Extensions in Mathematics Series

Transcription

1 CURRICULUM ASSOCIATES, Inc.

2 Grade 1 Mathematical Processes Standard 1-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book A Apply substantive mathematical problem-solving strategies. Featured throughout each Generate conjectures and exchange mathematical ideas. Featured in Extend Your Learning Explain and justify answers to simple problems. Featured throughout each Analyze patterns by reasoning systematically. Featured throughout each Generalize mathematical concepts. Featured throughout each Use a variety of forms of mathematical communication. Featured in Extend Your Learning Generalize connections among mathematics, the environment, and other subjects. Featured in Extend Your Learning Use multiple informal representations to convey mathematical ideas. Featured in Extend Your Learning Number and Operations Standard 1-2: The student will demonstrate through the mathematical processes a sense of quantity and numeral relationships; the relationships among addition, subtraction, and related basic facts; and the connections among numeric, oral, and written-word forms of whole numbers Recall basic addition facts through and corresponding subtraction facts. Applying Addition Generate strategies to add and subtract without regrouping through two-digit Applying Addition numbers Analyze the magnitude of digits through 999 on the basis of their place values. Building Number Sense 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

3 Algebra Standard 1-3: The student will demonstrate through the mathematical processes a sense of numeric patterns, the relationship between addition and subtraction, and change over time. Strategies Book A Applying Addition Analyze numeric patterns in addition and subtraction to develop strategies for acquiring basic facts Translate patterns into rules for simple addition and subtraction. Applying Addition Analyze numeric relationships to complete and extend simple patterns. Applying Addition Converting Time and Money Classify a number as odd or even. Building Number Sense Geometry Standard 1-4: The student will demonstrate through the mathematical processes a sense of two- and three-dimensional geometric shapes, symmetry, and relative positions and directions in space Analyze the two-dimensional shapes circle, square, triangle, and rectangle. Using Geometry Measurement Standard 1-5: The student will demonstrate through the mathematical processes a sense of the value of combinations of coins and the measurement of length, weight, time, and temperature Use a counting procedure to determine the value of a collection of pennies, nickels, Converting Time and Money dimes, and quarters totaling less than a dollar Represent a nickel, a dime, a quarter, a half-dollar, and a dollar in coins. Converting Time and Money Represent money by using the cent and dollar notations. Converting Time and Money Use analog and digital clocks to tell and record time to the half hour. Converting Time and Money Data Analysis and Probability Standard 1-6: The student will demonstrate through the mathematical processes a sense of collecting, organizing, and interpreting data and of making predictions on the basis of data Organize data in picture graphs, object graphs, bar graphs, and tables. Reading Math Pictures Interpret data in picture graphs, object graphs, bar graphs, and tables by using the Reading Math Pictures comparative terms more, less, greater, fewer, greater than, and less than. 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

4 Grade 2 Mathematical Processes Standard 2-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book B Apply substantive mathematical problem-solving strategies. Featured throughout each Generate conjectures and exchange mathematical ideas. Featured in Extend Your Learning Explain and justify answers to simple problems. Featured throughout each Analyze patterns by reasoning systematically. Featured throughout each Generalize mathematical concepts. Featured throughout each Use a variety of forms of mathematical communication. Featured in Extend Your Learning Generalize connections among mathematics, the environment, and other subjects. Featured in Extend Your Learning Use multiple informal representations to convey mathematical ideas. Featured in Extend Your Learning Number and Operations Standard 2-2: The student will demonstrate through the mathematical processes an understanding of the base-ten numeration system; place values; and accurate, efficient, and generalizable methods of adding and subtracting whole numbers Generate estimation strategies to determine the approximate number of objects in a Using Estimation set of no more than 1,000 objects Interpret models of equal grouping (multiplication) as repeated addition and arrays. Applying Multiplication Interpret models of sharing equally (division) in as repeated subtraction and arrays. Applying Division Generate strategies to add and subtract pairs of two-digit whole numbers with Applying Addition regrouping Generate addition and subtraction strategies to find missing addends and Applying Addition subtrahends in number combinations through Generate strategies to round numbers through 90 to the nearest 10. Using Estimation Analyze the magnitude of digits through 9,999 on the basis of their place values. Building Number Sense Applying Addition 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

