Grade 3

EALR 1: The student understands and applies the concepts and procedures of mathematics.

Number and numeration

1.1.1 Understand the concept of whole numbers.  W

·   Represent a number to at least 10,000 in different ways (e.g., words, numerals, pictures, physical models). [CU]

·   Translate from one representation of a whole number to another in standard, expanded, and word forms. [MC]

·   Generate equivalent representations for a given number by decomposing and composing. [MC]

·   Explain the difference between the natural numbers and the whole numbers.

·   Identify place values of digits of whole number to the hundreds or thousands place using words, pictures, or numbers.

·   Write whole numbers to 999.

·   Decompose whole numbers into components (e.g., 35 is made of 3 tens and 5 ones) using words, numbers, or pictures.

1.1.2 Understand the relative values of whole numbers.  W

·   Compare whole number values to at least 10,000 using the symbols for "greater than," "less than," and “equal to".

·   Order three or more numbers to at least 10,000 from smallest to largest. [CU]

·   Compare combined quantities (e.g., 50 + 3 is greater than 40 + 9). [RL]

1.1.3 Understand and apply the commutative and identity properties of addition on whole numbers.  W

·   Explain or show how the commutative property works with addition and not subtraction using words, numbers, or physical models. [CU]

·   Describe how the identity property works with addition. [CU]

·   Determine whether addition equations are true or false and explain, based on the commutative or identity properties for addition (e.g., 15+ 3+5 = 15+5 +3). [CU]

·   Identify an equivalent expression using the commutative property.

·   Show how the commutative property works using pictures or objects. [CU]

Computation

1.1.5 Understand the meaning of multiplication and division on whole numbers.  W

·   Illustrate multiplication and division using models and diagrams. [CU]

·   Illustrate and explain the inverse relationship between multiplication and division using physical diagrams, words, and symbols (e.g., arrays, fact families). [CU]

·   Describe and compare strategies to solve problems involving multiplication and division (e.g., alternative algorithms, different strategies, decomposition, properties of multiplication). [CU]

·   Demonstrate the relationship between multiplication and repeated addition.

·   Demonstrate the relationship between division and repeated subtraction.

1.1.6 Apply procedures of addition and subtraction on whole numbers with fluency.  W

·   Describe and compare strategies to solve three-digit addition and subtraction problems (e.g., child developed algorithms, decomposition). [RL, CU]

·   Use joining, separating, adding-on, and finding the difference to add and subtract.

·   Write and solve multi-step problem situations that involve addition and subtraction. [CU, MC]

·   Use calculators to compute with large numbers (e.g., adding three or more 3-digit numbers; subtracting 3 digit from 4 digit numbers).

1.1.7 Understand and apply strategies and tools as appropriate to tasks involving addition and subtraction on whole numbers.

·   Use appropriate strategies and tools from among mental computation, estimation, calculators, and paper and pencil to compute in a problem situation. [SP, RL]

·   Defend situations in which estimation is sufficient (e.g., grocery shopping or party supplies). [CU]

·   Use mental arithmetic, pencil and paper, or calculator as appropriate to the task involving addition and subtraction of whole numbers.

Estimation

1.1.8 Understand and apply estimation strategies to determine the reasonableness of answers in situations involving addition and subtraction on whole numbers.  W

·   Identify when an approximation is appropriate.

·   Use estimation to determine the reasonableness of answers in situations.  [RL]

·   Describe and justify reasonableness of an estimate in computation. [RL, CU]

·   Use a variety of estimation strategies (e.g., multiples of 10 and 100, rounding, front-end estimation, compatible numbers, clustering).

·   Describe and justify whether an approximation is or is not appropriate. {RL, CU]

Attributes, units, and systems

1.2.1 Understand how different attributes (length, perimeter, time, money value, weight/mass, and temperature) are used to describe objects.  W

·   Given an object, name the attributes that can be measured. [CU, MC]

·   Explain how length is used to describe objects. [CU]

·   Explain or show how height and weight are different. [CU]

·   Explain or show how clocks measure the passage of time. [CU]

·   Explain how money is used to describe the value of purchased items. [CU]

1.2.2 Understand the differences between non-standard and standard units of measurement for length and weight/mass in either U.S. or metric systems.  W

·   Identify when two unit measurements are not necessarily equal (e.g., one pace long can represent different lengths). [CU, MC]

·   Determine whether measurement can or cannot be compared based on whether the units are the same or different.

·   Show how length units are shown on rulers, tape measures, and other linear measuring tools. [MC, CU]

·   Show how weight units are shown on a grocery scale. [MC]

·   Explain why people created standard units for length or weight/mass. [CU]

1.2.3 Understand how measurement units of length (U.S.) and capacity (U.S.) are organized into systems.  W

·   Describe the various units of measurement for length and capacity and explain how they are organized.

