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Next Page Grade 6 Press for Link to NS Item Specs Grade 6 Press for Link to Press for Link to Press for Link to Grade 5 Grade 4 Grade 7 6 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Next Page Content Strand 1: Number Sense NS NS01 (Number and Number Theory) – 1.1.1 Understand the concept of integers as the set of natural numbers (1, 2, 3 …), their opposites (-1, -2, -3 …), and 0. – 1.1.2 Understand the relative values of integers and non-negative rational numbers. – 1.1.3 Apply properties of addition and multiplication to non-negative rational numbers. NS02 (Ratio and Proportion) – 1.1.4 Understand the concepts of ratio and percent. NS03 (Conceptual Understanding of Operations) – 1.1.5 Understand the meaning of multiplication and division on non-negative rational numbers. NS04 (Computation) – 1.1.6 Apply computational procedures with fluency for addition and subtraction on non- negative rational numbers. NS05 (Estimation) – 1.1.8 Apply estimation strategies to predict or determine the reasonableness of answers in situations involving addition and subtraction on non-negative rational numbers. 6 NS NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Content Strand 1: Number Sense Next Page NS NS01 (Number and Numeration) Demonstrate understanding of the concepts and symbolic representations of mixed numbers, proper and improper fractions, decimals, and integers as the set of natural numbers (1, 2, 3 …), their opposites (-1, -2, -3 …), and 0.; demonstrate understanding of the relative values of integers, non-negative fractions, decimals, and percents; use properties of addition and multiplication with non negative rational numbers; demonstrate understanding of the concept of divisibility including prime and composite numbers, factors and multiples.(1.1.1, 1.1.2, 1.1.3) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 NS01 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Stimulus, Stem, and Prompt Rules: Next Page NS • Stimulus may include integers, non-negative fractions, decimals, and percents presented in symbols, number lines, geometric representations, and pictorial models and/or real-world objects. • Stimulus may include illustrations of thousands blocks, hundreds blocks, tens blocks, and ones blocks, sticks, number lines, and other pictorial models for whole numbers, fractions, or decimals. • Stimulus may include numbers from the hundred millions place to the thousandths place. • Stimulus may include fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 25, 50, and/or 100. • Items will not require students to name, identify by name, or define properties. 6 NS01 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Mathematical Vocabulary and Terms: Next Page NS • Terms that may be used: =, ≠, <, >, ≤, or ≥, decimal, denominator, divisible, factor, fraction, greatest common factor, least common multiple, lowest terms, multiple, number line, numerator, percent, place value, prime, property • Terms that may be used with definitions or examples: compare (tell how they are alike and/or how they are different), evaluate, quotient, simplify • Terms that will not be used: associative, commutative, composite, identity, integer, rational number, reduce, relative value, zero property 6 NS01 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Item Characteristics: Next Page • Items may ask students to explain and/or illustrate the meaning of integer and NS integer values. • Items may ask students to explain when a fraction, decimal, or percent of one whole is not the same as the same fraction, decimal, or percent of another whole. • Items may ask students to convert between fractions, improper fractions, mixed numbers, and/or decimals. • Items may ask students to compare and/or order integers and non-negative proper and improper fractions, mixed numbers, percents, and decimals on a number line, with illustrations, or symbolically. • Items may ask students to explain why one integer, fraction, decimal, or percent is greater than, equal to, or less than another integer, fraction, decimal, or percent. • Items may ask students to identify, use, or illustrate the application of the following addition and multiplication properties with non-negative rational numbers: Properties of Addition Properties of Multiplication Commutative Property Commutative Property Associative Property Associative Property Identity Property Identity Property Zero Property 6 NS01 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 • Items may ask students to use addition and multiplication Next Page properties to assist in computation; NS e.g., 5 x 7 x 6 = 5 x 6 x 7 which is 30 x 7 or 210. • Items may ask students to identify or find numbers that are divisible by a given number and/or determine whether one number is divisible by another number. • Items may ask students to demonstrate understanding of divisibility rules for the factors of 2, 3, 5, 9, and 10 and/or use rules of divisibility to show if a quotient is an integer. • Items may ask students to identify or find prime or composite numbers or explain why a number is prime or composite. • Items may ask students to determine whether one number is a multiple of another number or identify the least common multiple of two numbers. • Items may ask students to identify or list factors or factor pairs for a given number or determine the greatest common factor of two numbers. 