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 4 pertain to these sets of numbers as well).

• Whole numbers through millions
• Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 16) as part of a whole, as a subset of a set, and as a location on a number line
• Decimals through hundredths

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

Number Sense 4.1.A.3 - Demonstrate a sense of the relative magnitudes of numbers.

Number Sense 4.1.A.4 - Understand the various uses of numbers.

• Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor)

Number Sense 4.1.A.5 - Use concrete and pictorial models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number.

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

Number Sense 4.1.A.7 - Explore settings that give rise to negative numbers.

• Temperatures below 0 degrees, debts
• Extension of the number line

Number Sense 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

Number Sense 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") and then commit them to memory.

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

• Pencil-and-paper
• Mental math
• Calculator

Number Sense 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
• Division of 3-digit numbers by 1-digit numbers

Number Sense 4.1.B.5 - Construct and use procedures for performing decimal addition and subtraction.

Number Sense 4.1.B.6 - Count and perform simple computations with money.

• Standard dollars and cents notation

Number Sense 4.1.B.7 - Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

Number Sense 4.1.B.8 - Check the reasonableness of results of computations.

Number Sense 4.1.B.9 - Use concrete models to explore addition and subtraction with fractions.

Number Sense 4.1.B.10 - Understand and use the inverse relationships between addition and subtraction and between multiplication and division.

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 results 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
• Shadows (projections) of everyday objects

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, quadrilateral, pentagon, hexagon, octagon
• Inclusive relationships – squares are rectangles, cubes are rectangular prisms

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

• Congruence
• Lines of symmetry

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

• Point, line, line segment, endpoint
• Parallel, perpendicular
• Angles – acute, right, obtuse
• Circles – diameter, radius, center

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

Transforming Shapes 4.2.B.1 - Use simple shapes to cover an area (tessellations).

Transforming Shapes 4.2.B.2 - Describe and use geometric transformations (slide, flip, turn).

Transforming Shapes 4.2.B.3 - 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.

Coordinate Geometry 4.2.C.2 - Use coordinates to give or follow directions from one point to another on a map or 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 (1/8, 1/4, 1/2), mile, decimeter, kilometer
• Area – square inch, square centimeter
• Volume – cubic inch, cubic centimeter
• Weight – ounce
• Capacity – fluid ounce, cup, gallon, milliliter

Units of Measurement 4.2.D.3 - Develop and use personal referents to approximate standard units of measure (e.g., a common paper clip is about an inch long).

Units of Measurement 4.2.D.4 - Incorporate estimation in measurement activities (e.g., estimate before measuring).

Units of Measurement 4.2.D.5 - Solve problems involving elapsed time.

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 - Distinguish between perimeter and area and use each appropriately in problem-solving situations.

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, number sentences/expressions, graphs, tables, variables (e.g., shape, blank, or letter)
• Sequences that stop or that continue infinitely
• 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, . . .)
• Sequences can often be extended in more than one way (e.g., the next term after 1, 2, 4, . . . could be 8, or 7, or … )

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
• Combining two function machines
• Reversing a function machine

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

• Graphs representing change over time (e.g., temperature, height)
• How change in one physical quantity can produce a corresponding change in another (e.g., pitch of a sound depends on the rate of vibration)

Modeling 4.3.C.2 - Construct and solve simple open sentences involving any one operation (e.g., 3 x 6 = __,

Procedures 4.3.D.1 - Understand, name, 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)
• Associative (e.g., 2 x 4 x 25 can be found by first multiplying either 2 x 4 or 4 x 25)
• Division by zero is undefined
• Any number multiplied by zero is zero.

Procedures 4.3.D.2 - Understand and use the concepts of equals, less than, and greater than in simple number sentences.

• 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 school environment

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

• Pictograph, bar graph, line plot, line graph, table
• Average (mean), most frequent (mode), middle term (median)

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, improbable, fair, unfair
• More likely, less likely, equally likely
• Probability of tossing "heads" does not depend on outcomes of previous tosses

Probability 4.4.B.2 - Determine probabilities of simple events based on equally likely outcomes and express them as fractions.

Probability 4.4.B.3 - 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)
• Analyze all possible outcomes to find the probability (theoretical)

Discrete Mathematics - Systematic Listing an 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 an 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, tree diagrams
• Dividing into categories (e.g., to find the total number of rectangles in a grid, find the number of rectangles of each size and add the results)

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 - Play two-person games and devise strategies for winning the games (e.g., "make 5" where players alternately add 1 or 2 and the person who reaches 5, or another designated number, is the winner).

Discrete Mathematics - Vertex-Edge Graphs and Algorithms 4.4.D.3 - Explore vertex-edge graphs and tree diagrams.

• Vertex, edge, neighboring/adjacent, number of neighbors
• Path, circuit (i.e., path that ends at its starting point)

Discrete Mathematics - Vertex-Edge Graphs and Algorithms 4.4.D.4 - Find the smallest number of colors needed to color a map or a graph.