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4.N
Number and Operations
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4
Students will understand numerical concepts and mathematical operations.
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4.N.1
Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
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4.N.1.1
Exhibit an understanding of the place-value structure of the base-ten number system by reading, modeling, writing, and interpreting whole numbers up to 100,000; compare and order the numbers:
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4.N.1.1.a
recognize equivalent representations for the same number and generate them by decomposing and combining numbers (e.g., 853 = 8 x 100 + 5 x 10 + 3; 853 = 85 x 10 + 3; 853 = 900 - 50 + 3)
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4.N.1.1.b
identify the numbers less than 0 by extending the number line and using negative numbers through familiar applications (e.g., temperature, money)
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4.N.1.2
Identify fractions as parts of unit wholes, as parts of groups, and as locations on number lines:
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4.N.1.2.a
use visual models and other strategies to compare and order commonly used fractions
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4.N.1.2.b
use models to show how whole numbers and decimals (to the hundredths place) relate to simple fractions (e.g., 1/2, 5/10, and 0.5)
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4.N.1.2.c
identify different interpretations of fractions:
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4.N.1.2.c.1
division of whole numbers by whole numbers
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4.N.1.2.c.2
ratio
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4.N.1.2.c.3
equivalence
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4.N.1.2.c.4
ordering of fractions
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4.N.1.2.c.5
parts of a whole or parts of a set
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4.N.1.3
Add and subtract fractions with common and uncommon denominators using a variety of strategies (e.g., manipulatives, numbers, pictures):
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4.N.1.3.a
recognize and generate equivalent decimal forms of commonly used fractions (e.g., halves, quarters, tenths, fifths)
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4.N.1.3.b
identify the numbers less than 0 by extending the number line and using negative numbers through familiar applications (e.g., temperature, money)
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4.N.1.4
Recognize classes of numbers (e.g., odd, even, factors, multiples, square numbers) and apply these concepts in problem-solving situations.
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4.N.2
Understand the meaning of operations and how they relate to one another.
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4.N.2.1
Demonstrate an understanding of and the ability to use:
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4.N.2.1.a
standard algorithms for the addition and subtraction of multi-digit numbers
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4.N.2.1.b
standard algorithms for multiplying a multi-digit number by a two-digit number and for dividing a multi-digit number by a one-digit number
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4.N.2.2
Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems.
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4.N.2.3
Extend the uses of whole numbers to the addition and subtraction of simple decimals (positive numbers to two places).
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4.N.2.4
Demonstrate commutative, associative, identity, and zero properties of operations on whole numbers (e.g., 37 x 46 = 46 x 37 and (6 x 2) x 5 = 6 x (2 x 5)).
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4.N.2.5
Demonstrate the concept of distributivity of multiplication over addition and subtraction (e.g., 7 x 28 is equivalent to (7 x 20) + (7 x 8) or (7 x 30) - (7 x 2)).
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4.N.3
Compute fluently and make reasonable estimates.
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4.N.3.1
Demonstrate multiplication combinations through 12 x 12 and related division facts, and use them to solve problems mentally and compute related problems (e.g., 4 x 5 is related to 40 x 50, 400 x 5, and 40 x 500).
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4.N.3.2
Add, subtract, and multiply up to two double-digits accurately and efficiently.
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4.N.3.3
Use a variety of strategies (e.g., rounding and regrouping) to estimate the results of whole number computations and judge the reasonableness of the answers.
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4.N.3.4
Use strategies to estimate computations involving fractions and decimals.
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4.A
Algebra
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4
Students will understand algebraic concepts and applications.
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4.A.1
Understand patterns, relations, and functions.
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4.A.1.1
Represent and analyze patterns and simple functions using words, tables, and graphs.
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4.A.1.2
Create and describe numeric and geometric patterns including multiplication and division patterns.
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4.A.1.3
Express mathematical relationships using equations.
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4.A.1.4
Use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:
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4.A.1.4.a
use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding of the concept of a variable)
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4.A.1.4.b
interpret and evaluate mathematical expressions using parentheses
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4.A.1.4.c
use and interpret formulas (e.g., Area = Length x Width or A = L x W) to answer questions about quantities and their relationships
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4.A.2
Represent and analyze mathematical situations and structures using algebraic symbols.
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4.A.2.1
Identify symbols and letters that represent the concept of a variable as an unknown quantity.
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4.A.2.2
Explore the uses of properties (commutative, distributive, associative) in the computation of whole numbers.
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4.A.2.3
Express mathematical relationships using equations.
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4.A.2.4
Determine the value of variables in simple equations (e.g., 80 x 15 = 40 x []).
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4.A.2.5
Develop simple formulas in exploring quantities and their relationships (e.g., A = L x W).
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4.A.3
Use mathematical models to represent and understand quantitative relationships.
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4.A.3.1
Solve problems involving proportional relationships (including unit pricing and map interpretations; e.g., one inch = five miles; therefore, five inches = [] miles).
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4.A.3.2
Model problem situations and use graphs, tables, pictures, and equations to draw conclusions (e.g., different patterns of change).
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4.A.3.3
Use and interpret formulas (e.g., Area = Length x Width or A = L x W) to answer questions about quantities and their relationships.
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4.A.4
Analyze changes in various contexts.