6 NS01 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Next Page NS Content Strand 1: Number Sense NS02 (Ratio and Proportion) Demonstrate understanding of the concepts of ratio and percent (1.1.4) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 NS02 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Stimulus, Stem, and Prompt Rules: Next Page NS • Stimulus may include numbers, tables, charts, and diagrams. • Stimulus may include whole numbers, ratios, and/or percents. 6 NS02 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Mathematical Vocabulary and Terms: Next Page NS • Terms that may be used: percent, ratio, scale • Terms that may be used with definitions or examples: • Terms that will not be used: rational number 6 NS02 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Item Characteristics: • Items may ask students to identify or write ratios in part/part and Next Page part/whole relationships using objects, pictures, and symbols NS • Items may ask students to create a ratio equivalent to a given ratio to determine an unknown value for a dimension or a number of events or objects. • Items may ask students to identify, demonstrate, or explain percent as 100 equal sized parts of a set. • Items may ask students to represent equivalent percentages using different objects, pictures, and/or symbols. • Items may ask students to identify or illustrate the use of percent. • Items may ask students to identify or represent equivalent ratios and/or percents. • Items may ask students to identify or determine a ratio or percent in a given situation. • Items may ask students to explain or show the meaning of a ratio or percent. • Items may ask students to give examples of ratio and/or percents in a situation. • Items may ask students to identify or determine fraction, decimal, or percent equivalents for common percents such as 90%, 75%, 66% 50%, 33%, 25%, and 10%. 6 NS02 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Next Page Content Strand 1: Number Sense NS NS03 (Conceptual Understanding of Operations) Demonstrate understanding of the meaning of addition, subtraction, multiplication, and division of non-negative decimals and fractions (1.1.5) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 NS03 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Stimulus, Stem, and Prompt Rules: Next Page NS • Stimulus may include words, numbers, mathematical expressions, symbols, illustrations, charts, graphs, or diagrams. • Fractions may include denominators of 2, 4, 8 or 2, 3, 6 or 2, 5, 10. • Decimals may include tenths, 0.25, 0.50, and 0.75. 6 NS03 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Vocabulary/Mathematical Terms: Next Page NS • Terms that may be used: addition, difference, division, equation, factor, multiple, multiplication, operation, product, remainder, subtraction • Terms that may be used with definitions or examples: quotient • Terms that will not be used: addend, dividend, divisor, minuend, multiplicand, subtrahend 6 NS03 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Item Characteristics: • . Items may ask students to explain or illustrate the meaning of addition Next Page or subtraction of non-negative decimals and fractions. NS • Items may ask students to explain or illustrate the meaning of multiplying or dividing non-negative fractions and decimals. • Items may ask students to select and/or use an appropriate operation to show understanding of addition, subtraction, multiplication, or division of non-negative decimals and fractions. • Items may ask students to explain, with words or pictures, why multiplication of fractions can be done by multiplying denominators. • Items may ask students to explain, with words or pictures, why addition of fractions requires finding a common denominator. • Items may ask students to translate a given picture or illustration into an equivalent symbolic representation of addition, subtraction, multiplication, or division of non- negative decimals or fractions 6 NS03 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Next Page NS Content Strand 1: Number Sense NS04 (Computation) Add and subtract non-negative decimals and fractions (1.1.6) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 NS04 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Stimulus, Stem, and Prompt Rules: Next Page NS • Stimulus may include words, numbers, mathematical expressions, illustrations, charts, graphs, or diagrams. • Working with fractions, mixed numbers, and decimals within the same item may be required. • NS04 items will be on a “no tools” day. • Items assessing addition and/or subtraction of non-negative decimals and/or fractions will use the following guidelines: – Numbers Session Without Tools – Non-negative decimals up to three numbers to the thousandths place – Non-negative fractions up to three fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 15. 6 NS04 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Mathematical Vocabulary and Terms: Next Page NS • Terms that may be used: addition, difference, equation, operation, subtraction, sum • Terms or phrases that may be used with definitions or examples: simplify • Terms that will not be used: addend, minuend, reduce, subtrahend 6 NS04 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Item Characteristics: Next Page NS • Items may ask students to find common denominators in order to add or subtract non-negative fractions. • Items may ask students to add or subtract non-negative decimals. • Items may ask students to do multiple step calculations requiring addition and/or subtraction using non-negative decimals and/or fractions. 