STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.

Number Sense 4.1.A.1 - Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well).

• Whole numbers through hundred thousands
• Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line

Number Sense 4.1.A.2 - Demonstrate an understanding of whole number place value concepts.

Number Sense 4.1.A.3 - Identify whether any whole number is odd or even.

Number Sense 4.1.A.4 - Explore the extension of the place value system to decimals through hundredths.

Number Sense 4.1.A.5 - Understand the various uses of numbers.

• Counting, measuring, labeling (e.g., numbers on baseball uniforms)

Number Sense 4.1.A.6 - Compare and order numbers.

Numberical Operations 4.1.B.1 - Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.

• Addition and subtraction: joining, separating, comparing
• Multiplication: repeated addition, area/array
• Division: repeated subtraction, sharing

Numberical Operations 4.1.B.2 - Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as "skip counting" and "repeated subtraction").

Numberical Operations 4.1.B.3 - Construct, use, and explain procedures for performing whole number calculations with:

• Pencil-and-paper
• Mental math
• Calculator

Numberical Operations 4.1.B.4 - Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.

• Addition of 3-digit numbers
• Subtraction of 3-digit numbers
• Multiplication of 2-digit numbers by 1-digit numbers

Numberical Operations 4.1.B.5 - Count and perform simple computations with money.

• Cents notation (¢)

Numberical Operations 4.1.B.6 - Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

Numberical Operations 4.1.B.7 - Check the reasonableness of results of computations.

Estimation 4.1.C.1 - Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

Estimation 4.1.C.2 - Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the result of computations.

Estimation 4.1.C.3 - Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

Estimation 4.1.C.4 - Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.

STANDARD 4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.

Geometric Properties 4.2.A.1 - Identify and describe spatial relationships of two or more objects in space.

• Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)
• Relative shapes and sizes

Geometric Properties 4.2.A.2 - Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.

• Vertex, edge, face, side, angle
• 3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid
• 2D figures – square, rectangle, circle, triangle, pentagon, hexagon, octagon

Geometric Properties 4.2.A.3 - Identify and describe relationships among two-dimensional shapes.

• Same size, same shape
• Lines of symmetry

Geometric Properties 4.2.A.4 - Understand and apply concepts involving lines, angles, and circles.

• Line, line segment, endpoint

Geometric Properties 4.2.A.5 - Recognize, describe, extend, and create space-filling patterns.

Transforming Shapes 4.2.B.1 - Describe and use geometric transformations (slide, flip, turn).

Transforming Shapes 4.2.B.2 - Investigate the occurrence of geometry in nature and art.

Coordinate Geometry 4.2.C.1 - Locate and name points in the first quadrant on a coordinate grid.

Units of Measurement 4.2.D.1 - Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.

Units of Measurement 4.2.D.2 - Select and use appropriate standard units of measure and measurement tools to solve real-life problems.

• Length – fractions of an inch (1/4, 1/2), mile, decimeter, kilometer
• Area – square inch, square centimeter
• Weight – ounce
• Capacity – fluid ounce, cup, gallon, milliliter

Units of Measurement 4.2.D.3 - Incorporate estimation in measurement activities (e.g., estimate before measuring).

Measuring Geometric Objects 4.2.E.1 - Determine the area of simple two-dimensional shapes on a square grid.

Measuring Geometric Objects 4.2.E.2 - Determine the perimeter of simple shapes by measuring all of the sides.

Measuring Geometric Objects 4.2.E.3 - Measure and compare the volume of three–dimensional objects using materials such as rice or cubes.

STANDARD 4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.

Patterns 4.3.A.1 - Recognize, describe, extend, and create patterns.

• Descriptions using words and number sentences/expressions
• Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11, . . . or 800, 400, 200, . . .)

Functions and Relationships 4.3.B.1 - Use concrete and pictorial models to explore the basic concept of a function.

• Input/output tables, T-charts

Modeling 4.3.C.1 - Recognize and describe change in quantities.

• Graphs representing change over time (e.g., temperature, height)

Modeling 4.3.C.2 - Construct and solve simple open sentences involving addition or subtraction (e.g., 3 + 6 = __, n = 15 – 3, 3 + __ = 3, 16 – c = 7).

Procedures 4.3.D.1 - Understand and apply the properties of operations and numbers.

• Commutative (e.g., 3 x 7 = 7 x 3)
• Identity element for multiplication is 1 (e.g., 1 x 8 = 8)
• Any number multiplied by zero is zero

Procedures 4.3.D.2 - Understand and use the concepts of equals, less than, and greater than to describe relations between numbers.

• Symbols ( = , < , > )

STANDARD 4.4 (DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS) ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF THE CONCEPTS AND TECHNIQUES OF DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL USE THEM TO MODEL SITUATIONS, SOLVE PROBLEMS, AND ANALYZE AND DRAW APPROPRIATE INFERENCES FROM DATA.

Data Analysis 4.4.A.1 - Collect, generate, organize, and display data in response to questions, claims, or curiosity.

• Data collected from the classroom environment

Data Analysis 4.4.A.2 - Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.

• Pictograph, bar graph, table

Probability 4.4.B.1 - Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability.

• Likely, unlikely, certain, impossible
• More likely, less likely, equally likely

Probability 4.4.B.2 - Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color).

• What students think will happen (intuitive)
• Collect data and use that data to predict the probability (experimental)

Discrete Mathematics - Systematic Listing and Counting 4.4.C.1 - Represent and classify data according to attributes, such as shape or color, and relationships.

• Venn diagrams
• Numerical and alphabetical order

Discrete Mathematics - Systematic Listing and Counting 4.4.C.2 - Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation.

• Organized lists, charts

Discrete Mathematics - Vertex-Edge Graphs and Algorithms 4.4.D.1 - Follow, devise, and describe practical sets of directions (e.g., to add two 2-digit numbers).

Discrete Mathematics - Vertex-Edge Graphs and Algorithms 4.4.D.2 - Explore vertex-edge graphs.

• Vertex, edge
• Path

Discrete Mathematics - Vertex-Edge Graphs and Algorithms 4.4.D.3 - Find the smallest number of colors needed to color a map.