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.
Dividing Mixed Numbers
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Multiplying Fractions
Multiplying Mixed Numbers
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: 9/16/2020