CRCT Content Descriptions Based on the Georgia Performance Standards Mathematics Grades 1 - 5

Georgia law requires the development and administration of the CRCT in the content areas of Reading, English/Language Arts, Mathematics, Science, and Social Studies. Each spring students in grades 1 through 8 take the Reading, English/Language Arts, and Mathematics CRCT, while students in grades 3 through 8 also take the Science and Social Studies CRCT. These tests are designed to measure student achievement of the Georgia Performance Standards (GPS).

Program Purpose:

The CRCT is designed to measure student acquisition and understanding of the knowledge, concepts, and skills set forth in the GPS. The testing program serves as a measure of the quality of education in the state. Reports yielding information on academic achievement at the student, class, school, system, and state levels are produced annually.

Mandated Grades for Mathematics:

Grades 1 through 8 are mandated to participate in the Mathematics CRCT each spring.

CRCT Content Descriptions:

The CRCT Content Descriptions are provided to acquaint Georgia educators with the content coverage of the CRCT. Only the knowledge, concepts, and skills reflected in the GPS will be assessed on the CRCT. Committees of Georgia educators reviewed the curriculum and provided guidance for the assessment program.
It is important to note that some curricular standards are better suited for classroom or individual assessment rather than large-scale, paper-pencil assessment. While those curricular standards designed for classroom/individual assessment are not included in the Content Descriptions, the knowledge, concepts, and skills outlined are often required for the mastery of the standards that are assessed. Therefore, the CRCT Content Descriptions are in no way intended to substitute for the GPS; they are provided to help educators better understand how the curriculum will be assessed. Further, the CRCT Content Descriptions by no means suggest when concepts and skills should be introduced in the instructional sequence; rather, their purpose is to communicate when concepts and skills will be assessed on the CRCT. Georgia law requires educators to teach the standards set forth in the state-adopted curriculum (i.e., the GPS). The GPS is located at http://www.georgiastandards.org.

Mathematics Content Domains:

To provide reliable measures as well as structure to the assessment program, the curricular standards provided in the GPS were grouped into content domains. Each domain is comprised of standards with similar content characteristics. The domains for Mathematics are for Grades 1–2 and Grades 3–5:
Number and Operations Number and Operations
Measurement Measurement
Geometry Geometry
Data Analysis and Probability Algebra
Data Analysis and Probability

The GPS in Mathematics requires that mathematical concepts be taught in the context of real-world phenomena. The mathematical process standards require students to solve single and multi-step routine and non-routine word problems while implementing a variety of problem-solving strategies. The process standards concepts and skills are taught and applied within context rather than merely following a prescribed algorithm. The concepts and skills inherent in the process standards are integrated in items across the five content domains.

Using the Mathematics CRCT Content Descriptions:

The Mathematics CRCT Content Descriptions provide information about the content and skills assessed by the CRCT. The documents are organized by grade and content domain. The curriculum standards assessed in each domain are provided as are the related concepts, skills, and abilities assessed. It is important to note the differences between the GPS and the former curriculum. The GPS is a conceptual curriculum, requiring instruction be integrated; the concepts, knowledge, skills, and abilities described in this document should not be viewed as discrete or taught in isolation. Deep understanding by students, resulting in higher achievement, is best achieved when the full curriculum is taught in an integrated, conceptual fashion.

Mathematics - Grade: 1

Domain: Number and Operations - Number and Operations refers to students’ skill in understanding and representing numbers, and being able to add and subtract small numbers.