·   Explain the benefits and appropriate uses of standard units of measurement for length and capacity using our customary (U.S.) system. [CU]

·   Demonstrate or explain how inches are organized into feet and feet are organized into yards. [CU]

·   Demonstrate or explain how cups are organized into pints, pints into quarts, and quarts into gallons. [CU]

Procedures, precision, and estimation

1.2.4 Understand and apply systematic procedures to measure length, time, weight, money value, and temperature.  W

·   Identify attribute to measure.

·   Select and use appropriate units (e.g., meters, minutes, pounds, dollars, degrees).

·   Select and use tools that match the unit (e.g., ruler, clock, scales, calculator, thermometer).

·   Count or compute and label measures.

·   Explain and use a method for making change with coins. [CU].

·   Compare measures of two or more like objects. [RL]

1.2.6 Understand and apply strategies to obtain reasonable estimates of length, time, weight, and temperature measurements.  W

·   Identify situations in which estimated measurements are sufficient; estimate length, time, money, weight or temperature.

·   Estimate a measurement using standard or non-standard units (e.g., fingers, arms, paper clips, inches, minutes, or foot lengths).

·   Create and use referents to standard units (e.g., width of pinkie finger is similar to a centimeter). [RL, MC]

·   Use estimation to decide whether standard or non-standard units of measurement have been used in a situation. [RL]

·   Determine when estimation is useful.

Properties and relationships

1.3.1 Understand the concept of congruence.  W

·   Identify, describe, and compare congruent two-dimensional geometric figures. [RL, CU]

·   Given a variety of figures, determine which figures are congruent.

·   Draw a shape that is congruent to a given two-dimensional shape. [CU]

·   Explain congruence and use an example to demonstrate it. [CU]

1.3.2 Understand and apply attributes and properties to two-dimensional shapes and figures.  W

·   Use attributes and properties to identify, name, draw, compare, and/or sort two-dimensional shapes and figures. [RL, CU]

·   Draw and label two-dimensional figures given particular attributes (e.g., triangle, rectangle with all sides the same length). [CU]

·   Identify, name, and describe the attributes and properties of polygons. [CU]

·   Given two polygons, explain how they are alike and different in terms of their attributes and properties (e.g., using a Venn diagram). [CU]

·   Give directions so that someone else can duplicate a design involving polygons (e.g., a friend who can’t see the design). [CU]

Locations and transformations

1.3.3 Understand relative locations including intervals of numbers on a positive number line.  W

·   Given directions for movement on a positive number line, identify the point of final destination using real-world examples (e.g., travel back and forth on a street, temperature variation at different times of the day, dance steps from diverse cultures). [SP, RL, MC]

·   Identify the interval on a given number line (e.g., describe the scale on a graph). [CU]

·   Describe the relative locations of points on a number line with positive coordinates. [CU]

·   Use unit values to describe the location of objects on a number line.

·   Draw points or objects on a number line based on unit values given.

Statistics

1.4.3 Understand how to use data collection and display methods to obtain desired information.  W

·   Interpret graphs for comparative information (e.g., find the difference in selected data). [RL, CU, MC]

·   Pose questions and gather data relevant to the questions posed.

·   Design a survey; collect, and record data in easy-to-use formats (e.g., use tally marks, make a table). [CU]

·   Organize category data into bar graphs with unit scales for ease of interpretation. [RL]

·   Organize data into picture graphs with unit scales for ease of interpretation. [RL]

·   Determine questions needed to gather data about themselves and their classmates.

1.4.4 Understand and apply mode to describe a set of data.  

·   Create and solve a problem situation where mode is meaningful for a set of data. [RL, CU, MC]

·   Explain what the mode represents and how to find it in a given set of data. [CU]

·   Identify the mode for a given set of data.

1.4.5 Understand representations of data from tables, charts, and bar graphs.  W

·   Pose questions that can be answered from a given graph. [CU, MC]

·   Make inferences based on the data or determine if the data can support inferences made. [CU, MC]

·   Read and report on data from tables, charts, and bar graphs. [CU]

·   Explain how types of graphs or the graph construction can support different points of view (e.g., starting the axis numbers at 50 rather than 0). [CU, SP, RL]

·   Create bar graphs including labels for title, both axes, scale units (e.g., 2’s, 5’s, 10’s), and key if needed. [SP, RL, CU, MC]

·   Interpret graphs for comparative information (e.g., find the difference in selected data). [RL, CU, MC]

Patterns, functions, and other relations

1.5.1 Understand patterns of objects including number patterns with a single addition or subtraction operation.  W

·   Recognize and extend patterns of numbers, figures, and objects using addition and subtraction based on a single arithmetic operation between the terms (e.g., stacking cans in a pyramid, observing textile patterns).

