State Board Adopted 2002-2003

State Board Adopted 2002-2003 Oregon Department of Education

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 2 MATHEMATICS Calculation and Estimations CCG: NUMBERS – Understand numbers, ways of representing numbers, relationships among numbers and number systems. 4th 5th 6th

Order, model, and compare Order, model, and compare Read, WRITE, order, model, common fractions, decimals positive rational numbers and compare whole numbers to and percentages. (fractions, decimals, and one million, common fractions, percentages). and decimals to hundredths.

Identify the place value and actual value of digits in a Apply factors and multiples to number to one million. express fractions in lowest terms and identify fraction equivalents.

Understand rates and ratios as comparisons of two quantities by division.

Differentiate between rates and ratios and express both as fractions.

Solve problems by calculating rates and ratios.

Locate decimals and Locate positive rational Locate common fractions and percentages on a number line. numbers (fractions, decimals, decimals on a number line. and percentages) on a number line.

Model, recognize AND Apply equivalent forms of Model, recognize, AND GENERAGE equivalent forms fractions and decimals to solve GENERATE equivalent forms of commonly used fractions, problems. of decimals to hundredths. decimals, and percents. Determine equivalent forms of fractions, mixed numbers and improper fractions.

Identify classes of numbers Model square numbers and (e.g., primes, composites, recognize their characteristics. even, odd, multiples) in a 1-to- 100 number chart AND DESCRIBE NUMERIC PATTERNS RELATED TO THEM.

Recognize characteristics of Identify prime and composite odd, even, prime, and numbers less than 100. composite numbers.

Solve problems using concepts Determine factors of whole related to factoring and numbers to 100 using models determining divisibility (e.g., such as arrays. 2,3,5,9, and 10).

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 3 CCG: COMPUTATION AND ESTIMATION - Compute fluently and make reasonable estimates. 4th 5th 6th

Develop and evaluate strategies Develop and evaluate strategies Develop and analyze algorithms for for multiplying and dividing whole for computing decimals and computing with fractions and mixed numbers and adding and fractions. numbers. subtracting fractions with like denominators.

Apply WITH FLUENCY efficient strategies for determining multiplication and division facts 0- 9.

Multiply a three digit number by a one digit number.

Divide a three digit number by a Divide by two digit numbers. one digit number with or without remainders.

Determine the meaning of whole Determine the meaning of a Add and subtract fractions with like number remainders in a problem remainder expressed as a whole and unlike denominators. situation. number, fraction, or decimal in a problem situation involving division.

Add and subtract commonly used Add and subtract fractions and fractions with like denominators mixed numbers with common (halves, thirds, fourths, eighths, fractions found on a ruler tenths) and decimals to (2,4,8,16). hundredths.

Add and subtract decimals to Add, subtract, multiply, and divide UNDERSTAND LINEAR, AREA, hundredths, including money decimals, including money AND DISCRETE MODELS TO amounts. amounts. multiply and divide fractions.

Solve problems involving common percentages.

Mentally multiply or divide Model percentages on a hundreds Convert mentally among common multiples of 10 (e.g., 40 X 70 or grid to determine equivalent decimals, fractions and 2700/30). decimals and percentages. percentages.

Identify the most efficient operation Determine the order of operations Apply grouping symbols to simplify (add, subtract, multiply, or divide) for multiple-step calculations calculations and evaluate for solving a problem. involving addition, subtraction, expressions. multiplication and division.

Select and use an appropriate Select and use an appropriate DEVELOP AND use strategies to estimation strategy (overestimate, estimation strategy (overestimate, estimate the results of positive underestimate, range of estimates) underestimate and range of rational number computations AND based on the problem situation estimates) based on the problem JUDGE THE REASONABLENESS when computing with whole situation when computing with OF RESULTS. numbers of money amounts. decimals.

