Grade 4 Math Proficiency Scales-T1

Transcription

1 Measurement & Data Geometry Critical Thinking Communication Grade 4 Math Proficiency Scales-T1 Novice 1 and of the Make mathematical arguments and critique the reasoning of others. Partially Proficient 2 Make mathematical arguments and critique the reasoning of others. Meeting Expectations 3 Make mathematical arguments and critique the reasoning of others. Meeting and Exceeding Expectations 4 Construct viable arguments and critique the reasoning of others. others mathematical thinking. and of the representations used. representations used. representations used. Choose appropriate tools and use them effectively to make sense of results. Create and justify rules, shortcuts, and generalizations. and of the Draw and label points, lines, line segments, and rays and correctly identify right angles. Identify properties of line segments and angles within quadrilaterals and identify right angles within triangles. Identify one line of symmetry in 2-dimensional symmetric figures. Draw and label points, lines, line segments, and rays and correctly identify right angles. Identify properties of line segments and angles within quadrilaterals and identify right angles within triangles. Identify one line of symmetry in 2- dimensional symmetric figures. Draw and label points, lines, line segments, and rays and correctly identify right angles. Identify properties of line segments and angles within quadrilaterals and identify right angles within triangles. Identify one line of symmetry in 2- dimensional symmetric figures. Understand that an ordered pair of numbers identifies an exact location on a coordinate grid; use coordinates to graph points and to name graphed points in the first quadrant of the coordinate plane. and of the Explain the relationship between and convert from yards to feet and feet to inches. Have a strategy to determine the perimeter. Explain the relationship between and convert from yards to feet and feet to inches. Have a strategy to determine the perimeter. Explain the relationship between and convert from yards to feet and feet to inches. Have a strategy to determine the perimeter. Understand and use unit cubes to find volume; find the volume of a partially packed prism when the dimensions of the prism are clearly shown. Understand that packing with unit cubes and multiplying dimensions are two strategies for finding the volume of a rectangular prism. Apply the appropriate volume formula when given the formulas and a set of whole-number dimensions. Understand that the volume of figures composed of two or more right rectangular prisms can be found by adding the volumes of individual parts. Perform one-step unit conversions within the same measurement system; use conversions to solve real-world problems when necessary conversions are identified.

2 Number & Operations in Base Ten and of the Recognize the relationship between the value of a place (under 1,000) that is ten times as large as the value of another place. Use place value to read numbers in expanded form. Compare and order multidigit whole numbers through hundred-thousands. Round numbers through the millions to the two largest places. Apply U.S. traditional addition and subtraction to 3-digit and 4-digit problems. Use fact extensions to multiply by a multiple of 10. Recognize the relationship between the value of a place (under 1,000) that is ten times as large as the value of another place. Use place value to read numbers in expanded form. Compare and order multidigit whole numbers through hundredthousands. Round numbers through the millions to the two largest places. Apply U.S. traditional addition and subtraction to 3-digit and 4- digit problems. Use fact extensions to multiply by a multiple of 10. Recognize the relationship between the value of a place (under 1,000) that is ten times as large as the value of another place. Use place value to read numbers in expanded form. Compare and order multidigit whole numbers through hundred-thousands. Round numbers through the millions to the two largest places. Apply U.S. traditional addition and subtraction to 3-digit and 4-digit problems. Use fact extensions to multiply by a multiple of 10. Use place-value understanding to write whole numbers in expanded form; identify the values of digits in a given whole number; write whole numbers in which digits represent given values; recognize that in a multi-digit whole number, a digit in one place represents 10 times what it represents in the place to its right. Translate between powers of 10 in exponential notation and standard notation; correctly multiply a whole number by a power of ten; notice patterns in the number of zeros in a produce when multiplying a whole number by a power of ten. Use a strategy to multiply whole numbers; understand the basic steps of the U.S. traditional multiplication algorithm and successfully apply it to 1-digit by multi-digit problems and 2- digit by 2-digit problems in which one factor is less than 20. Use the partial-quotients algorithm with up to 3-digit dividends and 1-digit or simple 2-digit divisors; make connections between written partial-quotients work and a given area model representing the same solution.

