Grade 3 Scoring Rubric/Curriculum Guide

Mathematics - Grade 3

Operations and Algebraic Thinking

Solves multiplication and division word problems

Essential Standard/Student Demonstration

3.OA.1  Interpret products of whole numbers, e.g., interpret 5    7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5    7.

3.OA.2 Interprets whole number quotients of whole numbers, e.g. interprets 56÷8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each

3.OA.3  Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

3.OA.6 Understand division as an unknown-factor problem.  For example, find 32÷8 by finding the number that makes 32 when multiplied by 8.

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g. 9 x 80) using strategies based on place value and properties of operations

End of Year Benchmark

Exceeding Standards

Represents and solves multiplication and division word problem situations beyond 100 involving equal groups, arrays and measurement quantities.

Meeting Standards

Represents and solves multiplication and division word problem situations within 100 involving equal groups, arrays and measurement quantities.

Working Toward the Standards

Represents and solves multiplication and division word problem situations with support within 100 involving equal groups, arrays and measurement quantities.

Limited Progress Toward the Standards

Represents and solve multiplication and division word problem situations with support within 100 involving equal groups and arrays. May or may not be able to solve some division word problem situations

Operations and Algebraic Thinking

Fluently multiplies and divides within 100

Essential Standard/Student Demonstration

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = x  3, 6 x6 = ?.

3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6x4=24 is known, then 4x6 =24 is also known. (Commutative property of multiplication.) 3x5x2 can be found by 3x5=15 then 15x2=30, or by 5x2=10 then 3x10=30. (Associative property of multiplication.) Knowing that 8x5=40 and 8x2=16, one can find 8x7 as 8x (5+2)=(8x5) + (8x2)=40+16=56. (Distributive property.)

3.OA.6 Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that makes 32 when multiplied by 8.

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8  5 = 40, one knows 40  5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.

3.OA.9  Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

End of Year Benchmark

Exceeding Standards

Fluently multiplies and divides beyond 100 using efficient strategies based on the numbers.

Meeting Standards

Fluently multiplies and divides within 100 using efficient strategies based on the numbers.

Working Toward the Standards

Understands the relationship between multiplication and division. With prompting and support can multiply and divide within 100 using appropriate efficient strategies baed on the numbers.

Limited Progress Toward the Standards

With prompting and support multiplies and divides within 50, relies on support to understand the relationship between multiplication and division.

Operations and Algebraic Thinking

Solves two step word problems

Essential Standard/Student Demonstration

3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g. 9 x 80) using strategies based on place value and properties of operations.

End of Year Benchmark

Exceeding Standards

Represents and solves multi-step word problems involving the 4 operations.

Meeting Standards

Represents and solves 2 step word problems involving the 4 operations.

Working Toward the Standards

With prompting and support represents and solves 2 step word problems involving all 4 operations.

Limited Progress Toward the Standards

With prompting and support represents and solves 2 step word problems involving addition and multiplication.

Numbers in Base Ten

Fluently adds and subtracts within1000

Essential Standard/Student Demonstration

3.NBT.A.2 Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [Note: A range of algorithms may be used.]

End of Year Benchmark

Exceeding Standards

Independently and consistently able to fluently add and subtract beyond 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [Note: A range of algorithms may be used.]

Meeting Standards

Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [Note: A range of algorithms may be used.]

Working Toward the Standards

With prompting and support, fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [Note: A range of algorithms may be used.]

Limited Progress Toward the Standards

Limited or unable to fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 

Numbers in Base Ten

Rounds whole numbers to the nearest 10 or 100

Essential Standard/Student Demonstration

3.NBT.1 Uses place value understanding to round whole numbers to the nearest 10 or hundred.

End of Year Benchmark

Exceeding Standards

Uses place value understanding to round whole numbers to the nearest 10 or 100 or 1,000

Meeting Standards

Uses place value understanding to round whole numbers to the nearest 10 or 100.

Working Toward the Standards

Uses place value understanding to round whole numbers within 100 to the nearest 10 and whole numbers within 1,000 to the nearest 100. With prompting and support, uses place value understanding to round whole numbers to the nearest 10 or 100.

Limited Progress Toward the Standards

Uses place value understanding to round whole numbers within 100 to the nearest 10. With prompting and support, uses place value understanding to round whole numbers within 1,000 to the nearest 100.