6 NS04 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Next Page Content Strand 1: Number Sense NS NS05 (Estimation) Identify when an approximation is appropriate; use estimation to determine the reasonableness of answers in situations involving addition and subtraction of non-negative decimals and fractions (1.1.8) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. Multiple-Choice items will not ask students to estimate and identify the answer. 6 NS05 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Stimulus, Stem, and Prompt Rules: Next Page NS • Stimulus may include tables, charts, diagrams, and illustrations. • Items will not require the use of a particular estimation strategy. • Items may present situations involving addition and subtraction of non- negative decimals and fractions. • NS05 items will be on a “no tools” day. 6 NS05 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Mathematical Vocabulary and Terms: Next Page NS • Terms that may be used: approximate (as an adjective), estimate, estimation, round • Terms that may be used with definitions or examples: evaluate • Terms that will not be used: approximate (as a verb), clustering, compatible numbers, front-end estimation or names of other estimation strategies 6 NS05 NS ME GS PS AS NS01 NS02 NS03 NS04 NS05 Item Characteristics: Next Page NS • Items may ask students to identify or explain whether estimation or exact calculation is appropriate in situations involving addition and subtraction of non-negative decimals and fractions. • Items may ask students to estimate in situations involving addition and/or subtraction of non-negative decimals and fractions. • Items may ask students to use estimation to determine whether a computation result is reasonable. • Items may ask students to describe or explain a strategy used for estimation involving addition and/or subtraction of non-negative decimals and fractions. • Note: Students will not receive credit in estimation items for computing and then rounding. 6 NS05 NS ME GS PS AS ME01 ME02 ME03 ME04 Next Page ME Content Strand 2: Measurement ME01 (Attributes and Dimensions) – 1.2.1 Understand the concepts of volume and extend the concept of area to surface area of rectangular prisms. ME02 (Units and Systems) – 1.2.2 Understand the differences between square and cubic units. ME03 (Procedures) – 1.2.4 Understand and apply systematic procedures to measure volume and capacity for solid shapes. ME04 (Estimated Measurements) – 1.2.6 Understand and apply strategies to obtain reasonable estimates of volume or capacity. 6 ME NS ME GS PS AS ME01 ME02 ME03 ME04 Next Page ME Content Strand 2: Measurement ME01 (Attributes and Dimensions) Demonstrate understanding of the concepts of volume and surface area of rectangular prisms; demonstrate understanding of the concept of angle measurement (1.2.1) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 ME01 NS ME GS PS AS ME01 ME02 ME03 ME04 Stimulus, Stem, and Prompt Rules: Next Page ME • Stimulus may include pictures, tables, charts, diagrams, figures, and illustrations. • Stimulus will include illustrations in items that involve finding area or volume. Items will not require students to convert from U.S. to metric or metric to U.S. • The answer and distractors will be stated in terms of the same system of measurement. • Items assessing understanding of measurement attributes and dimensions may use the following units: – Attribute – US Units – Metric (SI) Units – Length inch (in.), foot (ft), yard (yd), mile (mi) – millimeter (mm), centimeter (cm), meter (m), kilometer (km) – Angle measurementdegree (º) 6 ME01 NS ME GS PS AS ME01 ME02 ME03 ME04 Mathematical Vocabulary and Terms: Next Page ME • Terms that may be used: angle, area, centimeter, cube, cubic unit, degree, foot/feet, inch, kilometer, meter, mile, millimeter, perimeter, rectangle, prism, right angle, surface area, square unit, volume, yard • Terms that may be used with definitions or examples: compare (tell how they are alike and/or how they are different) • Terms that will not be used: • Students are expected to know how to determine the following: – Perimeter of a polygon – Area of a rectangle – Area of a triangle 6 ME01 NS ME GS PS AS Item Characteristics: ME01 ME02 ME03 ME04 • Items may ask students to identify or describe angles in a picture, diagram, or object. Next Page ME • Items may ask students to identify or describe angles by their relationship to a right angle. • Items may ask students to compare the meaning of surface area and volume of a rectangular prism • Items may ask students to compare the volume of two containers and explain the difference. • Items may ask students to identify the volume for a given rectangular prism from a picture or model. • Items may ask students to identify examples of surface area and/or volume. • Items may ask students to use the surface area and volume to describe a rectangular prism. • Items may ask students to label measurements of a rectangular prism to show understanding of the relationships among linear dimensions, surface area, and volume of rectangular prisms and that area is measured in square units and volume in cubic units. 