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File: Nys Math Standards Grade 6 Crosswalk
new york state next generation mathematics learning standards grade 6 crosswalk ratio and proportional reasoning cluster nys p 12 ccls nys next generation learning standard understand ratio 6 rp 1 ...

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                                                                             New York State Next Generation Mathematics Learning Standards 
                                                                                                                 Grade 6 Crosswalk 
                                                                                                    Ratio and Proportional Reasoning 
                                   Cluster                                            NYS P-12 CCLS                                                      NYS Next Generation Learning Standard  
                        Understand ratio                       6.RP.1 Understand the concept of a ratio and use ratio                        NY-6.RP.1 Understand the concept of a ratio and use ratio language to 
                        concepts and use ratio                 language to describe a ratio relationship between two                         describe a ratio relationship between two quantities. 
                        reasoning to solve                     quantities. For example, “The ratio of wings to beaks in                       
                        problems.                              the bird house at the zoo was 2:1, because for every 2                        e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, 
                                                               wings there was 1 beak.” “For every vote candidate A                          because for every 2 wings there was 1 beak.” “For every vote candidate 
                                                               received, candidate C received nearly three votes.”                           A received, candidate C received three votes.” 
                                                                                                                                              
                                                               6.RP.2 Understand the concept of a unit rate a/b                              NY-6.RP.2 Understand the concept of a unit rate a/b associated with a 
                                                               associated with a ratio a:b with b ≠ 0, and use rate                          ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the 
                                                               language in the context of a ratio relationship. For                          context of a ratio relationship.  
                                                               example, “This recipe has a ratio of 3 cups of flour to 4                      
                                                               cups of sugar, so there is 3/4 cup of flour for each cup of                   e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so 
                                                               sugar.” “We paid $75 for 15 hamburgers, which is a                            there are ¾ cup of flour for each cup of sugar.”  "We paid $75 for 15 
                                                               rate of $5 per hamburger.”                                                    hamburgers, which is a rate of $5 per hamburger."  
                                                                                                                                               
                                                               Note: Expectations for unit rates in this grade are limited to non-           Note:  Expectations for unit rates in this grade are limited to non-complex fractions. 
                                                               complex fractions.                                                             
                                                                                                                                              
                                                               6.RP.3 Use ratio and rate reasoning to solve real-world                       NY-6.RP.3 Use ratio and rate reasoning to solve real-world and 
                                                               and mathematical problems, e.g., by reasoning about                           mathematical problems. 
                                                               tables of equivalent ratios, tape diagrams, double number                      
                                                               line diagrams, or equations.                                                  Note: Strategies may include but are not limited to the following: tables of equivalent 
                                                                                                                                             ratios, tape diagrams, double number lines, and equations. 
                                                                                                                                              
                                                                
                                                                
                                                                
                                                                
                                                                
                                                                
                                                                
                        NYSED Grade 6 Draft 
                         
                                                              New York State Next Generation Mathematics Learning Standards 
                                                                                            Grade 6 Crosswalk 
                                                                                 Ratio and Proportional Reasoning 
                             Cluster                                  NYS P-12 CCLS                                         NYS Next Generation Learning Standard  
                   Understand ratio                6.RP.3a Make tables of equivalent ratios relating              NY-6.RP.3a Make tables of equivalent ratios relating quantities with 
                   concepts and use ratio          quantities with whole-number measurements, find                whole-number measurements, find missing values in the tables, and 
                   reasoning to solve              missing values in the tables, and plot the pairs of values     plot the pairs of values on the coordinate plane. Use tables to compare 
                   problems.                       on the coordinate plane. Use tables to compare ratios.         ratios. 
                                                                                                                   
                                                   6.RP.3b Solve unit rate problems including those               NY-6.RP.3b Solve unit rate problems. 
                                                   involving unit pricing and constant speed. For example,         
                                                   if it took 7 hours to mow 4 lawns, then at that rate, how      e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many 
                                                   many lawns could be mowed in 35 hours? At what rate            lawns could be mowed in 35 hours? At what rate were lawns being 
                                                   were lawns being mowed?                                        mowed? What is the unit rate? 
                                                                                                                   
