6.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

6.1.1.c: develop understanding of equivalent number representations (i.e., fractions, decimals, percents);

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

6.1.1.d: compare fractions, decimals, percents, and integers using the appropriate symbol (i.e., <, >, =);

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

6.1.1.e: connect whole numbers, fractions, decimals, percents, and integers on the number line;

Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

6.1.1.f: develop meaning for percents greater than 100 and less than one;

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

6.1.1.g: develop meaning for ratios using real-world models and/or situations;

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

6.1.1.h: use a variety of representations for ratios (e.g., 3 to 5; 3/5; 3:5);

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

6.1.1.i: develop and apply strategies to determine if two ratios form a proportion;

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers

6.1.1.j: develop the concept of prime and composite numbers;

Finding Factors with Area Models

6.1.2: Understand operations and how they relate to one another.

6.1.2.a: understand the meaning and effects of arithmetic operations on fractions and decimals;

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

6.1.2.b: apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals;

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

6.1.2.c: use the distributive property to simplify computations with integers, fractions, and decimals;

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

6.1.2.d: apply order of operations when computing with whole numbers and decimals;

Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

6.1.2.e: understand and use the inverse relationships of addition and subtraction and multiplication and division to simplify computations and solve problems.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

6.1.3: Solve problems, compute fluently and make reasonable estimates.

6.1.3.b: analyze procedures for computing with fractions, decimals, and integers;

Biconditional Statement
Conditional Statement
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

6.1.3.d: use strategies to estimate the results of computations involving whole numbers, fractions, and decimals in real-world situations;

Estimating Sums and Differences

6.2.1: Understand patterns, relations, and functions.

6.2.1.a: represent, analyze, and extend geometric and numerical patterns;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

6.2.1.c: apply function rules to complete tables.

Using Tables, Rules and Graphs

6.2.2: Represent and analyze mathematical situations and structures using algebraic symbols.

6.2.2.a: develop an initial conceptual understanding of different uses of variables;

Using Algebraic Equations

6.2.2.d: find missing addends or factors represented as variables in simple equations;

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

6.2.4: Analyze change in various contexts.

6.2.4.a: describe how changes in one quantity or variable result in changes in another.

Distance-Time Graphs

6.3.1: Analyze characteristics and properties of two- and three-dimensional geometric figures.

6.3.1.a: describe, classify, and understand relationships among types of two-dimensional figures;

Classifying Quadrilaterals - Activity A
Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

6.3.1.b: compare and classify angles as acute, obtuse, right, and straight;

Classifying Triangles

6.3.1.c: use appropriate mathematical language to describe characteristics of lines (e.g., parallel, perpendicular, intersecting);

Construct Parallel and Perpendicular Lines

6.3.1.d: compare and classify quadrilaterals using their defining properties;

Classifying Quadrilaterals - Activity A
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

6.3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

6.3.2.a: plot a given set of points in Quadrant I of a coordinate system.

Points in the Coordinate Plane - Activity A

6.3.3: Apply transformations and use symmetry to analyze mathematical situations.

6.3.3.a: investigate, predict, and describe the results of transformations of two-dimensional figures (e.g., slides, flips, turns);

Rotations, Reflections and Translations

6.3.3.b: describe line and rotational symmetry in two-dimensional figures;

Holiday Snowflake Designer

6.3.3.c: describe a motion or a series of motions that will show that two shapes are congruent.

Constructing Congruent Segments and Angles
Rotations, Reflections and Translations

6.3.4: Use visualization, spatial reasoning, and geometric modeling to solve problems.

6.3.4.b: build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa;

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

6.3.4.c: use visualization and spatial reasoning to solve real-world problems.

3D and Orthographic Views - Activity A

6.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

6.4.1.c: understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

6.4.2: Apply appropriate techniques, tools, and formulas to determine measurements.

6.4.2.a: use a variety of strategies to estimate length, perimeter, circumference, area, and volume;

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

6.4.2.b: use a variety of manipulatives to develop formulas to determine the circumference of circles;

Circle: Circumference and Area

6.4.2.c: use formulas to determine the area of triangles and parallelograms;

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B

6.4.2.d: use a variety of manipulatives to develop formulas to determine the area of trapezoids and circles;

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

6.4.2.e: explore surface area and volume of selected prisms and cylinders using models and manipulatives;

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

6.4.2.f: solve problems involving measurement using ratio and proportion;

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers

6.4.2.h: recognize the need for measurement precision.

Triple Beam Balance

6.5.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

6.5.1.c: examine various representations of data to evaluate how accurately the data is depicted;

Populations and Samples

6.5.2: Select and use appropriate statistical methods to analyze data.

6.5.2.a: find, use, and interpret measures of center and spread (e.g., mean, median, mode, interquartile range);

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

6.5.2.b: discuss and understand the relationship between data sets and their graphical representations.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

6.5.3: Develop and evaluate inferences and predictions that are based on data.

6.5.3.c: conduct a survey using random sampling;

Polling: Neighborhood

6.5.4: Understand and apply basic concepts of probability.

6.5.4.a: model situations by devising and carrying out experiments and simulations;

Probability Simulations

6.5.4.b: make and test conjectures about the results of experiments and simulations;

Probability Simulations