Standards Associated with Domain
M1N1 M1N2 M1N3 M1N4

Associated Concepts, Skills, and Abilities:
• Represent numbers up to 100 using a variety of models, diagrams, and number sentences, and use manipulatives and pictures to represent numbers larger than 10 in terms of tens and ones.
• Count and represent the number of objects in a set using numerals (up to 100).
• Compare small sets using the terms greater than, less than, and equal to.
• Understand the magnitude and order of numbers up to 100 by making ordered sequences and representing them on a number line.
• Exchange equivalent quantities of coins by making fair trades involving combinations of pennies, nickels, dimes, and quarters, and count out a combination needed to purchase items up to one dollar.
• Identify bills ($1, $5, $10, $20) by name and value, exchange equivalent quantities by making fair trades involving combinations of bills, and count out a combination of bills needed to purchase items that total up to twenty dollars.
• Determine to which ten a given number is closest using tools such as a sequential number line or chart.
• Represent collections of less than 30 objects with 2-digit numbers and understand the meaning of place value.
• Decompose numbers between 10 and 99 as one ten and the appropriate number of ones.
• Identify one more than, one less than, 10 more than, and 10 less than a given number.
• Skip-count by 2s, 5s, and 10s, forward and backwards; to and from numbers up to 100.
• Compose/decompose numbers up to 10 (e.g., 3 + 5 = 8, 8 = 5 + 2 + 1).
• Describe or identify a variety of situations to which subtraction may apply: taking away from a set, comparing two sets, and determining how many more or how many less.
• Identify and understand addition and subtraction number combinations using strategies such as counting on, counting back, doubles, and making tens.
• Know the single-digit addition facts to 18 and corresponding subtraction facts with understanding and fluency. (Use strategies such as relating to facts already known, applying the commutative property, and grouping facts into families.)
• Apply addition and subtraction to 2-digit numbers without regrouping (e.g., 15 + 4, 80 – 60, 56 + 10, 100 – 30, 52 + 5).
• Solve and create word problems involving addition and subtraction to 100 without regrouping. Use words, pictures, and concrete models to interpret story problems and reflect the combining of sets as addition and taking away or comparing elements of sets as subtraction.
• Use informal strategies to share objects (up to 100) equally between two to five people.
• Build number patterns, including concepts of even and odd numbers, using various concrete
representations. (Examples of concrete representations include a hundreds chart, ten grid frame, a place value chart, number line, counters, or other objects.)
• Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of objects or a whole using pictures and models.
• Understand halves and fourths as representations of equal parts of a whole.

Domain: Measurement - Measurement refers to students’ skill in understanding basic quantitative attributes of concrete objects.

Standards Associated with Domain
M1M1 M1M2

Associated Concepts, Skills, and Abilities:
• Compare and/or order length, weight, height, and capacity of concrete objects using direct comparison or a non-standard unit.
• Estimate and measure using a non-standard unit that is smaller than the object to be measured.
• Tell time to the nearest hour and half hour, and understand the movement of the minute hand and how it relates to the hour hand.
• Express a basic understanding of the relationship of calendar time by knowing the number of days in a week and the number of months in a year.
• Order and compare the sequence or duration of events (e.g., shorter/longer, before/after).

Domain: Geometry - Geometry refers to students’ skill in understanding the concepts of basic geometric shapes and spatial relationships of concrete objects.

Standards Associated with Domain
M1G1 M1G2 M1G3

Associated Concepts, Skills, and Abilities:
• Represent, name, and describe triangles, rectangles, pentagons, and hexagons.
• Represent, understand, name, and describe cylinders, cones, and rectangular prisms and identify the basic figures (squares, circles, triangles, and rectangles) within them.
• Compare, contrast, and classify geometric shapes by position, shape, size, number of sides, and number of corners.
• Arrange and describe objects in space by proximity, position, and direction (e.g., near, far, below, above, up, down, behind, in front of, next to, and left or right of).

Domain: Data Analysis and Probability - Data Analysis and Probability refers to students’ skill in posing questions and collecting, organizing, and interpreting data about themselves and their surroundings.

Standard Associated with Domain
M1D1

Associated Concepts, Skills, and Abilities:
• Interpret tally marks, picture graphs, and bar graphs.
• Pose questions and collect, sort, organize and record data using objects, pictures, tally marks, picture graphs, and bar graphs.

Mathematical Process Skills:

Mathematical Process Skills are integrated across the four domains. Mathematical Process Skills refers to students’ dexterity in applying concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures. Process skills are used to acquire and apply content knowledge. Process skills include solving problems that arise in mathematics and other contexts; reasoning and evaluating mathematical arguments; communicating mathematically; making connections among mathematical ideas and to other content areas; and representing mathematical ideas in multiple ways.

