Fourth Grade Math Grade Expectations

M4:1 Demonstrates conceptual understanding of rational numbers

with respect to:

whole numbers from 0 to 999,999 through equivalency,

composition, decomposition, or place value using models,

explanations, or other representations; and

positive fractional numbers (benchmark fractions: a/2, a/3, a/4,

a/5, a/6, a/8, or a/10, where a is a whole number greater than

0 and less than or equal to the denominator) as a part to whole

relationship in area, set, or linear models where the number of

parts in the whole are equal to, and a multiple or factor of the

denominator; and decimals as hundredths within the context of

money, or tenths within the context of metric measurements (e.g.,

2.3 cm) using models, explanations, or other representations.

M(N&O)–4–1

M4:2 Demonstrates understanding of the relative magnitude of

numbers from 0 to 999,999 by ordering or comparing whole

numbers; and ordering, comparing, or identifying equivalent proper

positive fractional numbers; or decimals using models, number

lines, or explanations.

M(N&O)–4–2

M4:3 Demonstrates conceptual understanding of mathematical

operations by describing or illustrating the relationship between

repeated subtraction and division (no remainders); the inverse

relationship between multiplication and division of whole numbers;

or the addition or subtraction of positive fractional numbers with like

denominators using models, number lines, or explanations.

M(N&O)–4–3

M4:4 Accurately solves problems involving multiple operations on

whole numbers or the use of the properties of factors and multiples;

and addition or subtraction of decimals and positive proper fractions

with like denominators. (Multiplication limited to 2 digits by 2 digits,

and division limited to 1 digit divisors.)

(IMPORTANT: Applies the conventions of order of operations

where the left to right computations are modified only by the use of

parentheses.)

M(N&O)–4–4

M4:5 No M4:5 at this grade level

M4:6 Mentally adds and subtracts whole numbers through twenty and

multiplies whole numbers through twelve with accuracy.

M4:7 Estimates and evaluates the reasonableness of solutions

Appropriate to grade level.

M4:8 Applied properties of numbers (odd, even, factor, multiple,

remainders, composition/decomposition) to solve problems and to

simplify computations.

M4:9 Uses properties or attributes of angles (number of angles)

or sides (number of sides, length of sides, parallelism, or perpendicularity)

to identify, describe, or distinguish among triangles squares, rectangles,

rhombi, trapezoids, hexagons, or octagons; or classify angles relative to 90o as

more than, less than, or equal to.

M(G&M)-4-1

Recognizes symmetrical figures and uses symmetry to identify and classify figures.

M4:10 No M4:10 at this grade level

M4:11 Uses properties or attributes (shape of bases or number of lateral

faces) to identify, compare, or describe three-dimensional

shapes (rectangular prisms, triangular prisms, cylinders, or

spheres). M(G&M)–4–3

Identifies components (faces, edges, and vertices) of three dimensional

shapes (cubes and rectangular prisms).

M4:12 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.

M(G&M)–5–4

M4:13 Demonstrates conceptual understanding of similarity by

applying scales on maps, or applying characteristics of similar

figures (same shape, but not necessarily the same size) to identify

similar figures, or to solve problems involving similar figures.

Describes relationships using models or explanations.

M(G&M)–4–5

M4:14 Demonstrates conceptual understanding of perimeter of

polygons, and the area of rectangles, polygons, or irregular shapes

on grids using a variety of models, manipulatives, or formulas.

Expresses all measures using appropriate units.

M(G&M)–4–6

M4:15 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)–4–7

M4:16 Determines elapsed and accrued time to the ¼ hour.

M4:17 No M4:17 at this grade level

M4:18 Solves problems using the Cartesian coordinate system

(Quadrant I) to locate coordinates and to represent data from tables.

M4:19 Identifies and extends to specific cases a variety of patterns

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

and writes a rule in words or symbols to find the next case.

M(F&A)–4–1

M4:20 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.

M4:21 Demonstrates conceptual understanding of algebraic

expressions by using letters or symbols to represent unknown

quantities to write simple linear algebraic expressions involving any

one of the four operations; or by evaluating simple linear algebraic

expressions using whole numbers.

M(F&A)–4–3

M4:22 Demonstrates conceptual understanding of equality by showing

equivalence between two expressions using models or different

representations of the expressions, by simplifying numerical

expressions where left to right computations may be modified

only by the use of parentheses [e.g., 14 – (2 × 5)] (expressions

consistent with the parameters of M(F&A)–4–3), and by solving

one-step linear equations of the form ax = c, x ± b = c, where a, b,

and c are whole numbers with a . 0.

M(F&A)–4–4

M4:23 Interprets a given representation (line plots, tables, bar graphs,

pictographs, or circle 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

M4:24.)

M(DSP)–4–1

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

M4:24 Analyzes patterns, trends, or distributions in data in a variety

of contexts by determining or using measures of central

tendency (median or mode), or range.

M(DSP)–4–2

M4:25 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, or

to make predictions.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M4:24.)

M4:26 Uses counting techniques to solve problems in context involving

combinations or simple permutations (e.g., given a map, determines

the number of paths from point A to point B) using a variety of

strategies (e.g., organized lists, tables, tree diagrams, or others).

M(DSP)–4–4

M4:27 For a probability event in which the sample space may or may

not contain equally likely outcomes, determines the theoretical

probability of an event and expresses the result as part to whole

(e.g., two out of five).

M(DSP)–4–5

M4:28 In response to a teacher- or student-generated question or

hypothesis, collects appropriate data, organizes the data, displays/

represents the data, analyzes the data to draw conclusions about

the questions or hypothesis being tested.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M4:24.)

M4:29 Uses experimental probability, records the outcomes, and

describes the likelihood of an event as a value from 0 through 1

(for events that are certain to occur) written as either a ratio or as

part to whole (e.g., 7 out of 10).

M4:30 Demonstrate understanding of mathematical problem solving2

and communication through:3

• 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.