6 ME01 • Note: Students are expected to determine and label units. NS ME GS PS AS ME01 ME02 ME03 ME04 Content Strand 2: Measurement Next Page ME ME02 (Units and Systems) Demonstrate understanding of the concept of degrees in angles as a unit of measurement – specifically 30o, 45 o, 60 o, 90 o, and 180 o angle measurements; demonstrate understanding of the differences between square and cubic units; demonstrate understanding of how capacity, mass, and length units are organized in the metric system (1.2.2, 1.2.3) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 ME02 NS ME GS PS AS ME01 ME02 ME03 ME04 Stimulus, Stem, and Prompt Rules: Next Page • Stimulus may include pictures, tables, charts, diagrams, figures, and ME illustrations. • Items will not require students to convert from U.S. to metric or metric to U.S. • The answer and distractors will be stated in terms of the same system of measurement. • Items assessing understanding of measurement units and systems may use the following units: – Attribute – US Units – Metric (SI) Units – Length inch (in.), foot (ft), yard (yd), mile (mi) – millimeter (mm), centimeter (cm), meter (m), kilometer (km) – Weight/mass milligram (mg), gram (g), kilogram (kg) – Capacity (liquid volume)milliliter (mL), liter (L) – Angle measurementdegree (º) 6 ME02 NS ME GS PS AS ME01 ME02 ME03 ME04 Mathematical Vocabulary and Terms: Next Page ME • Terms that may be used: angle, area, centimeter, cubic unit, degree, foot/feet, gram, inch, kilogram, kiloliter, kilometer, liter, mass, meter, mile, milligram, milliliter, millimeter, perimeter, right angle, square unit, volume, yard • Terms that may be used with definitions or examples: • Terms that will not be used: metric system, U.S. system 6 ME02 NS ME GS PS AS ME01 ME02 ME03 ME04 Item Characteristics: • Items may ask students to identify or describe angles or angle measures of 30º Next Page , 45 º, 60 º, 90 º, and/or 180 º in a picture, diagram, or object. ME • Items may ask the student to draw angles or polygons with angles of 30 º, 45 º , 60 º , and/or 90 º . • Items may ask the student to identify cubic units as a measure of volume. • Items may ask the student to explain why area and volume are measured in square units and cubic units vs. circular or triangular units. • Items may ask the student to explain how the selected unit of length affects the size of square or cubic units. • Items may ask students to explain the relationship of units within the metric system using milli-, centi-, and/or kilo-. • Items may ask students to convert between units in the metric system in order to answer a question using capacity, weight/mass, or length. • Note: Students are expected to determine and label units. 6 ME02 NS ME GS PS AS ME01 ME02 ME03 ME04 Content Strand 2: Measurement Next Page ME03 (Procedures) Use systematic procedures to ME measure, describe, and compare the area of rectangles and right triangles and the volume of rectangular prisms - identify area or volume as the attribute to be measured, select and use appropriate unit for area or volume, select and use tool that matches the unit chosen, count to determine the number of units; use formulas to find the perimeter and area of rectangles and right triangles (1.2.4, 1.2.5) Item Format(s): Multiple-Choice and Short-Answer items may be used to test this learning target. 6 ME03 NS ME GS PS AS ME01 ME02 ME03 ME04 Stimulus, Stem, and Prompt Rules: Next Page ME • Stimulus may include illustrations of tools that are familiar to sixth-grade students, e.g., meter sticks, rulers, and grids. • Illustrations of rectangular prisms will be used in items that involve finding volume. • The answer and distractors will be stated in terms of the same system of measurement. • Items will not require students to convert from U.S. to metric or metric to U.S. Conversion facts may be given in an item, e.g., 1 mile = 5,280 feet. 6 ME03 NS ME GS PS AS ME01 ME02 ME03 ME04 Mathematical Vocabulary and Terms: Next Page ME • Terms that may be used: $, cm, ft, or other common abbreviations, area, attribute, centimeter, foot/feet, inch, kilometer, length, meter, mile, millimeter, perimeter, square unit, unit, volume, yard • Terms that may be used with definitions or examples: acre, compare (tell how they are alike and/or how they are different) • Terms that will not be used: metric system, U.S. system, • Students are expected to know how to determine the following: – Perimeter of a polygon – Area of a rectangle – Area of a right triangle 6 ME03 NS ME GS PS AS ME01 ME02 ME03 ME04 Item Characteristics: Next Page • Items may ask students to identify or describe the appropriate units and/or tools for measuring area or volume. ME • Items may ask students to count or compare the attribute to the units on the measurement tool to determine the number of units. • Items may ask students to use and/or describe procedures for measuring length, perimeter, and area of a rectangle or right triangle and/or the volume of a rectangular prism: • identify the attribute to be measured; select and use appropriate unit of measurement; select and use a tool that matches the unit chosen; count or compare the attribute to the units on the tool to determine the number of units. • Items may ask students to determine whether measurement has been done correctly in a given situation. • Items may ask students to find the perimeter and/or area of a rectangle or right triangle. • Items may ask students to determine linear dimensions of a rectangle or right triangle based on a given perimeter or area. • Items may ask the student to use area or volume to compare rectangles, right triangles, or rectangular prisms. • Note: Students are expected to determine and label units. 