Fractions

Breaks wholes into equal parts

Essential Standard/Student Demonstration

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

End of Year Benchmark

Exceeding Standards

Partitions wholes into equal parts beyond 8 shares

Meeting Standards

Partitions wholes into 2,4,8,3, and 6 equal parts

Working Toward the Standards

With prompting and support partitions wholes into 2,4,8,3,6 equal parts

Limited Progress Toward the Standards

Partitions wholes into 2 equal parts. With prompting and support partition wholes in 4 and 8 equal parts

Fractions

Compares fractions

Essential Standard/Student Demonstration

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

1. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
2. Recognize and generate simple equivalent fractions, e.g., ½ = 2/4,

4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

1. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. (e.g. Express 3 in the form 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.)
2. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

End of Year Benchmark

Exceeding Standards

Compares fractions with denominators beyond 8 and fractions beyond one whole by using visual fraction models and or by reasoning about their size

Meeting Standards

Compares fractions with denominators beyond 8 and fractions beyond one whole by using visual fraction models and or by reasoning about their size

Working Toward the Standards

Compares fractions with denominators of 2,4 and 8 by using visual fraction models and/or by reasoning about their size. With prompting and support can compare fractions with denominators of 3 and 6.

Limited Progress Toward the Standards

Compares fractions with denominators of 2 and 4 by using visual fraction models and/or by reasoning about their size, can compare fractions with denominators of 8.

Fractions

Shows fractions on a number line

Essential Standard/Student Demonstration

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

1. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
2. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

End of Year Benchmark

Exceeding Standards

Represents unit fractions on a number line with denominators beyond 8 and fractions beyond 1 whole.

Meeting Standards

Represents unit fractions on a number line with denominators of 2, 4, 8, 3, and 6.

Working Toward the Standards

Represents unit fractions on a number line with a denominator of 2, 4, and 8. With prompting and support is able to represent unit fractions on a number line with denominators of 3 and 6.

Limited Progress Toward the Standards

Represents unit fractions on a number line with a denominator of 2. With prompting and support is able to represent unit fractions on a number line with a denominator of 4.

Measurement and Data

Tells time to the nearest minute and elapsed time

Essential Standard/Student Demonstration

3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

End of Year Benchmark

Exceeding Standards

Tells and writes time to the nearest minute and solves 2-step elapsed time problems to the nearest minute involving addition and subtraction, by representing the problem on a number line diagram.

Meeting Standards

Tells and writes time to the nearest minute and solves elapsed time problems to the nearest minute, involving addition and subtraction, by representing the problem on a numberline diagram

Working Toward the Standards

Tells and writes time to the nearest minute and solves elapsed time problems, to the nearest hour, half hour and quarter hour, involving addition and subtraction by representing the problem on a number line diagram. With prompting and support, solves elapsed time problems, to the nearest minute, involving addition and subtraction, by representing the problem on a number line diagram.

Limited Progress Toward the Standards

Tells and writes time to the nearest minute and solves elapsed time problems, to the nearest hour and half hour, involving addition and subtraction by representing the problem on a number line diagram. With prompting and support, solves elapsed time problems, to the nearest quarter hour, involving addition and subtraction, by representing the problem on a number line diagram.

Measurement and Data

Shows measurement data on a line plot

Essential Standard/Student Demonstration

3.MD.4 Generate measurement data by measuring lengths of objects using rulers marked with halves and fourths of an inch. Record and show the data by making a line plot (dot plot), where the horizontal scale is marked off in appropriate units— whole numbers, halves, or fourths

End of Year Benchmark

Exceeding Standards

Independently generates, records, and shows data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or fourths. Provides analysis of data represented by line plot.

Meeting Standards

Independently generates, records, and shows data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or fourths.

Working Toward the Standards

WIth prompting and support, generates, records, and shows data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or fourths.

Limited Progress Toward the Standards

Unable to generate, record, and show data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or fourths.

Measurement and Data

Solves problems involving mass and liquid volume

Essential Standard/Student Demonstration

3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent problems.

End of Year Benchmark

Exceeding Standards

Uses addition, subtraction, multiplication, and division to solve 2 step problems involving mass and liquid volume.

Meeting Standards

Uses addition, subtraction, multiplication, and division to solve problems involving mass and liquid volume.

Working Toward the Standards

Uses addition, subtraction, and multiplication to solve problems involving mass and liquid volume. With prompting and support, uses division to solve problems involving mass and liquid volume.

