday, February 3, 2005 TAKS Math Prep. 66 7th Grade Objective 3 (cont.) (7.8) The student uses geometry to model and describe the physical world. The student is expected to: (A) sketch a solid when given the top, side, and front views; (B) make a net (two-dimensional model) of the surface area of a solid; and (C) use geometric concepts and properties to solve problems in fields such as art and architecture. Thursday, February 3, 2005 TAKS Math Prep. 67 7th Grade Objective 4 (7.9) The student solves application problems involving estimation and measurement. The student is expected to: (A) estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume. Thursday, February 3, 2005 TAKS Math Prep. 68 7th Grade Objective 5 (7.10) The student recognizes that a physical or mathematical model can be used to describe the probability of real- life events. The student is expected to (A) construct sample spaces for compound events (dependent and independent). Thursday, February 3, 2005 TAKS Math Prep. 69 7th Grade Objective 5 (cont.) (7.11) The student understands that the way a set of data is displayed influences its interpretation. The student is expected to (A) select and use an appropriate representation for presenting collected data and justify the selection; and (B) make inferences and convincing arguments based on an analysis of given or collected data. Thursday, February 3, 2005 TAKS Math Prep. 70 7th Grade Objective 5 (cont.) (7.12) The student uses measures of central tendency and range to describe a set of data. The student is expected to: (A) describe a set of data using mean, median, mode, and range; and (B) choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation. Thursday, February 3, 2005 TAKS Math Prep. 71 7th Grade Objective 6 (7.13) The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; and (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. Thursday, February 3, 2005 TAKS Math Prep. 72 7th Grade Objective 6 (cont.) (7.14) The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Thursday, February 3, 2005 TAKS Math Prep. 73 7th Grade Objective 6 (cont.) (7.15) The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships. Thursday, February 3, 2005 TAKS Math Prep. 74 8th Grade Objective 1 (8.1) The student understands that different forms of numbers are appropriate for different situations. The student is expected to: (A) compare and order rational numbers in various forms, including integers, percents, and positive and negative fractions and decimals; (B) select and use appropriate forms of rational numbers to solve real-life problems, including those involving proportional relationships; (C) approximate mentally [and with calculators] the value of irrational numbers as they arise from problem situations (π,√2); and (D) express numbers in scientific notation, including negative exponents, in appropriate problem situations [using a calculator]. Thursday, February 3, 2005 TAKS Math Prep. 75 8th Grade Objective 1 (cont.) (8.2) The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to: (A) select and use appropriate operations to solve problems and justify the selections; (B) add, subtract, multiply, and divide rational numbers in problem situations; (C) evaluate a solution for reasonableness; and (D) use multiplication by a constant factor (unit rate) to represent proportional relationships; for example, the arm span of a gibbon is about 1.4 times its height, a = 1.4h. Thursday, February 3, 2005 TAKS Math Prep. 76 8th Grade Objective 2 (8.3) The student identifies proportional relationships in problem situations and solves problems. The student is expected to: (A) compare and contrast proportional and non-proportional relationships; and (B) estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates. Thursday, February 3, 2005 TAKS Math Prep. 77 8th Grade Objective 2 (cont.) (8.4) The student makes connections among various representations of a numerical relationship. The student is expected to: (A) generate a different representation given one representation of data, such as a table, graph, equation, or verbal description. Thursday, February 3, 2005 TAKS Math Prep. 78 8th Grade Objective 2 (cont.) (8.5) The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to: (A) estimate, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and (B) use an algebraic expression to find any term in a sequence. Thursday, February 3, 2005 TAKS Math Prep. 79 8th Grade Objective 3 (8.6) The student uses transformational geometry to develop spatial sense. The student is expected to: (A) generate similar shapes using dilations including enlargements and reductions; and (B) graph dilations, reflections, and translations on a coordinate plane. Thursday, February 3, 2005 TAKS Math Prep. 80 8th Grade Objective 3 (cont.) (8.7) The student uses geometry to model and describe the physical world. The student is expected to: (A) draw solids from different perspectives; (B) use geometric concepts and properties to solve problems in fields such as art and architecture; (C) use pictures or models to demonstrate the Pythagorean Theorem; and (D) locate and name points on a coordinate plane using ordered pairs of rational numbers. Thursday, February 3, 2005 TAKS Math Prep. 81 8th Grade Objective 4 (8.8) The student uses procedures to determine measures of solids. The student is expected to: (A) find surface area of prisms and cylinders using [concrete] models and nets (two- dimensional models); and (C) estimate answers and use formulas to solve application problems involving surface area and volume. Thursday, February 3, 2005 TAKS Math Prep. 82 8th Grade Objective 4 (cont.) (8.9) The student uses indirect measurement to solve problems. The student is expected to: (A) use the Pythagorean Theorem to solve real-life problems; and (B) use proportional relationships in similar shapes to find missing measurements. Thursday, February 3, 2005 TAKS Math Prep. 83 8th Grade Objective 4 (cont.) (8.10) The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to: (A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and (B) describe the resulting effect on volume when dimensions of a solid are changed proportionally. Thursday, February 3, 2005 TAKS Math Prep. 84 8th Grade Objective 5 (8.11) The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: (A) find the probabilities of compound events (dependent and independent); and (B) use theoretical probabilities and experimental results to make predictions and decisions. Thursday, February 3, 2005 TAKS Math Prep. 85 8th Grade Objective 5 (cont.) (8.12) The student uses statistical procedures to describe data. The student is expected to: (A) select the appropriate measure of central tendency to describe a set of data for a particular purpose; (B) draw conclusions and make predictions by analyzing trends in scatterplots; and (C) construct circle graphs, bar graphs, and histograms, [with and] without technology. Thursday, February 3, 2005 TAKS Math Prep. 86 8th Grade Objective 5 (cont.) (8.13) The student evaluates predictions and conclusions based on statistical data. The student is expected to: (A) evaluate methods of sampling to determine validity of an inference made from a set of data; and (B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. Thursday, February 3, 2005 TAKS Math Prep. 87 8th Grade Objective 6 (8.14) The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; and (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. Thursday, February 3, 2005 TAKS Math Prep. 88 8th Grade Objective 6 (cont.) (8.15) The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Thursday, February 3, 2005 TAKS Math Prep. 89 8th Grade Objective 6 (cont.) (8.16) The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships. Thursday, February 3, 2005 TAKS Math Prep. 90

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