5 Algebra Standard 2-3: The student will demonstrate through the mathematical processes an understanding of numeric patterns and quantitative and qualitative change. Strategies Book B Analyze numeric patterns in skip counting that uses the numerals 1 through 10. Applying Multiplication Using Algebra Analyze relationships to complete and extend growing and repeating patterns Using Algebra involving numbers, symbols, and objects Identify quantitative and qualitative change over time. Using Algebra Analyze quantitative and qualitative change over time. Using Algebra Geometry Standard 2-4: The student will demonstrate through the mathematical processes an understanding of basic spatial reasoning and the connection between the identification of basic attributes and the classification of three-dimensional shapes Identify multiple lines of symmetry. Using Geometry Predict the results of combining and subdividing polygons and circles. Using Geometry Measurement Standard 2-5: The student will demonstrate through the mathematical processes an understanding of the value of combinations of coins and bills and the measurement of length, weight, time, and temperature Use a counting procedure to determine the value of a collection of coins and bills. Converting Time and Money Use appropriate tools to measure objects to the nearest whole unit: measuring length Converting Customary and Metric in centimeters, feet, and yards; measuring liquid volume in cups, quarts, and gallons Predict whether the measurement will be greater or smaller when different units are Converting Customary and Metric used to measure the same object Use analog and digital clocks to tell and record time. Converting Time and Money Match a.m. and p.m. to familiar situations. Converting Time and Money Recall equivalencies associated with length and time: 12 inches = 1 foot, 3 feet = 1 Converting Customary and Metric yard, 60 minutes = 1 hour, and 24 hours = 1 day. Data Analysis and Probability Standard 2-6: The student will demonstrate through the mathematical processes an understanding of creating questions to collect data, organizing data, describing trends of a data set, and making predictions based on data Organize data in charts, pictographs, and tables. Interpreting Graphs and Charts Predict on the basis of data whether events are more likely or less likely to occur. Determining Probability and 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

6 Grade 3 Mathematical Processes Standard 3-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book C Analyze information to solve increasingly more sophisticated problems. Featured throughout each Construct arguments that lead to conclusions about general mathematical properties Featured throughout each and relationships Explain and justify answers on the basis of mathematical properties, structures, and Featured throughout each relationships Generate descriptions and mathematical statements about relationships between and Featured throughout each among classes of objects Use correct, complete, and clearly written and oral mathematical language to pose Featured in Extend Your Learning questions, communicate ideas, and extend problem situations Generalize connections between new mathematical ideas and related concepts and Featured in Extend Your Learning subjects that have been previously considered Use flexibility in mathematical representations. Featured in Extend Your Learning Recognize the limitations of various forms of mathematical representations. Featured in Extend Your Learning 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

7 Number and Operations Standard 3-2: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts. Strategies Book C Apply an algorithm to add and subtract whole numbers fluently. Applying Addition Apply procedures to round any whole number to the nearest 10, 100, or 1,000. Using Estimation Understand fractions as parts of a whole. Building Number Sense Represent fractions that are greater than or equal to 1. Converting Customary and Metric Recall basic multiplication facts through 12 x 12 and the corresponding division facts. Applying Multiplication Applying Division Compare the inverse relationship between multiplication and division. Applying Division Analyze the effect that adding, subtracting, or multiplying odd and/or even numbers Using Estimation has on the outcome Generate strategies to multiply whole numbers by using one single-digit factor and Applying Multiplication one multi-digit factor Use basic number combinations to compute related multiplication problems that Applying Multiplication involve multiples of Analyze the magnitude of digits through 999,999 on the basis of their place value. Building Number Sense Using Estimation Applying Addition Algebra Standard 3-3: The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time Create numeric patterns that involve whole-number operations. Using Algebra Apply procedures to find missing numbers in numeric patterns that involve wholenumber Using Algebra operations Use symbols to represent an unknown quantity in a simple addition, subtraction, or Using Algebra multiplication equation. 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

