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.1.2.1.4.1  reads, writes, and identifies whole numbers through millions or more.

MA.A.1.2.1.4.2  reads, writes, and identifies fractions and mixed numbers with denominators including 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 100, and 1000.

MA.A.1.2.1.4.3  reads, writes, and identifies decimals through hundredths.

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

MA.A.1.2.2.4.1  uses language and symbols (>, <, =) to compare numbers in the same form and in two different forms such as _ < 1.

MA.A.1.2.2.4.2  compares and orders whole numbers through millions or more, using concrete materials, number lines, drawings, and numerals.

MA.A.1.2.2.4.3  compares and orders commonly used fractions and decimals to hundredths using concrete materials, drawings, and numerals.

MA.A.1.2.2.4.4  locates whole numbers, fractions, mixed numbers, and decimals on a 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.1.2.3.4.1  translates problem situations into diagrams and models using whole numbers, fractions, mixed numbers and decimals to hundredths including money notation.

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.1.2.4.4.1  uses concrete materials to model equivalent forms of whole numbers, fractions, and decimals.

MA.A.1.2.4.4.2  identifies equivalent forms of numbers.

MA.A.1.2.4.4.3  knows that two numbers in different forms are equivalent or nonequivalent, using whole numbers, decimals, fractions, and mixed numbers.

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.2.2.1.4.1  knows the value of a given digit in numbers from hundredths to millions, including writing and interpreting expanded forms of numbers.

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.2.2.2.4.1  uses concrete materials and symbolic notation to represent numbers in bases other than base ten, such as base five.

MA.A.2.2.2.4.2  reads, writes, and compares the decimal number system to the Roman numeral system using the Roman numerals I, V, X, L, C, D, and M.

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.3.2.1.4.1  recalls (from memory) basic multiplication facts and related division facts.

MA.A.3.2.1.4.2  knows the inverse relationship of multiplication and division and demonstrates that relationship by writing related fact families.

MA.A.3.2.1.4.3  explains and demonstrates the multiplication and division of whole numbers using manipulatives, drawings, and algorithms.

MA.A.3.2.1.4.4  explains and demonstrates the addition and subtraction of common fractions using concrete materials, drawings, story problems, and algorithms.

MA.A.3.2.1.4.5  5. explains and demonstrates the addition and subtraction of decimals (to hundredths) using concrete materials, drawings, story problems, and algorithms.

MA.A.3.2.1.4.6  knows the properties of numbers including the following:
the identity, commutative, and associative properties of addition
the zero and identity properties of multiplication
the commutative, associative, and distributive properties of multiplication

MA.A.3.2.1.4.7  predicts the relative size of solutions in the following:
addition, subtraction, multiplication, and division of whole numbers

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.3.2.2.4.1  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 and subtraction 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.3.2.3.4.1  solves realworld problems involving addition, subtraction, multiplication, and division of whole numbers, and addition and subtraction of decimals and fractions using an appropriate method (for example, mental math, pencil and paper, calculator).

MA.A.3.2.3.4.2  explains the reason for choosing a particular computing method for a particular problem.

MA.A.3.2.3.4.3  solves realworld multiplication problems with whole numbers (three digits by one digit) using concrete materials, drawings, and pencil and paper.

MA.A.3.2.3.4.4  solves realworld division problems having divisors of one digit and dividends of three digits, with or without remainders.

MA.A.3.2.3.4.5  solves realworld problems involving the addition or subtraction of decimals (to hundredths) or common fractions with like or unlike denominators.

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

MA.A.4.2.1.4.2  estimates quantities of objects to 500 or more and justifies and explains the reasoning for the estimates (for example, using compatible numbers, 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.5.2.1.4.1  knows factors and multiples of numbers to 100.

MA.A.5.2.1.4.2  multiplies by 10, 100, and 1,000 recognizing and demonstrating patterns.

MA.A.5.2.1.4.3  knows rules of divisibility for 2, 3, 5, 9, and 10.

MA.A.5.2.1.4.4  uses models to identify perfect squares to 100.

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.1.2.1.4.1  knows measurement concepts and can use oral and written language to communicate them.

MA.B.1.2.1.4.2  uses a wide variety of models (for example, manipulatives, diagrams) and applies counting procedures to investigate measurements of length, area, volume, and perimeter.

MA.B.1.2.1.4.3  knows about varied time intervals, including decades, hours, minutes, and seconds.

MA.B.1.2.1.4.4  4. investigates angle measures using models and manipulatives for the common angles of 45°, 90°, and 180° (straight angle) and uses these angles as reference points for measures of other angles.

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

MA.B.1.2.2.4.1  solves realworld problems involving measurement of the following:
length (for example, millimeter, quarterinch, foot, yard, meter)
weight (for example, pounds, ounces, kilograms, grams)
capacity (for example, cup, milliliters)
temperature (Fahrenheit and Celsius)
angles (right and straight)

MA.B.1.2.2.4.2  solves realworld problems involving perimeter, area, and volume using concrete, graphic, or pictorial models.

MA.B.1.2.2.4.3  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.2.2.1.4.1  devises nonstandard, indirect ways to compare lengths (for example, compare the height of a cylinder to the distance around it).

MA.B.2.2.1.4.2  uses customary and metric units to compare length, weight, and capacity or volume.

MA.B.2.2.1.4.3  uses multiplication or division to convert units of measure within either the customary or metric system (for example: 100 cm = 1 m).

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.2.2.2.4.1  knows an appropriate unit of measure to determine the dimension(s) of a given object (for example, standard  student chooses feet or inches instead of yards to measure a classroom desk; nonstandard  student chooses a pencil or his or her hand to measure a classroom desk).

MA.B.2.2.2.4.2  knows an appropriate unit of measure (standard or nonstandard) to measure weight 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.3.2.1.4.1  knows how to determine whether an accurate or estimated measurement is needed for a solution.

MA.B.3.2.1.4.2  using realworld settings, objects, graph paper, or charts, solves problems involving estimated measurements, including the following:
length to nearest halfinch, centimeter
weight to nearest ounce, gram
time to nearest fiveminute interval
temperature to nearest fivedegree interval
money to nearest $1.00 (combination of coin and currency)

MA.B.3.2.1.4.3  knows how to estimate the area and perimeter of regular and irregular polygons using graph paper, geoboard, or other objects.

MA.B.3.2.1.4.4  knows how to estimate the volume of a rectangular prism using manipulatives or graphic representation.

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.4.2.1.4.1  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.4.2.2.4.1  selects and uses the appropriate tool for situational measures (for example, measuring sticks, scales and balances, thermometers, measuring cups, gauges).

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.1.2.1.4.1  uses appropriate geometric vocabulary to describe properties and attributes of two and threedimensional figures (for example, faces, edges, vertices, diameter).

MA.C.1.2.1.4.2  draws and classifies twodimensional figures having up to eight or more sides.

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.2.2.1.4.1  uses manipulatives to solve problems requiring spatial visualization.

MA.C.2.2.1.4.2  knows symmetry, congruency, and reflections in geometric figures using drawings and concrete materials (for example, pattern blocks, mirrors).

MA.C.2.2.1.4.3  knows and creates congruent and similar figures.

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.2.2.2.4.1  identifies and performs flips, slides, and turns given angle (90°, 180°) and direction (clockwise or counterclockwise) of turn, using concrete and graphic materials (for example, pattern blocks, geoboards, grid paper).

MA.C.2.2.2.4.2  knows the effect of a flip, slide, or turn (90°, 180°) on a geometric figure.

MA.C.2.2.2.4.3  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.3.2.1.4.1  compares the concepts of area and perimeter using concrete materials (for example, color tiles, grid paper) and realworld situations (for example, carpeting a floor, fencing a yard).

MA.C.3.2.1.4.2  applies the concepts of area and perimeter to solve realworld and mathematical problems.

MA.C.3.2.1.4.3  knows how area and perimeter are affected when geometric figures are combined.

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

MA.C.3.2.2.4.1  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.1.2.1.4.1  describes, extends, and creates numerical and geometric patterns using a variety of models (for example, lists, tables, charts).

MA.D.1.2.1.4.2  poses, solves, and explains problems by identifying a predictable visual or numerical pattern such as:
Input 1 2 3 7
Output $3 $6 $9 ?

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.1.2.2.4.1  knows mathematical relationships in patterns (for example, the second shape is the first shape turned 90°).

MA.D.1.2.2.4.2  analyzes number patterns and states rules for relationships (for example, 2, 4, 7, 9, 12, …; the rule is: +2, +3, +2, +3, …).

MA.D.1.2.2.4.3  discusses, explains, and analyzes the rule that applies to the pattern.

MA.D.1.2.2.4.4  applies the appropriate rule to complete a table or a chart such as:
Input Output
2 8
9 36
? 16
7 28

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.2.2.1.4.1  solves problems involving equations or simple inequalities using manipulatives, diagrams, or models, symbolic expressions, or written phrases.

MA.D.2.2.1.4.2  uses a variable to represent a given verbal expression (for example, seven times a number is 7n).

MA.D.2.2.1.4.3  translates problemsolving situations into expressions and equations using a variable for the unknown.

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.2.2.2.4.1  uses physical or pictorial models and graphs (for example, cubes, number lines) to solve equations or inequalities.

MA.D.2.2.2.4.2  uses information from physical models, graphs, or tables 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.1.2.1.4.1  knows the purpose of different parts of a graph (for example, titles, labels, intervals, key).

MA.E.1.2.1.4.2  chooses reasonable titles and labels for graphs.

MA.E.1.2.1.4.3  interprets and compares information from different types of graphs including graphs from contentarea materials and periodicals.

MA.E.1.2.1.4.4  generates questions, collects responses, and displays data on a pictograph, circle graph, bar, double bar, or line graph.

MA.E.1.2.1.4.5  interprets and completes circle graphs using common fractions.

MA.E.1.2.1.4.6  analyzes and explains orally or in writing the implications of data displays.

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

MA.E.1.2.2.4.1  identifies the mean, median and mode from a set of data.

MA.E.1.2.2.4.2  identifies the range on a line graph.

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.1.2.3.4.1  uses a calculator to determine the range and mean of a set of data.

MA.E.1.2.3.4.2  uses computer applications to examine and evaluate data.

MA.E.1.2.3.4.3  uses computer applications to construct graphs.

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

MA.E.2.2.1.4.2  represents all possible outcomes for a simple probability situation or event using models such as organized lists, charts, or tree diagrams.

MA.E.2.2.1.4.3  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.2.2.2.4.1  identifies and records using common fractions, the possible outcomes of simple experiments using concrete materials (for example, spinners, number cubes, coin toss).

MA.E.2.2.2.4.2  determines and predicts which outcomes are likely to occur and expresses those expected outcomes as fractions.

MA.E.2.2.2.4.3  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.3.2.1.4.1  designs a class survey to collect data.

MA.E.3.2.1.4.2  creates an appropriate graph to display data (for example, pictographs, bar graphs, line graphs, circle graphs).

MA.E.3.2.1.4.3  determines appropriate statistical measures for data (range, mean, median, mode).

MA.E.3.2.1.4.4  explains 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.3.2.2.4.1  uses statistical data to identify trends.

MA.E.3.2.2.4.2  applies statistical data to make generalizations.

MA.E.3.2.2.4.3  justifies and explains generalizations.