Use place value concepts such as Use referent numbers and Use referent numbers in estimating rounding to nearest 10, 100, and rounding to estimate the answers to adding and subtracting 1000 to estimate and check magnitude of calculations with fractions and mixed numbers (e.g., reasonableness of answers. decimals. 2 ¼ + 3/8 <3, since both ¼ and 3/8 are less than ½).

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 4 CCG: OPERATIONS AND PROPERTIES – Understand meanings of operations and how they relate to one another. 4th 5th 6th

Demonstrate the meaning of fractions as part of a unit whole or as parts of a collection or set Use inverse operations Use the inverse operations Use inverse operations (addition and subtraction, of addition and subtraction, (addition and subtraction, multiplications and to solve problems AND multiplications and division) to solve problems CHECK SOLUTIONS division) to solve problems AND CHECK SOLUTIONS involving adding and AND CHECK SOLUTIONS involving calculations with subtracting fractions and involving calculations with decimals. mixed numbers. whole numbers. Apply the commutative, Apply the associative, Apply the commutative, associative and identify commutative, and associative and identify properties of addition and distributive properties to properties of addition and multiplication and the simplify computations with multiplication and the distributive property to positive rational numbers. distributive property to simplify calculations with simplify calculations with decimals. whole numbers.

Statistics and Probability Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 5 CCG: STATISTICS - Select and use appropriate statistical methods to analyze data.

4th 5th 6th Find, use and interpret Determine the median for Compare two related sets measures of center and a set of data AND of data using measures of spread. UNDERSTAND WHAT center (mean, median, EACH STATISTIC DOES and mode) and spread AND DOES NOT (range). INDICATE ABOUT THE DATA.

CCG: PROBABILITY - Understand and apply basic concepts of probability.

4th 5th 6th Determine probability of a Determine experimental single event. probability of an event from a set of data.

Connect simple fractional Express probability using probabilities to events fractions, ratios, decimals, (e.g., heads is 1 out of 2; and percents. rolling a 5 on a six-sided number cube is 1/6).

Understand that the Understand that probability of an event can probability cannot be represented by a determine an individual number from 0 outcome, but can be used (impossible) to 1 (certain). to predict the frequency of an outcome.

Determine the number of possible combinations of two or more classes of objects (e.g., shirts, pants, and shoes).

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 6 CCG: COLLECT AND DISPLAY DATA - Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them. . 4th 5th 6th

Conduct experiments and Design investigations to Design experiments and simulations to determine address a question and simulations to determine experimental probability of recognize how data collection experimental probability of different outcomes. methods affect the nature of a different outcomes. set of data.

Understand basic concepts of Understand that experimental sampling (e.g., larger samples probability approaches yield better results, the need for theoretical probability as the representative samples). number of trials increases.

Recognize and understand the connections among concepts of independent outcomes, picking at random, and fairness.

REPRESENT and interpret the REPRESENT and interpret REPRESENT and interpret outcome of a probability data collected from probability data using tables, circle experiment using a frequency experiments and simulations graphs, bar graphs, and line distribution, including using tallies, charts, graphs or plots (first quadrant). determining experimental pictograms, and bar graphs, probabilities. including determining Compare different probabilities of single events. representations of the same data and evaluate how well each representation shows important aspects of the data (e.g., circle and bar graphs, histograms with different widths).

Evaluate the appropriateness of representations of categorical and numeric data (e.g., categorical: types of lunch food, and numerical: heights of students in a class).

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 7 CCG: DATA ANALYSIS AND PREDICTIONS – Develop and evaluate inferences and predictions that are based on data.

4th 5th 6th

Predict the degree of Analyze data from tables Make predictions for likelihood of a single and bar graphs using succeeding trials of a event occurring using mean, median, mode, and probability experiment words such as certain, range, and draw given the outcome of impossible, most often, conclusions. preceding repeated trials. least often, likely, and unlikely.

