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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