·   Identify, extend, and describe numerical patterns (e.g., skip counting, 100 chart, multiplication table). [RL, CU]

·   Describe the pattern in a number sequence (e.g., Guess My Rule, Function Machine). [CU]

·   Identify the rule for a pattern based on a single operation (e.g., add 3). [RL]

·   Explain what makes a given pattern a pattern. [CU]

·   Complete a pattern by supplying missing elements in the pattern.

·   Compare two patterns to determine whether they are alike or different and explain the decision. [RL, CU]

Symbols and representations

1.5.3 Apply understanding of the concept of mathematical equality.  W

·   Write an equation or expression for a given situation (e.g., there are 23 dogs at a kennel; if 15 are present, how many are absent?). [SP, RL, CU]

·   Explain equality and the use of “=” in equations. [CU]

·   Compare expressions to determine whether they are equal (e.g., 3+4 and 2+5). [RL]

·   Write a situation that represents it given an equation involving addition or subtraction. [CU, MC]

·   Identify a situation that represents it given an equation involving addition or subtraction. [CU, MC]

1.5.4 Understand and apply operational and relational symbols and notations to write equations involving addition and subtraction.  W

·   Write and explain mathematical statements (e.g., 7 + £ = 8 or £ +8 = 10). [CU]

·   Identify and use mathematical symbols and notations in reading and writing expressions and equations involving addition and subtraction.

·   Write an equation for a given situation (e.g., there are 23 children in class; if 15 are present, how many are absent?). [CU]

Evaluating and solving

1.5.6 Understand and apply strategies to solve equations that include addition or subtraction.  W

·   Solve problems involving equality (e.g., 5 + 3 = £ + 2). [SP, RL]

·   Solve equations with addition and subtraction using manipulatives, pictures, and symbols. [SP, RL, CU]

·   Describe a strategy used to solve an equation with addition or subtraction. [CU]

EALR 2: The student uses mathematics to define and solve problems.

Example: Miguel’s reading class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his nine classmates to determine about how many minutes they read each night to see if they have met the goal. Miguel likes to read books by Matt Christopher.

2.1.1 Analyze a situation to define a problem.  W

·   Use strategies/approaches to examine the situation and determine if there is a problem to solve (e.g., ask questions, or paraphrase information provided: Miguel is taking a survey to determine about how many minutes students read on school nights. The class goal is at least 30 minutes each night).

·   Determine the problem using information from investigation (e.g., has the class met its reading goal for the week?).

·   Generate questions that would need to be answered in order to solve the problem (e.g., about how many minutes did each person read? Can we estimate or do we need an exact number? What is the difference between the goal and the minutes read?).

·   Identify known and unknown information (e.g., known: who the students are, the class goal [30 minutes x 5 nights x 10 students is 1500 total minutes]; unknown: the number of minutes each student read, if the class reached the goal).

·   Identify information that is needed and not needed to solve the problem (e.g., needed: the class goal; not needed: Miguel likes Matt Christopher books).

2.2.1 Apply strategies, concepts, and procedures to devise a plan to solve the problem.  W

·   Gather and organize data and information (e.g., create a survey to find out about how many minutes students are watching TV; organize data on a two-column chart).

·   Determine what strategy will be used to solve the problem (e.g., estimate minutes read per night per week from data gathered).

2.2.2 Apply mathematical tools to solve the problem.  W

·   Use strategies to solve problems (e.g., use number estimation ─ if one student reads 45 minutes [around 50] one night and if the same student reads 18 [around 20] minutes the next night, that is about 70 minutes).

·   Use appropriate tools to estimate solution (e.g., mental math or paper and pencil).

·   Recognize when an approach is unproductive and try a new approach.

EALR 3: The student uses mathematical reasoning.

Example: Miguel’s reading class has set a goal to increase nightly reading to at least 30 minutes. He is taking a survey of his nine classmates to determine about how many minutes they read each night to see if they have met the goal. Miguel likes to read books by Matt Christopher.

3.1.1 Analyze information presented in familiar situations.  W

·   Break down results from data to determine about how many minutes per night students are reading in order to estimate whether the class has met 30 minutes each night goal.

3.2.1 Apply prediction and inference skills.  W

·   Make a reasonable prediction based on prior knowledge and investigation of situation (e.g., after collecting survey data and before estimation, predict whether the class will meet its goal).

·    Defend prediction with evidence from the situation.

·   Make inferences (conjectures) using information from the situation to support the inference (e.g., the class probably did not make the reading goal because the community softball league has started up and most kids are involved in the evenings).

