Mathematics – Grade 3
In third grade, students develop their fluency with addition and subtraction, while beginning to understand multiplication as repeated addition and division as repeated subtraction and equal sharing. Students use standard units of measure for length, perimeter, time, money value, weight/mass, and temperature. They gain a broader understanding of geometry by using line segments and identifying properties of shapes. Algebraic sense grows through their understanding of equality and by identifying missing numbers in addition and subtraction expressions and equations. Students analyze, interpret and compare information in familiar situations.
EALR 1: The student understands and applies the concepts and procedures of mathematics.
COMPONENT 1.1: Understand and apply concepts and procedures from number sense.
1.1.1 Understand the concept and symbolic representation of whole numbers to at least 10,000. W
EXAMPLES
EX Represent a number to at least 10,000 in different ways including numerals, words, pictures, and physical models and translate from one representation to another.
EX Represent and show numbers in standard and expanded forms.
EX State equivalent representations for a given number by decomposing and composing into sums for that number.
EX Represent and discusses place values of digits of whole numbers using words, pictures, or numbers.
1.1.2 Understand the relative values of whole numbers to at least 10,000. W
EXAMPLES
EX Sort and order whole number values to at least 10,000 from least to greatest.
EX Order three or more numbers to at least 10,000 from least to greatest on number lines, symbolically, or with illustrations.
EX Explain why one whole number is greater than or less than another whole number.
1.1.3 Understand and use the commutative and identity properties of addition on whole numbers. W
EXAMPLES
EX Explain or show how the commutative property works for addition and not subtraction using words, pictures, physical models, or numbers.
EX Identify equivalent expressions using the commutative property.
EX Explain the identity property of addition and give examples.
EX Show whether addition equations are true or false and provides an explanation, based on the commutative or identity property of addition.
1.1.5 Understand the meaning of multiplication and division of whole numbers. W
EXAMPLES
EX Illustrate multiplication and division using words, pictures, models, and/or numbers.
EX Illustrate and explain the inverse relationship between multiplication and division using words, pictures, models, and/or numbers.
EX Show and explain the relationship between multiplication and repeated addition.
EX Show and explain the relationship between division and repeated subtraction.
EX Explain the use of division to find the number of equal shares or the quantity in each equal share.
EX Identify and explain fact families for multiplication and division.
EX Explain the meaning of a remainder in a division problem.
EX Select and/or use an appropriate operation to show understanding of addition, subtraction, multiplication, or division of whole numbers.
1.1.6 Use computational procedures for addition and subtraction of whole numbers. W
EXAMPLES
EX Apply a variety of strategies to add and subtract three-digit numbers in a given situation.
EX Describe and show relationships between strategies and procedures for multiplying and dividing.
EX Complete multi-step computations that involve addition and subtraction and explain strategies.
EX Explain and apply strategies or use procedures to add three 2-digit or two 3-digit numbers, and/or subtract numbers with 1, 2, or 3 digits.
EX Explain and apply strategies or use procedures to add 5 one-digit whole numbers.
1.1.7 Applies strategies and use tools appropriate to tasks involving addition and subtraction of whole numbers.
EXAMPLES
EX Select and use appropriate tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation.
EX Explain why a selected tool is most efficient for a given situation.
1.1.8 Understand and apply estimation strategies involving addition and subtraction of whole numbers to predict or determine the reasonableness of answers in situations. W
EXAMPLES
EX Explain when an estimation or exact answer is or is not appropriate.
EX Apply and explain a variety of estimation strategies, including multiples of 10 and 100, rounding, and compatible numbers prior to computation.
EX Use estimation to check the reasonableness of calculated results.
EX Explain an appropriate adjustment when an estimate and a calculation don’t agree.
COMPONENT 1.2: Understand and apply concepts and procedures from measurement.1.2.1 Understand how attributes of length, perimeter, time, money value, weight/mass, capacity, and temperature are used to describe objects or events. W
EXAMPLES
EX Name the attributes that can be measured for a given object.
EX Show how measurable attributes are used to describe objects or events.
EX Show how clocks and/or the environment measure the passage of time.
EX Show how money is used to describe the value of an object.
