MATHEMATICS

1) Understands and applies mathematical concepts.

Trimester 1 2 3 4

1st

Numeration: Student is unable or rarely able to demonstrate understanding of numeration concepts.

Numeration: Student demonstrates partial understanding of numeration concepts.

Numeration:● Student consistently understands

place value concepts in the base ten numeration system; that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.A.1

● Student can apply and explain patterns in zeros when multiplying by powers of 10. 5.NBT.A.2

● Student can explain patterns in the placement of a decimal point when multiplying or dividing by a power of 10. 5.NBT.A.2

● Student uses whole number exponents to denote powers of 10. 5.NBT.A.2

● Student is able to read and write

Numeration: Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Multiplication and Division with Multi-Digit Whole Numbers: Student is unable or rarely able to use concepts of multiplication and division of whole numbers.

Multiplication and Division with Multi-Digit Whole Numbers: Student sometimes uses concepts of multiplication and division of whole numbers.

decimals to thousandths using base-ten numerals, number names, and expanded form. 5.NBT.A.3.A

● Student can compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 5.NBT.A.3.B

● Student uses place value understanding to round decimals to any place. 5.NBT.A.4

Multiplication and Division with Multi-Digit Whole Numbers:

● Student can fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.B.5

● Student consistently finds whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 5.NBT.B.6

● Student consistently applies strategies based on place value, the properties of operations, and/or the relationship between multiplication and division to

Multiplication and Division with Multi-Digit Whole Numbers: Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Operations with Decimals to Hundredths: Student is unable or rarely able to use concepts of decimal operations.

Operations with Decimals to Hundredths: Student sometimes uses concepts of decimal operations.

solve problems. 5.NBT.B.6● Student can illustrate and explain

calculations by using equations, rectangular arrays, and/or area models. 5.NBT.B.6

Operations with Decimals to Hundredths:

● Student fluently adds, subtracts, multiplies and divides decimals tohundredths. 5.NBT.B.7

● Student uses concrete models or drawings and consistently applies strategies based on place value, the properties of operations, and/or the relationship between inverse operations to solve problems. 5.NBT.B.7

Operations with Decimals to Hundredths: Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

2nd

Adding and Subtracting Fractions:Student is unable or rarely able to use concepts of addition and subtraction of fractions.

Adding and Subtracting Fractions:Student sometimes uses concepts of addition and subtraction of fractions.

Adding and Subtracting Fractions:● Student can add and subtract

fractions and mixed numbers by using equivalent fractions. 5.NF.A.1

● Student uses visual fraction models and equations to solve problems. 5.NF.A.2

● Student consistently uses benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 5.NF.A.2

Multiplying Fractions:● Student can interpret the product

Adding and Subtracting Fractions:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Multiplying Fractions:Student is unable or rarely able to use concepts of multiplication of fractions.

Multiplying Fractions:Student sometimes uses concepts of multiplication of fractions.

(a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. 5.NF.B.4.A

● Student can find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. 5.NF.B.4.B

● Student can multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.NF.B.4.B

● Student can interpret multiplication as scaling by:- comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5.NF.B.5.A- explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. 5.NF.B.5.B

Multiplying Fractions:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

● Student can solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. 5.NF.B.6

Dividing Fractions:● Student can interpret a fraction as

division of the numerator by the denominator (a/b = a ÷ b). 5.NF.B.3

● Student can solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, by using visual fraction models or equations to represent the problem. 5.NF.B.3

● Student can interpret division of a unit fraction by a non-zero whole number, and compute such quotients. 5.NF.B.7.A

● Student can interpret division of a whole number by a unit fraction, and compute such quotients. 5.NF.B.7.B

● Student can solve real world problems involving division of unit

Grading Benchmarks – FIFTH GRADE

Dividing Fractions:Student is unable or rarely able to use concepts of dividing fractions.

Dividing Fractions:Student sometimes uses concepts of division of fractions.

fractions by non-zero whole numbers and division of whole numbers by unit fractions, by using visual fraction models and equations to represent the problem. 5.NF.B.7.C

Volume Concepts:● Student recognizes that a cube with

side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. 5.MD.C.3.A

● Student recognizes that a solid figure, which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.C.3.B

● Student can measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.C.4

● Student can find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying

Dividing Fractions:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Volume Concepts:Student is unable or rarely able to use volume concepts.

Volume Concepts:Student sometimes uses volume concepts.

the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. 5.MD.C.5.A

● Student can apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. 5.MD.C.5.B

● Student recognizes volume as additive and can find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. 5.MD.C.5.C

Converting Measurements:● Student is able to convert among

different-sized standard measurement units within a given measurement system. 5.MD.5.A.1

● Student uses these conversions in solving multi-step, real world

Volume Concepts:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

problems. 5.MD.5.A.1

Writing and Interpreting Numerical Expressions:

● Student is able to use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.A.1

● Student is able to write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 5.OA.A.2

Grading Benchmarks – FIFTH GRADE

Converting Measurements:Student is unable or rarely able to use concepts of converting measurements.

Converting Measurements:Student sometimes uses concepts of converting measurements.

Converting Measurements:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Writing and Interpreting Numerical Expressions:Student is unable or rarely able to use concepts of writing and interpreting numerical expressions.

Writing and Interpreting Numerical Expressions:Student sometimes uses concepts of writing and interpreting numerical expressions.