8 Measurement Standard 3-5: The student will demonstrate through the mathematical processes an understanding of length, time, weight, and liquid volume measurements; the relationships between systems of measure; accurate, efficient, and generalizable methods of determining the perimeters of polygons; and the values and combinations of coins required to make change. Strategies Book C Use the fewest possible number of coins when making change. Converting Time and Money Use appropriate tools to measure objects to the nearest unit: measuring length in Converting Customary and Metric meters and half inches; measuring liquid volume in fluid ounces, pints, and liters; and measuring mass in grams Recognize the relationship between meters and yards, kilometers and miles, liters and Converting Customary and Metric quarts, and kilograms and pounds Use analog and digital clocks to tell time to the nearest minute. Converting Time and Money Recall equivalencies associated with time and length: 60 seconds = 1 minute and 36 Converting Time and Money inches = 1 yard. Data Analysis and Probability Standard 3-6: The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability Organize data in tables, bar graphs, and dot plots. Interpreting Graphs and Charts Interpret data in tables, bar graphs, pictographs, and dot plots. Interpreting Graphs and Charts Analyze dot plots and bar graphs to make predictions about populations. Interpreting Graphs and Charts Predict on the basis of data whether events are likely, unlikely, certain, or impossible to occur. Determining Probability and 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

9 Grade 4 Mathematical Processes Standard 4-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book D Analyze information to solve increasingly more sophisticated problems. Featured throughout each Construct arguments that lead to conclusions about general mathematical properties Featured in Extend Your Learning and relationships Explain and justify answers to problems on the basis of mathematical properties, Featured throughout each structures, and relationships on mathematical properties, structures, and relationships Generate descriptions and mathematical statements about relationships between and Featured throughout each among classes of objects Use correct, complete, and clearly written and oral mathematical language to pose Featured throughout each questions, communicate ideas, and extend problem situations Generalize connections between new mathematical ideas and related concepts and Featured in Extend Your Learning subjects that have been previously considered Use flexibility in mathematical representations. Featured in Extend Your Learning Recognize the limitations of various forms of mathematical representations. Featured in Extend Your Learning 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

10 Number and Operations Standard 4-2: The student will demonstrate through the mathematical processes an understanding of decimal notation as an extension of the place-value system; the relationship between fractions and decimals; the multiplication of whole numbers; and accurate, efficient, and generalizable methods of dividing whole numbers, adding decimals, and subtracting decimals. Strategies Book D Recognize the period in the place-value structure of whole numbers: units, thousands, Building Number Sense millions, and billions Apply an algorithm to multiply whole numbers fluently. Applying Multiplication Generate strategies to divide whole numbers by single-digit divisors. Applying Division Analyze the magnitude of digits through hundredths on the basis of their place value. Building Number Sense Apply strategies and procedures to find equivalent forms of fractions. Building Number Sense 1 Building Number Sense Compare the relative size of fractions to the benchmarks 0,, and Identify common the fraction/decimal equivalents 2 1 =.5, 4 1 =.25, 4 3 =.75, 3 1!.33, 2 1 1!.67, multiples of, and multiples of Building Number Sense Using Estimation Represent improper fractions, mixed numbers, and decimals. Building Number Sense Using Estimation Generate strategies to add and subtract decimals through hundredths. Algebra Standard 4-3: The student will demonstrate through the mathematical processes an understanding of numeric and nonnumeric patterns, the representation of simple mathematical relationships, and the application of procedures to find the value of an unknown Analyze numeric, nonnumeric, and repeating patterns involving all operations and Using Algebra decimal patterns through hundredths Generalize a rule for numeric, nonnumeric, and repeating patterns involving all Using Algebra operations Use a rule to complete a sequence or a table. Using Algebra Translate among, letters, symbols, and words to represent quantities in simple Using Algebra mathematical expressions or equations Apply procedures to find the value of an unknown letter or symbol in a whole-number Using Algebra equation. 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

