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3.N
Number and Operations
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1
Students will understand numerical concepts and mathematical operations.
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3.N.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
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3.N.1.1
Exhibit an understanding of the place-value structure of the base-ten number system by:
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3.N.1.1.a
reading, modeling, writing, and interpreting whole numbers up to 10,000
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3.N.1.1.b
comparing and ordering numbers up to 1,000
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3.N.1.1.c
recognizing the position of a given number in the base-ten number system and its relationship to benchmark numbers such as 10, 50, 100, 500
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3.N.1.2
Use whole numbers by using a variety of contexts and models (e.g., exploring the size of 1,000 by skip- counting to 1,000 using hundred charts or strips 10 or 100 centimeters long).
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3.N.1.3
Identify some representations for some numbers and generate them by decomposing and recombining numbers (e.g., 853 = 8 x 100 + 5 x 10 + 3; 85 x 10 + 3 = 853; 853 = 900 - 50 + 3)
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3.N.1.4
Identify the relationship among commonly encountered factors and multiples (e.g., factor pairs of 12 are 1 x 12, 2 x 6, 3 x 4; multiples of 12 are 12, 24, 36).
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3.N.1.5
Use visual models and other strategies to recognize and generate equivalents of commonly used fractions and mixed numbers (e.g., halves, thirds, fourths, sixths, eighths, and tenths).
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3.N.1.6
Demonstrate an understanding of fractions as parts of unit wholes, parts of a collection or set, and as a location on a number line.
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3.N.1.7
Use common fractions for measuring and money (e.g., using fractions and decimals as representations of the same concept, such as half of a dollar = 50 cents).
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3.N.2
Understand the meaning of operations and how they relate to one another.
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3.N.2.1
Use a variety of models to show an understanding of multiplication and division of whole numbers (e.g., charts, arrays, diagrams, and physical models [i.e., modeling multiplication with a variety of pictures, diagrams, and concrete tools to help students learn what the factors and products represent in various contexts]).
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3.N.2.2
Find the sum or difference of two whole numbers between 0 and 10,000.
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3.N.2.3
Solve simple multiplication and division problems (e.g., 135 รท 5 = []).
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3.N.2.4
Identify how the number of groups and the number of items in each group equals a product.
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3.N.2.5
Demonstrate the effects of multiplying and dividing on whole numbers (e.g., to find the total number of legs on 12 cats, 4 represents the number of each [cat] unit, so 12 x 4 = 48 [leg] units).
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3.N.2.6
Identify and use relationship between multiplication and division (e.g., division is the inverse of multiplication) to solve problems.
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3.N.2.7
Select and use operations (e.g., addition, multiplication, subtraction, division) to solve problems.
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3.N.3
Compute fluently and make reasonable estimates.
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3.N.3.1
Choose computational methods based on understanding the base-ten number system, properties of multiplication and division, and number relationships.
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3.N.3.2
Use strategies (e.g., 6 x 8 is double 3 x 8) to become fluent with the multiplication pairs up to 10 x 10.
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3.N.3.3
Compute with basic number combinations (e.g., multiplication pairs up to 10 x 10 and their division counterparts).
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3.N.3.4
Demonstrate reasonable estimation strategies for measurement, computation, and problem solving.
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3.A
Algebra
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3
Students will understand algebraic concepts and applications.
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3.A.1
Understand patterns, relations, and functions.
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3.A.1.1
Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities
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3.A.1.2
Solve problems involving numeric equations.
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3.A.1.3
Select appropriate operational and relational symbols to make an expression true (e.g., 'If 4 [] 3 = 12, what operational symbol goes in the box?').
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3.A.1.4
Use models of feet and inches to express simple unit conversions in symbolic form (e.g., 36 inches = [] feet x 12) that develop conceptual understanding versus procedural skills.
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3.A.1.5
Recognize and use the commutative property of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5?).
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3.A.1.6
Create, describe, and extend numeric and geometric patterns including multiplication patterns.
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3.A.1.7
Represent simple functional relationships:
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3.A.1.7.a
solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit)
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3.A.1.7.b
extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s, by multiplying the number of horses by 4, or through the use of tables)
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3.A.2
Represent and analyze mathematical situations and structures using algebraic symbols.
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3.A.2.1
Determine the value of variables in missing part problems (e.g., 139 + [] = 189).
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3.A.2.2
Recognize and use the commutative and associative properties of addition and multiplication (e.g., 'If 5 x 7 = 35, then what is 7 x 5? And if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?').
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3.A.2.3
Explore the ways that commutative, distributive, identity, and zero properties are useful in computing with numbers.
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3.A.3
Use mathematical models to represent and understand quantitative relationships.
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3.A.3.1
Model problem situations with objects and use representations such as pictures, graphs, tables, and equations to draw conclusions.
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3.A.3.2
Solve problems involving proportional relationships including unit pricing (e.g., four apples cost 80 cents; therefore, one apple costs 20 cents).
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3.A.3.3
Describe relationships of quantities in the form of mathematical expressions, equations, or inequalities.