Standards Associated with Domain
M1P1 M1P2 M1P3 M1P4 M1P5

Associated Concepts, Skills, and Abilities:
• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
• Recognize reasoning and proof as fundamental aspects of mathematics.
• Make and investigate mathematical conjectures.
• Develop and evaluate mathematical arguments and proofs.
• Select and use various types of reasoning and methods of proof.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.
• Recognize and use connections among mathematical ideas.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Recognize and apply mathematics in contexts outside of mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.

Mathematics - Grade: 2

Domain: Number and Operations - Number and Operations refers to students’ skill in developing their understanding of numbers including fractions and how to represent them; in understanding and applying addition, subtraction, and multiplication through concrete manipulation; and in performing basic calculations.

Standards Associated with Domain
M2N1 M2N2 M2N3 M2N4 M2N5

Associated Concepts, Skills, and Abilities:
• Represent numbers using a variety of models, diagrams, and number sentences (e.g., 4,703 represented as 4,000 + 700 + 3, and units, 47 hundreds + 3, or 4,500 + 203).
• Understand the relative magnitudes of numbers using 10 as a unit, 100 as a unit, or 1,000 as a unit. Represent 2-digit numbers with drawings of tens and ones and 3-digit numbers with drawings of hundreds, tens, and ones.
• Use money as a medium of exchange. Make change and use decimal notation and the dollar and cent symbols to represent a collection of coins and currency.
• Add and subtract two whole numbers up to three digits each with regrouping.
• Understand and use the inverse relation between addition and subtraction to solve problems and check solutions.
• Use mental math strategies such as benchmark numbers to solve problems.
• Use basic properties of addition (commutative, associative, and identity) to simplify problems (e.g., 98 + 17 by taking two from 17 adding to 98 to make 100 and replacing the original problem by the sum 100 + 15).
• Estimate to determine if solutions are reasonable for addition and subtraction.
• Understand multiplication as repeated addition.
• Use repeated addition, arrays, and counting by multiples (skip-counting) to correctly multiply 1-digit numbers and construct the multiplication table.
• Determine the product of two numbers using a multiplication table.
• Use repeated subtraction, equal sharing, and forming equal groups to divide large collections of objects and determine factors for multiplication.
• Model, identify, label, and compare fractions (thirds, sixths, eighths, and tenths) as a representation of equal parts of a whole or of a set.
• Know that when all fractional parts are included, such as three-thirds, the result is equal to the whole.
• Include the use of boxes or ____ to represent a missing value.
• Represent problem-solving situations where addition, subtraction, or multiplication may be applied using mathematical expressions, including equality and inequality signs (=, <, or >, ≠).

Domain: Measurement - Measurement refers to students’ skill in understanding length, time, and temperature and choosing an appropriate tool to measure them.

Standards Associated with Domain
M2M1 M2M2 M2M3

Associated Concepts, Skills, and Abilities:
• Measure length to the nearest inch or centimeter.
• Compare the relationship of one unit to another by measuring objects twice using different units each time (inch, foot, yard, centimeter, and meter).
• Estimate lengths and then measure to determine if estimations were reasonable.
• Determine an appropriate tool and unit for measuring.
• Tell time to the nearest five minutes and know the relationships of time such as the number of seconds in a minute, the number of minutes in an hour, and the number of hours in a day.
• Determine a reasonable temperature for a given situation.
• Read a thermometer.

Domain: Geometry - Geometry refers to students’ skill in understanding basic and compound geometric shapes together with the elements from which they are composed.

Standards Associated with Domain
M2G1 M2G2 M2G3

Associated Concepts, Skills, and Abilities:
• Describe and classify plane figures (triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, hexagons, and irregular polygonal shapes) according to the number of sides and vertices and the sizes of angles (right, obtuse, or acute angle).
• Describe and classify solid figures (prisms, pyramids, cylinders, cones, and spheres) according to such things as the number of edges and vertices and the number and shape of faces and angles.
• Recognize the (plane) shapes of the faces of a geometric solid and count the number of faces of
each type.
• Recognize the shape of an angle as right, obtuse, or acute.
• Describe the change in attributes as two- and three-dimensional shapes are cut and rearranged.

Domain: Data Analysis and Probability - Data Analysis and Probability refers to students’ skill in posing questions and collecting, organizing, and interpreting data about themselves and their surroundings.

