A: Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.

A.1: Represent, extend and compare geometric and numeric patterns using words, tables, graphs and equations.

Function Machines 1 (Functions and Tables)

A.2: Analyze patterns and data to make generalizations, make predictions and to identify trends.

Pattern Finder
Pattern Flip (Patterns)

A.3: Represent and describe mathematical relationships using variables or symbols in expressions, equations and inequalities

Comparing and Ordering Decimals

N: Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

N.1: Compare, order and round whole numbers to 1,000,000 using number patterns, number lines and diagrams.

Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rounding Whole Numbers (Number Line)

N.2: Represent whole numbers up to 1,000,000 in expanded and regrouped forms and use the forms to support computation.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)

N.3: Construct and use models, number patterns and pictorial representations to extend place value concepts and patterns to decimals, e.g., 0.1 is one-tenth of one and 0.01 is one one-hundredth of one and one-tenth of 0.1.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

N.5: Classify numbers as prime, composite or perfect squares and identify factor pairs using rectangular arrays.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)

N.6: Represent equivalent fractions, decimals, ratios and percents using models, pictures, number patterns and common factors.

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

N.9: Use models and pictures to identify and compare ratios and represent ratios in equivalent fraction and decimal forms.

Fraction, Decimal, Percent (Area and Grid Models)

N.12: Develop and use strategies involving place value relationships, inverse operations and algebraic properties (commutative, associative and distributive) to simplify addition, subtraction and multiplication problems with three-, four- and five-digit numbers and money amounts and division by one-digit factors.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)

N.13: Multiply and divide decimals and money amounts by whole numbers.

Multiplying Decimals (Area Model)

N.14: Write and solve multistep problems for all four operations involving multidigit whole numbers and money amounts and explain how answers were determined, orally and in writing.

Adding Whole Numbers and Decimals (Base-10 Blocks)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

N.16: Add and subtract fractions, decimals and mixed numbers using a variety of strategies, e.g., models, mental math, equivalence and substitution: 1/2 + 3/4 can also be solved using 0.5 + 0.75.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

N.18: Use ratios and proportions to solve practical problems, e.g., interpreting scale drawings and maps and determining the probability of an event.

Road Trip (Problem Solving)

N.19: Use estimation to predict results and to recognize when an answer is or is not reasonable, or will result in an overestimate or underestimate and explain the reasoning used orally and in writing.

Cannonball Clowns (Number Line Estimation)

G: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.

G.2: Develop formulas for finding the perimeter and area of squares, rectangles and triangles and use them to solve problems.

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

G.3: Use the attributes of parallel sides, perpendicular sides, congruent sides/angles, number and length of sides or faces and number and kinds of angles (right, acute or obtuse) to describe, classify and sort polygons and solids (cube, prism, pyramid and sphere).

Classifying Quadrilaterals

G.5: Use an x, y coordinate system to plot points, to estimate the distance between points and to determine the horizontal or vertical distance between two points.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

G.6: Analyze and describe the effect that changing the dimensions (perimeter) of a polygon has on its area and vice versa.

Fido's Flower Bed (Perimeter and Area)

G.7: Use calendars and clocks to plan and sequence events and to solve problems involving the conversion of measures of time and elapsed time using days, hours, minutes and seconds.

Elapsed Time

G.10: Solve length problems involving conversions of measure within the customary (inches, feet, yards and miles) or metric systems (millimeters, centimeters, meters and kilometers).

Cannonball Clowns (Number Line Estimation)

D: Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.

D.1: Represent sets of data using line plots, bar graphs, double bar graphs, pictographs, simple circle graphs, stem and leaf plots and scatter plots.

Forest Ecosystem
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

D.2: Compare different representations of the same data set and evaluate how well each kind of display represents the features of the data.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

D.4: Determine the mean, mode and median of a data set and explain in writing, how they are affected by a change in the data set.

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

D.5: Design and conduct probability experiments and simple games of chance to test predictions about outcomes and fairness.

Spin the Big Wheel! (Probability)

D.6: Determine and describe possible outcomes and express the likelihood of events as a fraction.

Spin the Big Wheel! (Probability)
Estimating Population Size
Spin the Big Wheel! (Probability)

D.3: Design and conduct surveys of a representative sample of a population and use the data collected to begin to make inferences about the general population.

Real-Time Histogram