4.1: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

4.1.4 A: Number Sense

4.1.4 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).

4.1.4 A.1.a: Whole numbers through millions

Modeling Whole Numbers and Decimals (Base-10 Blocks)

4.1.4 A.1.b: 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

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

4.1.4 A.1.c: Decimals through hundredths

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Treasure Hunter (Decimals on the Number Line)

4.1.4 A.2: Demonstrate an understanding of place value concepts.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cannonball Clowns (Number Line Estimation)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Rounding Whole Numbers (Number Line)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)
Treasure Hunter (Decimals on the Number Line)

4.1.4 A.3: Demonstrate a sense of the relative magnitudes of numbers.

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Treasure Hunter (Decimals on the Number Line)

4.1.4 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.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

4.1.4 A.6: Compare and order numbers.

Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

4.1.4 B: Numerical Operations

4.1.4 B.1: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.

4.1.4 B.1.a: Addition and subtraction: joining, separating, comparing

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Equivalent Fractions (Fraction Tiles)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)

4.1.4 B.1.b: Multiplication: repeated addition, area/array

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

4.1.4 B.1.c: Division: repeated subtraction, sharing

No Alien Left Behind (Division with Remainders)

4.1.4 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.

No Alien Left Behind (Division with Remainders)

4.1.4 B.3: Construct, use, and explain procedures for performing whole number calculations and with:

4.1.4 B.3.a: Pencil-and-paper

Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)

4.1.4 B.3.b: Mental math

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

4.1.4 B.4: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.

4.1.4 B.4.c: Multiplication of 2-digit numbers

Multiplying Decimals (Area Model)

4.1.4 B.4.d: Division of 3-digit numbers by 1-digit numbers

No Alien Left Behind (Division with Remainders)

4.1.4 B.5: Construct and use procedures for performing decimal addition and subtraction.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

4.1.4 B.9: Use concrete models to explore addition and subtraction with fractions.

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

4.1.4 B.10: Understand and use the inverse relationships between addition and subtraction and between multiplication and division.

Factor Trees (Factoring Numbers)
Function Machines 3 (Functions and Problem Solving)

4.1.4 C: Estimation

4.1.4 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.

Cannonball Clowns (Number Line Estimation)
Rounding Whole Numbers (Number Line)

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

Cannonball Clowns (Number Line Estimation)
Multiplying Decimals (Area Model)

4.2: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

4.2.4 A: Geometric Properties

4.2.4 A.2: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.

4.2.4 A.2.b: 3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid

Pyramids and Cones

4.2.4 A.2.c: 2D figures - square, rectangle, circle, triangle, quadrilateral, pentagon, hexagon, octagon

Classifying Quadrilaterals

4.2.4 A.2.d: Inclusive relationships - squares are rectangles, cubes are rectangular prisms

Classifying Quadrilaterals

4.2.4 A.3: Identify and describe relationships among two-dimensional shapes.

4.2.4 A.3.a: Congruence

Classifying Quadrilaterals
Rock Art (Transformations)

4.2.4 A.3.b: Lines of symmetry

Quilting Bee (Symmetry)

4.2.4 A.4: Understand and apply concepts involving lines, angles, and circles.

4.2.4 A.4.a: Point, line, line segment, endpoint

City Tour (Coordinates)
Elevator Operator (Line Graphs)

4.2.4 A.5: Recognize, describe, extend, and create space-filling patterns.

Pattern Finder
Pattern Flip (Patterns)

4.2.4 B: Transforming Shapes

4.2.4 B.2: Describe and use geometric transformations (slide, flip, turn).

Rock Art (Transformations)

4.2.4 C: Coordinate Geometry

4.2.4 C.1: Locate and name points in the first quadrant on a coordinate grid.

City Tour (Coordinates)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

4.2.4 C.2: Use coordinates to give or follow directions from one point to another on a map or grid.

City Tour (Coordinates)

4.2.4 D: Units of Measurement

4.2.4 D.2: Select and use appropriate standard units of measure and measurement tools to solve real-life problems

4.2.4 D.2.b: Area - square inch, square centimeter

Fido's Flower Bed (Perimeter and Area)

4.2.4 D.2.c: Volume - cubic inch, cubic centimeter

Cannonball Clowns (Number Line Estimation)

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

Cannonball Clowns (Number Line Estimation)

4.2.4 D.4: Incorporate estimation in measurement activities (e.g., estimate before measuring).

Cannonball Clowns (Number Line Estimation)

4.2.4 D.5: Solve problems involving elapsed time.

Elapsed Time

4.2.4 E: Measuring Geometric Objects

4.2.4 E.1: Determine the area of simple two-dimensional shapes on a square grid.

Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

4.2.4 E.2: Distinguish between perimeter and area and use each appropriately in problem-solving situations.

Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

4.2.4 E.3: Measure and compare the volume of three-dimensional objects using materials such as rice or cubes.

Balancing Blocks (Volume)
Pyramids and Cones

4.3: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

4.3.4 A: Patterns

4.3.4 A.1: Recognize, describe, extend, and create patterns.

4.3.4 A.1.c: 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,...)

Pattern Flip (Patterns)

4.3.4 A.1.d: 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 ...)

Pattern Flip (Patterns)

4.3.4 B: Functions and Relationships

4.3.4 B.1: Use concrete and pictorial models to explore the basic concept of a function.

4.3.4 B.1.a: Input/output tables, T-charts

Function Machines 1 (Functions and Tables)

4.3.4 B.1.b: Combining two function machines

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

4.3.4 B.1.c: Reversing a function machine

Function Machines 3 (Functions and Problem Solving)

4.3.4 C: Modeling

4.3.4 C.1: Recognize and describe change in quantities.

4.3.4 C.1.a: Graphs representing change over time (e.g., temperature, height)

Elevator Operator (Line Graphs)

4.3.4 C.2: Construct and solve simple open sentences involving any one operation (e.g., 3 x 6 = __, n = 15 ÷ 3, 3 x __ = 0, 16 - c = 7).

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

4.3.4 D: Procedures

4.3.4 D.1: Understand, name, and apply the properties of operations and numbers.

4.3.4 D.1.a: Commutative (e.g., 3 x 7 = 7 x 3)

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

4.4: 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.

4.4.4 A: Data Analysis

4.4.4 A.1: Collect, generate, organize, and display data in response to questions, claims, or curiosity.

4.4.4 A.1.a: Data collected from the school environment

Graphing Skills

4.4.4 A.2: Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.

4.4.4 A.2.a: Pictograph, bar graph, line plot, line graph, table

Forest Ecosystem
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.4.4 A.2.b: Average (mean), most frequent (mode), middle term (median)

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.4.4 B: Probability

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

4.4.4 B.1.a: Likely, unlikely, certain, impossible, improbable, fair, unfair

Spin the Big Wheel! (Probability)

4.4.4 B.1.b: More likely, less likely, equally likely

Spin the Big Wheel! (Probability)

4.4.4 B.1.c: Probability of tossing "heads" does not depend on outcomes of previous tosses

Spin the Big Wheel! (Probability)

4.4.4 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).

4.4.4 B.3.c: Analyze all possible outcomes to find the probability (theoretical)

Spin the Big Wheel! (Probability)