OREGON MATH STANDARDS (2021): [6.NS]
Overview
The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.
Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.
2021 Oregon Math Guidance: 6.NS.A.1
Cluster: 6.NS.A - Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
STANDARD: 6.NS.A.1
Standards Statement (2021):
Represent, interpret, and compute quotients of fractions to solve problems in authentic contexts involving division of fractions by fractions.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.NF.B.6, 5.NF.B.7, 6.NS.B.4 | 7.NS.A.2 | 3.OA.B.6, 6.AEE.B.6 | 6.NS.A.1 6.NS.A Crosswalk |
Standards Guidance:
Clarifications
- Students should use their understanding of equivalency to flexibly reason with equivalent fractions based on the context of the problem. Simplifying fractions is not an expectation of this grade level.
- Students should be able to use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of multiplying and dividing fractions.
Terminology
- Fraction quotients can be represented visually by fraction diagram, concretely with manipulatives, or symbolically with equations to represent the problem.
Teaching Strategies
- Students should be able to utilize fractions with denominators including 2, 3, 4, 5, 6, 8, 10, and 12.
- Students should be able to use numerical reasoning to interpret contextual, mathematical situations involving fractions.
- Students can use a variety of strategies, including but not limited to concrete models, visual fraction models, student-generated strategies, a standard algorithm, or other strategies based on numerical reasoning to represent and solve problems.
Progressions
- Students should use flexible, accurate, and efficient written methods to express computational thinking based on numerical reasoning and sense-making developed from learning experiences that focus on the numbers as quantities. (Please reference pages 5 and 6 in the Progression document).
Examples
- Reason and solve problems with quotients of fractions using both the measurement and partition models of division (based on what is most appropriate for the fractions in the quotient).
- For example, (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)
- How many 3/4-cup servings are in 2/3 of a cup of yogurt?
- How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.NS.B.2
Cluster: 6.NS.B - Compute fluently with multi-digit numbers and find common factors and multiples.
STANDARD: 6.NS.B.2
Standards Statement (2021):
Fluently divide multi-digit numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.NBT.B.6, 5.NF.A.2 | 6.NS.B.3 | 5.NF.B.4 | 6.NS.B.2 6.NS.B Crosswalk |
Standards Guidance:
Clarifications
- Fluently/Fluency – Students choose flexibly among methods and strategies to solve mathematical problems accurately and efficiently.
Terminology
- Decimal number – a number whose whole number part and fractional part are separated by a decimal point.
Teaching Strategies
- Students should be able to use a variety of part- whole strategies to compute efficiently (area model, partial product, partial quotient).
- The part-whole strategies used should be flexible and extend from previous computation strategies and future work with computation.
- Students should use models and student-selected strategies as an efficient written method of demonstrating place value understanding for each operation (addition, subtraction, multiplication, and division).
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.NS.B.3
Cluster: 6.NS.B - Compute fluently with multi-digit numbers and find common factors and multiples.
STANDARD: 6.NS.B.3
Standards Statement (2021):
Fluently add, subtract, multiply, and divide positive rational numbers using accurate, efficient, and flexible strategies and algorithms.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7, 5.NF.A.2, 6.NS.B.2 | 7.NS.A.3 | 6.AEE.A.3 | 6.NS.B.3 6.NS.B Crosswalk |
Standards Guidance:
Terminology
- Positive rational numbers includes numbers that can be represented by a ratio a/b where a is positive whole number greater than or equal to zero, and b is a non-zero whole number. Such numbers include whole numbers, fractions, and decimals greater than or equal to zero.
- Fluently/Fluency – Students choose flexibly among methods and strategies to solve mathematical problems accurately and efficiently.
Boundaries
- Students should be allowed to choose an appropriate strategy to demonstrate fluency.
Teaching Strategies
- Students should be able to use numerical reasoning to interpret contextual, mathematical situations involving fractions.
- Students should be given the opportunity to apply reasoning strategies while solving problems.
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.NS.B.4
Cluster: 6.NS.B - Compute fluently with multi-digit numbers and find common factors and multiples.
STANDARD: 6.NS.B.4
Standards Statement (2021):
Determine greatest common factors and least common multiples using a variety of strategies. Apply the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.OA.B.4 | 6.NS.A.1, 6.AEE.A.3 | 5.OA.A.2, 7.AEE.A.1 | 6.NS.B.4 6.NS.B Crosswalk |
Standards Guidance:
Clarification
- Students should also be able to apply the least common multiple of two whole numbers less than or equal to 12 to solve contextual, mathematical problems.
- Students should be able to determine the greatest common factor of 2 whole numbers (from 1-100) and use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factors (GCF).
Boundaries
- Find the greatest common factor of two whole numbers less than or equal to 100
- Find the least common multiple of two whole numbers less than or equal to 12.
Teaching Strategies
- Investigate the distributive property using sums and its use in adding numbers 1-100 with a common factor.
- Students should apply these strategies to solve real- life, mathematical problems.
- Note GCF & LCM support use of distributive property.
Examples
- Express 36 + 8 as 4 (9 + 2).
- Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
- Hotdogs come in a package of 8 and buns in a package of 12. How many packages of hot dogs and packages of buns would you need to purchase to have an equal number of hot dogs and buns?
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.NS.C.5
Cluster: 6.NS.C - Apply and extend previous understandings of numbers to the system of rational numbers.