EX Show how the attributes of length, perimeter, time, money value, weight/mass, capacity, and temperature can be measured without a standard measurement tool.
EX Describe objects using U.S. units of measurement.
o Length – inch, foot, yard, mile
o Money – cent/penny, nickel, dime, quarter, dollar
o Weight – ounce, pound, ton
o Capacity (liquid volume) – cup, pint, quart, gallon
o Temperature – degree Fahrenheit
o Time – second, minute, hour, day, week, month, year
EX Describe objects using metric units of measurement.
o Length – centimeter, meter
o Mass – gram, kilogram
o Capacity (liquid volume) – milliliter, liter
o Temperature – degree Celsius
1.2.2 Understand the differences between non-standard and standard units of measurement for length and weight/mass in either the U.S. or metric system. W
EXAMPLES
EX Describe the benefits of standard units of measurement.
EX Explain whether standard units of measurement are necessary in a situation.
EX Explain when measurements can or cannot be compared, based on the units being the same or different.
EX Describe appropriate units, standard and non-standard, for measuring length and weight/mass.
1.2.3 Understand how measurement units of money value, length, and capacity are organized in the U.S. system. W
Understand how time and weight are organized in the U.S. system.
EXAMPLES
EX Explain the system of standard U.S. units for measurement of money value, length, and capacity.
EX Show how to convert standard units within the U.S. system in order to answer a question.
EX Converts between units in the U.S. system:
o Length – inch, foot, yard
o Money – penny, nickel, dime, quarter, dollar
o Capacity (liquid capacity) – cup, pint, quart, gallon
EX Explain the system of standard U.S. units for measurement of weight.
EX Explain and cites examples of the system of standard units for time including seconds, minutes, hours, days, weeks, months, and years.
EX Show how to convert time units in order to answer a question.
1.2.4 Use a procedure to measure length, perimeter, time, money value, weight/mass, capacity, and temperature. W
EXAMPLES
Suggested Procedure:
— Identifies the attribute to measure.
— Selects an appropriate unit to measure the attribute identified.
— Selects a tool that matches the unit chosen.
— Uses the selected tool to determine the number of units.
— Reports or records the number of units and a label.
EX Measure length, perimeter, time, weight/mass, capacity, and temperature in the U.S. or metric system using the suggested procedure.
EX Identify the value of each coin or bill in a given situation and calculates the total amount of money.
EX Use passage of time to identify or determine an answer to a question.
1.2.6 Understand and apply strategies to obtain reasonable estimates of length, perimeter, time, money, weight/mass, capacity, and temperature measurements. W
EXAMPLES
EX Describe situations in which estimated measurements are appropriate.
EX Use estimation to determine length, perimeter, time, money value, mass/weight, capacity, or temperature and records the number of units with a label.
EX Describe a procedure for estimating length, perimeter, time, money value, weight/mass, capacity, or temperature.
EX Use estimation to determine the perimeter of a rectangle or right triangle and records the number of units with a label.
COMPONENT 1.3: Understands and applies concepts and procedures from geometric sense.
1.3.1 Understand the concept of congruence. W
EXAMPLES
EX Draw congruent figures.
EX Indicate whether two figures are congruent and explains why or why not.
EX Explain congruence and uses examples to demonstrate it.
1.3.2 Use the properties of 2-dimensional figures including polygons. W
EXAMPLES
EX Use attributes and properties to sort, classify, and label
2-dimensional figures.
EX Draw and label a 2-dimensional figure with given attributes.
EX Describe a 2-dimensional figure using geometric attributes.
1.3.3 Determine relative locations, including intervals, of points on a positive number line. W
EXAMPLES
EX Describe the relative locations of points on a horizontal or vertical number line with positive coordinates.
EX Describe the location of objects on a number line using numbers or letters.
EX Draw or locate points or objects on a number line based on the coordinates given.
1.3.4 Understand the movement of points on a number line.
EXAMPLES
EX Locate the point of final destination for movement on a positive number line.
COMPONENT 1.4: Understand and apply concepts and procedures from probability and statistics.
1.4.3 Understand how ask questions to collect data about a specific topic. W
EXAMPLES
EX Determine or develop questions needed to gather data about themselves and their classmates.