6 ME03 NS ME GS PS AS ME01 ME02 ME03 ME04 Next Page ME Content Strand 2: Measurement ME04 (Estimated Measurements) Identify situations in which estimated measurements are sufficient; estimate volume using manipulatives and/or drawings; estimate measures of angles and areas of rectangles and right triangles (1.2.6) Item Format: Multiple Choice and Short-Answer items may be used to assess this learning target. Multiple-Choice items will not ask students to estimate and identify the answer. 6 ME04 NS ME GS PS AS ME01 ME02 ME03 ME04 Stimulus, Stem, and Prompt Rules: Next Page ME • Pictorial representations of objects and figures, tables, charts, and graphs may be used. • Items should focus on the appropriate use of estimation rather than particular estimation strategies. • Items will not require students to convert from U.S. to metric or metric to U.S. • The answer and distractors will be stated in terms of the same system of measurement. • ME04 items will be on a “no tools” day. 6 ME04 NS ME GS PS AS ME01 ME02 ME03 ME04 Mathematical Vocabulary and Terms: Next Page ME • Terms that may be used: accurate, accuracy, area, centimeters, cubic unit, degree, estimate, estimation, foot/feet, inch, kilometer, meter, mile, millimeter, perimeter, square unit, volume, yard • Terms that may be used with definitions or examples: approximation • Terms that will not be used: metric system, U.S. system • Students are expected to know how to determine the following: – Perimeter of a polygon – Area of a rectangle – Area of a triangle 6 ME04 NS ME GS PS AS ME01 ME02 ME03 ME04 Item Characteristics: Next Page • Items may ask students to determine when or whether estimation is appropriate ME in a given situation. • Items may ask students to determine if a given angle, area, or volume measurement is reasonable in a situation. • Items may ask students to identify or describe a procedure that would be an appropriate way to estimate angle measures, area, or volume. • Items may ask students to explain why they would use estimation rather than an exact measurement. • Items may ask students to estimate volume using drawings. • Items may ask students to estimate measures of angles or areas of rectangles and/or triangles. • Note: Students will not receive credit in estimation items for computing and then rounding. • Note: Students are expected to determine and label units. 6 ME04 NS ME GS PS AS GS01 GS02 Next Page GS Content Strand 3: Geometric Sense GS01 (Properties and Relationships) – 1.3.1 Understand the characteristics of circles and rectangular prisms. – 1.3.2 Apply understanding of angles and polygons. GS02 Locations and Transformations) – 1.3.3 Understand the relative location of integers on a number line. – 1.3.4 Apply understanding of rotations (turns) to two-dimensional figures. 6 GS NS ME GS PS AS GS01 GS02 Content Strand 3: Geometric Sense Next Page GS GS01 (Properties and Relationships) Demonstrate understanding of the characteristics of angles, polygons, circles, and rectangular prisms; use properties of parallel and perpendicular lines and line of symmetry and the characteristics of angles and polygons to describe, draw, and compare objects, shapes, and figures (1.3.1, 1.3.2) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 GS01 NS ME GS PS AS GS01 GS02 Stimulus, Stem, and Prompt Rules: Next Page GS • Stimulus will include a box drawn in figures for right angles, hash marks on line segments to indicate equal lengths, and the symbol to indicate perpendicular lines. • Stimulus may include illustrations of 2-dimensional and 3- dimensional figures or objects. 6 GS01 NS ME GS PS AS GS01 GS02 Mathematical Vocabulary and Terms: Next Page GS • Terms that may be used: acute angle, angle, attribute, base, circle, circumference, cube, diagonal, diameter, dimensions, edge, equilateral, face, figure, height, hexagon, intersecting, isosceles, obtuse angle, octagon, parallel, parallelogram, pentagon, perpendicular, polygon, quadrilateral, prism, radius/radii, rectangle, rhombus, right angle, side, square, symmetry, 3-dimensional, trapezoid, triangle, 2-dimensional, vertex/vertices • Terms that may be used with definitions or examples: compare (tell how they are alike and/or how they are different) • Terms that will not be used: plane figure, solid figure 6 GS01 NS ME GS PS AS GS01 GS02 Item Characteristics: • Items may ask students to identify or describe angles, polygons, and/or circles Next Page using geometric properties including parallel, perpendicular, and line of symmetry. GS • Items may ask students to compare, sort, and/or label angles, polygons, and/or circles according to their geometric properties including parallel, perpendicular, and line of symmetry. • Items may ask students to identify, describe, compare, sort, and/or label rectangular prisms using geometric properties. • Items may ask students to draw a figure with given characteristics. • Items may ask students to draw symmetrical figures or to complete a picture or design given the line of symmetry. • Items may ask students to identify and/or draw one or more lines of symmetry in a given geometric figure. • Items may ask students to describe lines of symmetry for angles, polygons, and/or circles. 