6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.

6.6.01: Read, write, recognize, and model equivalent representations of whole numbers and their place values.

Modeling Whole Numbers and Decimals (Base-10 Blocks)

6.6.02: Read, write, recognize, model, and interpret numerical expressions from a given description or situation.

Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6.6.03: Read, write, recognize, and model equivalent representations of fractions, including improper fractions and mixed numbers.

Adding Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

6.6.04: Recognize, translate between, and apply multiple representations of decimals, fractions, percents (less than 100%), and mixed numbers (halves, quarters, fifths, and tenths).

Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

6.6.05: Read, write, recognize, and model equivalent representations of decimals and their place values through thousandths.

Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)

6.6.07: Order and compare whole numbers.

Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values

6.6.08: Order and compare decimals through thousandths.

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)
Rational Numbers, Opposites, and Absolute Values
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

6.6.09: Order and compare fractions and mixed numbers having like or unlike denominators.

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

6.6.10: Identify and locate decimals, fractions, and mixed numbers on a number line.

Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Treasure Hunter (Decimals on the Number Line)

6.6.11: Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than, square numbers, primes).

Chocomatic (Multiplication, Arrays, and Area)
Comparing and Ordering Decimals
Factor Trees (Factoring Numbers)
Rational Numbers, Opposites, and Absolute Values

6.6.12: Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

6.6.13: Solve problems and number sentences involving addition, subtraction, and multiplication of decimals.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Square Roots
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

6.6.14: Solve problems involving addition and subtraction of fractions and mixed numbers, and express answers in simplest form.

Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Modeling Fractions (Area Models)

6.6.15: Identify and apply order of operations to simplify numeric expressions involving whole numbers.

Order of Operations

6.6.16: Solve problems involving the commutative, distributive, and associative properties of operations on whole numbers [e.g., (5×7)×2 = 5×(7×2)].

Chocomatic (Multiplication, Arrays, and Area)

6.6.18: Identify and express ratios using appropriate notation (i.e., a/b, a to b, a:b), identify equivalent ratios, and explain ratios that represent a given situation.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Rational Numbers, Opposites, and Absolute Values
Road Trip (Problem Solving)

6.6.19: Solve problems involving proportional relationships, including unit pricing (e.g., seven apples cost $1.40, so nine apples cost $1.80).

Beam to Moon (Ratios and Proportions)
Geometric Probability
Percents and Proportions
Proportions and Common Multipliers

6.6.20: Read, write, recognize, and model percents from 0% to 100%.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

6.6.21: Solve number sentences and problems involving percents.

Percent of Change
Percents, Fractions, and Decimals
Real-Time Histogram
Time Estimation

7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy.

7.6.01: Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles.

Beam to Moon (Ratios and Proportions)
Measuring Trees

7.6.02: Solve problems involving the perimeter and area of a triangle, parallelogram, or irregular shape using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).

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

7.6.03: Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0° to 180°) using referents.

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

7.6.04: Determine the volume of a right rectangular prism using an appropriate formula or strategy.

Balancing Blocks (Volume)
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

7.6.05: Solve problems involving unit conversions within the same measurement system for time, length, and weight/mass, including compound units (e.g., 5ft 5in, 2lbs 2oz).

Unit Conversions

7.6.06: Solve problems involving scale drawings and maps.

Points in the Coordinate Plane

8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results.

8.6.01: Determine a missing term in a sequence, extend a sequence, and construct and identify a rule that can generate the terms of a given sequence (e.g., 3, 6, 9,... is explained by the rule 3n, for n is greater than or equal to 1).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Multiplying Fractions

8.6.02: Write an expression using variables to represent unknown quantities.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

8.6.03: Evaluate algebraic expressions with up to two whole number variable values (e.g., evaluate 3m + n + 3 when m = 4 and n = 2).

Solving Equations on the Number Line

8.6.04: Determine a rule having two operations from an input-output table (e.g., multiply by 3 and add 2).

Function Machines 1 (Functions and Tables)

8.6.05: Select a table of values that satisfies a linear equation, and recognize the ordered pairs on a rectangular coordinate system.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations

8.6.06: Translate between different representations (table, written, or pictorial) of whole number relationships.

Function Machines 1 (Functions and Tables)
Geometric Sequences

8.6.07: Identify graphs of inequalities on a number line.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

8.6.08: Represent problems with equations and inequalities.

Comparing and Ordering Decimals
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Using Algebraic Equations

8.6.09: Solve for the unknown in an equation with one operation (e.g., 8x = 24, m÷2=25).

Solving Equations on the Number Line

9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.6.03: Solve problems using properties of triangles and quadrilaterals (e.g., sum of interior angles of a quadrilateral is 360°).

Concurrent Lines, Medians, and Altitudes
Similarity in Right Triangles
Triangle Angle Sum
Triangle Inequalities

9.6.05: Graph, locate, identify points, describe paths, and plot figures using ordered pairs (first quadrant).

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

9.6.06: Identify, describe, and predict results of reflections, translations, and rotations of two-dimensional shapes.

Circles
Holiday Snowflake Designer
Rock Art (Transformations)
Rotations, Reflections, and Translations

9.6.09: Identify a three-dimensional object from its net.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

9.6.11: Identify congruent and similar figures by visual inspection.

Rock Art (Transformations)

9.6.12: Determine if figures are similar, and identify relationships between corresponding parts of similar figures.

Similarity in Right Triangles

10: Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability.

10.6.01: Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph.

Compound Inequalities
Elevator Operator (Line Graphs)
Graphing Skills
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)

10.6.02: Compare different representations of the same data.

Box-and-Whisker Plots
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

10.6.03: Create a bar graph, chart/table, line graph, or circle graph with common referents (1/4, 50%, .75) for a given set of data.

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

10.6.04: Determine the mode, range, median, and mean, given a set of data or a graph.

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

10.6.05: Solve problems involving the probability of a simple event, including representing the probability as a fraction, decimal, or percent.

Independent and Dependent Events
Theoretical and Experimental Probability