Standard Associated with Domain
M2D1

Associated Concepts, Skills, and Abilities:
• Create, organize, and display data using pictographs, Venn diagrams, bar graphs, picture graphs, simple charts, and tables to record results with scales of 1, 2, and 5.
• Interpret picture graphs, Venn diagrams, and bar graphs.

Mathematical Process Skills:

Mathematical Process Skills are integrated across the four domains. Mathematical Process Skills refers to students’ dexterity in applying concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures. Process skills are used to acquire and apply content knowledge. Process skills include solving problems that arise in mathematics and other contexts; reasoning and evaluating mathematical arguments; communicating mathematically; making connections among mathematical ideas and to other content areas; and representing mathematical ideas in multiple ways.

Standards Associated with Domain
M2P1 M2P2 M2P3 M2P4 M2P5

Associated Concepts, Skills, and Abilities:
• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
• Recognize reasoning and proof as fundamental aspects of mathematics.
• Make and investigate mathematical conjectures.
• Develop and evaluate mathematical arguments and proofs.
• Select and use various types of reasoning and methods of proof.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.
• Recognize and use connections among mathematical ideas.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Recognize and apply mathematics in contexts outside of mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.

Mathematics - Grade: 3

Domain: Number and Operations - Number and Operations refers to students’ skill in using decimal fractions and common fractions to represent parts of a whole. This domain also refers to students’ skill in understanding the four arithmetic operations for whole numbers, using them in basic calculations, and applying them in problem-solving situations.

Standards Associated with Domain
M3N1 M3N2 M3N3 M3N4 M3N5

Associated Concepts, Skills, and Abilities:
• Identify place values from tenths through ten thousands.
• Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10 of a single digit whole number) and ways to represent them including word name, standard form, and expanded form.
• Use the properties of addition and subtraction to compute and verify the results of computation.
• Use mental math and estimation strategies to add and subtract.
• Solve problems requiring addition and subtraction.
• Model addition and subtraction by counting back change using the fewest number of coins.
• Describe the relationship between addition and multiplication, i.e., multiplication is defined as repeated addition.
• Know the multiplication facts with understanding and fluency to 10 x 10.
• Use arrays and area models to develop understanding of the distributive property and to determine partial products for multiplication of 2- or 3-digit numbers by a 1-digit number.
• Understand the effect on the product when multiplying by multiples of 10.
• Apply the identity, commutative, and associative properties of multiplication and verify the results.
• Use mental math and estimation strategies to multiply.
• Solve problems requiring multiplication.
• Understand the relationship between division and multiplication and between division and subtraction.
• Recognize that division may be two situations: the first is determining how many equal parts of a given size or amount may be taken away from the whole as in repeated subtraction, and the second is determining the size of the parts when the whole is separated into a given number of equal parts as in a sharing model.
• Recognize problem-solving situations in which division may be applied, and write corresponding mathematical expressions.
• Explain the meaning of a remainder in division in different circumstances.
• Divide a 2- or 3-digit number by a 1-digit divisor.
• Solve problems requiring division.
• Use mental math strategies to divide.
• Identify fractions that are decimal fractions and/or common fractions.
• Understand that a decimal fraction (i.e., 3/10) can be written as a decimal (i.e., 0.3).
• Understand the fraction a/b represents a equal sized parts of a whole that is divided into b equal sized parts.
• Know and use decimal fractions and common fractions to represent the size of parts created by equal divisions of a whole.
• Understand the concept of addition and subtraction of decimal fractions and common fractions with like denominators.
• Model addition and subtraction of decimal fractions and common fractions with like denominators.
• Use mental math and estimation strategies to add and subtract decimal fractions and common fractions with like denominators.
• Solve problems involving decimal fractions and common fractions with like denominators.

Domain: Measurement - Measurement refers to students’ skill in understanding and measuring time and length. This domain also refers to students’ skill in modeling and calculating perimeters and areas of simple geometric figures.

Standards Associated with Domain
M3M1 M3M2 M3M3 M3M4

Associated Concepts, Skills, and Abilities:
• Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter hour.
• Use the units kilometer (km) and mile (mi) to discuss the measure of long distances.
• Measure to the nearest 1/4 inch, 1/2 inch, and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.
• Estimate length and represent it using appropriate units.
• Compare one unit to another within a single system of measurement.
• Understand the meaning of the linear unit and measurement in perimeter.
• Understand the concept of perimeter as being the boundary of a geometric figure.
• Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.
• Understand the meaning of the square unit and measurement in area.
• Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot, etc.).
• Determine the area of squares and rectangles by counting, addition, and multiplication with models.