Predict the likelihood of Predict the outcome of a an outcome prior to an probability experiment by experiment AND computing and using COMPARE PREDICTED theoretical probability. PROBABILITY WITH THE ACTUAL RESULTS.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 8 Algebraic Relationships

CCG: PATTERNS AND FUNCTIONS - Understand patterns, relations and functions. 4th 5th 6th DESCRIBE, extend, and REPRESENT and REPRESENT, analyze make generalizations analyze patterns and and determine rules for about patterns and functions using words, finding patterns involving sequences and supply table, graphs or simple positive rational numbers missing elements in chart algebraic expressions. with tables, graphs, or table format. words, and when possible, symbolic rules.

Supply a missing element Supply a missing element in or determine a rule that in or determine a rule that extends number patterns extends number patterns involving addition or involving multiplication or subtraction of decimals. division.

CCG: ALGEBRAIC RELATIONSHIPS - Represent and analyze mathematical situations and structures using algebraic symbols. 4th 5th 6th

Select operational and Use letters, boxes, or other relational symbols to make a symbols to stand for an number sentence true (e.g., unknown quantity in 4_3 = 12, 5 + 17_25) expressions or equations.

Represent and solve open Represent the idea of a Develop an understanding of sentences or problems variable as an unknown different uses of variables involving numeric equations quantity using a letter or (e.g., as a placeholder for a or inequalities (e.g., 3+?=4; symbol. specific unknown, as 2+1>?; 4<2+?). representative of a range of values).

Represent and evaluate Represent and evaluate algebraic expressions algebraic expressions involving a single variable involving two variables (e.g., (e.g., 4s, .05n) bh/2, 2w +2I).

Translate between different Identify AND REPRESENT DESCRIBE and interpret representations (words, whole number data on a relationships using numeric, pictorial) of a coordinate graph (first information from tables and simple quantitative quadrant). graphs including coordinate relationship (e.g., match a graphs (first quadrant). table of values to its rule). Graph linear equations on a coordinate grid by making a table using whole number coordinates.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 9 CCG: MODELING - Use mathematical models to represent and understand quantitative relationships. 4th 5th 6th Model and solve contextualized problems using various representations such as graphs, tables, and equations.

Recognize and represent direct variation using tables and graphs.

Identify or DESCRIBE a Identify and sketch a situation which may be graph that models a given modeled by a given situation. graph.

CCG: CHANGE – Analyze change in various contexts. 4th 5th 6th

Identify and describe Investigate how a change situations with constant or in one variable relates to a varying rates of change change in a second and compare them. variable.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 10 Measurement CCG: UNITS AND TOOLS - Understand measurable attributes of objects and the units, systems, and processes of measurement. 4th 5th 6th

Select the most Select the most appropriate appropriate tool and US unit to measure area and customary unit to measure perimeter. length, perimeter, weight, and volume. Carry out unit conversions Carry out simple unit Using estimation, in the US customary conversions within the US convert from a system as a result of customary system (e.g., in measurement expressed calculations involving to ft, oz to lb). using one unit within a measurements of length, system to one using a perimeter, volume and comparable unit within weight (e.g., 6 ½” + 3 3/4” the other system (e.g., + 6 ½” = 16 ¾” or 1 ft 4 inches to centimeters). ¾”).

Understand that measurements are approximations and understand how differences in units and tools affect precision. Convert from a measurement expressed in one unit within a system to another using a different unit within the same system to measure perimeter and area.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 11 CCG: DIRECT AND INDIRECT MEASUREMENT - Apply appropriate techniques, tools and formulas to determine measurements.. 4th 5th 6th

Determine elapsed time requiring unit conversions (e.g., weeks to months, minutes to hours).

Read temperature Know common referents for measurements of thermometers Fahrenheit and Celsius with Fahrenheit and Celsius temperatures (e.g., freezing units and RECOGNIZE point, boiling point). REASONABLE RANGES OF TEMPERATURES FOR DIFFERENT EVENTS (e.g., COLD OR HOT DAY).

