Academic Standards

6.1.1: Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.

6.1.1.1: Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.

Adding and Subtracting Integers

Adding on the Number Line

City Tour (Coordinates)

Elevator Operator (Line Graphs)

Integers, Opposites, and Absolute Values

Points in the Coordinate Plane

Points, Lines, and Equations

Rational Numbers, Opposites, and Absolute Values

6.1.1.2: Compare positive rational numbers represented in various forms. Use the symbols < and >.

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

6.1.1.3: Understand that percent represents parts out of 100 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

Real-Time Histogram

Road Trip (Problem Solving)

6.1.1.4: Determine equivalences among fractions, decimals and percents; select among these representations to solve problems.

Modeling Decimals (Area and Grid Models)

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

6.1.1.5: Factor whole numbers; express a whole number as a product of prime factors with exponents.

Chocomatic (Multiplication, Arrays, and Area)

Factor Trees (Factoring Numbers)

Finding Factors with Area Models

Operations with Radical Expressions

6.1.1.6: Determine greatest common factors and least common multiples. Use common factors and common multiples to do arithmetic with fractions and find equivalent fractions.

Factor Trees (Factoring Numbers)

Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Fractions with Unlike Denominators

Modeling Fractions (Area Models)

Multiplying Fractions

Multiplying Mixed Numbers

6.1.1.7: Convert between equivalent representations of positive rational numbers.

Percents, Fractions, and Decimals

6.1.2: Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.

6.1.2.2: Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations.

Adding Fractions (Fraction Tiles)

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Factor Trees (Factoring Numbers)

Fraction Artist 1 (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)

Part-to-part and Part-to-whole Ratios

Percent of Change

Percents, Fractions, and Decimals

Proportions and Common Multipliers

Real-Time Histogram

Road Trip (Problem Solving)

Time Estimation

Toy Factory (Set Models of Fractions)

6.1.2.3: Determine the rate for ratios of quantities with different units.

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

6.1.2.4: Use reasoning about multiplication and division to solve ratio and rate problems.

Proportions and Common Multipliers

6.1.3: Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.

6.1.3.1: Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

6.1.3.3: Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts.

Percent of Change

Polling: Neighborhood

6.1.3.4: Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers.

Improper Fractions and Mixed Numbers

Modeling Decimals (Area and Grid Models)

Multiplying with Decimals

Percents, Fractions, and Decimals

Sums and Differences with Decimals

6.2.1: Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

6.2.1.1: Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts.

6.2.2: Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.

6.2.2.1: Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers.

Adding and Subtracting Integers

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Order of Operations

Simplifying Algebraic Expressions II

Square Roots

6.2.3: Understand and interpret equations and inequalities involving variables and positive rational numbers. Use equations and inequalities to represent real-world and mathematical problems; use the idea of maintaining equality to solve equations. Interpret solutions in the original context.

6.2.3.1: Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers.

Solving Equations on the Number Line

6.2.3.2: Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results.

Solving Algebraic Equations II

Solving Equations on the Number Line

6.3.1: Calculate perimeter, area, surface area and volume of two- and three-dimensional figures to solve real-world and mathematical problems.

6.3.1.1: Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models.

Surface and Lateral Areas of Prisms and Cylinders

6.3.1.2: Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.

Area of Parallelograms

Area of Triangles

Chocomatic (Multiplication, Arrays, and Area)

Fido's Flower Bed (Perimeter and Area)

Perimeter and Area of Rectangles

Square Roots

6.3.2: Understand and use relationships between angles in geometric figures.

6.3.2.1: Solve problems using the relationships between the angles formed by intersecting lines.

6.3.2.2: Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180°. Use models of triangles to illustrate this fact.

Isosceles and Equilateral Triangles

Triangle Angle Sum

6.3.3: Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

6.3.3.1: Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.

6.4.1: Use probabilities to solve real-world and mathematical problems; represent probabilities using fractions, decimals and percents.

6.4.1.1: Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Independent and Dependent Events

Permutations and Combinations

Spin the Big Wheel! (Probability)

6.4.1.2: Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

6.4.1.3: Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

6.4.1.4: Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

Correlation last revised: 1/20/2017