11 Geometry Standard 4-4: The student will demonstrate through the mathematical processes an understanding of the relationship between two- and three-dimensional shapes, the use of transformations to determine congruency, and the representation of location and movement within the first quadrant of a coordinate system Predict the results of multiple transformations of the same type translation, reflection, or rotation on a two-dimensional geometric shape. Strategies Book D Using Geometry Measurement Standard 4-5: The student will demonstrate through the mathematical processes an understanding of elapsed time; conversions within the U.S. Customary System; and accurate, efficient, and generalizable methods of determining area Use equivalencies to convert units of measure within the U.S. Customary System: converting length in inches, feet, yards, and miles; converting weight in ounces, pounds, and tons; converting liquid volume in cups, pints, quarts, and gallons; and converting time in years, months, weeks, days, hours, minutes, and seconds. Converting Customary and Metric Analyze the perimeter of a polygon. Using Geometry Generate strategies to determine the area of rectangles and triangles. Using Geometry Apply strategies and procedures to determine the amount of elapsed time in hours Converting Time and Money and minutes within a 12-hour period, either a.m. or p.m Recall equivalencies associated with liquid volume, time, weight, and length. Converting Customary and Metric Converting Time and Money Data Analysis and Probability Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event Interpret data in tables, line graphs, bar graphs, and double bar graphs whose scale Interpreting Graphs and Charts increments are greater than or equal to Organize data in tables, line graphs, and bar graphs whose scale increments are Interpreting Graphs and Charts greater than or equal to Predict on the basis of data whether events are likely, unlikely, certain, impossible, or Determining Probability and equally likely to occur Analyze possible outcomes for a simple event. Determining Probability and Grade 5 Mathematical Processes 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

12 Standard 5-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book E Analyze information to solve increasingly more sophisticated problems. Featured throughout each Construct arguments that lead to conclusions about general mathematical properties Featured in Extend Your Learning and relationships Explain and justify answers based on mathematical properties, structures, and Featured throughout each relationships Generate descriptions and mathematical statements about relationships between and Featured throughout each among classes of objects Use correct, clear, and complete oral and written mathematical language to pose Featured throughout each questions, communicate ideas, and extend problem situations Generalize connections between new mathematical ideas and related concepts and Featured in Extend Your Learning subjects that have been previously considered Use flexibility in mathematical representations. Featured in Extend Your Learning Recognize the limitations of various forms of mathematical representations. Featured in Extend Your Learning Number and Operations Standard 5-2: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions Apply an algorithm to divide whole numbers fluently. Applying Division Understand the relationship among the divisor, dividend, and quotient. Applying Division Generate strategies to find the greatest common factor and the least common multiple of two whole numbers. Building Number Sense Applying Addition Generate strategies to add and subtract fractions with like and unlike denominators. Applying Addition 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

13 Algebra Standard 5-3: The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts. Strategies Book E Represent numeric, algebraic, and geometric patterns in words, symbols, algebraic Using Algebra expressions, and algebraic equations Analyze situations that show change over time. Interpreting Graphs and Charts Geometry Standard 5-4: The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among the properties of quadrilaterals Apply the relationships of quadrilaterals to make logical arguments about their Using Geometry properties Compare the angles, side lengths, and perimeters of congruent shapes. Using Geometry Measurement Standard 5-5: The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements Use appropriate tools and units to measure objects to the precision of one-eighth inch. Converting Customary and Metric Use a protractor to measure angles from 0 to 180 degrees. Using Geometry Use equivalencies to convert units of measure within the metric system: converting length in millimeters, centimeters, meters, and kilometers; converting liquid volume in milliliters, centiliters, liters, and kiloliters; and converting mass in milligrams, centigrams, grams, and kilograms. Converting Customary and Metric Apply procedures to determine the amount of elapsed time in hours, minutes, and Converting Time and Money seconds within a 24-hour period Recall equivalencies associated with length, liquid volume, and mass. Converting Customary and Metric 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

14 Data Analysis and Probability Standard 5-6: The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability. Strategies Book E Determining Probability and Apply procedures to calculate the measures of central tendency (mean, median, and mode) Interpret the meaning and application of the measures of central tendency. Determining Probability and Represent the probability of a single-stage event in words and fractions. Determining Probability and Conclude why the sum of the probabilities of the outcomes of an experiment must equal 1. Determining Probability and 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