Writing and Interpreting Numerical Expressions:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Grading Benchmarks – FIFTH GRADE

3rd Representing and Interpreting Data:Student is unable or rarely able to use concepts of representing and interpreting data.

Points on the Coordinate Plane:Student is unable or rarely able to use concepts of points on the coordinate plane.

Representing and Interpreting Data:Student sometimes uses concepts of representing and interpreting data.

Points on the Coordinate Plane:Student sometimes uses concepts of points on the coordinate plane.

Representing and Interpreting Data:● Student can make a line plot to

display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). 5.MD.B.2

● Student can use operations on fractions for fifth grade (5.NF.A.2, 5.NF.B.6) to solve problems involving information presented in line plots.  5.MD.B.2

Points on the Coordinate Plane:● Student can use a pair of

perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. 5.G.A.1

● Student understands that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates

Representing and Interpreting Data:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Points on the Coordinate Plane:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 5.G.A.1

● Student can represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. 5.G.A.2

● Student can interpret coordinate values of points in the context of the situation. 5.G.A.2

Analyzing Patterns and Relationships:● Student can generate two numerical

patterns using two given rules and identify apparent relationships between corresponding terms. 5.OA.B.3

● Student can form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. 5.OA.B.3 (5.G.A.2)

Classifying Two-Dimensional Figures:● Student understands that attributes

belonging to a category of two-dimensional figures also belong to all subcategories of that category. (For example, all rectangles have four

Grading Benchmarks – FIFTH GRADE

Analyzing Patterns and Relationships:Student is unable or rarely able to use concepts of analyzing patterns and relationships.

Classifying Two-Dimensional Figures:Student is unable or rarely able to use concepts of classifying two-dimensional figures.

Analyzing Patterns and Relationships:Student sometimes uses concepts of analyzing patterns and relationships.

Classifying Two-Dimensional Figures:Student sometimes uses concepts of classifying two-dimensional figures.

right angles and squares are rectangles, so all squares have four right angles.) 5.G.B.3

● Student can classify two-dimensional figures in a hierarchy based on properties. 5.G.B.4

Analyzing Patterns and Relationships:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Classifying Two-Dimensional Figures:Student consistently makes insightful connections to other ideas and concepts and independently challenges him/herself.

Grading Benchmarks – FIFTH GRADE

Grading Benchmarks – FIFTH GRADE

2)Recalls math facts with speed and accuracy.

Trimester 1 2 3 4

ALLStudent is unable or rarely able to recall multiplication and division facts with 1 through 12.

Student is unable or rarely able to

Student can sometimes recall multiplication and division facts with 1 through 12.

Student can sometimes mentally

Student can consistently recall multiplication and division facts with 1 through 12.

Student mentally calculates products with multiples of

Student is able to apply and extend

content knowledge independently.

Grading Benchmarks – FIFTH GRADE

mentally calculate products with multiples of 10.

Student is unable to mentally calculate whole number quotients with divisors that are of powers of 10.

calculate products with multiples of 10.

Student can sometimes mentally calculate whole number quotients with divisors that are powers of 10.

10.

Student mentally calculates whole number quotients with divisors that are of powers of 10.

3) Understands and solves word problems accurately.

Trimester 1 2 3 4

ALL

● Student is unable or rarely able to apply math content knowledge and skills to solve problems.

● Student is unable or rarely able to choose appropriate tools (diagrams,

● Student sometimes applies math content knowledge and skills to solve problems.

● Student sometimes chooses appropriate tools (diagrams, pictures, equations/numbe

● Student consistently applies math content knowledge and skills to solve problems.

● Student consistently chooses appropriate tools (diagrams, pictures, equations/number sentences, tables, graphs, number lines, formulas, etc.) to solve problems.

● Student work includes all necessary calculations and labels.

● Student applies content knowledge independently to life experiences.

● Student consistently uses a variety of processes including problem solving,

Grading Benchmarks – FIFTH GRADE

pictures, equations/number sentences, tables, graphs, number lines, formulas, etc.) to solve problems.

● Student work rarely includes all necessary calculations and labels.

r sentences, tables, graphs, number lines, formulas, etc.) to solve problems.

● Student work sometimes includes all necessary calculations and labels.

reasoning, communicating, connecting, and representing to extend solutions to other situations, to design other strategies, and/or to apply strategies to life experiences.

4) Computes accurately.

Trimester 1 2 3 4

ALLStudent is unable or rarely able to identify appropriate operations and mathematically compute the correct answer.

Student sometimes identifies appropriate operations and mathematically computes the correct answer.

Student consistently identifies appropriate operations and mathematically computes the correct answer.

Student consistently applies appropriate operations and computes accurately on more complex problems, mental math, and/or other mathematical concepts.

Grading Benchmarks – FIFTH GRADE

5) Clearly expresses mathematical thinking in written and oral form.

Trimester 1 2 3 4

ALLStudent is unable or rarely able to communicate mathematical thinking precisely and with accurate vocabulary.

Student sometimes, but not consistently, communicates mathematical thinking precisely and with accurate vocabulary.

Student communicates all mathematical thinking precisely and with accurate vocabulary.

Student communicates all mathematical thinking precisely and with accurate vocabulary.

Student communicates logical arguments clearly in oral, written, and/or graphic form toshow why a result makes sense.

Grading Benchmarks – FIFTH GRADE