Strand A: Number Sense, Concepts, and Operations

Standard 1: The student understands the different ways numbers are represented and used in the real world.

Benchmark MA.A.1.2.1: The student names whole numbers combining 3digit numeration (hundreds, tens, ones) and the use of number periods, such as ones, thousands, and millions and associates verbal names, written word names, and standard numerals with whole numbers, commonly used fractions, decimals, and percents.

MA.A.1.2.1.5.1  reads, writes, and identifies whole numbers, fractions, and mixed numbers.

MA.A.1.2.1.5.2  reads, writes, and identifies decimals through thousandths.

MA.A.1.2.1.5.3  reads, writes, and identifies common percents including 10%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, 75% , 80%, 90%, and 100%.

Benchmark MA.A.1.2.2: The student understands the relative size of whole numbers, commonly used fractions, decimals, and percents.

MA.A.1.2.2.5.1  uses symbols (>, <, =) to compare numbers in the same and different forms such as 0.5 < 3/4.

MA.A.1.2.2.5.2  compares and orders whole numbers using concrete materials, number lines, drawings, and numerals.

MA.A.1.2.2.5.3  compares and orders commonly used fractions, percents, and decimals to thousandths using concrete materials, number lines, drawings, and numerals.

MA.A.1.2.2.5.4  locates whole numbers, fractions, mixed numbers, and decimals on the same number line.

Benchmark MA.A.1.2.3: The student understands concrete and symbolic representations of whole numbers, fractions, decimals, and percents in realworld situations.

MA.A.1.2.3.5.1  translates problem situations into diagrams, models, and numerals using whole numbers, fractions, mixed numbers, decimals, and percents.

Benchmark MA.A.1.2.4: The student understands that numbers can be represented in a variety of equivalent forms using whole numbers, decimals, fractions, and percents.

MA.A.1.2.4.5.1  knows that numbers in different forms are equivalent or nonequivalent, using whole numbers, decimals, fractions, mixed numbers, and percents.

Standard 2: The student understands number systems.

Benchmark MA.A.2.2.1: The student uses placevalue concepts of grouping based upon powers of ten (thousandths, hundredths, tenths, ones, tens, hundreds, thousands) within the decimal number system.

MA.A.2.2.1.5.1  knows that place value relates to powers of 10.

MA.A.2.2.1.5.2  expresses numbers to millions or more in expanded form using powers of ten, with or without exponential notation.

Benchmark MA.A.2.2.2: The student recognizes and compares the decimal number system to the structure of other number systems such as the Roman numeral system or bases other than ten.

MA.A.2.2.2.5.1  explains the similarities and differences between the decimal (base 10) number system and other number systems that do or do not use place value.

Standard 3: The student understands the effects of operations on numbers and the relationship among these operations, selects appropriate operations, and computes for problem solving.

Benchmark MA.A.3.2.1: The student understands and explains the effects of addition, subtraction, and multiplication on whole numbers, decimals, and fractions, including mixed numbers, and the effects of division on whole numbers, including the inverse relationship of multiplication and division.

MA.A.3.2.1.5.1  explains and demonstrates the multiplication of common fractions using concrete materials, drawings, story problems, symbols, and algorithms.

MA.A.3.2.1.5.2  explains and demonstrates the multiplication of decimals to hundredths using concrete materials, drawings, story problems, symbols, and algorithms.

MA.A.3.2.1.5.3  predicts the relative size of solutions in the following:
addition, subtraction, multiplication, and division of whole numbers
addition, subtraction, and multiplication of fractions, decimals, and mixed numbers, with particular attention given to fraction and decimal multiplication (for example, when two numbers less than one are multiplied, the result is a number less than either factor)

MA.A.3.2.1.5.4  explains and demonstrates the inverse nature of multiplication and division, with particular attention to multiplication by a fraction (for example, multiplying by _ yields the same result as dividing by 4).

MA.A.3.2.1.5.5  explains and demonstrates the commutative, associative, and distributive properties of multiplication.

