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

6.7.02: Read, write, recognize, model, and interpret integers, including translating numerical expressions.

Adding and Subtracting Integers
Order of Operations

6.7.03: Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%).

Fraction Garden (Comparing Fractions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

6.7.04: Represent repeated factors using exponents.

Exponents and Power Rules

6.7.05: Order and compare integers, terminating decimals, fractions, and mixed numbers.

Adding Fractions (Fraction Tiles)
Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

6.7.06: Identify and locate integers, decimals, and fractions/mixed numbers on a number line, and estimate the locations of square roots.

Adding on the Number Line
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Square Roots

6.7.07: Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple).

Chocomatic (Multiplication, Arrays, and Area)
Finding Factors with Area Models
Square Roots

6.7.08: Solve problems and number sentences involving addition, subtraction, multiplication, and division using integers, fractions, and decimals.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Addition of Polynomials
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Square Roots
Sums and Differences with Decimals

6.7.09: Identify and apply order of operations to simplify numeric expressions involving whole numbers (including exponents), fractions, and decimals.

Order of Operations

6.7.10: Identify and apply the following properties of operations with rational numbers:

6.7.10.a: the commutative and associative properties for addition and multiplication;

Adding and Subtracting Integers
Adding on the Number Line
Equivalent Algebraic Expressions I

6.7.10.b: the distributive property;

Equivalent Algebraic Expressions II
Square Roots

6.7.10.d: the additive and multiplicative inverse properties; and

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.7.11: Demonstrate and apply the relationships between addition/subtraction and multiplication/division with rational numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

6.7.13: Estimate the square root of a number less than 1,000 between two whole numbers (e.g., the square root of 41 is between 6 and 7).

Square Roots

6.7.14: Create 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
Road Trip (Problem Solving)

6.7.15: Use proportional reasoning to model and solve problems.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

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

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

6.7.17: Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5×10, sales tax, tips, interest, discounts).

Comparing and Ordering Decimals
Compound Interest
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Multiplying with Decimals
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Sums and Differences with Decimals
Time Estimation
Toy Factory (Set Models of Fractions)

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

7.7.01: Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles. Sketch, with given specifications, line segments, angles, triangles, and quadrilaterals.

Beam to Moon (Ratios and Proportions)
Classifying Quadrilaterals
Measuring Trees
Special Parallelograms

7.7.02: Solve problems involving the perimeter and area of polygons and composite figures 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
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

7.7.03: 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)

7.7.04: Determine the volume and surface area of a right rectangular prism using an appropriate formula or strategy.

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

7.7.05: Solve problems involving unit conversions within the same measurement system for length, weight/mass, capacity, and square units (e.g., 1 ft² = 144 in²).

Unit Conversions

7.7.06: Solve problems involving scale drawings and maps.

Dilations
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.

8.7.01: Determine a missing term in a sequence, extend a sequence, and construct and identify a rule that can generate the terms of an arithmetic or geometric sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

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

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

8.7.03: Simplify algebraic expressions by identifying and combining like terms.

Addition of Polynomials
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

8.7.04: Recognize equivalent forms of algebraic expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

8.7.07: Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph.

Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Standard Form of a Line

8.7.08: Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions.

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

8.7.09: Identify, graph, and interpret inequalities on a number line.

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

8.7.10: Represent and analyze problems with linear equations and inequalities.

Linear Inequalities in Two Variables
Solving Equations by Graphing Each Side

8.7.11: Solve linear equations in one variable (e.g., 2x + 3 = 13) and inequalities involving < or > (e.g., 2x<6, x+7>10).

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side

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

9.7.01: Classify, describe, and sketch regular and irregular two-dimensional shapes according to the number of sides, length of sides, number of vertices, and interior angles.

Classifying Quadrilaterals

9.7.02: Solve problems involving two- and three-dimensional shapes.

Classifying Quadrilaterals

9.7.03: Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent).

Concurrent Lines, Medians, and Altitudes
Triangle Inequalities

9.7.04: Identify, describe, and determine the radius and diameter of a circle.

Chords and Arcs
Circles

9.7.05: Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).

City Tour (Coordinates)
Points in the Coordinate Plane

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

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

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

Similar Figures
Similarity in Right Triangles

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

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

Correlation
Graphing Skills
Histograms
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

10.7.02: Compare different representations of the same data.

Correlation
Graphing Skills

10.7.03: Create a bar graph, chart/table, line graph, or circle graph for a given set of data.

Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

10.7.04: Identify a reasonable approximation of the line of best fit from a set of data or a scatter plot.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

10.7.05: Determine and use the mode, range, median, and mean to interpret data.

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

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

Independent and Dependent Events
Theoretical and Experimental Probability

10.7.07: Represent all possible outcomes for simple events.

Independent and Dependent Events
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

10.7.08: Solve simple problems involving the number of ways objects can be arranged (permutations and combinations).

Permutations and Combinations