                                                                                                                  Note: Problems may include unit pricing and constant speed. 
                                                   6.RP.3c Find a percent of a quantity as a rate per 100         NY-6.RP.3c Find a percent of a quantity as a rate per 100.  Solve 
                                                   (e.g., 30% of a quantity means 30/100 times the                problems that involve finding the whole given a part and the percent, 
                                                   quantity); solve problems involving finding the whole,         and finding a part of a whole given the percent. 
                                                   given a part and the percent.                                                                   30
                                                                                                                  e.g., 30% of a quantity means        times the quantity. 
                                                                                                                                                  100
                                                   6.RP.3d Use ratio reasoning to convert measurement             NY-6.RP.3d Use ratio reasoning to convert measurement units; 
                                                   units; manipulate and transform units appropriately when       manipulate and transform units appropriately when multiplying or 
                                                   multiplying or dividing quantities.                            dividing quantities. 
                                                                                                                    
                                                                                                                  Note: Conversion of units occur within a given measurement system, not across 
                                                                                                                  different measurement systems. 
                    
                    
                    
                    
                   NYSED Grade 6 Draft 
                    
                                                                                    
                                                                                                                                                                                                                                                                            New York State Next Generation Mathematics Learning Standards 
                                                                                                                                                                                                                                                                                                                                                                                                           Grade 6 Crosswalk 
                                                                                                                                                                                                                                                                                                                                                                                                        The Number System 
                                                                                                                           Cluster                                                                                                                                                                                                     NYS P-12 CCLS                                                                                                                                                                                                                             NYS Next Generation Learning Standard 
                                                                                   Apply and extend                                                                                                                        6.NS.1 Interpret and compute quotients of fractions, and solve word                                                                                                                                                                                                                                                                  NY-6.NS.1 Interpret and compute quotients of fractions, 
                                                                                   previous understandings                                                                                                                 problems involving division of fractions by fractions, e.g., by using                                                                                                                                                                                                                                                                and solve word problems involving division of fractions by 
                                                                                   of multiplication and                                                                                                                   visual fraction models and equations to represent the problem. For                                                                                                                                                                                                                                                                   fractions. 
                                                                                   division to divide                                                                                                                      example, create a story context for (2/3) ÷ (3/4) and use a visual                                                                                                                                                                                                                                                                    
                                                                                   fractions by fractions.                                                                                                                 fraction model to show the quotient; use the relationship between                                                                                                                                                                                                                                                                    Note:  Strategies may include but are not limited to the following: using 
                                                                                                                                                                                                                           multiplication and division to explain that (2/3) ÷ (3/4) = 8/9                                                                                                                                                                                                                                                                      visual fraction models, a standard algorithm, and equations to represent 
                                                                                                                                                                                                                           because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How                                                                                                                                                                                                                                                                  the problem. 
                                                                                                                                                                                                                           much chocolate will each person get if 3 people share 1/2 lb of                                                                                                                                                                                                                                                                                                                                                                                                                      2                       3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                e.g., Create a story context for ( ) ÷ ( ) and use a visual 
                                                                                                                                                                                                                           chocolate equally? How many 3/4-cup servings are in 2/3 of a cup                                                                                                                                                                                                                                                                                                                                                                                                                     3                       4
                                                                                                                                                                                                                           of yogurt? How wide is a rectangular strip of land with length 3/4                                                                                                                                                                                                                                                                   fraction model to show the quotient; use the relationship 
                                                                                                                                                                                                                           mi and area 1/2 square mi?                                                                                                                                                                                                                                                                                                           between multiplication and division to explain that 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2                       3                    8                                                     3                     8                   2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 ( ) ÷ ( ) =   because      of    is  . 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      3                       4                    9                                                     4                      9                  3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                In general, ( ) ÷ ( ) =                                                                                        . 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                e.g.,  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    •                    How much chocolate will each person get if 3 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     1 lb of chocolate equally?  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         people share 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              3 2                                                                                               2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    •                    How many   cup servings are in    of a cup of 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         yogurt?                                              4                                                                                                 3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    •                    How wide is a rectangular strip of land with length 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         3                                                                 1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              mi and area    square mi?  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         4                                                                 2
                                                                                   Compute fluently with                                                                                                                   6.NS.2 Fluently divide multi-digit numbers using the standard                                                                                                                                                                                                                                                                        NY-6.NS.2 Fluently divide multi-digit numbers using a 
                                                                                   multi-digit numbers and                                                                                                                 algorithm.                                                                                                                                                                                                                                                                                                                           standard algorithm. 
                                                                                   find common factors and                                                                                                                                                                                                                                                                                                                                                                                                                                                       
                                                                                   multiples.                                                                                                                              6.NS.3 Fluently add, subtract, multiply, and divide multi-digit                                                                                                                                                                                                                                                                      NY-6.NS.3 Fluently add, subtract, multiply, and divide 
                                                                                                                                                                                                                           decimals using the standard algorithm for each operation.                                                                                                                                                                                                                                                                            multi-digit decimals using a standard algorithm for each 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                operation. 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                    
                                                                                   NYSED Grade 6 Draft 
                                                                                    
                    
                    
                                                            New York State Next Generation Mathematics Learning Standards 
                                                                                        Grade 6 Crosswalk 
                                                                                       The Number System 
                            Cluster                                NYS P-12 CCLS                                       NYS Next Generation Learning Standard 
                   Compute fluently with         6.NS.4 Find the greatest common factor of two whole          NY-6.NS.4 Find the greatest common factor of two whole numbers 
                   multi-digit numbers and       numbers less than or equal to 100 and the least common       less than or equal to 100. Use the distributive property to express a sum 
                   find common factors and       multiple of two whole numbers less than or equal to 12.      of two whole numbers 1–100 with a common factor as a multiple of a 
                   multiples.                    Use the distributive property to express a sum of two        sum of two whole numbers with no common factor other than 1. 
                                                 whole numbers 1–100 with a common factor as a                Find the least common multiple of two whole numbers less than or 
                                                 multiple of a sum of two whole numbers with no               equal to 12. 
                                                 common factor. For example, express 36 + 8 as 4 (9 +                   
                                                 2).                                                          e.g.,    Express 36 + 8 as 4 (9 + 2). 
                                                                                                                        
                   Apply and extend              6.NS.5 Understand that positive and negative numbers         NY-6.NS.5 Understand that positive and negative numbers are used 
                   previous understandings       are used together to describe quantities having opposite     together to describe quantities having opposite directions or values. 
                   of numbers to the system      directions or values (e.g., temperature above/below zero,    Use positive and negative numbers to represent quantities in real-world 
                   of rational numbers.          elevation above/below sea level, credits/debits,             contexts, explaining the meaning of 0 in each situation.   
                                                 positive/negative electric charge); use positive and          
                                                 negative numbers to represent quantities in real-world       e.g., temperature above/below zero, elevation above/below sea level, 
                                                 contexts, explaining the meaning of 0 in each situation.         debits/credits, positive/negative electric charge. 
                                                                                                               
                                                 6.NS.6 Understand a rational number as a point on the        NY-6.NS.6 Understand a rational number as a point on the number 
                                                 number line. Extend number line diagrams and                 line. Use number lines and coordinate axes to represent points on a 
                                                 coordinate axes familiar from previous grades to             number line and in the coordinate plane with negative number 
                                                 represent points on the line and in the plane with           coordinates. 
                                                 negative number coordinates. 
                    
                    
                   NYSED Grade 6 Draft 
                    
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