Benchmark MA.A.3.2.2: The student selects the appropriate operation to solve specific problems involving addition, subtraction, and multiplication of whole numbers, decimals, and fractions, and division of whole numbers.

MA.A.3.2.2.5.1  uses problemsolving strategies to determine the operation(s) needed to solve one and twostep problems involving addition, subtraction, multiplication, and division of whole numbers, and addition, subtraction, and multiplication of decimals and fractions.

Benchmark MA.A.3.2.3: The student adds, subtracts, and multiplies whole numbers, decimals, and fractions, including mixed numbers, and divides whole numbers to solve realworld problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

MA.A.3.2.3.5.1  solves realworld problems involving addition, subtraction, multiplication, and division of whole numbers, and addition, subtraction, and multiplication of decimals, fractions, and mixed numbers using an appropriate method (for example, mental math, pencil and paper, calculator).

Standard 4: The student uses estimation in problem solving and computation.

Benchmark MA.A.4.2.1: The student uses and justifies different estimation strategies in a realworld problem situation and determines the reasonableness of results of calculations in a given problem situation.

MA.A.4.2.1.5.1  chooses, describes, and explains estimation strategies used to determine the reasonableness of solutions to realworld problems.

MA.A.4.2.1.5.2  estimates quantities of objects to 1000 or more and justifies and explains the reasoning for the estimate (for example, using benchmark numbers, unitizing).

Standard 5: The student understands and applies theories related to numbers.

Benchmark MA.A.5.2.1: The student understands and applies basic number theory concepts, including primes, composites, factors, and multiples.

MA.A.5.2.1.5.1  finds factors of numbers to 100 to determine if they are prime or composite.

MA.A.5.2.1.5.2  expresses a whole number as a product of its prime factors.

MA.A.5.2.1.5.3  determines the greatest common factor of two numbers.

MA.A.5.2.1.5.4  determines the least common multiple of two numbers up to 100 or more.

MA.A.5.2.1.5.5  multiplies by powers of 10 (100, 1,000, and 10,000) demonstrating patterns.

MA.A.5.2.1.5.6  identifies and applies rules of divisibility for 2, 3, 4, 5, 6, 9, and 10.

MA.A.5.2.1.5.7  uses models to identify perfect squares to 144.

Strand B: Measurement


Standard 1: The student measures quantities in the real world and uses the measures to solve problems.

Benchmark MA.B.1.2.1: The student uses concrete and graphic models to develop procedures for solving problems related to measurement including length, weight, time, temperature, perimeter, area, volume, and angle.

MA.B.1.2.1.5.1  knows measurement concepts and can use oral and written language to communicate them.

MA.B.1.2.1.5.2  extends conceptual experiences into patterns to develop formulas for determining perimeter, area, and volume.

MA.B.1.2.1.5.3  knows varied units of time that include centuries and seconds.

MA.B.1.2.1.5.4  classifies angle measures as acute, obtuse, right, or straight.

MA.B.1.2.1.5.5  investigates measures of circumference using concrete materials (for example, uses string or measuring tape to measure the circumference of cans or bottles).

Benchmark MA.B.1.2.2: The student solves realworld problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles.

MA.B.1.2.2.5.1  solves realworld problems involving measurement of the following:
length (for example, eighthinch, kilometer, mile)
weight or mass (for example, milligram, ton)
temperature (comparing temperature changes within the same scale using either a Fahrenheit or a Celsius thermometer)
angles (acute, obtuse, straight)

MA.B.1.2.2.5.2  solves realworld problems involving perimeter, area, capacity, and volume using concrete, graphic or pictorial models.

MA.B.1.2.2.5.3  uses schedules, calendars, and elapsed time to solve realworld problems.

Standard 2: The student compares, contrasts, and converts within systems of measurement (both standard/nonstandard and metric/customary).