Domain: Geometry - Geometry refers to students’ skill in further understanding of characteristics of previously studied geometric figures.

Standard Associated with Domain
M3G1

Associated Concepts, Skills, and Abilities:
• Draw and classify previously learned fundamental geometric figures as well as scalene, isosceles, and equilateral triangles.
• Identify and compare the properties of fundamental geometric figures.
• Examine and compare angles of fundamental geometric figures.
• Identify the center, diameter, and radius of a circle.

Domain: Algebra - Algebra refers to students’ skill in understanding how to express mathematical relationships as mathematical expressions.

Standard Associated with Domain
M3A1

Associated Concepts, Skills, and Abilities:
• Describe and extend numeric and geometric patterns.
• Describe and explain a quantitative relationship represented by a formula (such as the perimeter of a geometric figure).
• Use a symbol, such as ?? and Δ, to represent an unknown, and find the value of the unknown in a number sentence.

Domain: Data Analysis - Data Analysis refers to students’ skill in gathering, organizing, and displaying data and interpreting graphs.

Standard Associated with Domain
M3D1

Associated Concepts, Skills, and Abilities:
• Solve problems by organizing and displaying data in charts, tables, and graphs.
• Construct and interpret line plot graphs, pictographs, Venn diagrams, and bar graphs using scale increments of 1, 2, 5, and 10.

Mathematical Process Skills:

Mathematical Process Skills are integrated across the five domains. Mathematical Process Skills refers to students’ dexterity in applying concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures. Process skills are used to acquire and apply content knowledge. Process skills include solving problems that arise in mathematics and other contexts; reasoning and evaluating mathematical arguments; communicating mathematically; making connections among mathematical ideas and to other content areas; and representing mathematical ideas in multiple ways.

Standards Associated with Domain
M3P1 M3P2 M3P3 M3P4 M3P5

Associated Concepts, Skills, and Abilities:
• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
• Recognize reasoning and proof as fundamental aspects of mathematics.
• Make and investigate mathematical conjectures.
• Develop and evaluate mathematical arguments and proofs.
• Select and use various types of reasoning and methods of proof.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.
• Recognize and use connections among mathematical ideas.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Recognize and apply mathematics in contexts outside of mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.

Mathematics - Grade: 4

Domain: Number and Operations - Number and Operations refers to students’ skill in further developing understanding of whole numbers and mastering the four basic operations with whole numbers by solving problems. This domain also refers to students’ skill in understanding rounding and its appropriate use and adding and subtracting decimals and common fractions with like denominators.

Standards Associated with Domain
M4N1 M4N2 M4N3 M4N4 M4N5 M4N6 M4N7

Associated Concepts, Skills, and Abilities:
• Identify place value names and places from hundredths through one million.
• Equate a number’s word name, its standard form, and its expanded form.
• Round numbers to the nearest ten, hundred, or thousand.
• Describe situations in which rounding numbers would be appropriate and determine whether to round to the nearest ten, hundred, or thousand.
• Determine to which whole number or tenth a given decimal is closest using tools such as a number line and/or charts.
• Round a decimal to the nearest whole number or tenth.
• Represent the results of computation as a rounded number when appropriate and estimate a sum or difference by rounding numbers.
• Solve problems involving multiplication of 2- to 3-digit numbers by 1- or 2-digit numbers.
• Know the division facts with understanding and fluency.
• Solve problems involving division by a 1- or 2-digit number (including those that generate a remainder).
• Understand the relationship between dividend, divisor, quotient, and remainder.
• Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number (2050 ÷ 50 yields the same answer as 205 ÷ 5).
• Understand decimals are a part of the base-ten system.
• Understand the relative size of numbers and order 2-digit decimals.
• Add and subtract both 1- and 2-digit decimals.
• Model multiplication and division of decimals by whole numbers.
• Multiply and divide both 1- and 2-digit decimals by whole numbers.
• Understand representations of simple equivalent common fractions and/or decimal fractions.
• Add and subtract fractions and mixed numbers with common denominators. (Denominators should not exceed twelve.)
• Use mixed numbers and improper fractions interchangeably.
• Describe situations in which the four operations may be used and the relationships among them.
• Compute using the order of operations, including parentheses.
• Compute using the commutative, associative, and distributive properties.
• Use mental math and estimation strategies to compute.

