FOURTH GRADE MATH STANDARDS BASED RUBRIC NUMBER SENSE Essential Standard: 1.0 STUDENTS UNDERSTAND THE PLACE VALUE OF WHOLE NUMBERS AND DECIMALS TO TWO DECIMAL PLACES AND HOW WHOLE NUMBERS AND DECIMALS RELATE TO SIMPLE FRACTIONS. First Trimester  1.1  1.2  1.3  1.4

FAR BELOW/BELOW BASIC Unable read and write whole numbers in millions. Unable to order and compare whole numbers. Unable to round whole numbers through the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Unable to decide when a rounded solution is called for and explain why such a solution may be appropriate.

  



BASIC Inconsistently read and write whole numbers in the millions. Inconsistently order and compare whole numbers. Inconsistently round whole numbers through the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Inconsistently decide when a rounded solution is called for and explain why such a solution may be appropriate.

  

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PROFICIENT Read and write whole numbers in the millions. Order and compare whole numbers through millions Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Decide when a rounded solution is called for and explain why such a solution may be appropriate.

  

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ADVANCED Apply concepts of millions to the real world. Order and compare whole numbers and decimals. Round fractions to the nearest benchmark number.

Create problems that require a rounded answer.

Second Trimester  1.2

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Unable to explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers; explain equivalents of fractions.

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Unable to write tenths and hundredths in decimal and fraction notation and know the fraction equivalents for halves and fourths.

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1.5

1.6

FAR BELOW/BELOW BASIC Unable to order and compare whole numbers and decimals to two decimal places.

BASIC Inconsistently order and compare whole numbers and decimals to two decimal places. Inconsistently explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers; explain equivalents of fractions. Inconsistently write tenths and hundredths in decimal and fraction notation and know the fraction equivalents for halves and fourths.

6-09

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

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PROFICIENT Order and compare whole numbers and decimals to two decimal places. Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions. Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths.

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ADVANCED Order and compare whole numbers and decimals to three decimal places.

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Compare and order fractions on a number line.

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Understand the equivalents of tenths and hundredths and their relationships.

1

 1.7

 1.8  1.9

Unable to write a fraction represented by a drawing of parts of a figure; represent a given fraction by using a drawing; and relate a fraction to a simple decimal on a number line. Unable to use concepts of negative numbers (e.g. number line, in counting, in temperature, and in “owing”). Unable to identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

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

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Inconsistently write a fraction represented by a drawing of parts of a figure; represent a given fraction by using a drawing; and relate a fraction to a simple decimal on a number line. Inconsistently use concepts of negative numbers (e.g. number line, in counting, in temperature, and in “owing”). Inconsistently identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

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Write a fraction represented by a drawing of parts of a figure; represent a given fraction by using a drawings; and relate a fraction to a simple decimal on a number line.

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Combine like fractions.

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Use concepts of negative numbers (e.g. number line, in counting, in temperature, and in “owing”). Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

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Add negative numbers on a number line.

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Identify how much larger or how much smaller one fraction or decimal is from another.

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Esstential Standard:

2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals: 2.2

FAR BELOW/BELOW BASIC  Unable to round decimals

BASIC  Inconsistently rounds deicmals to two places or can only round to one place.

PROFICIENT  Able to round two-place decimals to one decimal or the nearest whole number

ADVANCED  Able to round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer

Essential Standard: 3.0 STUDENT USES MULTIPLE STRATEGIES TO SOLVE PROBLEMS INVOLVING ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF WHOLE NUMBERS AND UNDERSTAND THE RELATIONSHIPS AMONG THE OPERATIONS. First Trimester FAR BELOW/BELOW BASIC BASIC PROFICIENT ADVANCED  Unable to use the operations of  Inconsistently use the  Use the operations of addition  Use multiple strategies with 3.1 addition and subtraction and operations of addition and and subtraction and addition and subtraction and understand their relationships subtraction and understand understand their relationships understand their relationships up to hundred thousands. their relationships up to up to hundred thousands. up to hundred thousands. hundred thousands.