6 GS01 NS ME GS PS AS GS01 GS02 Content Strand 3: Geometric Sense Next Page GS GS02 (Locations and Transformations) Describe the relative location of points and objects on a positive- negative number line; recognize or draw a translation (slide) or reflection (flip) of a 2-dimensional shape or figure; rotate (turn) a simple 2-dimensional figure 90° or 180° about the center or a vertex of the figure (1.3.3, 1.3.4) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 GS02 NS ME GS PS AS GS01 GS02 Stimulus, Stem, and Prompt Rules: Next Page GS • Number lines will have the necessary reference points labeled using integers, fractions, and/or decimals. • When rotating figures, the center of the figure must be marked and labeled. • When figures that are rotated are on a coordinate grid, each vertex and the center of the figure must be on the intersection of a horizontal and a vertical grid line. • Only the first quadrant of a Cartesian plane may be used. • Grids will be provided in items that require students to plot a point. • Location grids may use ordered number pairs or letter and number combinations. • Grids will have the origin and scales labeled. 6 GS02 NS ME GS PS AS GS01 GS02 Mathematical Vocabulary and Terms: Next Page GS • Terms that may be used: angle, axis/axes, clockwise, coordinate(s), counterclockwise, degree, diagonal, figure, intersect, ordered pair, origin, parallel, perpendicular, point, vertex/vertices, x-axis, y-axis • Terms that may be used with definitions or examples: reflection (flip), rotation (turn), translation (slide) • Terms that will not be used: Cartesian plane, plane, quadrant • Terms related to transformations: – Translation (slide): the image of a figure in which every point in the figure moves the same distance in the same direction. – Reflection (flip): the mirror image of a figure on the opposite side of a line. – Rotation (turn): the image of a figure moved through an angle around a point. 6 GS02 NS ME GS PS AS Item Characteristics: GS01 GS02 • Items may ask students to place integers, fractions, and/or decimals on a number line. Next Page GS • Items may ask students to identify or name the location of objects or points on a number line using coordinates and/or labels. • Items may ask students to determine and/or describe the relative position - to the right, to the left, number of spaces apart – of points or objects on a positive/negative number line. • Items may ask students to identify the point of final destination on an integer number line, given a starting point and a movement right/left or up/down. • Items may ask students to use ordered pairs to identify or describe the location of a given object rotated 90° or 180° about the center or vertex of the figure in the first quadrant of a coordinate grid. • Items may ask students to identify, describe, or classify whether an object has been transformed by a translation reflection, or rotation with or without a grid. • Items may ask students to identify a picture or diagram of a particular translation, reflection, or rotation of 90° or 180° about the center or vertex of a figure, with or without a grid. • Items may ask students to draw a translation, a reflection, or a rotation of 90° or 180° about the center or vertex of a figure. • Items may ask students to describe a 90o or 1800 rotation about the center or vertex of a figure so that another person could draw it. 6 GS02 NS ME GS PS AS PS01 PS02 PS03 Next Page PS Content Strand 4: Probability and Statistics PS01 (Probability) – 1.4.1 Understand probability as a ratio between and including 0 and 1. – 1.4.2 Understand various ways to determine outcomes of events or situations. PS02 (Data Collection and Central Tendencies) – 1.4.3 Analyze how data collection methods affect the data collected. – 1.4.4 Apply measures of central tendency to interpret a set of data. PS03 (Data Representation and Interpretation) – 1.4.5 Understand how to organize, display, and interpret data in text from single line graphs and scatter plots. – 1.4.6 Evaluate a data set to determine how it can be, or has been, used to support a point of view. 6 PS NS ME GS PS AS PS01 PS02 PS03 Next Page Content Strand 4: Probability and Statistics PS PS01 (Probability) Demonstrate understanding of the likelihood of simple events; demonstrate understanding that probability is a ratio between and including 0 and 1; determine all possible outcomes and/or the probabilities for simple experiments or situations (1.4.1, 1.4.2) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 PS01 NS ME GS PS AS PS01 PS02 PS03 Stimulus, Stem, and Prompt Rules: Next Page PS • Pictures of objects such as game spinners, coins, chips, marbles, number cubes, diagrams, tables, charts, and graphs may be used. • A probability may be expressed as a ratio, decimal, or percent. 6 PS01 NS ME GS PS AS PS01 PS02 PS03 Mathematical Vocabulary and Terms: Next Page PS • Terms that may be used: outcome, probability, random • Terms that may be used with definitions or examples: event, experiment, sample space • Terms that will not be used: expected value, experimental probability, permutation, theoretical probability 6 PS01 NS ME GS PS AS PS01 PS02 PS03 Item Characteristics: Next Page • Items may ask students to explain why some outcomes are equally PS likely or more or less likely to happen than others and how much more or less. • Items may ask students to identify, predict, or determine the probability of an event in a simple experiment or situation as a ratio, decimal, or percent. • Items may ask students to demonstrate an understanding that probability is a ratio between and including 0 and 1 or a percent between and including 0% and 100%. • Items may ask students to determine the sample space of simple experiments or activities. • Items may ask students to translate between representations of probability. • Items may ask students to create a spinner, game, or situation that would produce a given, fair or unfair, outcome. • Items may ask students to explain why a game is fair or unfair. 