STANDARD: 6.NS.C.5
Standards Statement (2021):
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in authentic contexts, explaining the meaning of zero in each situation.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
N/A | 6.NS.C.6, 7.NS.A.1 | N/A | 6.NS.C.5 6.NS.C Crosswalk |
Standards Guidance:
Clarifications
- Students should be able to explain that zero is its own opposite.
- Students should be able to explain that the sign of an integer represents its position relative to zero on a number line.
- Students should be able to show and explain why –(–a) = a. Which is read as, “The opposite of the opposite of a is the same as a.”
Terminology
- Rational numbers are numbers that can be written as a fraction where the numerator and denominator are integers.
Teaching Strategies
- Students should be able to use numerical reasoning to interpret and explain the meaning of numerical statements of inequality as the relative position of two integers positioned on a number line.
- Students are introduced to rational numbers. Students should connect their understanding of fractions and integers to comprehend rational numbers as numbers that can be written as a fraction where the numerator and denominator are integers.
Progressions
- The Standards do not introduce integers separately from the entire system of rational numbers, and examples of negative fractions or decimals can be included from the beginning. (Please reference page 7 in the Progression document).
Examples
- Example contexts: Temperature above/below zero; Elevation above/below sea level; Debits/credit; Positive/negative electric charge.
- Write –3 degrees Celsius > –7 degrees Celsius to express the fact that ─3 degree Celsius is warmer than –7 degrees Celsius.
- Illustrative Mathematics:
2021 Oregon Math Guidance: 6.NS.C.6
Cluster: 6.NS.C - Apply and extend previous understandings of numbers to the system of rational numbers.
STANDARD: 6.NS.C.6
Standards Statement (2021):
Represent a rational number as a point on the number line. Extend number line diagrams and coordinate axes to represent points on the line and in the coordinate plane with negative number coordinates.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.NS.C.5 | 6.NS.C.7, 6.NS.C.8, 7.NS.A.1 | 6.AEE.B.7, 3.NF.A.2, 5.GM.A.1 | 6.NS.C.6 6.NS.C Crosswalk |
Standards Guidance:
Clarifications
- Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.
- Recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
- Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.
- Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
- Students should use numerical and graphical reasoning to plot points in all four quadrants on the coordinate plane.
Teaching Strategies
- Students should have opportunities to explore this concept using visual models to develop a deeper understanding.
- Number lines should be indicated both vertically and horizontally.
- Students should use numerical and graphical reasoning to show and explain the relationship between ordered pairs and location in quadrants of the coordinate plane.
- Students should extend understanding of number lines and coordinate axes from previous grades to represent points on the line and in the plane with negative number coordinates.
Progressions
- Students come to see p as the opposite of p, located an equal distance from 0 in the opposite direction. In order to avoid the common misconception later in algebra that any symbol with a negative sign in front of it should be a negative number, it is useful for students to see examples where p is a positive number, for example if p = -3 then -p = -(-3) = 3. (Please reference page 7 in the Progression document).
Examples
- Find and position integers and rational numbers on a horizontal or vertical number line diagram.
- Find and position pairs of integers and other rational numbers on a coordinate plane.
- Students should be able to recognize that -a is the same distance from zero as a, and therefore, are opposites of each other.
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.NS.C.7
Cluster: 6.NS.C - Apply and extend previous understandings of numbers to the system of rational numbers.
STANDARD: 6.NS.C.7
Standards Statement (2021):
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers and absolute value in authentic applications.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.NS.C.6 | 6.NS.C.8, 7.NS.A.1 | 6.AEE.B.7 | 6.NS.C.7 6.NS.C Crosswalk |
Standards Guidance:
Clarifications
- Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation
- Distinguish comparisons of absolute value from statements about order.
- Students should be introduced to the absolute value symbol with this learning objective, i.e., |−3/4|.
- Students should conclude through exploration that absolute value and distance are always expressed as a positive value.
Terminology
- Absolute value is a number’s distance from zero (0) on a number line.
Progressions
- Comparing negative numbers requires closer attention to the relative positions of the numbers on the number line rather than their magnitudes.
- Comparisons such as -7 < -5 can initially be confusing to students, because -7 is further away from 0 than -5, and is therefore larger in magnitude. (Please reference page 8 in the Progression document).
Examples
- Interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
- Write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.
- For an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
- Recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
- For an account balance of –51.25 dollars, write |– 51.25| = 51.25 to describe the size of the debt in dollars.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.NS.C.8
Cluster: 6.NS.C - Apply and extend previous understandings of numbers to the system of rational numbers.
STANDARD: 6.NS.C.8
Standards Statement (2021):
Graph points in all four quadrants of the coordinate plane to solve problems in authentic contexts. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.GM.A.2, 6.NS.C.6, 6.NS.C.7 | 7.NS.A.1, 8.GM.B.7, 8.GM.B.8 | 6.GM.A.3 | 6.NS.C.8 6.NS.C Crosswalk |
Standards Guidance:
Teaching Strategies
- Students should be expected to solve problems within the context of a graph only.
Progressions
- Students should be able to solve contextual, mathematical problems when graphing points.
Examples
- Rectangle RSTU has vertices at (−4,3), 𝑆𝑆(−4, −2), 𝑇𝑇(5, −2) and 𝑈𝑈(5,3).
- Plot the rectangle on a coordinate plane and find the perimeter of the figure.
- Illustrative Mathematics:
- Student Achievement Partners: