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

A.1: Analyze, describe in writing and extend a variety of patterns to justify predictions and identify trends.

Polling: City

A.2: Create tables of values and scatterplots from mathematical relationships and equations and vice versa to solve problems.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Points, Lines, and Equations
Trends in Scatter Plots

A.3: Examine tables, graphs and equations to determine patterns of change in linear relationships.

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations

A.4: Write expressions, formulas, equations or inequalities using symbols or variables to denote a pattern or represent a contextual situation.

Compound Interest
Using Algebraic Expressions

A.5: Evaluate algebraic expressions and formulas using substitution.

Compound Interest

A.6: Write, model and solve one-step equations using mental math, tables, substitution and concrete models that demonstrate equivalence and justify the solution.

Solving Equations on the Number Line

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: Locate and label whole numbers, fractions, decimals and positive and negative integers on number lines, scales, coordinate grids (all four quadrants) and measurement tools.

Elevator Operator (Line Graphs)
Points in the Coordinate Plane

N.2: Compare and order whole numbers, fractions, decimals and positive and negative integers in context using number lines and scales.

Integers, Opposites, and Absolute Values

N.3: Represent and compare whole numbers (to a billion) and decimals (to thousandths) in expanded notation, e.g., 75.654 = (7 × 10) + (5 × 1) + (6 × 0.1) + (5 × 0.01) + (4 × 0.001).

Comparing and Ordering Decimals

N.5: Factor composite numbers and express them as a product of primes using exponents.

Finding Factors with Area Models

N.6: Determine equivalent fraction, decimal, and percentage representations and choose among these forms to solve problems.

Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Part-to-part and Part-to-whole Ratios
Toy Factory (Set Models of Fractions)

N.10: Estimate and find percentages of a number in context using benchmarks and number patterns and ratios to 100.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

N.11: Solve practical problems involving rates, ratios, percentages and proportionality.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Road Trip (Problem Solving)

N.12: Add, subtract, multiply and divide by fractions and decimals in context.

Dividing Mixed Numbers
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

N.19: Write and solve multistep problems in context involving addition, subtraction, multiplication and division with whole numbers, fractions, decimals, money and simple percentages.

Cargo Captain (Multi-digit Subtraction)
Dividing Mixed Numbers
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percents, Fractions, and Decimals
Sums and Differences with Decimals

N.20: Understand and use divisibility rules, factors of composite numbers and powers of 10 to find products and quotients.

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

N.21: Apply the order of operations and algebraic properties; i.e., commutative, associative, distributive, inverse operations, and the additive and multiplicative identities; to compute and solve multistep problems and explain solutions in writing.

Chocomatic (Multiplication, Arrays, and Area)
Order of Operations
Square Roots

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

G.3: Identify lines of symmetry and reflections, rotations and translations of geometric figures.

Holiday Snowflake Designer
Quilting Bee (Symmetry)
Rock Art (Transformations)
Rotations, Reflections, and Translations

G.4: Use rectangles as basic shapes to model and develop formulas for finding the area of triangles, parallelograms and trapezoids.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

G.5: Recognize the relationships among radius, diameter, circumference and area of circles and develop formulas for finding circumference and area based on these relationships.

Circumference and Area of Circles

G.8: Select and use appropriate strategies, tools and units to estimate and solve measurement problems involving length, perimeter, area, volume, capacity, mass and weight.

Area of Triangles
Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

G.9: Use ratios to convert between customary units of length, mass, capacity and time.

Unit Conversions

G.10: Use ratios and powers of 10 to convert between metric units.

Unit Conversions

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

D.1: Compare sets of data between two populations, e.g., heights of two classes of students, or within a population, e.g., height vs. arm length of sixth-grade students, using a variety of graphical representations.

Polling: City
Populations and Samples

D.2: Select, create and use appropriate graphical representations of data including, circle graphs, scatter plots, histograms, and stem and leaf plots.

Graphing Skills
Histograms
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots
Trends in Scatter Plots

D.3: Describe the shape of numerical data sets using measures of spread (range) and central tendency (mean, median, mode) and outliers.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

D.5: Investigate and describe the relationship between the number of trials in an experiment and the predicted outcomes.

Independent and Dependent Events

D.6: Design and conduct probability experiments to test predictions about outcomes and fairness.

Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability
Estimating Population Size
Spin the Big Wheel! (Probability)

D.7: Express probabilities as fractions, ratios, decimals and percentages.

Estimating Population Size
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability