#### MA.A: Number Sense, Concepts, and Operations

MA.A.1.2: The student understands the different ways numbers are represented and used in the real world.

MA.A.1.2.1: The student names whole numbers combining three-digit 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.1.2.1.2: reads, writes, and identifies proper fractions with denominators including 2, 3, 4, 5, 6, 8, 10, and 100.

MA.A.1.2.1.3: reads, writes, and identifies decimal notation in the context of money.

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

MA.A.1.2.2.1: uses language and symbols (> , < , =) to compare the relative size of numbers in the same form.

MA.A.1.2.2.2: compares and orders whole numbers through hundred thousands or more, using concrete materials, number lines, drawings, and numerals.

MA.A.1.2.2.3: compares and orders commonly used fractions, including halves, thirds, fourths, fifths, sixths and eighths, using concrete materials.

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

MA.A.1.2.3.1: translates problem situations into diagrams and models using whole numbers, fractions, and decimal notation in the context of money.

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.1.2.4.1: uses concrete materials to model equivalent forms of whole numbers and common fractions.

MA.A.1.2.4.3: knows that two numbers in different forms are equivalent or non-equivalent, using whole numbers, fractions, and decimals in the context of money.

MA.A.2.2: The student understands number systems.

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

MA.A.2.2.1.1: knows the value of a given digit in whole numbers to hundred thousands, including writing and interpreting expanded forms of numbers.

MA.A.2.2.1.2: knows that the value of each place is 10 times that of the place to its right (for example, 1,000 = 10 x 100).

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.2.2.2.1: compares the decimal (base 10) number system to the Roman numeral system using the Roman numerals I, V, X, L, and C.

MA.A.3.2: The student understands the effects of operations on numbers and the relationships among these operations, selects appropriate operations, and computes for problem solving.

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.3.2.1.1: explains and demonstrates the addition and subtraction of whole numbers (up to three digits or more) using concrete materials, drawings, symbols, and algorithms.

MA.A.3.2.1.2: explains the inverse relationship of addition and subtraction and demonstrates that relationship by writing related fact families.

MA.A.3.2.1.3: explains and demonstrates the meaning of multiplication (for the repeated addition, array, and area models) using manipulatives, drawings, number sentences, and story problems.

MA.A.3.2.1.4: explains and demonstrates the meaning of division and of remainders (for the repeated subtraction and partitive models) using manipulatives, drawings, number sentences, and story problems.

MA.A.3.2.1.5: solves multiplication basic facts using various strategies including the following:

MA.A.3.2.1.5.b: skip counting, for example, to find 4 x 5, count 5, 10, 15, 20

MA.A.3.2.1.5.c: using doubles and near doubles, such as 3 x 8 = (2 x 8) + 8

MA.A.3.2.1.5.d: applying the commutative property of multiplication, such as 7 x 3 = 3 x 7

MA.A.3.2.1.5.e: applying the distributive property of multiplication, such as 8 x 7 = (8 x 5) + (8 x 2)

MA.A.3.2.1.5.f: noting and applying patterns in the facts tables, such as the regularity in the nines

MA.A.3.2.1.5.g: using the zero and identity properties of multiplication

MA.A.3.2.1.6: explains the inverse relationship of multiplication and division and writes related fact families.

MA.A.3.2.1.7: predicts the relative size of solutions in addition, subtraction, multiplication, and division of whole numbers (for example, dividing a whole number by a smaller whole number results in another number that is smaller than the original number).

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.3.2.2.1: writes number sentences for given situations involving the addition, subtraction, multiplication, and division of whole numbers.

MA.A.3.2.2.2: uses problem-solving strategies to determine the operation needed to solve one-step problems involving addition, subtraction, multiplication, and division of whole numbers.

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 real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

MA.A.3.2.3.1: solves real-world problems involving addition, subtraction, multiplication, and division of whole numbers using an appropriate method (for example, mental math, paper and pencil, concrete materials, calculator).

MA.A.4.2: The student uses estimation in problem solving and computation.

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

MA.A.4.2.1.1: uses estimation strategies to determine a reasonable estimate of a quantity.

MA.A.4.2.1.3: chooses estimation strategies (for example, front-end, rounding) in real-world problem situations and explains the choice.

MA.A.5.2: The student understands and applies theories related to numbers.

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

MA.A.5.2.1.2: uses a model to determine factors of whole numbers through 100 (for example, array).

#### MA.B: Measurement

MA.B.1.2: The student measures quantities in the real world and uses the measures to solve problems.

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.1.2.1.2: uses a wide variety of concrete objects to investigate measurement of length, weight, capacity, area, perimeter, and volume (for example, cubes, grid paper, string, squares).

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

MA.B.1.2.2.1: solves real-world problems involving measurement using concrete and pictorial models for the following:

MA.B.1.2.2.1.a: length (for example, half-inch, centimeter)

MA.B.1.2.2.2: solves real-world problems involving perimeter, area, and volume using concrete materials or graphic models.

MA.B.3.2: The student estimates measurements in real-world problem situations.

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

MA.B.3.2.1.1: knows how to determine whether an accurate or estimated measurement is needed for a solution.

MA.B.3.2.1.2: using real-world settings, objects, graph paper, or charts, solves problems involving estimated measurements including the following:

MA.B.3.2.1.2.a: length to nearest inch, centimeter

MA.B.3.2.1.3: knows how to estimate the area and perimeter of square and rectangular shapes using graph paper, geoboard or other manipulatives.

MA.B.3.2.1.4: knows how to estimate the volume of a rectangular prism using manipulatives.

#### MA.C: Geometry and Spatial Sense

MA.C.2.2: The student visualizes and illustrates ways in which shapes can be combined, subdivided, and changed.

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

MA.C.2.2.1.2: knows symmetry, congruency, and reflections in geometric figures using concrete materials (for example, pattern blocks, geoboards, mirrors).

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.2.2.2.1: explores flips, slides, and 180 degree turns (either clockwise or counterclockwise) using concrete and graphic materials (for example, pattern blocks, geoboards, dot paper).

MA.C.2.2.2.2: knows the effect of a flip, slide, and 180 degree turn on a geometric figure.

MA.C.3.2: The student uses coordinate geometry to locate objects in both two and three dimensions and to describe objects algebraically.

MA.C.3.2.1: The student represents and applies a variety of strategies and geometric properties and formulas for two- and three-dimensional shapes to solve real-world and mathematical problems.

MA.C.3.2.1.1: compares the concepts of area and perimeter through the use of concrete and graphic materials (for example, geoboards, color tiles, grid paper).

MA.C.3.2.1.2: applies the concepts of area and perimeter of rectangles to solve real-world and mathematical problems through the use of concrete materials (for example, framing a photograph).

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

MA.C.3.2.2.1: knows how to identify, locate, and plot ordered pairs of whole numbers on a graph.

#### MA.D: Algebraic Thinking

MA.D.1.2: The student describes, analyzes, and generalizes a wide variety of patterns, relations, and functions.

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.1.2.1.1: identifies missing parts in patterns.

MA.D.1.2.1.2: describes, extends, and creates numerical and geometric patterns through models (for example, concrete objects, drawings, simple number sequences).

MA.D.1.2.1.3: poses and solves problems by identifying a predictable visual or numerical pattern (for example: Continue this pattern: + , -, = , + , + , -, -, _ _ _ , _ _ _ ,).

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.1.2.2.1: knows mathematical relationships in patterns (for example, the second number is two more than the first).

MA.D.1.2.2.2: analyzes number patterns and states the rule for relationships (for example, 2, 4, 6, 8, ...; the rule: + 2).

MA.D.1.2.2.3: discusses and explains the choice of the rule that applies to the pattern.

MA.D.1.2.2.4: identifies and extends a pattern according to the given rule.

MA.D.1.2.2.5: applies and explains the appropriate rule to complete a table or chart.

MA.D.2.2: The student uses expressions, equations, inequalities, graphs, and formulas to represent and interpret situations.

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.2.2.1.2: creates a simple word problem for a given number sentence, diagram, or model.

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

MA.D.2.2.2.1: uses physical models and graphs (for example, cubes, number lines) to solve real-world equations and inequalities.

#### MA.E: Data Analysis and Probability

MA.E.1.2: The student understands and uses the tools of data analysis for managing information.

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.1.2.1.2: interprets and compares information from picto-and bar graphs including graphs from content-area materials and periodicals.

MA.E.1.2.1.3: generates questions, collects responses, and displays data in a table, pictograph or bar graph.

MA.E.1.2.1.4: interprets and explains orally and in writing displays of data.

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

MA.E.1.2.2.1: uses concrete materials to determine the mean in a set.

MA.E.1.2.2.2: identifies the median and mode from a set of numerical data.

MA.E.1.2.2.3: identifies the range in a set of numerical data.

MA.E.1.2.2.4: uses concrete materials, pictures, or graphs to display data and identify range, median, and mode.

MA.E.1.2.3: The student analyzes real-world 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.1.2.3.2: in class projects, constructs and discusses patterns in computer-generated graphs using real- world problems (for example, identify most popular pizza topping).

MA.E.2.2: The student identifies patterns and makes predictions from an orderly display of data using concepts of probability and statistics.

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

MA.E.2.2.1.3: calculates the probability of a particular event occurring from a set of all possible outcomes.

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

MA.E.2.2.2.2: determines which outcomes are most likely to occur in certain situations (for example, spinning red is most likely to occur when a spinner is divided equally among red, blue, green, and red).

MA.E.3.2: The student uses statistical methods to make inferences and valid arguments about real-world situations.

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.3.2.1.1: designs appropriate questions for a survey.

MA.E.3.2.1.2: creates a pictograph or bar graph to present data from a given survey.

MA.E.3.2.1.3: explains the results from the data of a given survey.

Correlation last revised: 6/20/2014

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.