Domain: Measurement - Measurement refers to students’ skill in measuring weight, using appropriate metric and standard units, and in measuring angles.

Standards Associated with Domain
M4M1 M4M2

Associated Concepts, Skills, and Abilities:
• Use standard and metric units to measure the weight of objects.
• Know units used to measure weight (gram, kilogram, ounce, pound, and ton).
• Compare one unit to another within a single system of measurement.
• Use tools, such as a protractor or angle ruler, and other methods, such as paper folding or drawing a diagonal in a square, to measure angles.
• Understand the meaning and measure of a half rotation (180°) and a full rotation (360°).
• Determine that the sum of the three angles of a triangle is always 180°.

Domain: Geometry - Geometry refers to students’ understanding of and ability to build plane and solid geometric figures. This domain also refers to students’ skill in graphing points on the coordinate plane.

Standards Associated with Domain
M4G1 M4G2 M4G3

Associated Concepts, Skills, and Abilities:
• Examine and compare angles in order to classify and identify triangles by their angles.
• Describe parallel and perpendicular lines in plane geometric figures.
• Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties.
• Compare and contrast the relationships among quadrilaterals.
• Compare and contrast a cube and a rectangular prism in terms of the number and shape of their faces, edges, and vertices.
• Describe parallel and perpendicular lines and planes in connection with rectangular prisms.
• Build/collect models for solid geometric figures (cubes, prisms, cylinders, pyramids, spheres, and cones) using nets and other representation.
• Understand and apply ordered pairs in the first quadrant of the coordinate system.
• Locate a point in the first quadrant in the coordinate plane and name the ordered pair.
• Graph ordered pairs in the first quadrant.

Domain: Algebra - Algebra refers to students’ skill in understanding and representing mathematical relationships between quantities using mathematical expressions in problem-solving situations.

Standard Associated with Domain
M4A1

Associated Concepts, Skills, and Abilities:
• Understand and apply patterns and rules to describe relationships and solve problems.
• Represent unknowns using symbols, such as ?? and Δ.
• Write and evaluate mathematical expressions using symbols and different values.

Domain: Data Analysis - Data Analysis refers to students’ skill in gathering, organizing, and displaying data. This domain also refers to students’ skill in comparing features of graphs.

Standard Associated with Domain
M4D1

Associated Concepts, Skills, and Abilities:
• Construct and interpret line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs.
• Investigate the features and tendencies of graphs.
• Compare different graphical representations for a given set of data.
• Identify missing information and duplications in data.
• Determine and justify the range, mode, and median of a set of data.

Mathematical Process Skills:

Mathematical Process Skills are integrated across the five domains. Mathematical Process Skills refers to students’ dexterity in applying concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures. Process skills are used to acquire and apply content knowledge. Process skills include solving problems that arise in mathematics and other contexts; reasoning and evaluating mathematical arguments; communicating mathematically; making connections among mathematical ideas and to other content areas; and representing mathematical ideas in multiple ways.

Standards Associated with Domain
M4P1 M4P2 M4P3 M4P4 M4P5

Associated Concepts, Skills, and Abilities:
• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
• Recognize reasoning and proof as fundamental aspects of mathematics.
• Make and investigate mathematical conjectures.
• Develop and evaluate mathematical arguments and proofs.
• Select and use various types of reasoning and methods of proof.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.
• Recognize and use connections among mathematical ideas.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Recognize and apply mathematics in contexts outside of mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.
CRCT Content Descriptions – Mathematics

Mathematics - Grade: 5

Domain: Number and Operations - Number and Operations refers to students’ skill in further developing understanding of numbers, the meanings of multiplication and division of decimals, and the use of decimals and common fractions in computation and problem solving.