3 Number & Operations in Fractions and of the Recognize two equivalent fractions through 12ths using a using a model. Use a preferred model to represent decimals to hundredths, name decimals using base-10 numerals, and translate between decimal notation and fractions with denominators 10 or 100. Compare decimals using a model. Compare two fractions. Recognize two equivalent fractions through 12ths using a using a model. Use a preferred model to represent decimals to hundredths, name decimals using base-10 numerals, and translate between decimal notation and fractions with denominators 10 or 100. Compare decimals using a model. Compare two fractions. Recognize two equivalent fractions through 12ths using a using a model. Use a preferred model to represent decimals to hundredths, name decimals using base-10 numerals, and translate between decimal notation and fractions with denominators 10 or 100. Compare decimals using a model. Compare two fractions. Find the area of a rectangle with one fractional side length by tiling it with unit squares of side length 1 and counting full and partial tiles; understand that unit squares with fractional side lengths is different from the measure of area in square units. Use tools and visual models to generate equivalent fractions and to add fractions with unlike denominators when only one fraction needs to be replaced with an equivalent fraction. Use tools and visual models to solve number stories involving addition and subtraction of fractions and mixed numbers with the like denominators; identify benchmarks close to fractions less than or equal to 2 and use them to make reasonable estimates for fraction sums and differences. Recognize that a fraction a/b is the result of dividing a by b; use tools and visual models to solve whole-number division problems that have fraction or mixed-number answers; use tools and visual models to rename mixed numbers and fractions greater than one. Solve fraction-of problems to build a conceptual foundation for multiplication of fractions by whole numbers. Find a unit fraction of a whole number by partitioning the whole number into the appropriate number of parts and taking one of the parts. Use tools and visual models to solve real-world fractions-of problems with unit fractions and whole numbers.

4 Operations & Algebraic Thinking and of the addition and subtraction multistep number stories and estimate to generate a reasonable answer to a problem before solving. Identify a number story as additive or multiplicative and explain how they know. Identify more than one factor pair for composite numbers less than 40, write multiples of a 1- digit number, and identify prime and composite numbers less than 40. addition and subtraction multistep number stories and estimate to generate a reasonable answer to a problem before solving. Identify a number story as additive or multiplicative and explain how they know. Identify more than one factor pair for composite numbers less than 40, write multiples of a 1-digit number, and identify prime and composite numbers less than 40. addition and subtraction multistep number stories and estimate to generate a reasonable answer to a problem before solving. Identify a number story as additive or multiplicative and explain how they know. Identify more than one factor pair for composite numbers less than 40, write multiples of a 1- digit number, and identify prime and composite numbers less than 40. Understand the purpose of grouping symbols and evaluate expressions with one set of symbols; place one set of grouping symbols to make a number sentence true. Write simple expressions to model situations in which no more than two operations are involved; reason about the relative value of simple expressions without evaluating them.

5 Geometry Critical Thinking Communication Grade 4 Math Proficiency Scales-T2 Novice 1 some of the Explain mathematical thinking clearly and precisely. Partially Proficient 2 Explain mathematical thinking clearly and precisely. Meeting Expectations 3 Explain mathematical thinking clearly and precisely. Meeting and Exceeding Expectations 4 Construct viable arguments and critique the reasoning of others. others mathematical thinking. some of the representations used. a problem. Check whether the answer makes sense. representations used. Make sense of a problem. Check whether the answer makes sense. representations used. a problem. Check whether the answer makes sense. Use tools effectively and justify results. Use mathematical models to solve problems and answer questions. Check whether an answer makes sense. some of the Draw and label points, lines, line segments, and rays and correctly identify right angles. Identify properties of line segments and angles within quadrilaterals and identify right angles within triangles. Identify one line of symmetry in 2-dimensional symmetric figures. Draw and label points, lines, line segments, and rays and correctly identify right angles. Identify properties of line segments and angles within quadrilaterals and identify right angles within triangles. Identify one line of symmetry in 2- dimensional symmetric figures. Draw and label points, lines, line segments, and rays and correctly identify right angles. Identify properties of line segments and angles within quadrilaterals and identify right angles within triangles. Identify one line of symmetry in 2- dimensional symmetric figures. Understand that an ordered pair of numbers identifies an exact location on a coordinate grid; use coordinates to graph points and to name graphed points in the first quadrant of the coordinate plane. Understand that information from some real-world and mathematical problems can be represented as ordered pairs and graphed on a coordinate grid; plot points to represent given information.