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4.A.4.1
Identify and describe situations with constant or varying rates of change and compare them.
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4.A.4.2
Determine how a change in one variable relates to a change in a second variable (e.g., data tables, input-output machines).
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4.A.4.3
Find and analyze patterns using data tables (e.g., T tables).
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4.A.4.4
Demonstrate and describe varying rates of change in relation to real-world situations (e.g., plant growth, students' heights).
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4.G
Geometry
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4
Students will understand geometric concepts and applications.
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4.G.1
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
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4.G.1.1
Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes:
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4.G.1.1.a
build, draw, create, and describe geometric objects
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4.G.1.1.b
identify lines that are parallel or perpendicular
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4.G.1.1.c
identify and compare congruent and similar figures
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4.G.1.2
Classify two- and three-dimensional shapes according to their properties and develop definitions of classes like triangles and pyramids:
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4.G.1.2.a
visualize, describe, and make models of geometric solids in terms of the number of faces, edges, and vertices
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4.G.1.2.b
interpret two-dimensional representations of three-dimensional objects
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4.G.1.3
Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.
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4.G.2
Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
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4.G.2.1
Describe location and movement using common language and geometric vocabulary.
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4.G.2.2
Use ordered pairs to graph, locate, identify points, and describe paths in the first quadrant of the coordinate plane.
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4.G.2.3
Use a variety of methods for measuring distances between locations on a grid.
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4.G.3
Apply transformations and use symmetry to analyze mathematical situations.
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4.G.3.1
Create and describe rotational designs using language of transformational symmetry.
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4.G.3.2
Describe a motion or set of motions that will show that two shapes are congruent.
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4.G.4
Use visualization, spatial reasoning, and geometric modeling to solve problems.
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4.G.4.1
Develop and use mental images of geometric shapes to solve problems (e.g., represent three-dimensional shapes in two dimensions).
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4.G.4.2
Use geometric models such as number lines, arrays, and computer simulations to investigate number relationships (e.g., patterns).
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4.G.4.3
Explore relationships involving perimeter and area:
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4.G.4.3.a
measure area of rectangular shapes and use appropriate units
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4.G.4.3.b
recognize that area can have the same perimeter but different areas and vice versa
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4.G.4.3.c
use models and formulas to solve problems involving perimeter and area of rectangles and squares (e.g., arrays)
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4.M
Measurement
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4
Students will understand measurement systems and applications.
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4.M.1
Understand measurable attributes of objects and the units, systems, and process of measurement.
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4.M.1.1
Select the appropriate type of unit for measuring perimeter and size of an angle.
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4.M.1.2
Understand the need for measuring with standard units and become familiar with the standard units in customary and metric system.
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4.M.1.3
Identify the inverse relationship between the size of the units and the number of units.
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4.M.1.4
Develop formulas to determine the surface areas of rectangular solids.
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4.M.1.5
Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms.
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4.M.1.6
Carry out simple conversions within a system of measurement (e.g., hours to minutes, meters to centimeters).
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4.M.2
Apply appropriate techniques, tools, and formulas to determine measurements.
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4.M.2.1
Estimate perimeters, areas of rectangles, triangles, and irregular shapes.
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4.M.2.2
Find the area of rectangles, related triangles, and parallelograms.
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4.M.2.3
Estimate, measure, and solve problems involving length, area, mass, time, and temperature using appropriate standard units and tools.
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4.M.2.4
Identify common measurements of turns (e.g., 360 degrees in one turn, 90 degrees in a quarter-turn).
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4.M.2.5
Compute elapsed time and make and interpret schedules.
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4.M.2.6
Use tools to measure angles (e.g., protractor, compass).
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4.D
Data Analysis and Probability
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4
Students will understand how to formulate questions, analyze data, and determine probabilities.
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4.D.1
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
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4.D.1.1
Organize, represent, and interpret numerical and categorical data and clearly communicate findings:
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4.D.1.1.a
choose and construct representations that are appropriate for the data set
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4.D.1.1.b
recognize the differences in representing categorical and numerical data
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4.D.1.2
Design investigations and represent data using tables and graphs (e.g., line plots, bar graphs, line graphs).
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4.D.2
Select and use appropriate statistical methods to analyze data.
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4.D.2.1
Compare and describe related data sets.
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4.D.2.2
Use the concepts of median, mode, maximum, minimum, and range and draw conclusions about a data set.
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4.D.2.3
Use data analysis to make reasonable inferences/predictions and to develop convincing arguments from data described in a variety of formats (e.g. bar graphs, Venn diagrams, charts, tables, line graphs, and pictographs).
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4.D.3
Develop and evaluate inferences and predictions that are based on data.
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4.D.3.1
Propose and justify conclusions and predictions based on data.
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4.D.3.2
Develop convincing arguments from data displayed in a variety of formats.
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4.D.4
Understand and apply basic concepts of probability.
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4.D.4.1
Describe events as 'likely,' 'unlikely,' or 'impossible' and quantify simple probability situations:
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4.D.4.1.a
represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams)
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4.D.4.1.b
express outcomes of experimental probability situations verbally and numerically (e.g., three out of four, 3/4)
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4.D.4.2
List all the possible combinations of objects from three sets (e.g., spinners, number of outfits from three different shirts, two skirts, and two hats).
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