EX Design a survey and collects, and records data in easy-to-use formats such as tally marks, charts, or tables.
1.4.4 Understand, determine, and use mode to describe a set of data. W
EXAMPLES
EX Describe a situation where mode is meaningful for a set of data.
EX Explain why mode is useful for describing a set of data.
EX Explain what the mode represents and how to find it in a given set of data.
EX Use pictures to demonstrate understanding of mode.
EX Determine the mode for a set of data.
1.4.5 Read and understand data from tables, charts, pictographs, and bar graphs. W
EXAMPLES
EX Make inferences based on the data or determine if the data can support inferences made.
EX Read, explain, and summarize data from tables, charts, pictographs, and bar graphs.
EX Read and interpret data from pictographs and bar graphs for comparative information.
COMPONENT1.5: Understand and apply concepts and procedures from algebraic sense.
1.5.1 Recognize, understand, and extend a pattern of shapes and /or objects or a pattern of numbers with a single addition or subtraction between terms. W
EXAMPLES
EX Identify, describe, extend, or construct patterns of numbers based on a single addition or subtraction between terms.
EX Identify, describe, extend, or construct patterns of figures or objects.
EX Identify or write the missing elements in the beginning, middle, and/or end of a pattern.
EX Identify a pattern that fits a given rule.
1.5.3 Understand the concept of mathematical equality and uses the symbol = in equations. W
EXAMPLES
EX Explain equality and the use of = in equations.
EX Identify or write an equation for a given situation involving addition or subtraction.
EX Identify or describe a situation that represents a given equation involving addition or subtraction.
EX Determine when two expressions are equal and use = to denote equality.
EX Describe a situation in which two expressions are equal.
1.5.4 Use a single variable to write simple expressions and equations that represent situations involving addition and subtraction of whole numbers. W
EXAMPLES
EX Read expressions and equations involving a single variable.
EX Use mathematical symbols, including a single variable, to write expressions and equations to represent a given situation.
EX Describe a situation that represents a given expression or equation that includes a single variable.
1.5.6 Apply algebraic properties to solve equations involving addition and subtraction. W
EXAMPLES
EX Solve a one-step equation with addition or subtraction using manipulatives, pictures, physical models, and/or symbols.
EX Write and solves a one-step equation using addition or subtraction in a given situation.
EX Explain the meaning of the solution for an equation.
EALR 2: The student uses mathematics to define and solve problems.
COMPONENT 2.1: Define problems.
2.1.1 Identify questions to be answered to solve a problem in familiar situations. W
EXAMPLES
EX Investigate the situation and determine if there is a problem to solve.
EX Define or clarify the question the problem presents.
EX Generate questions that would need to be answered in order to solve the problem.
2.1.2 Determine what information is missing or extraneous in familiar situations. W
EXAMPLES
EX Identify missing information that is needed to solve the problem.
EX Differentiate between information that is needed or not needed to solve the problem.
2.1.3 Identify what is known and unknown in familiar situations. W
EXAMPLES
EX Examine information to identify what is known and unknown.
COMPONENT 2.2: Construct solutions.
2.2.1 Select and use relevant information to construct solutions. W
EXAMPLES
EX Select and use relevant data and information in a problem situation.
2.2.2 Select and use appropriate concepts and procedures from number sense, measurement, geometric sense, or statistics to construct solutions. W
EXAMPLES
EX Use addition and subtraction of whole numbers to construct a solution.
EX Use measurements related to length, perimeter, time, money value, weight/mass, capacity, and temperature to construct a solution.
EX Use properties of 2-dimensional figures or relative position on a positive number, line to construct a solution.
EX Use mode to construct a solution.
2.2.3 Apply a variety of strategies to construct solutions. W
EXAMPLES
EX Use tools such as manipulatives, pictures, charts, calculators, or measurement tools to construct a solution.
EX Select and applies appropriate strategies to construct a solution.
EX Determine when an approach is unproductive and try a new approach.
EX Explain whether a given solution applies strategies appropriately.
2.2.4 Determine whether a solution is viable, is mathematically correct, and answers the question. W