6 Number & Operations in Base Ten Measurement & Data some of the Solve number stories involving metric units of capacity and mass. Use a formula to find the perimeters and areas of rectangles. Organize and represent data in ½ and ¼ units on line plots and solve addition and subtraction problems about line plot data in ½ and ¼ units. Identify benchmark rotations such as ¼, ½, ¾, and full turns and recognize that the degree is the standard unit of measure for angles. Recognize that angles are measured in iterations of one-degree angles. Solve number stories involving metric units of capacity and mass. Use a formula to find the perimeters and areas of rectangles. Organize and represent data in ½ and ¼ units on line plots and solve addition and subtraction problems about line plot data in ½ and ¼ units. Identify benchmark rotations such as ¼, ½, ¾, and full turns and recognize that the degree is the standard unit of measure for angles. Recognize that angles are measured in iterations of one-degree angles. Solve number stories involving metric units of capacity and mass. Use a formula to find the perimeters and areas of rectangles. Organize and represent data in ½ and ¼ units on line plots and solve addition and subtraction problems about line plot data in ½ and ¼ units. Identify benchmark rotations such as ¼, ½, ¾, and full turns and recognize that the degree is the standard unit of measure for angles. Recognize that angles are measured in iterations of one-degree angles. Understand and use unit cubes to find volume; find the volume of a partially packed prism when the dimensions of the prism are clearly shown. Understand that packing with unit cubes and multiplying dimensions are two strategies for finding the volume of a rectangular prism. Apply the appropriate volume formula when given the formulas and a set of whole-number dimensions. Understand that the volume of figures composed of two or more right rectangular prisms can be found by adding the volumes of individual parts. Perform one-step unit conversions within the same measurement system; use conversions to solve real-world problems when necessary conversions are identified. some of the Read and identify places in numbers through the hundred-thousands. Read and write number names through millions. Read and write numbers in expanded form through millions. Compare and order multidigit whole numbers, and record comparisons using or or = and explain. Use and explain the standard algorithm to add and subtract multidigit whole numbers. Accurately multiply 2-digit by 1- digit whole numbers. Read and identify places in numbers through the hundred-thousands. Read and write number names through millions. Read and write numbers in expanded form through millions. Compare and order multidigit whole numbers, and record comparisons using or or = and explain. Use and explain the standard algorithm to add and subtract multidigit whole numbers. Accurately multiply 2-digit by 1-digit whole numbers. Read and identify places in numbers through the hundred-thousands. Read and write number names through millions. Read and write numbers in expanded form through millions. Compare and order multidigit whole numbers, and record comparisons using or or = and explain. Use and explain the standard algorithm to add and subtract multidigit whole numbers. Accurately multiply 2-digit by 1-digit whole numbers. Recognize that in multi-digit whole numbers, a digit in one place represents 10 times what it represents in the place to its right and 1/10 of what it represents in the place to its left; recognize that place-value patterns with whole numbers extend to decimals. Represent, read and write decimals through thousandths with no placeholder zeros and in expanded form as sums of decimals (e.g., = ). Use materials to compare and order decimals through thousandths and record comparisons using, and = symbols. Use materials to round decimals to the nearest tenth or hundredth and to add and subtract decimals; use algorithms to add and subtract decimals. Estimate and find products and quotients of decimals. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole number quotients using strategies based and illustrate and explain the calculation. Use whole-number exponents to denote powers of 10; multiply whole numbers by whole numbers by powers of 10 and explain the number of zeros in the product; multiply or divide a decimal by a power of 10.