6-09

2

 3.2

 3.3  3.4  4.2

Unable to demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a two digit number and for dividing a multi-digit number by a one digit number; use relationships between them to simplify computations and to check results. Unable to solve problems involving multiplication of multi-digit numbers by twodigit numbers. Unable to solve problems involving division of multi-digit numbers by two-digit numbers. Unable to demonstrate that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

Second Trimester FAR BELOW/BELOW BASIC  Unable to demonstrate an 3.2 understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a two digit number and for dividing a multi-digit number by a one digit number; use relationships between them to simplify computations and to check results.  Unable to solve problems 3.4 involving division of multi-digit numbers by two-digit numbers.

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

 

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Inconsistently demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a twodigit number and for dividing a multi-digit number by a onedigit number; use relationships between them to simplify computations and to check results. Inconsistently solve problems involving multiplication of multi-digit numbers by twodigit numbers. Inconsistently solve problems involving division of multi-digit numbers by two-digit numbers. Inconsistently demonstrates that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers. BASIC Inconsistently demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a twodigit number and for dividing a multi-digit number by a onedigit number; use relationships between them to simplify computations and to check results. Inconsistently solve problems involving division of multi-digit numbers by two-digit numbers.

6-09

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Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results.

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Explain and demonstrate the standard multiplication and division algorithm.

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Solve problems involving multiplication of multi-digit numbers by two-digit numbers.

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Apply understanding of multidigit multiplication to abstract situations.

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Solve problems involving division of multi-digit numbers by one-digit numbers. Know that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

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Apply understanding of multidigit division to abstract situations. Know that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers and can apply to higher numbers.

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PROFICIENT Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number; use relationships between them to simplify computations and to check results. Solve problems involving division of multi-digit numbers by one-digit numbers.

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ADVANCED Explain and demonstrate the standard multiplication and division algorithm.

Apply understanding of multidigit division to abstract situations.

3

Essential Standard: 4.0 STUDENT KNOW HOW TO FACTOR SMALL Second Trimester FAR BELOW/BELOW BASIC  Unable to demonstrate that  4.2 numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

WHOLE NUMBERS. BASIC Inconsistently demonstrates that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

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PROFICIENT Know that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

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ADVANCED Know that numbers such as 2,3,5,7 and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers and can apply to higher numbers.

ALGEBRA AND FUNCTIONS Essential Standard: 1.0 STUDENTS USE AND INTERPRET VARIABLES, MATHEMATICAL SYMBOLS AND PROPERTIES TO WRITE AND SIMPLIFY EXPRESSIONS AND SENTENCES. First Trimester: Benchmarks  1.1

 1.2  1.3

 1.5

FAR BELOW/BELOW BASIC Unable to use letters, boxes, or other symbols to stand for any number in simple expressions or equations.

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Unable to interpret and evaluate mathematical expressions that now use parentheses. Unable to use parentheses to indicate which operation to perform first when writing expressions containing more than 2 terms and different operations.

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Unable to understand that an equation such a y=3x + 5 is a prescription for determining a second number when the first number is given.

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BASIC Inconsistently use letters, boxes, or other symbols to stand for any number in simple expressions or equations.

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PROFICIENT Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g. demonstrate an understanding and the use of the concept of a variable). Interpret and evaluate mathematical expressions that now use parentheses.

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Inconsistently interpret and evaluate mathematical expressions that now use parentheses. Inconsistently use parentheses to indicate which operation to perform first when writing expressions containing more than 2 terms and different operations.

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Use parentheses to indicate which operation to perform first when writing expressions containing more than 2 terms and different operations.

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Inconsistently understand that an equation such a y=3x + 5 is a prescription for determining a second number when the first number is given.

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Understand that an equation such a y=3x + 5 is a prescription for determining a second number when the first number is given.

