Fifth Grade Math Grade Expectations

M5:1 Demonstrates conceptual understanding of rational numbers

with respect to:

whole numbers from 0 to 9,999,999 through equivalency,

composition, decomposition, or place value using models,

explanations, or other representations;

positive fractional numbers (proper, mixed number, and

improper) (halves, fourths, eighths, thirds, sixths, twelfths, fifths,

or powers of ten [10, 100, 1000]), decimals (to thousandths), or

benchmark percents (10%, 25%, 50%, 75% or 100%) as a part

to whole relationship in area, set, or linear models using models,

explanations, or other representations.*

M(N&O)–5–1

*Specifications for area, set, and linear models for grades 5–8: Fractions: The number of parts in the whole is equal to the denominator, a multiple of the denominator, or a factor of the denominator. Percents: The number of parts in the whole is equal to 100, a multiple of 100, or a factor of 100 (for grade 5); the number of parts in the whole is a multiple or a factor of the numeric value representing the whole (for grades 6–8). Decimals (including powers of ten): The number of parts in the whole is equal to the denominator of the fractional equivalent of the decimal, a multiple of the denominator of the fractional equivalent of the decimal, or a factor of the denominator of the fractional equivalent of the decimal.

M5:2 Demonstrates understanding of the relative magnitude of

numbers by ordering, comparing, or identifying equivalent positive

fractional numbers, decimals, or benchmark percents within number

formats (fractions to fractions, decimals to decimals, or percents to

percents); or integers in context using models or number lines.

M(N&O)–5–2

M5:3 Demonstrates conceptual understanding of mathematical

operations by describing or illustrating the meaning of a

remainder with respect to division of whole numbers using models,

explanations, or solving problems.

M(N&O)–5–3

M5:4 Accurately solves problems involving multiple operations on

whole numbers or the use of the properties of factors, multiples,

prime, or composite numbers; and addition or subtraction of

fractions (proper) and decimals to the hundredths place. (Division of

whole numbers by up to a two-digit divisor.)

(IMPORTANT: Applies the conventions of order of operations with

and without parentheses.)

M(N&O)–5–4

M5:5 No M5:5 at this grade level

M5:6 Mentally multiplies and divides whole numbers through twelve

with accuracy.

M5:7 Estimates and evaluates the reasonableness of solutions

appropriate to grade level.

M5:8 Applies properties of numbers (odd, even, factor, multiple, prime,

composite, divisibility, remainders, composition/decomposition) to

solve problems and to simplify computations.

M5:9 Uses properties or attributes of angles (right, acute, or

obtuse) or sides (number of congruent sides, parallelism, or

perpendicularity) to identify, describe, classify, or distinguish

among different types of triangles (right, acute, obtuse,

equiangular, or equilateral) or quadrilaterals (rectangles, squares,

rhombi, trapezoids, or parallelograms).

M(G&M)–5–1

M5:10 No M5:10 at this grade level

M5:11 Uses properties or attributes (shape of bases, number of lateral

faces, or number of bases) to identify, compare, or describe

three-dimensional shapes (rectangular prisms, triangular prisms,

cylinders, spheres, pyramids, or cones).

M(G&M)–5–3

M5:12 Demonstrates conceptual understanding of congruency by

matching congruent figures using reflections, translations, or

rotations (flips, slides, or turns), or as the result of composing or

decomposing shapes using models or explanations.

M5:13 Demonstrates conceptual understanding of similarity by

describing the proportional effect on the linear dimensions of

polygons when scaling up or down while preserving the angles of

polygons, or by solving related problems (including applying scales

on maps). Describes effects using models or explanations.

M5:14 Demonstrates conceptual understanding of perimeter of

polygons, and the area of rectangles or right triangles through

models, manipulatives, or formulas, the area of polygons or

irregular figures on grids, and volume of rectangular prisms

(cubes) using a variety of models, manipulatives, or formulas.

Expresses all measures using appropriate units.