3.2.2 Apply the skills of drawing conclusions and support the conclusions using evidence.  W

·   Draw conclusions from displays, texts, or oral discussions and justify those conclusions with logical reasoning or other evidence.

3.2.3 Analyze procedures used to solve problems in familiar situations.  W

·   Describe and compare estimation strategies used (e.g., front end estimation vs. using compatible numbers). [1.1.8]

3.3.1 Understand how to justify results using evidence.  W

·   Check for reasonableness of results by using a different strategy or tool to solve the problem (e.g., use front end estimation to determine about how many minutes students were reading each night).

·   Justify whether estimation is appropriate for the situation.

3.3.2 Understand how to validate thinking about numerical, measurement, geometric, or statistical ideas by using models, known facts, patterns, or relationships.  W

·   Explain how comparisons can be used to draw a conclusion (e.g., the class won’t have met the reading goal because fewer students read less than more this week and didn’t make the goal last week).

EALR 4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.1.1 Understand how to follow a plan for collecting information for a given purpose.  W

·   Determine how to collect information for a specific purpose or audience (e.g., to convince a parent or other adult, to demonstrate a need for change, to provide information).

·   Develop and follow a plan based on the kind of information needed, the purpose, and the audience (e.g., survey, gather data from a chart or graph, read in a text to gather information).

4.1.2 Understand how to extract information for a given purpose from one or two different sources using reading, listening, and observation.  W

·   Read and report on data from tables, charts, and bar graphs. [1.4.5]

·   Read directions for movement on a positive number line, identify the point of final destination using real–world examples (e.g., travel back and forth on a street, temperature variations during the day). [1.3.3]

4.2.1 Understand how to organize information for a given purpose.  W

·   Create a display to represent information from survey results (e.g., the approximate number of minutes read and whether or not the goal was met).

·   Create bar graphs including labels for title, both axes, scale units (e.g., 2’s, 5’s, 10’s), and key if needed. [1.4.2]

·   Create and solve a problem situation where mode is meaningful for a set of data. [1.4.4]

·   Display information to be shared.

4.2.2 Understand how to communicate or represent ideas using mathematical language or notation.  W

·   Translate from one representation of a whole number to another in standard, expanded, and word forms. [1.1.1]

·   Name attributes of an object that can be measured. [1.2.4]

·   Identify, describe, and compare congruent two-dimensional geometric shapes. [1.3.1]

·   Make a survey and collect data (e.g., use tally marks, make a table). [1.4.3]

·   Identify and use appropriate symbols and notation in reading and writing simple expressions and equations involving addition and subtraction. [1.5.4]

EALR 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

5.1.1 Understand how to use concepts and procedures from any two of the content components in a given problem or situation.  W

·   Conduct a survey for a question, collect data, and use three-digit addition and subtraction to compute the results of the survey. [1.1.6, 1.4.4]

·   Explain and use a method for making change with coins. [1.1.1, 1.2.4]

5.1.2 Understand how to recognize equivalent mathematical models and representations in familiar situations.  W

·   Translate from one representation of a whole number to another in standard, expanded, and word forms. [1.1.1]

·   Compare strategies to solve problems involving multiplication and division (e.g., alternative algorithms, use of properties of multiplication). [1.1.5]

·   Use the inverse relationship between multiplication and division using physical diagrams, words, and symbols (e.g., arrays, fact families). [1.1.5]

5.2.1 Apply mathematical patterns and ideas in familiar situations in other disciplines.

·   Given an object, identify geometric attributes that can be measured.

·   Interpret graphs for comparative information. [1.4.3]

·   Pose questions and gather data about self and surroundings. [1.4.3]

·   Make inferences based on data or determine if the data can support inferences made. [1.4.5]

5.2.2 Know the contributions of individuals and cultures to the development of mathematics.

·   Recognize the contributions to the development of mathematics by women, men, and various cultures (e.g., complete a mathematically based project that researches the history of 0?).

5.3.1 Understand that mathematics is used in daily life and extensively outside the classroom.

·   Write and solve multi-step situations that involve addition and subtraction. [1.1.6]

·   Use referents to standard units (e.g., width of pinkie finger is similar to a centimeter). [1.2.6]

·   Identify the point of final destination using real-world examples given directions for movement on a positive number line (e.g., travel back and forth on a street, temperature variation at different times of the day, climbing up and down stairs). [1.3.3]

·   Pose questions and gather data about self and surroundings. [1.4.2]

·   Create and solve a problem situation where mode is meaningful for a set of data. [1.4.4]

·   Make inferences on data from a real-world context and then use the context to determine if the inference is valid. [1.4.5]