7 Number & Operations in Fractions some of the Using manipulatives add fractions and subtract fractions with no regrouping. Decompose fractions, represent decompositions with an equation, and explain using a visual fraction model. Add and subtract mixed numbers with no regrouping using manipulatives and visual fraction models. Add two fractions with denominators 10 and 100 using a model. Using manipulatives add fractions and subtract fractions with no regrouping. Decompose fractions, represent decompositions with an equation, and explain using a visual fraction model. Add and subtract mixed numbers with no regrouping using manipulatives and visual fraction models. Add two fractions with denominators 10 and 100 using a model. Using manipulatives add fractions and subtract fractions with no regrouping. Decompose fractions, represent decompositions with an equation, and explain using a visual fraction model. Add and subtract mixed numbers with no regrouping using manipulatives and visual fraction models. Add two fractions with denominators 10 and 100 using a model. Recognize that a common denominator makes it easier to add and subtract fractions and mixed numbers; use a strategy to identify a common denominator; add and subtract fractions and mixed numbers when one of the following is required, but not both: finding a common denominator, or renaming the sum or starting number to have a smaller or larger fraction part. Use models to solve number stories involving addition and subtraction of fractions and mixed numbers that require one, but not both, of the finding a common denominator, or renaming the sum or starting number; use benchmark fractions and number sense to make reasonable estimates for fraction and mixed-number sums and differences. Find a fraction of a whole number, when the answer is a whole number, by partitioning the whole number into equal parts and taking the appropriate number of parts or by multiplying the whole number by the numerator of the fraction and dividing by the denominator; use paper-folding and other visual representations to visualize partitioning a fraction into equal parts and finding the value of one or more parts; connect fractionof problems to fraction multiplication. Find the area of a rectangle with fractional side lengths by counting the number of unit-fraction tiles that cover the rectangle and relating the count to how many tiles cover a unit square; use area models to represent and find fraction products. Predict that a product of a whole number and a fraction less than 1 will be less than the whole number and informally explain why this is so; understand that multiplying a fraction by another fraction equal to 1 creates an equivalent fraction. Use tools and models to solve real-world problems involving multiplication of fractions by whole numbers or fractions by fractions. Use models to solve problems involving division of a unit fraction by a whole number or division of a whole number by a unit fraction when the problems are in context.

8 Operations & Algebraic Thinking some of the and articulate a plan for solving multistep number stories involving addition, subtraction, and multiplication, and assess the reasonableness of their answers by comparing them to an estimate. and articulate a plan for solving multistep number stories involving addition, subtraction, and multiplication, and assess the reasonableness of their answers by comparing them to an estimate. and articulate a plan for solving multistep number stories involving addition, subtraction, and multiplication, and assess the reasonableness of their answers by comparing them to an estimate. Understand the purpose of grouping symbols and evaluate expressions with one set of symbols; place one set of grouping symbols to make a number sentence true. Write simple expressions to model situations in which no more than two operations are involved; reason about the relative value of simple expressions without evaluating them.

9 Geometry Critical Thinking Communication Grade 4 Math Proficiency Scales-T3 Novice 1 Make mathematical arguments and critique the reasoning of others. Explain mathematical thinking clearly and precisely. Partially Proficient 2 Make mathematical arguments and critique the reasoning of others. Explain mathematical thinking clearly and precisely. Meeting Expectations 3 Make mathematical arguments and critique the reasoning of others. Explain mathematical thinking clearly and precisely. Meeting and Exceeding Expectations 4 Construct viable arguments and critique the reasoning of others. others mathematical thinking. problems and persevere in solving them. Use appropriate tools strategically. problems and persevere in solving them. Use appropriate tools strategically. problems and persevere in solving them. Use appropriate tools strategically. Look for mathematical structures such as categories, patterns, and properties. Draw, represent, and identify angles, including right, acute, and obtuse angles. Identify linesymmetric figures and draw lines of symmetry. Draw, represent, and identify angles, including right, acute, and obtuse angles. Identify linesymmetric figures and draw lines of symmetry. Draw, represent, and identify angles, including right, acute, and obtuse angles. Identify linesymmetric figures and draw lines of symmetry. Understand that attributes can be used to define categories and subcategories of shapes; recognize when one category is a subcategory of another. Understand the basic structure of a hierarchy; classify two-dimensional figures in a correct category according to a hierarchy, although not necessarily the most specific category. Understand and use a Cartesian coordinate grid in two dimensions. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