Benchmark MA.B.2.2.1: The student uses direct (measured) and indirect (not measured) measures to calculate and compare measurable characteristics.

MA.B.2.2.1.5.1  finds the length or height of “hardtoreach” objects by using the measure of a portion of the objects (for example, find the height of a room or building by finding the height of one block or floor and multiplying by the number of blocks or floors).

MA.B.2.2.1.5.2  uses customary and metric units to compare length, weight or mass, and capacity or volume.

MA.B.2.2.1.5.3  uses multiplication and division to convert units of measure within the customary or metric system.

Benchmark MA.B.2.2.2: The student selects and uses appropriate standard and nonstandard units of measurement, according to type and size.

MA.B.2.2.2.5.1  knows an appropriate unit of measure to determine the dimension(s) of a given object (for example, standard  student chooses feet or yards instead of inches to measure a room; nonstandard  student chooses a length of yarn instead of a pencil to measure a room).

MA.B.2.2.2.5.2  knows an appropriate unit of measure (standard or nonstandard) to measure weight, mass, and capacity.

Standard 3: The student estimates measurements in realworld problem situations.

Benchmark MA.B.3.2.1: The student solves realworld problems involving estimates of measurements, including length, time, weight, temperature, money, perimeter, area, and volume.

MA.B.3.2.1.5.1  knows how to determine whether an accurate or estimated measurement is needed for a solution.

MA.B.3.2.1.5.2  solves realworld problems involving estimated measurements, including the following:
length to nearest quarterinch, centimeter
weight to nearest ounce, gram
time to nearest oneminute interval
temperature to nearest fivedegree interval
money to nearest $1.00

MA.B.3.2.1.5.3  knows how to estimate the area and perimeter of regular and irregular polygons.

MA.B.3.2.1.5.4  knows how to estimate the volume of a rectangular prism.

Standard 4: The student selects and uses appropriate units and instruments for measurement to achieve the degree of precision and accuracy required in realworld situations.

Benchmark MA.B.4.2.1: The student determines which units of measurement, such as seconds, square inches, dollars per tankful, to use with answers to realworld problems.

MA.B.4.2.1.5.1  selects an appropriate measurement unit for labeling the solution to realworld problems.

Benchmark MA.B.4.2.2: The student selects and uses appropriate instruments and technology, including scales, rulers, thermometers, measuring cups, protractors, and gauges, to measure in realworld situations.

MA.B.4.2.2.5.1  selects and uses the appropriate tool for situational measures (for example, measuring sticks, scales and balances, thermometer, measuring cups, gauges, protractors).

Strand C: Geometry and Spatial Sense

Standard 1: The student describes, draws, identifies, and analyzes two and threedimensional shapes.

Benchmark MA.C.1.2.1: The student given a verbal description, draws and/or models two and threedimensional shapes and uses appropriate geometric vocabulary to write a description of a figure or a picture composed of geometric figures.

MA.C.1.2.1.5.1  uses appropriate geometric vocabulary to describe properties and attributes of two and threedimensional figures (for example, obtuse and acute angles; radius; equilateral, scalene, and isosceles triangles.).

MA.C.1.2.1.5.2  draws and classifies twodimensional figures having up to ten or more sides and threedimensional figures (for example, cubes, rectangular prisms, pyramids).

MA.C.1.2.1.5.3  knows the characteristics of and relationships among points, lines, line segments, rays, and planes.

Standard 2: The student visualizes and illustrates ways in which shapes can be combined, subdivided, and changed.

Benchmark MA.C.2.2.1: The student understands the concepts of spatial relationships, symmetry, reflections, congruency, and similarity.

MA.C.2.2.1.5.1  uses manipulatives to solve problems requiring spatial visualization.

MA.C.2.2.1.5.2  knows symmetry, congruency, and reflections in geometric figures.

MA.C.2.2.1.5.3  knows how to justify that two figures are similar or congruent.

Benchmark MA.C.2.2.2: The student predicts, illustrates, and verifies which figures could result from a flip, slide, or turn of a given figure.