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3.A.3.4
Select appropriate operational and relational symbols to make an expression true (e.g.,' If 4 [] 3 = 12), what operational symbol goes in the box?').
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3.D
Analyze changes in various contexts.
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3.A.4.1
Demonstrate how change in one variable can relate to a change in a second variable (e.g., input-output machines, data tables).
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3.G
Geometry
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3
Students will understand geometric concepts and applications.
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3.G.1
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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3.G.1.1
Describe and compare the attributes of plane and solid geometric figures to show relationships and solve problems:
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3.G.1.1.a
identify, describe, and classify polygons (e.g., pentagons, hexagons, and octagons)
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3.G.1.1.b
identify lines of symmetry in two-dimensional shapes
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3.G.1.1.c
explore attributes of quadrilaterals (e.g., parallel and perpendicular sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square)
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3.G.1.1.d
identify right angles
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3.G.1.1.e
identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder)
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3.G.2
Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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3.G.2.1
Describe location and movement using common language and geometric vocabulary (e.g., directions from classroom to gym).
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3.G.2.2
Use ordered pairs to graph, locate specific points, create paths, and measure distances within a coordinate grid system.
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3.G.2.3
Use a two-dimensional grid system (e.g., a map) to locate positions representing actual places.
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3.G.3
Apply transformations and use symmetry to analyze mathematical situations.
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3.G.3.1
Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.
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3.G.3.2
Identify and describe the line of symmetry in two- and three-dimensional shapes.
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3.G.4
Use visualization, spatial reasoning, and geometric modeling to solve problems.
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3.G.4.1
Visualize, build, and draw geometric objects.
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3.G.4.2
Create and describe mental images of objects, patterns, and paths.
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3.G.4.3
Recognize geometric shapes and structures (e.g., in the environment).
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3.G.4.4
Use geometric models to solve problems in other areas of mathematics (e.g., using arrays as models of multiplication or area).
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3.G.4.5
Identify and build three-dimensional objects from two-dimensional representations of that object.
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3.G.4.6
Investigate two-dimensional representations of three-dimensional shapes.
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3.G.4.7
Explore geometric ideas and relationships as they apply to other disciplines and to problems that arise in the classroom or in everyday life.
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3.M
Measurement
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3
Students will understand measurement systems and applications.
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3.M.1
Understand measurable attributes of objects and the units, systems, and process of measurement.
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3.M.1.1
Demonstrate understanding of the need for measuring with standard units and become familiar with standard units in the U.S. customary system.
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3.M.1.2
Choose and use the appropriate units and measurement tools to quantify the properties of objects (e.g., length [ruler], width [ruler], or mass [balance scale]).
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3.M.1.3
Identify time to the nearest minute (elapsed time) and relate time to everyday events.
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3.M.1.4
Identify and use time intervals (e.g., hours, days, weeks, months, years).
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3.M.1.5
Identify properties (e.g., length, area, weight, volume) and select the appropriate type of unit for measuring each property.
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3.M.1.6
Demonstrate understanding that measurements are approximations, investigate differences in units and their effect on precision, and consider the degree of accuracy for different situations.
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3.M.2
Apply appropriate techniques, tools, and formulas to determine measurements.
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3.M.2.1
Find the area of rectangles using appropriate tools (e.g., grid paper, tiles).
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3.M.2.2
Estimate measurements.
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3.M.2.3
Use appropriate standard units and tools to estimate, measure, and solve problems (e.g., length, area, weight).
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3.M.2.4
Recognize a 90-degree angle and use it as a strategy to estimate the size of other angles.
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3.D
Data Analysis and Probability
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3
Students will understand how to formulate questions, analyze data, and determine probabilities.
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3.D.1
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
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3.D.1.1
Collect and organize data using observations, measurements, surveys, or experiments.
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3.D.1.2
Represent data using tables and graphs (e.g., line plots, bar graphs, and line graphs).
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3.D.1.3
Conduct simple experiments by determining the number of possible outcomes and make simple predictions:
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3.D.1.3.a
identify whether events are certain, likely, unlikely, or impossible
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3.D.1.3.b
record the outcomes for a simple event and keep track of repetitions
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3.D.1.3.c
summarize and record the results in a clear and organized way
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3.D.1.3.d
use the results to predict future events
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3.D.2
Select and use appropriate statistical methods to analyze data.
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3.D.2.1
Apply and explain the uses of sampling techniques (e.g., observations, polls, tally marks) for gathering data.
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3.D.3
Develop and evaluate inferences and predictions that are based on data.
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3.D.3.1
Analyze data displayed in a variety of formats to make reasonable inferences and predictions, answer questions, and make decisions.
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3.D.4
Understand and apply basic concepts of probability.
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3.D.4.1
Discuss the degree of likelihood of events and use terminology such as 'certain,' 'likely,' 'unlikely'.
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3.D.4.2
Predict the outcomes of simple experiments (e.g., coin tossing) and test the predictions using concrete objects (e.g., coins, counters, number cubes, spinners).
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3.D.4.3
Record the probability of a specific outcome for a simple probability situation (e.g., probability is three out of seven for choosing a black ball; 3/7).
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