6 PS01 NS ME GS PS AS PS01 PS02 PS03 Next Page Content Strand 4: Probability and Statistics PS PS02 (Data Collection and Central Tendencies) Identify and/or describe how different collection methods or different questions affect the data collected; determine and use mean, median, and mode to describe or interpret a set of data (1.4.3, 1.4.4) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 PS02 NS ME GS PS AS PS01 PS02 PS03 Stimulus, Stem, and Prompt Rules: Next Page PS • Items may include descriptive scenarios that involve survey questions and collection methods. • Items may include tables, charts, diagrams, pictures, bar graphs, line plots, pictographs, circle graphs, histograms, and line graphs. 6 PS02 NS ME GS PS AS PS01 PS02 PS03 Mathematical Vocabulary and Terms: Next Page PS • Terms that may be used: data, population, questionnaire, survey • Terms that may be used with definitions or examples: bias, mean (average), median (middle number), mode (most common or most common number), variable • Terms that will not be used: measures of central tendency, reliability 6 PS02 NS ME GS PS AS PS01 PS02 PS03 Item Characteristics: Next Page PS • Items may ask students to identify or write survey questions that will obtain the appropriate information and will avoid bias. • Items may ask students to identify or describe how to collect data about a given population, taking into account collection methods. • Items may ask students to describe how a question or data collection method may affect the data. • Items may ask students to identify, calculate, and/or use mean, median, and mode as appropriate to describe a set of data. • Items may ask students to explain the difference between mode, median, and/or mean for a set of data in a given situation. 6 PS02 NS ME GS PS AS PS01 PS02 PS03 Content Strand 4: Probability and Statistics Next Page PS PS03 (Data Representation and Interpretation) Read and interpret data presented in text, circle graphs, histograms, and single line graphs and determine when using these is appropriate; demonstrate understanding of how data can be used to support a point of view (1.4.5, 1.4.6) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 PS03 NS ME GS PS AS PS01 PS02 PS03 Stimulus, Stem, and Prompt Rules: Next Page PS • Stimulus may include text, tables, charts, diagrams, pictures, circle graphs, histograms, and line graphs. 6 PS03 NS ME GS PS AS PS01 PS02 PS03 Mathematical Vocabulary and Terms: Next Page PS • Terms that may be used: axis/axes, circle graph, graph, histogram, horizontal axis, line graph, origin, scale, vertical axis, x-axis, y-axis • Terms that may be used with definitions or examples: compare (tell how they are alike and/or how they are different), evaluate, trend • Terms that will not be used: continuous, discrete, intercept, slope 6 PS03 NS ME GS PS AS Item Characteristics: PS01 PS02 PS03 Next Page • Items may ask students to read and interpret data from text, circle graphs, PS histograms, and single line graphs. • Items may ask students to describe the accuracy and completeness of the data in a circle graph, histogram, or line graph. • Items may ask students to identify and/or explain whether a circle graph, histogram, or line graph is more appropriate for a given set of data, a particular situation or purpose, or answers a question most effectively. • Items may ask students to identify or describe trends or patterns in data represented in a circle graph, histogram, or line graph. • Items may ask students to compare or evaluate multiple interpretations of the same data. • Items may ask students to read and interpret data from a circle graph, histogram, or single line graph. • Items may ask students to evaluate the appropriateness of an inference made from a set of data. • Items may ask students to determine whether the title, labels, and/or scale(s) on a circle graph, histogram, or line graph accurately and appropriately represent the data, to explain why or why not, and/or to correct it as needed. 6 PS03 NS ME GS PS AS AS01 AS02 AS03 Next Page AS Content Strand 5: Algebraic Sense AS01 (Patterns and Functions) – 1.5.1 Apply rules for number patterns based on two arithmetic operations. – 1.5.2 Apply understanding of patterns involving two arithmetic operations to develop a rule. AS02 (Symbols and Notations) – 1.5.3 Apply understanding of equalities and inequalities to interpret and represent relationships between quantities. – 1.5.4 Apply understanding of tables, graphs, expressions, equations, or inequalities to represent situations involving two arithmetic operations. AS03 (Evaluating and Solving) – 1.5.5 Understand and apply procedures to evaluate expressions and formulas. – 1.5.6 Understand and apply a variety of strategies to solve one-step equations. 