Standards Associated with Domain
M5N1 M5N2 M5N3 M5N4 M5N5

Associated Concepts, Skills, and Abilities:
• Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite).
• Find multiples and factors.
• Analyze and use divisibility rules.
• Understand place value.
• Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, 0.01, and 0.001.
• Use <, >, or = to compare decimals and justify the comparison.
• Model multiplication and division of decimals.
• Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimals.
• Multiply and divide with decimals including decimals less than one and greater than one.
• Understand that the relationships and rules for multiplication and division of whole numbers also apply to decimals.
• Understand division of whole numbers can be represented as a fraction (a/b = a ÷ b).
• Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one.
• Find equivalent fractions and simplify fractions.
• Model the multiplication and division of common fractions.
• Explore finding common denominators using concrete, pictorial, and computational models.
• Use <, >, or = to compare fractions and justify the comparison.
• Add and subtract common fractions and mixed numbers with unlike denominators.
• Use fractions (proper and improper) and decimals interchangeably.
• Estimate products and quotients.
• Explore and model percents using multiple representations.
• Apply percents to circle graphs.

Domain: Measurement - Measurement refers to students’ skill in understanding and computing the areas of geometric plane figures, the volumes of simple geometric solids, and the measurement of capacity. This domain also refers to students’ skill in converting measures from one unit to another within a system of measurement.

Standards Associated with Domain
M5M1 M5M3 M5M4

Associated Concepts, Skills, and Abilities:
• Estimate the area of geometric plane figures.
• Derive the formula for the area of a parallelogram.
• Derive the formula for the area of a triangle.
• Find the areas of triangles and parallelograms using formulae.
• Estimate the area of a circle through partitioning and tiling.
• Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles, and find the sum of the areas of those shapes.
• Find the area of a circle using the formula and pi ≈ 3.14.
• Find the circumference of a circle using the formula and pi ≈ 3.14.
• Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to measure capacity.
• Compare one unit to another within a single system of measurement.
• Understand a cubic unit (u3) is represented by a cube in which each edge has the length of 1 unit.
• Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3).
• Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.
• Compute the volume of a cube and a rectangular prism using formulae.
• Estimate the volume of a simple geometric solid.
• Understand the similarities and differences between volume and capacity.

Domain: Geometry - Geometry refers to students’ skill in understanding geometric figures.

Standards Associated with Domain
M5G1 M5G2

Associated Concepts, Skills, and Abilities:
• Understand congruence of geometric figures and the correspondence of their vertices, sides, and angles.
• Understand the relationship of the circumference of a circle to its diameter is pi (π ≈ 3.14).

Domain: Algebra - Algebra refers to students’ skill in representing and investigating mathematical expressions algebraically by using variables.

Standard Associated with Domain
M5A1

Associated Concepts, Skills, and Abilities:
• Use variables, such as n or x, for unknown quantities in algebraic expressions.
• Investigate simple algebraic expressions by substituting numbers for the unknown.

Domain: Data Analysis - Data Analysis refers to students’ skill in gathering, organizing, and displaying data. This domain also refers to students’ skill in interpreting graphs.

Standards Associated with Domain
M5D1 M5D2

Associated Concepts, Skills, and Abilities:
• Analyze data presented in a graph.
• Compare and contrast multiple graphic representations (circle graphs, line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs) for a single set of data and discuss the advantages/disadvantages of each.
• Collect, organize, and display data using the most appropriate graph.

Mathematical Process Skills:

Mathematical Process Skills are integrated across the five domains. Mathematical Process Skills refers to students’ dexterity in applying concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures. Process skills are used to acquire and apply content knowledge. Process skills include solving problems that arise in mathematics and other contexts; reasoning and evaluating mathematical arguments; communicating mathematically; making connections among mathematical ideas and to other content areas; and representing mathematical ideas in multiple ways.

Standards Associated with Domain
M5P1 M5P2 M5P3 M5P4 M5P5

Associated Concepts, Skills, and Abilities:
• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
• Recognize reasoning and proof as fundamental aspects of mathematics.
• Make and investigate mathematical conjectures.
• Develop and evaluate mathematical arguments and proofs.
• Select and use various types of reasoning and methods of proof.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.
• Recognize and use connections among mathematical ideas.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Recognize and apply mathematics in contexts outside of mathematics.
• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.

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last updated September 2, 2009