15 Grade 6 Mathematical Processes Standard 6-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book F Featured throughout each Generate and solve complex abstract problems that involve modeling physical, social, and/or mathematical phenomena Evaluate conjectures and pose follow-up questions to prove or disprove conjectures. Featured in Extend Your Learning Use inductive and deductive reasoning to formulate mathematical arguments. Featured throughout each Understand equivalent symbolic expressions as distinct symbolic forms that represent Featured throughout each the same relationship Generalize mathematical statements based on inductive and deductive reasoning. Featured throughout each Use correct and clearly written or spoken words, variables, and notations to Featured in Extend Your Learning communicate about significant mathematical tasks Generalize connections among a variety of representational forms and real-world Featured in Extend Your Learning situations Use standard and nonstandard representations to convey and support mathematical Featured in Extend Your Learning relationships. Number and Operations Standard 6-2: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers Understand whole-number percentages through 100. Using Estimation Understand integers. Applying Addition Compare rational numbers and whole-number percentages through 100 by using the Building Number Sense symbols,, <, >, and = Generate strategies to multiply and divide fractions and decimals. Applying Multiplication Applying Division Represent whole numbers in exponential form. Applying Multiplication 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

16 Algebra Standard 6-3: The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities Apply order of operations to simplify whole-number expressions. Using Algebra Represent algebraic relationships with variables in expressions, simple equations, and Using Algebra simple inequalities Use inverse operations to solve one-step equations that have whole-number solutions Using Algebra and variables with whole-number coefficients. Strategies Book F Geometry Standard 6-4: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry Apply strategies and procedures to find the coordinates of the missing vertex of a Using Geometry square, rectangle, or right triangle when given the coordinates of the polygon s other vertices Compare the angles, side lengths, and perimeters of similar shapes. Using Geometry Measurement Standard 6-5: The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance Explain the relationships among the circumference, diameter, and radius of a circle. Using Geometry 22 Using Geometry Apply strategies and formulas with an approximation of pi (3.14, or ) to find the circumference and area of a circle Use proportions to determine unit rates. Using Geometry 7 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

17 Data Analysis and Probability Standard 6-6: The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample. Strategies Book F Analyze which measure of central tendency (mean, median, or mode) is the most Determining Probability and appropriate for a given purpose Use theoretical probability to determine the sample space and probability for one- and Determining Probability and two-stage events such as tree diagrams, models, lists, charts, and pictures Apply procedures to calculate the probability of complementary events. Determining Probability and 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

18 Grade 7 Mathematical Processes Standard 7-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book G Featured throughout each Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena Evaluate conjectures and pose follow-up questions to prove or disprove conjectures. Featured in Extend Your Learning Use inductive and deductive reasoning to formulate mathematical arguments. Featured throughout each Understand equivalent symbolic expressions as distinct symbolic forms that represent Featured throughout each the same relationship Generalize mathematical statements based on inductive and deductive reasoning. Featured throughout each Use correct and clearly written or spoken words, variables, and notation to Featured in Extend Your Learning communicate about significant mathematical tasks Generalize connections among a variety of representational forms and real-world Featured in Extend Your Learning situations Use standard and nonstandard representations to convey and support mathematical Featured in Extend Your Learning relationships. 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

19 Number and Operations Standard 7-2: The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems; accurate, efficient, and generalizable methods for operations with integers; the multiplication and division of fractions and decimals; and the inverse relationship between squaring and finding the square roots of perfect squares. Strategies Book G Understand fractional percentages and percentages greater than one hundred. Applying Division Apply ratios, rates, and proportions to discounts, taxes, tips, interest, unit costs, and Converting Time and Money similar shapes Translate between standard form and exponential form. Building Number Sense Translate between standard form and scientific notation. Building Number Sense Generate strategies to add, subtract, multiply, and divide integers. Applying Addition Applying Multiplication Applying Division Apply an algorithm to multiply and divide fractions and decimals. Applying Multiplication Applying Division Algebra Standard 7-3: The student will demonstrate through the mathematical processes an understanding of proportional relationships Analyze geometric patterns and pattern relationships. Using Algebra Use inverse operations to solve two-step equations and two-step inequalities. Using Algebra Represent proportional relationships with graphs, tables, and equations. Using Algebra Geometry Standard 7-4: The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments Explain the results of the intersection of two or more geometric shapes in a plane. Using Geometry 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

