6.1: Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and factors.

6.1.1: Understand and apply the basic concept of negative numbers (e.g., on a number line, in counting, in temperature, in “owing”).

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

6.1.2: Interpret the absolute value of a number as the distance from zero on a number line, and find the absolute value of real numbers.

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

6.1.3: Compare and represent on a number line positive and negative integers, fractions, decimals (to hundredths), and mixed numbers.

Adding and Subtracting Integers
Adding on the Number Line
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Integers, Opposites, and Absolute Values
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

6.1.4: Convert between any two representations of numbers (fractions, decimals, and percents) without the use of a calculator.

Modeling Decimals (Area and Grid Models)
Percents, Fractions, and Decimals

6.1.5: Recognize decimal equivalents for commonly used fractions without the use of a calculator.

Modeling Decimals (Area and Grid Models)

6.1.6: Use models to represent ratios.

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

6.1.7: Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

Adding Fractions (Fraction Tiles)

6.2: Students solve problems involving addition, subtraction, multiplication, and division of integers. They solve problems involving fractions, decimals, ratios, proportions, and percentages.

6.2.1: Add and subtract positive and negative integers.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values

6.2.2: Multiply and divide positive and negative integers.

Adding and Subtracting Integers

6.2.3: Multiply and divide decimals.

Multiplying Decimals (Area Model)
Multiplying with Decimals
Square Roots

6.2.4: Explain how to multiply and divide positive fractions and perform the calculations.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

6.2.7: Understand proportions and use them to solve problems.

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

6.2.8: Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

Compound Interest
Percent of Change

6.2.9: Use estimation to decide whether answers are reasonable in decimal problems.

Multiplying Decimals (Area Model)

6.2.10: Use mental arithmetic to add or subtract simple fractions and decimals.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Subtracting Decimals (Base-10 Blocks)
Sums and Differences with Decimals

6.3: Students write verbal expressions and sentences as algebraic expressions and equations. They evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. They investigate geometric relationships and describe them algebraically.

6.3.1: Write and solve one-step linear equations and inequalities in one variable and check the answers.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

6.3.3: Interpret and evaluate mathematical expressions that use grouping symbols such as parentheses.

Order of Operations
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

6.3.4: Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.

Order of Operations

6.3.6: Apply the correct order of operations and the properties of real numbers (e.g., identity, inverse, commutative, associative, and distributive properties) to evaluate numerical expressions. Justify each step in the process.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Solving Equations on the Number Line

6.3.7: Identify and graph ordered pairs in the four quadrants of the coordinate plane.

Points in the Coordinate Plane
Points, Lines, and Equations

6.3.8: Solve problems involving linear functions with integer values. Write the equation and graph the resulting ordered pairs of integers on a grid.

Points, Lines, and Equations

6.4: Students identify, describe, and classify the properties of plane and solid geometric shapes and the relationships between them.

6.4.1: Identify and draw vertical, adjacent, complementary, and supplementary angles and describe these angle relationships.

Triangle Angle Sum

6.4.2: Use the properties of complementary, supplementary, and vertical angles to solve problems involving an unknown angle. Justify solutions.

Triangle Angle Sum

6.4.4: Understand that the sum of the interior angles of any triangle is 180º and that the sum of the interior angles of any quadrilateral is 360º. Use this information to solve problems.

Polygon Angle Sum
Triangle Angle Sum

6.4.6: Draw the translation (slide) and reflection (flip) of shapes.

Rotations, Reflections, and Translations

6.4.7: Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

Surface and Lateral Areas of Prisms and Cylinders

6.5: Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems. They calculate with temperature and money, and choose appropriate units of measure in other areas.

6.5.1: Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

Area of Triangles
Balancing Blocks (Volume)
Beam to Moon (Ratios and Proportions)
Fido's Flower Bed (Perimeter and Area)
Measuring Trees

6.5.4: Understand the concept of the constant pi as the ratio of the circumference to the diameter of a circle. Develop and use the formulas for the circumference and area of a circle.

Circumference and Area of Circles

6.5.5: Know common estimates of PI (3.14, 22/7 ) and use these values to estimate and calculate the circumference and the area of circles. Compare with actual measurements.

Circumference and Area of Circles

6.5.7: Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area of these objects.

Surface and Lateral Areas of Prisms and Cylinders

6.5.8: Use strategies to find the surface area and volume of right prisms and cylinders using appropriate units.

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

6.6: Students compute and analyze statistical measures for data sets. They determine theoretical and experimental probabilities and use them to make predictions about events.

6.6.1: Organize and display single-variable data in appropriate graphs and stem-and-leaf plots, and explain which types of graphs are appropriate for various data sets.

Describing Data Using Statistics
Graphing Skills
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

6.6.3: Compare the mean, median, and mode for a set of data and explain which measure is most appropriate in a given context.

Reaction Time 1 (Graphs and Statistics)

6.6.4: Show all possible outcomes for compound events in an organized way and find the theoretical probability of each outcome.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability