6.NR.4:  Solve a variety of contextual problems involving ratios, unit rate, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. 

• 6.NR.4.1 Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.

  • K1: I can write ratio notation in multiple ways. (For example, as 2:3, 2 to 3, 2/3) 

  • K2: I can demonstrate how ratios compare two quantities. 

  • K3: I can generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship. 

  • K4: I can use ratio language to describe the relationship between two quantities. 

  • R2: I can explain ratio reasoning using tables of equivalent ratios, tape diagrams (bar models), double number line diagrams or equations and standard fractional notation.

6.NR.4.2 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

• K1: I can write and plot the ordered pairs from the ratio table that represent equivalent ratios on the coordinate plane. 

• R1: I can make a table of equivalent ratios with whole number measurements.

• R2: I can find the missing values in a table of equivalent ratios. 

6.NR.4:  Solve a variety of contextual problems involving ratios, unit rate, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning

• 6.NR.4.3 Solve problems involving proportions using a variety of student selected strategies.

  • R1: I can solve proportions using ratio reasoning with a variety of strategies: tables of equivalent ratios, tape diagrams (bar models), double number line diagrams or equations and standard fractional notation.

  • R2:  I can choose a strategy from a variety of strategies developed to solve a specific problem depending on the situation presented in the problem

• 6.NR.4.4 Describe the concept of rates and unit rate in the context of a ratio relationship.

  • K1: I can use appropriate math terminology as related to rate.

  • K2: I can identify and calculate a unit rate. 

  • K3: I can define independent and dependent variables. 

  • K4: I can plot the ordered pairs from the ratio table that represent equivalent ratios on the coordinate plane.

6.NR.4.5 Solve unit rate problems including those involving unit pricing and constant speed.6.NR.4.3 (Solve Proportions).

• R1: I can apply the concept of unit rate to solve problems involving unit pricing and speed.

• R2: I can list and graph the ordered pairs of distances and times, and write the equation  d = rt to represent the relationship between distance and time, in problems involving motion at a constant speed.

• R3: I can list and graph the ordered pairs of items and price, and write the equation using y = kx to represent the unit pricing.

6.NR.4.8 Solve problems involving ratios found in everyday situations.

• R1: I can solve problems involving ratios in context using computational skills.

• R2: I can make connections to the classroom beyond the school day exploring unit rate, ratios, and calculate percentages using proportional reasoning.

6.NR.4:  Solve a variety of contextual problems involving ratios, unit rate, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. 

• 6.NR.4.6 Calculate a percent of a quantity as a rate per 100 and solve real-life problems given a percent.

  • R1: I can calculate the percentage of a number using proportional reasoning.

  • R2. I can solve contextual problems involving finding the whole given a part and the part given the whole. 

  • R3. I can determine what percent one number is of another number to solve authentic, mathematical problems.

6.NR.4.7 Use ratios to convert within measurement systems (customary and metric) to solve real-life problems. 

• R1: I can convert measurement units when given a conversion factor within one system of measurement and between two systems of measurement (customary and metric) using proportional reasoning. 

6.NR.4.8 Solve problems involving ratios found in everyday situations.

• R1: I can solve problems involving ratios in context using computational skills.

• R2: I can make connections to the classroom beyond the school day exploring unit rate, ratios, and calculate percentages using proportional reasoning. 

6.PAR.7: Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations

• 6.PAR.7.1 Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable.

  • K1: I can recognize solving an equation or inequality as a process of answering “Which values from a specified set, if any, make the equation or inequality true?” 

  • R1: I can use algebraic reasoning to solve an equation to answer an authentic question and explain my reasoning.

  • R2: I can solve an inequality and I can explain why a specific set of values makes an inequality true.

  • R3: I can use substitution to determine whether a given number in a specified set makes an equation or inequality true.

• 6.PAR.7.2 Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number oK1: I can explain that a variable can represent an unknown number or any number in a specified set.

  • K2: I can represent equations involving positive variables and rational numbers. 

  • R1: I can write and solve one step equations and inequalities with variables in all positions in relevant authentic mathematical problems. r any number in a specified set. 

6.PAR.7: Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations

• 6.PAR.7.3 Solve problems by writing and solving equations of the form xp=q, px = q and xp=q for cases in which p, q and x are all nonnegative rational numbers.

  • R1: I can use various strategies to solve addition, subtraction, multiplication, and division when solving one-step equations

  • R2: I am able to solve one step equations presented in applicable mathematical problems involving positive rational numbers by maintaining equality on both sides of the equation.  inverse operations

  •  R3: I can interpret a solution in the original context and assess the reasonableness of results.

• 6.PAR.7.4 Recognize and generate inequalities of the form  x>c, xc, x<c, or xc  to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line.

  • K1: I can recognize and explain the different inequalities.   <, >,  ≤, ≥.

  • K2: I can represent solutions of such inequalities on a number line.

  • R1: I can represent authentic, mathematical situations using inequalities involving variables. 

  • R2: I can explain situations that have infinitely many solutions.