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6-09

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ADVANCED Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution (e.g. 3x + 2 =14. What is x?). Write equations to word problems using mathematical expressions using parentheses. Create equation to real life problems using parentheses to indicate which operation to perform first when writing expressions containing more than 2 terms and different operations.. Apply understanding that an equation (such as y=3x + 5) is a prescription for determining a second number when the first number is given to real life situations.

4

Essential Standard: 2.0 STUDENTS KNOW HOW TO MANIPULATE EQUATIONS First Trimester

2.1

FAR BELOW/BELOW BASIC  Does not understand the concept of equality.

 2.2

Does not understand the concept of equality.

BASIC Understands the concept of equality, but has limited understanding of the properties (e.g. 3+3=6, when 2 is added to both sides the sum is still equal).  Understands the concept of equality, but has limited understanding of the properties (e.g. (7-3) x 5 = 4 X ___). 

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PROFICIENT Know and understand that equals added to equals are equal.

Know and understand that equals multiplied by equals are equal (e.g. (7-3) x 5 = 4 X ___). 

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

ADVANCED Apply understanding of equality to real life situations. Apply understanding of equality to real life situations.

MEASUREMENT AND GEOMETRY Essential Standard: 1.0 STUDENT UNDERSTANDS PERIMETER AND AREA. Third Trimester

1.1

FAR BELOW/BELOW BASIC  Unable to measure the area of rectangular shapes by using appropriate units. 

1.2  1.3  1.4

Unable to recognize that triangles that have the same area can have different perimeters. Unable to understand that rectangles that have the same perimeter can have different areas. Unable to use formulas to find the areas of more complex figures by dividing the figures into basic shapes.

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BASIC Inconsistently measure the area of rectangular shapes by using appropriate units.

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Inconsistently recognize that triangles that have the same area can have different perimeters.

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Inconsistently understand that rectangles that have the same perimeter can have different areas.

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Inconsistently use formulas to find the areas of more complex figures by dividing the figures into basic shapes.

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6-09

PROFICIENT Calculate the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2). Recognize that rectangles that have the same area can have different perimeters.

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ADVANCED Predict, calculate and compare areas of different rectangular shapes.

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Predict and estimate the perimeter of rectangles based on the area.

Understand that rectangles that have the same perimeter can have different areas.

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Predict and estimate the area of triangles based on the perimeter.

Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

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Apply the use of formulas including perimeter and area of rectangles and squares to real life situations.

5

Essential Standard:

2.0 STUDENTS USE TWO-DIMENSIONAL COORDINATE GRIDS TO REPRESENT POINTS AND GRAPH LINES AND SIMPLE FIGURES. Second Trimester  2.1

 2.2  2.3

FAR BELOW/BELOW BASIC Unable to plot the points corresponding to linear relationships on graph paper

Does not understand that the length of a horizontal line segment equals the difference of the “x” coordinates. Does not understand that the length of a vertical line segment equals the difference of the “y” coordinates.

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BASIC Inconsistently plot the points corresponding to linear relationships on graph paper

Inconsistently understand that the length of a horizontal line segment equals the difference of the “x” coordinates. Inconsistently understands that the length of a vertical line segment equals the difference of the “y” coordinates.

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PROFICIENT Plot the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y=3x and connect them by using a straight line). Understand that the length of a horizontal line segment equals the difference of the “x” coordinates. Understand that the length of a vertical line segment equals the difference of the “y” coordinates.

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ADVANCED Apply to real life situations.

Apply to real life situations.

Apply to real life situations.

Essential Standard: 3.0 STUDENTS DEMONSTRATE AN UNDERSTANDING OF PLANE AND SOLID GEOMETRIC OBJECTS AND USE THIS KNOWLEDGE TO SHOW RELATIONSHIPS AND SOLVE PROBLEMS. Third Trimester  3.1

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Unable to identify the radius and diameter of a circle.

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Unable to identify congruent figures.

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Inconsistently identify attributes of triangles.

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Does not know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

3.2 3.3 3.7

3.8

FAR BELOW/BELOW BASIC Unable to identify lines that are parallel and perpendicular.