Determine measurements of Determine measurements of Determine measurements of length and perimeter to the length and perimeter to the length and perimeter to the nearest inch and nearest foot. nearest tenth centimeter nearest eighth inch (for length (millimeter) and nearest tenth less than one foot) and nearest Estimate the length of objects in meter. inch (for lengths greater than inches, feet, and yards. one foot).

Determine measurement of volume to the nearest ¼ cup, quart, or gallon of measuring cups, beakers, or graduated cylinders.

Estimate the volume of objects in cups, quarts, and gallons.

Determine measurements of weight to the nearest ounce and pound.

Estimate the weight of objects in ounces and pounds. Estimate the measure of Estimate the measures of angles acute, right and obtuse greater than 180 degrees. angles in degrees using referent angles of 45 and 90 degrees and determine the measurement of angles between 0 and 180 degrees to the nearest degree. DEVELOP and use formulas for Relate the area of a rectangle DEVELOP and use formulas finding perimeter and area of and its dimensions to area for determining the perimeter polygons. models for multiplication and and area of rectangles, and division. related triangles and parallelograms. Calculate the area and Determine perimeter and area Develop strategies to circumference of a circle using pi of rectangles given lengths of measure the perimeter of as well as common sides. simple polygons and approximations of pi (e.g., 3.14, everyday objects. 22/7).

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 12 Develop strategies for determining approximate perimeter and area of irregular shapes.

Determine the area of a complex Analyze the effects on area figure representative of a and perimeter by combining problem situation composed of a two simple geometric figures combination of two or more (e.g., two right triangles and a geometric figures (e.g., attach a rectangle). triangle to a parallelogram).

Compare and contrast the formulas for area of rectangles, related triangles, and parallelograms. Recognize that two-dimensional shapes having the same perimeter may have different areas and that shapes having the same area may have different perimeters.

Analyze how changes in area of a figure affect the dimensions of the figure.

Estimate and measure the area Estimate and measure of a rectangular surface using volume of a rectangular solid unit squares. using unit cubes. Use referents to make estimates Use referents for US customary Use referents for metric of area AND EVALUATE THE measurements to make measurements to make REASONABLENESS OF THE estimates of length, weight, and estimates of length, weight, ESTIMATE (e.g., ESTIMATE volume AND EVALUATE THE and volume AND EVALUATE AREA OF CLASSROOM BY REASONABLENESS OF THE THE REASONABLENESS MEASURING AREA OF ONE ESTIMATE (e.g., LENGTH OF OF THE ESTIMATE (e.g., FLOOR TILE). ONE FLOOR TILE AND HEIGHT OF TEACHER ESTIMATE LENGTH OF ESTIMATED IN HEIGHT OF Calculate rates (e.g., miles per CLASSROOM). STUDENT LENGTHS). hour, miles per gallon, people per square mile) to solve problems.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 13 Geometry CCG: PROPERTIES AND RELATIONSHIPS - Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. 4th 5th 6th Identify, DESCRIBE, Identify, DESCRIBE, Identify, DESCRIBE, compare and classify compare and classify compare and classify quadrilaterals by their triangles by their sides polygons by their sides and sides and angles. and angles. angles.

Identify right, acute, and Identify and represent the obtuse angles in isolation radius, center, diameter, and in geometric figures. chord and circumference of circle.

Identify combinations of angles that are complementary or supplementary and determine their measures.

Use properties of Use properties of Use properties of polygons quadrilaterals to determine triangles to determine to determine the lengths of the lengths of their sides the lengths of their sides sides and perimeters. and perimeters. and perimeters.

DEVELOP, DEVELOP, DEVELOP, UNDERSTAND, and apply UNDERSTAND, and UNDERSTAND, and apply the property of the sum of apply the property of the the property of the sum of the angle measures in a sum of the angle the measures of the interior quadrilateral is 360 measures in a triangle is angles in a polygon as well degrees. 180 degrees. as the sum of the exterior angles.