6 AS NS ME GS PS AS AS01 AS02 AS03 Content Strand 5: Algebraic Sense Next Page AS AS01 (Patterns and Functions) Extend or create patterns of numbers, shapes, and/or objects that use one arithmetic operation – addition, subtraction, multiplication, or division – to move from one term to the next; recognize or extend patterns and sequences that use two different alternating arithmetic operations to move from one term to the next; describe a rule for a pattern with combinations of two arithmetic operations in the rule (1.5.1, 1.5.2) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 AS01 NS ME GS PS AS AS01 AS02 AS03 Stimulus, Stem, and Prompt Rules: Next Page AS • Stimulus may include numbers, tables, charts, pictorial, and/or geometric patterns. • A given pattern must have a minimum of four elements or terms. • Number patterns may use one operation to move from one term in a pattern to the next. • Number patterns may use two different operations that alternate between terms. • Number patterns may include addition, subtraction, multiplication, or division with whole numbers OR addition or subtraction of non-negative decimals or fractions. 6 AS01 NS ME GS PS AS AS01 AS02 AS03 Mathematical Vocabulary and Terms: Next Page AS • Terms that may be used: pattern, predict, rule, sequence • Terms that may be used with definitions or examples: function, interval • Terms that will not be used: 6 AS01 NS ME GS PS AS AS01 AS02 AS03 Item Characteristics: Next Page AS • Items may ask students to extend a pattern by identifying or supplying missing elements in the beginning, middle and/or end and/or describe the pattern or write a rule with one operation. • Items may ask students to identify a pattern that is equivalent to a given pattern. • Items may ask students to identify or describe a number pattern given in tables, graphs, rules, or words. • Items may ask students to extend a pattern by identifying or supplying missing elements in the beginning, middle, and/or end and/or describe the pattern or write a rule with alternating operations between terms. • Items may ask students to create a pattern that uses the same rule as a given pattern. • Items may ask students to create a pattern and explain what makes it a pattern. 6 AS01 NS ME GS PS AS AS01 AS02 AS03 Content Strand 5: Algebraic Sense Next Page AS AS02 (Symbols and Notations) Express relationships between quantities using =, ≠, <, >, ≤, and ≥; use variables to write expressions, equations, and inequalities that represent situations involving two arithmetic operations with non-negative decimals and fractions (1.5.3, 1.5.4) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 AS02 NS ME GS PS AS AS01 AS02 AS03 Stimulus, Stem, and Prompt Rules: Next Page AS • Stimulus may include pictorial representations, tables, charts, or graphs. • Stimulus may include the use of variables to represent an unknown quantity in expressions or equations. • Stimulus may use addition and subtraction of non-negative decimals and fractions. • Stimulus should avoid the use of the letters a, b, c, d, or x as variables. 6 AS02 NS ME GS PS AS AS01 AS02 AS03 Mathematical Vocabulary and Terms: Next Page AS • Terms that may be used: =, ≠, <, >, ≤, ≥, equation, expression, relationship • Terms that may be used with definitions or examples: function, inequality, interval, variable • Terms that will not be used: 6 AS02 NS ME GS PS AS AS01 AS02 AS03 Item Characteristics Next Page AS • Items may ask students to identify or write a simple expression, using variables, to represent a given situation. • Items may ask students to identify or write a simple equation or simple inequality, with variables, to represent a given situation, using =, ≠, <, >, ≤, or ≥. • Items may ask students to explain the meaning of a variable in a formula, expression, equation, or inequality. • Items may ask students to identify a situation that corresponds to a given expression, equation, or inequality. 6 AS02 NS ME GS PS AS AS01 AS02 AS03 Next Page AS Content Strand 5: Algebraic Sense AS03 (Evaluating and Solving) Evaluate simple expressions and formulas using pictures and/or symbols; solve one-step equations using pictures and symbols (1.5.5, 1.5.6) Item Format: Multiple-Choice and Short-Answer items may be used to test this learning target. 6 AS03 NS ME GS PS AS AS01 AS02 AS03 Stimulus, Stem, and Prompt Rules: Next Page AS • Stimulus may include pictorial representations, tables, charts, or graphs. • Stimulus may include the use of a variable to represent an unknown quantity in an expression or equation. • Equations will require a maximum of one step to solve and will have whole number solutions. • Stimulus should avoid the use of the letters a, b, c, d, or x as variables. 6 AS03 NS ME GS PS AS AS01 AS02 AS03 Mathematical Vocabulary and Terms: Next Page AS • Terms that may be used: equation, expression, formula, solve, symbol, unknown • Terms that may be used with definitions or examples: evaluate, function, variable • Terms that will not be used: set up 6 AS03 NS ME GS PS AS AS01 AS02 AS03 Item Characteristics: • Items may ask students to write a simple expression for a given situation and evaluate the expression given the values for the variables. • Items may ask students to evaluate an expression or formula given the values for the variables. • Items may ask students to solve one-step single-variable equations for a given situation. • Items may ask students to write and solve one-step single-variable equations for a given situation. 6 AS03 NS ME GS PS AS