Limited Progress Toward the Standards

Uses addition and subtraction to solve problems involving mass and liquid volume. With prompting and support, solves problems using multiplication involving mass and liquid volume. May or may not be able to solve division problems involving mass or liquid volume even with support.

Measurement and Data

Uses a variety of strategies to find area

Essential Standard/Student Demonstration

3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

1. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

1. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3.MD.7 Relate area to the operations of multiplication and addition.

1. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
2. Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
3. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning.
4. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

End of Year Benchmark

Exceeding Standards

Uses multiplication and division to find the missing length, width or area of a region (rectangles and regions that can be decomposed into rectangles) using the given length or width or area.

Meeting Standards

Uses a variety of strategies to find the area of regions (rectangles and regions that can be decomposed into rectangles).

Working Toward the Standards

Uses counting and tiling to find the area of regions (rectangles and regions that can be decomposed into rectangles). With prompting and support, uses multiplication to find the area of regions, (rectangles and regions that can be decomposed into rectangles).

Limited Progress Toward the Standards

Uses counting and tiling to find the area of rectangles. With prompting and support, uses counting and tiling to find the area of regions that can be decomposed into rectangles.

Measurement and Data

Creates and understands bar graphs and pictographs

Essential Standard/Student Demonstration

3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. solves one- and two- step “how many more” and “how many less” problems using information presented in scaled bar graphs.

End of Year Benchmark

Exceeding Standards

Independently and consistently, represents and interprets data on various graphs.  Independently and consistently able to solve multi-step problems using information presented in the graphs.

Meeting Standards

Represents and interprets data on a scaled picture graph and scaled bar graph. Independently solves one step problems using information presented in the graphs.

Working Toward the Standards

With prompting and support, represents and interprets data on a scaled picture graph and scaled bar graph. With prompting and support, solves one step problems using information presented in the graphs.

Limited Progress Toward the Standards

Limited or unable to represent and interpret data on a scaled picture graph and scaled bar graph. Limited or unable to solve one step problems using information presented in the graphs.

Measurement and Data

Solves problems to determine the perimeter

Essential Standard/Student Demonstration

3.MD.8 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

End of Year Benchmark

Exceeding Standards

Solves problems involving perimeter of polygons including missing side length problems and exhibits rectangles with the same perimeter and different areas or with the same areas and different perimeters. Uses the perimeter formula using multiplication and addition to solve perimeter problems of rectangles. e.g. of 2 (4 cm) + 2 (6cm) = 14cm

Meeting Standards

Solves problems involving perimeter of polygons including missing side length problems and exhibits rectangles with the same perimeter and different areas or with the same areas and different perimeters. Uses the perimeter formula using multiplication and addition to solve perimeter problems of rectangles. e.g. of 2 (4 cm) + 2 (6cm) = 14cm

Working Toward the Standards

Solves problems involving perimeter of polygons. With prompting and support, solves problems involving perimeter with missing side lengths in rectangles.

Limited Progress Toward the Standards

Solves problems involving perimeter of rectangles. With prompting and support solves problems involving perimeter of other polygons.

Geometry

Compares and Classifies shapes

Essential Standard/Student Demonstration

3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories

End of Year Benchmark

Exceeding Standards

Compares classifies shapes by their sides (presence or absence of parallel or perpendicular) and angles (right, acute, obtuse).

Meeting Standards

Compares classifies shapes by their sides(number of) and angles (right angle/non-right angle- square corner/on-square corner).

Working Toward the Standards

With prompting and support, compares and classifies shapes by their sides (number of) and angles (right angle/non-right angle).

Limited Progress Toward the Standards

With prompting and support, compares and classifies shapes by their sides (number of).

Geometry

Breaks shapes into parts with equal areas

Essential Standard/Student Demonstration

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal areas and describe the area of each part as ¼ of the area of the shape

End of Year Benchmark

Exceeding Standards

Partitions shapes into parts with equal areas and express the area of each part as a unit fraction beyond the denominator of 8. Expresses the area of multiple parts together as a fraction

Meeting Standards

Partitions shapes into parts with equal areas and express the area of each part as a unit fraction (limited to denominators of 2, 4, 8, 3, and 6).

Working Toward the Standards

With prompting and support, partitions shapes into parts with equal areas and express the area of each part as a unit fraction (limited to denominators of 2, 4, 8, 3, and 6).

Limited Progress Toward the Standards

With prompting and support, partitions shapes into parts with equal areas with up to 4 parts.