10 Number & Operations in Base Ten Measurement & Data Correctly identify the type of angle and obtain measurements within the correct range. Recognize angle measures as additive within benchmark angles measuring 90 and 180 degrees, and add and subtract to find unknown angle measures within benchmark angles measuring 90 and 180 degrees. Express conversions of units of capacity in a 2-column table. Organize and represent data in 1/8 units on line plots and solve addition and subtraction problems about line plot data in 1/8 units. Use the four operations to solve number stories involving whole numbers of measured quantities. Solve addition and subtraction problems to find unknown angle measures on a diagram in real world and mathematical problems. Correctly identify the type of angle and obtain measurements within the correct range. Recognize angle measures as additive within benchmark angles measuring 90 and 180 degrees, and add and subtract to find unknown angle measures within benchmark angles measuring 90 and 180 degrees. Express conversions of units of capacity in a 2-column table. Organize and represent data in 1/8 units on line plots and solve addition and subtraction problems about line plot data in 1/8 units. Use the four operations to solve number stories involving whole numbers of measured quantities. Solve addition and subtraction problems to find unknown angle measures on a diagram in real world and mathematical problems. Correctly identify the type of angle and obtain measurements within the correct range. Recognize angle measures as additive within benchmark angles measuring 90 and 180 degrees, and add and subtract to find unknown angle measures within benchmark angles measuring 90 and 180 degrees. Express conversions of units of capacity in a 2- column table. Organize and represent data in 1/8 units on line plots and solve addition and subtraction problems about line plot data in 1/8 units. Use the four operations to solve number stories involving whole numbers of measured quantities. Solve addition and subtraction problems to find unknown angle measures on a diagram in real world and mathematical problems. Place fractional data on a line plot when the number line and scale are provided; use information in line plots to solve single-step problems. Convert among different-sized standard measurement units within a given measurement system, and use these conversions to solve multi-step, real world problems. Multiply a 4-digit by a 1-digit number and a 2-digit number by a 2- digit number and attempt to illustrate and explain multiplication by a 1- digit number and a 2- digit number by 2-digit number. Accurately divide a 3-digit number by a 1-digit number and illustrate and explain division of a 3-digit number by a 1-digit number. Multiply a 4-digit by a 1- digit number and a 2-digit number by a 2-digit number and attempt to illustrate and explain multiplication by a 1-digit number and a 2- digit number by 2-digit number. Accurately divide a 3-digit number by a 1-digit number and illustrate and explain division of a 3-digit number by a 1-digit number. Multiply a 4-digit by a 1- digit number and a 2-digit number by a 2-digit number and attempt to illustrate and explain multiplication by a 1-digit number and a 2-digit number by 2-digit number. Accurately divide a 3-digit number by a 1-digit number and illustrate and explain division of a 3-digit number by a 1-digit number. Use place value understanding to round decimals to any place. Add, subtract, multiply and divide decimals to hundredths, using manipulatives, drawings, or placevalue strategies; explain their computation methods.

11 Operations & Algebraic Thinking Number & Operations in Fractions Find a multiple of 1/b using strategies. Write a multiplication equation with a letter standing for an unknown to represent a number story involving multiplication of a fraction by a whole number. Add and subtract mixed numbers. Multiply a fraction by a whole number. Add two fractions with denominators 10 and 100. Use decimal notation for fractions with denominators 10 or 100. Solve and articulate a plan for solving multistep number stories involving addition, subtraction, and multiplication, and assess the reasonableness of their answers by comparing them to an estimate. Continue and describe number patterns. Find a multiple of 1/b using strategies. Write a multiplication equation with a letter standing for an unknown to represent a number story involving multiplication of a fraction by a whole number. Add and subtract mixed numbers. Multiply a fraction by a whole number. Add two fractions with denominators 10 and 100. Use decimal notation for fractions with denominators 10 or 100. Solve and articulate a plan for solving multistep number stories involving addition, subtraction, and multiplication, and assess the reasonableness of their answers by comparing them to an estimate. Continue and describe number patterns. Find a multiple of 1/b using strategies. Write a multiplication equation with a letter standing for an unknown to represent a number story involving multiplication of a fraction by a whole number. Add and subtract mixed numbers. Multiply a fraction by a whole number. Add two fractions with denominators 10 and 100. Use decimal notation for fractions with denominators 10 or 100. Solve and articulate a plan for solving multistep number stories involving addition, subtraction, and multiplication, and assess the reasonableness of their answers by comparing them to an estimate. Continue and describe number patterns. Use tools and visual models to generate equivalent fractions and to add fractions with unlike denominators when only one fraction needs to be replaced with an equivalent fraction. Solve fraction-of problems to build a conceptual foundation for multiplication of fractions by whole numbers. Find the area of a rectangle with fractional side lengths by counting the number of unit-fraction tiles that cover the rectangle and relating the count to how many tiles cover a unit square; use area models to represent and find fraction products. Use models to solve problems involving division of a unit fraction by a whole number or division of a whole number by a unit fraction when the problems are in context. Multiply a fraction or a whole number by a fraction. Compare the size of a product to one factor, based on the size of the other factor; explain the effects of multiplying by fractions greater than or less than 1; explain the effects of multiplying fractions by 1. Solve real-world problems involving multiplication of fractions and mixed numbers. Generate a pattern using a given rule; form ordered pairs from corresponding terms in a table; graph ordered pairs on a coordinate plane.