BASIC Inconsistently identify lines that are parallel and perpendicular. Inconsistently identify the radius and diameter of a circle.

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PROFICIENT Identify lines that are parallel and perpendicular.

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Identify the radius and diameter of a circle.

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Inconsistently identify congruent figures.

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Identify congruent figures.

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Identify attributes of triangles.

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Inconsistently verbalize the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

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Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes. Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

6-09



ADVANCED Construct parallel and perpendicular lines using appropriate tools. Measure the radius and diameter of a circle using appropriate tools. From an existing figure, draw a congruent figure using appropriate tools. Know the sum of the angles of any triangle is 180 . Know the sum of the angles of any quadrilateral is 360 .

6

Third Trimester

 3.4  3.5

3.6



FAR BELOW/BELOW BASIC Unable to identify figures that have bilateral and rotational symmetry. Inconsistently identify right angles and determine whether angles are greater than, less than, or equal to a right angle. Inconsistently identify, describe, and classify common three-dimensional geometric objects (cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

 

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BASIC Inconsistently identify figures that have bilateral and rotational symmetry. Identify right angles in geometric figures or in appropriate objects and determine whether triangles are greater than or less than a right angle. Identify, describe, and classify common three-dimensional geometric objects (cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

 

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PROFICIENT Identify figures that have bilateral and rotational symmetry. Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90 , 180 , 270 , and 360 are associated respectively with ¼, ½, ¾, and full turns. Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shapes of faces, edges, and vertices; interpret twodimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.

 



ADVANCED Visualize and draw figures that have bilateral and rotational symmetry. Use the properties of complimentary and supplementary angles and the sum to solve problems involving and unknown angle. Visualize and draw twodimensional views of threedimensional objects made from rectangular solids.

STATISTICS, DATA ANALYSIS, AND PROABILITY Essential Standard: 1.0 STUDENTS ORGANIZE, REPRESENT, AND INTERPRET NUMERICAL AND CATEGORICAL DATA AND CLEARLY COMMUNICATE THEIR FINDINGS. Third Trimester 

FAR BELOW/BELOW BASIC Unable to read and interpret data from a graph..

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BASIC Read and interpret data from one type of graph.



1.1 

Unable to identify the mode(s) for sets of categorical data or the mode(s), median, and any apparent outliers for numerical data sets.

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

Unable to Interpret variable data graphs.



1.2

1.3

Inconsistently identify the mode(s) for sets of categorical data and/or the mode(s), median, and any apparent outliers for numerical data sets. Inconsistently interpret one and two variable data graphs to answer questions about a situation. 6-09



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PROFICIENT Read and interpret data from various types of graphs (e.g., using pictures, bar graphs, tally charts, real graphs, and picture graphs). Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets. Interpret one and two variable data graphs to answer questions about a situation.

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ADVANCED Collect and represent data using various types of graphs (e.g., using picture, bar graphs, tally charts, real graphs, and picture graphs). Apply understanding of mode and median to real life situations.

Formulate questions about a situation shown on one and two variable data graphs. 7

STATISTICS, DATA ANALYSIS, AND PROBABILITY Essential Standard: 2.0 STUDENTS MAKE PREDICTIONS FOR SIMPLE PROBABILITY SITUATIONS. Third Trimester  2.1

 2.2

FAR BELOW/BELOW BASIC Unable to represent outcomes for a simple probability situation. Unable to express outcomes of an experimental probability situation.

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BASIC Inconsistently represent outcomes for a simple probability situation.

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Inconsistently express outcomes of experimental probability.

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PROFICIENT Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams). Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; ¾).

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ADVANCED Use data to predict outcomes of a future event.

Express the theoretical probability of the outcomes.

K:\dleal\website\WORD\CURRICULUM ALIGNMENT\BENCHMARKS & ESSENTIAL STDS. - LANG & MATH K-6 FINAL 11-01\K-6 MATH\GRADE 4 FINAL MATH.doc

6-09

8