MA.C.2.2.2.5.1  identifies and performs flips, slides, and turns given angle (90°, 180°, 270°) and direction (clockwise or counterclockwise) of turn.

MA.C.2.2.2.5.2  knows the effect of a flip, slide or turn (90°, 180°, 270°) on a geometric figure.

MA.C.2.2.2.5.3  explores tessellations.

Standard 3: The student uses coordinate geometry to locate objects in both two and three dimensions and to describe objects algebraically.

Benchmark MA.C.3.2.1: The student represents and applies a variety of strategies and geometric properties and formulas for two and threedimensional shapes to solve realworld and mathematical problems.

MA.C.3.2.1.5.1  compares the concepts of area, perimeter, and volume using concrete materials (for example, geoboards, grid paper) and realworld situations (for example, tiling a floor, bordering a room, packing a box).

MA.C.3.2.1.5.2  applies the concepts of area, perimeter, and volume to solve realworld and mathematical problems using studentdeveloped formulas.

MA.C.3.2.1.5.3  knows how area and perimeter are affected when geometric figures are combined, rearranged, enlarged, or reduced (for example, What happens to the area of a square when the sides are doubled?).

Benchmark MA.C.3.2.2: The student identifies and plots positive ordered pairs (whole numbers) in a rectangular coordinate system (graph).

MA.C.3.2.2.5.1  knows how to identify, locate, and plot ordered pairs of whole numbers on a graph or on the first quadrant of a coordinate system.

Strand D: Algebraic Thinking

Standard 1: The student describes, analyzes, and generalizes a wide variety of patterns, relations, and functions.

Benchmark MA.D.1.2.1: The student describes a wide variety of patterns and relationships through models, such as manipulatives, tables, graphs, rules using algebraic symbols.

MA.D.1.2.1.5.1  describes, extends, creates, predicts, and generalizes numerical and geometric patterns using a variety of models (for example, lists, tables, graphs, charts, diagrams, calendar math).

MA.D.1.2.1.5.2  poses and solves problems by identifying a predictable visual or numerical pattern such as:
Day 1 2 3 4 ..... n
Number of Calls 4 7 10 ? ?

MA.D.1.2.1.5.3  explains and expresses numerical relationships and pattern generalizations, using algebraic symbols (for example, in the problem above, the number of calls on the nth day can be expressed as 3n+1).

Benchmark MA.D.1.2.2: The student generalizes a pattern, relation, or function to explain how a change in one quantity results in a change in another.

MA.D.1.2.2.5.1  knows mathematical relationships in patterns (for example, Fibonacci numbers: 1, 1, 2, 3, 5, 8,…).

MA.D.1.2.2.5.2  analyzes and generalizes number patterns and states the rule for relationships (for example, 1, 4, 9, 16, …; the rule: +3, +5, +7, …; or “squares of the whole numbers”).

MA.D.1.2.2.5.3  applies the appropriate rule to complete a table or a chart, such as:
IN 1 2 3 9
OUT 1 4 9 ?

Standard 2: The student uses expressions, equations, inequalities, graphs, and formulas to represent and interpret situations.

Benchmark MA.D.2.2.1: The student represents a given simple problem situation using diagrams, models, and symbolic expressions translated from verbal phrases, or verbal phrases translated from symbolic expressions, etc.

MA.D.2.2.1.5.1  solves problems involving simple equations or inequalities using diagrams or models, symbolic expressions, or written phrases.

MA.D.2.2.1.5.2  uses a variable to represent a given verbal expression (for example, 5 more than a number is n + 5).

MA.D.2.2.1.5.3  translates equations into verbal and written problem situations.

Benchmark MA.D.2.2.2: The student uses informal methods, such as physical models and graphs to solve realworld problems involving equations and inequalities.

MA.D.2.2.2.5.1  uses concrete or pictorial models and graphs (for example, drawings, number lines) to solve equations or inequalities.