Identify congruent Find and use congruent quadrilaterals using polygons which will cover a concrete methods. surface without overlapping (tessellation). Draw conclusions about Draw conclusions about the measures of the measures of corresponding sides and corresponding sides and angles of two congruent angles of two congruent quadrilaterals. and similar triangles.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 14 CCG: MODELING - Use visualization, spatial reasoning and geometric modeling to solve problems. 4th 5th 6th

Model, sketch, draw, and Accurately draw and label Model, sketch, draw and label points, lines, line triangles, angles, and line label polygons, circles segments, angles, rays, segments using (including the center, radius quadrilaterals, and parallel, measurement tools. and diameter), perpendicular, and complementary angles, intersecting lines. supplementary angles, vertical angles, and adjacent angles.

Identify AND DESCRIBE the intersection of two or more geometric figures in the place (e.g., the intersection Build three-dimensional Identify AND BUILD three- of a circle and a line). objects and sketch two- dimensional objects from dimensional representations two-dimensional of the object. representations.

CCG: COORDINATE GEOMETRY - Specify locations and describe spatial relationships using coordinate geometry and other representational systems. 4th 5th 6th

Locate coordinates of points MAKE and use coordinate Plot polygons on coordinate on graph paper, maps, systems to specify location graphs (first quadrant). globes and other charts. and describe paths.

Determine the shortest path Find the distance between Determine lengths and of horizontal and vertical points along the horizontal areas of simple polygons movement between two and vertical lines of a from coordinate graphs. locations grid. coordinate system.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 15 CCG: TRANSFORMATIONS AND SYMMETRY - Apply transformations and use symmetry to analyze mathematical situations. 4th 5th 6th

Identify AND DESCRIBE line and rotational symmetry in two- dimensional shapes and designs. Build or sketch a shape that has a given number of lines of symmetry, or rotational symmetries (e.g., sketch a simple polygon with a given number of lines of symmetry).

Predict AND DESCRIBE the results of performing reflections, rotations and translations of quadrilaterals.

Identify AND DESCRIBE Identify AND DESCRIBE a a motion or series of motion or series of motions that will show motions that will show two two quadrilaterals are quadrilaterals are congruent. congruent.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 16 Mathematical Problem Solving CCG: CONCEPTUAL UNDERSTANDING - Select, apply and translate among mathematical representations to solve problems. 4th 5th 6th Interpret the concepts of Interpret the concepts of a Interpret the concepts of a a problem-solving task problem-solving task and problem-solving task and and translate them into translate them into translate them into mathematics. mathematics. mathematics. CCG: PROCESSES AND STRATEGIES – Apply and adapt a variety of appropriate strategies to solve problems. 4th 5th 6th Choose strategies that Choose strategies that can Choose strategies that can can work and then carry work and then carry out work and then carry out out the strategies the strategies chosen. the strategies chosen. chosen.

CCG: VERIFICATION – Monitor and reflect on the process of mathematical problem solving.

4th 5th 6th Produce identifiable Produce identifiable Produce identifiable evidence of a second evidence of a second look evidence of a second look look at the concepts/ at the concepts/strategies/ at the concepts/strategies/ strategies/calculations to calculations to defend the calculations to defend the defend a solution. solution. solution.

CCG: COMMUNICATION – Communicate mathematical thinking coherently and clearly. Use the language of mathematics to express mathematical ideas precisely. 4th 5th 6th Use pictures, symbols Use pictures, symbols Use pictures, symbols and/or vocabulary to and/or vocabulary to and/or vocabulary to convey the path to the convey the path to the convey the path to the identified solution. identified solution. identified solution.

CCG: ACCURACY – Accurately solve problems that arise in mathematics and other contests. 4th 5th 6th Accurately solve Accurately solve problems Accurately solve problems problems using using mathematics. using mathematics. mathematics.

Indicates content may appear on Oregon State Assessment. (CAPS = only classroom assessment) 17