M(G&M)–5–6

M5:15 Measures and uses units of measures appropriately and

consistently, and makes conversions within systems when

solving problems across the content strands. (Benchmarks in

Appendix B.)

M(G&M)–5–7

M5:16 Determines elapsed and accrued time to the nearest minute.

M5:17 No M5:17 at this grade level

M5:18 Solves problems using the Cartesian coordinate system (all

quadrants) to locate coordinates and to represent data from tables.

M5:19 Identifies and extends to specific cases a variety of patterns

(linear and nonlinear) represented in models, tables, sequences,

or in problem situations; and writes a rule in words or symbols for

finding specific cases of a linear relationship.

M(F&A)–5–1

M5:20 Demonstrates a conceptual understanding of linear

relationships ( y = kx) as a constant rate of change by

identifying, describing, or comparing situations that represent

constant rates of change.

M5:21 Demonstrates conceptual understanding of algebraic

expressions by using letters to represent unknown quantities to

write linear algebraic expressions involving any two of the four

operations; or by evaluating linear algebraic expressions using

whole numbers.

M(F&A)–5–3

M5:22 Demonstrates conceptual understanding of equality by showing

equivalence between two expressions using models or different

representations of the expressions (expressions consistent with the

parameters of M(F&A)–5–3), by solving one-step linear equations

of the form ax = c, x ± b = c, or x/ a = c, where a, b, and c are

whole numbers with a . 0; or by determining which values of a

replacement set make the equation (multistep of the form ax ±

b = c where a, b, and c are whole numbers with a . 0) a true

statement (e.g., 2 x + 3 = 11, { x: x = 2, 3, 4, 5}).

M(F&A)–5–4

M5:23 Interprets a given representation (tables, bar graphs, circle

graphs, or line graphs) to answer questions related to the data,

to analyze the data to formulate or justify conclusions, to make

predictions, or to solve problems.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M5:24.)

M(DSP)–5–1

And (tally charts, frequency charts, line graphs, Venn diagrams,

pictographs, line plots, histograms).

M5:24 Analyzes patterns, trends, or distributions in data in a variety

of contexts by determining or using measures of central

tendency (mean, median, or mode) or range to analyze situations,

or to solve problems.

M(DSP)–5–2

M5:25 Identifies or describes representations or elements of

representations that best display a given set of data or

situation, consistent with the representations required in M5:23.

M(DSP)–5–3

Organizes and displays data using line plots, bar graphs, tally

charts and frequency charts, or tables to answer question related to

the data, to analyze the data to formulate or justify conclusions, to

make predictions, or to solve problems.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M5:24.)

M5:26 Uses counting techniques to solve problems in context involving

combinations using a variety of strategies (e.g., organized lists,

tables, tree diagrams, or others); or determines the possible

outcomes for a sample space that contains equally likely outcomes.

M5:27 For a probability event in which the sample space may or

may not contain equally likely outcomes, determines the

experimental or theoretical probability of an event and expresses

the result as a fraction.

M(DSP)–5–5

M5:28 In response to a teacher- or student-generated question

or hypothesis, collects appropriate data, organizes the data,

appropriately displays/represents numerical and/or categorical

data, analyzes the data to draw conclusions about the questions or

hypothesis being tested, and when appropriate makes predictions,

asks new questions, or makes connections to real-world situations.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M5:24.)

M5:29 Uses experimental probability, evaluates the possible

outcomes, and describes the likelihood or chance of an event

as a ratio of actual times the event occurred to the number of trials

written as either a ratio or as part to whole.

M5:30 Demonstrate understanding of mathematical problem solving2

and communication through:

• Approach & Reasoning—The reasoning, strategies, and skills

used to solve the problem;

• Connections—Demonstration of observations, applications,

extensions, and generalizations;

• Solution—All of the work that was done to solve the problem,

including the answer;

• Mathematical Language—The use of mathematical language

in communicating the solution;

• Mathematical Representation—The use of mathematical

representation to communicate the solution; and

• Documentation—Presentation of the solution.