MA.D.2.2.2.5.2  uses information from concrete or pictorial models or graphs to solve problems.

Strand E: Data Analysis and Probability

Standard 1: The student understands and uses the tools of data analysis for managing information.

Benchmark MA.E.1.2.1: The student solves problems by generating, collecting, organizing, displaying, and analyzing data using histograms, bar graphs, circle graphs, line graphs, pictographs, and charts.

MA.E.1.2.1.5.1  knows which types of graphs are appropriate for different kinds of data (for example, bar graphs, line, or circle graphs).

MA.E.1.2.1.5.2  interprets and compares information from different types of graphs including graphs from contentarea materials and periodicals.

MA.E.1.2.1.5.3  chooses reasonable titles, labels, scales and intervals for organizing data on graphs.

MA.E.1.2.1.5.4  generates questions, collects responses, and displays data on a graph.

MA.E.1.2.1.5.5  interprets and completes circle graphs using common fractions or percents.

MA.E.1.2.1.5.6  analyzes and explains orally or in writing the implications of graphed data.

Benchmark MA.E.1.2.2: The student determines range, mean, median, and mode from sets of data.

MA.E.1.2.2.5.1  uses a stemandleaf plot from a set of data to identify the range, median, mean, and mode.

MA.E.1.2.2.5.2  uses range and measures of central tendency in realworld situations.

Benchmark MA.E.1.2.3: The student analyzes realworld data to recognize patterns and relationships of the measures of central tendency using tables, charts, histograms, bar graphs, line graphs, pictographs, and circle graphs generated by appropriate technology, including calculators and computers.

MA.E.1.2.3.5.1  uses a calculator to determine the range and mean of a set of data.

MA.E.1.2.3.5.2  uses computer applications to examine and evaluate data.

MA.E.1.2.3.5.3  uses computer applications to construct labeled graphs.

MA.E.1.2.3.5.4  uses computergenerated spreadsheets to record and display realworld data.

Standard 2: The student identifies patterns and makes predictions from an orderly display of data using concepts of probability and statistics.

Benchmark MA.E.2.2.1: The student uses models, such as tree diagrams, to display possible outcomes and to predict events.

MA.E.2.2.1.5.1  determines the number of possible combinations of given items and displays them in an organized way.

MA.E.2.2.1.5.2  represents all possible outcomes for a simple probability situation or event using models such as organized lists, charts, or tree diagrams.

MA.E.2.2.1.5.3  calculates the probability of a particular event occurring from a set of all possible outcomes.

Benchmark MA.E.2.2.2: The student predicts the likelihood of simple events occurring.

MA.E.2.2.2.5.1  identifies and records the possible outcomes of an experiment using concrete materials (for example, spinners, marbles, number cubes).

MA.E.2.2.2.5.2  explains and predicts which outcomes are most likely to occur and expresses the probabilities as fractions.

MA.E.2.2.2.5.3  conducts experiments to test predictions.

Standard 3: The student uses statistical methods to make inferences and valid arguments about realworld situations.

Benchmark MA.E.3.2.1: The student designs experiments to answer class or personal questions, collects information, and interprets the results using statistics (range, mean, median, and mode) and pictographs, charts, bar graphs, circle graphs, and line graphs.

MA.E.3.2.1.5.1  designs a survey to collect data.

MA.E.3.2.1.5.2  as a class project, discusses ways to choose a sample representative of a large group such as a sample representative of the entire school.

MA.E.3.2.1.5.3  creates an appropriate graph to display data, including titles, labels, scales, and intervals.

MA.E.3.2.1.5.4  interprets the results using statistics (range and measures of central tendency).

Benchmark MA.E.3.2.2: The student uses statistical data about life situations to make predictions and justifies reasoning.

MA.E.3.2.2.5.1  uses statistical data to predict trends.

MA.E.3.2.2.5.2  applies statistical data to make generalizations.

MA.E.3.2.2.5.3  justifies and explains generalizations.