20 Measurement Standard 7-5: The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary System and the metric system. Strategies Book G Use ratio and proportion to solve problems involving scale factors and rates. Using Algebra Apply strategies and formulas to determine the surface area and volume of the threedimensional Using Geometry shapes prism, pyramid, and cylinder Recall equivalencies associated with length, mass and weight, and liquid volume. Converting Customary and Metric Use one-step unit analysis to convert between and within the U.S. Customary System Converting Customary and Metric and the metric system. Data Analysis and Probability Standard 7-6: The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples Organize data in box plots or circle graphs as appropriate. Interpreting Graphs and Charts Apply procedures to calculate the probability of mutually exclusive simple or compound events. Determining Probability and 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

21 Grade 8 Mathematical Processes Standard 8-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Strategies Book H Featured throughout each Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena Evaluate conjectures and pose follow-up questions to prove or disprove conjectures. Featured in Extend Your Learning Use inductive and deductive reasoning to formulate mathematical arguments. Featured throughout each Understand equivalent symbolic expressions as distinct symbolic forms that represent Featured throughout each the same relationship Generalize mathematical statements based on inductive and deductive reasoning. Featured throughout each Use correct and clearly written or spoken words, variables, and notations to Featured in Extend Your Learning communicate about significant mathematical tasks Generalize connections among a variety of representational forms and real-world Featured in Extend Your Learning situations Use standard and nonstandard representations to convey and support mathematical Featured in Extend Your Learning relationships. Number and Operations Standard 8-2: The student will demonstrate through the mathematical processes an understanding of operations with integers, the effects of multiplying and dividing with rational numbers, the comparative magnitude of rational and irrational numbers, the approximation of cube and square roots, and the application of proportional reasoning Apply an algorithm to add, subtract, multiply, and divide integers. Applying Addition Applying Multiplication Applying Division Understand the effect of multiplying and dividing a rational number by another rational Applying Multiplication number. Applying Division Apply strategies and procedures to approximate between two whole numbers the Using Estimation square roots or cube roots of numbers less than 1, Apply ratios, rates, and proportions. Interpreting Graphs and Charts 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

22 Algebra Standard 8-3: The student will demonstrate through the mathematical processes an understanding of equations, inequalities, and linear functions. Strategies Book H Translate among verbal, graphic, tabular, and algebraic representations of linear Using Algebra functions Represent algebraic relationships with equations and inequalities. Using Algebra Apply procedures to solve multi-step equations. Using Algebra Geometry Standard 8-4: The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation in a coordinate plane Apply the Pythagorean theorem. Using Geometry Use ordered pairs, equations, intercepts, and intersections to locate points and lines Using Geometry in a coordinate plane. Measurement Standard 8-5: The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system Apply strategies and formulas to determine the volume of the three-dimensional Converting Customary and Metric shapes cone and sphere Apply formulas to determine the perimeters and areas of trapezoids. Using Geometry Use multi-step unit analysis to convert between and within U.S. Customary System and the metric system. Converting Customary and Metric 8/10/07 CURRICULUM ASSOCIATES, Inc Fax

23 Data Analysis and Probability Standard 8-6: The student will demonstrate through the mathematical processes an understanding of the relationships between two variables within one population or sample. Strategies Book H Generalize the relationship between two sets of data by using scatterplots and lines of Interpreting Graphs and Charts best fit Organize data in matrices or scatterplots as appropriate. Interpreting Graphs and Charts Use theoretical and experimental probability to make inferences and convincing Determining Probability and arguments about an event or events Apply procedures to calculate the probability of two dependent events. Determining Probability and Interpret the probability for two dependent events. Determining Probability and Apply procedures to compute the odds of a given event. Determining Probability and Interpret graphic and tabular data representations by using range and the measures of central tendency (mean, median, and mode). Determining Probability and 8/10/07 CURRICULUM ASSOCIATES, Inc Fax