Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Middle School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [7.NS]

OREGON MATH STANDARDS (2021): [7.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: 7.NS.A.1

ODE and Oregon Math Project Logo

Cluster: 7.NS.A - Apply and extend previous understandings of operations with fractions.

STANDARD: 7.NS.A.1

 Standards Statement (2021):

Apply and extend previous understandings of addition, subtraction and absolute value to add and subtract rational numbers in authentic contexts. Understand subtraction as adding the additive inverse, p – q = p + (–q).

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.NS.C.5, 6.NS.C.6, 6.NS.C.7, 6.NS.C.8

7.NS.A.2, 7.NS.A.3

5.NF.A.1

7.NS.A.1

7.NS.A Crosswalk

 Standards Guidance:

Terminology

  • Part-whole reasoning refers to how numbers can be split into parts to add and subtract numbers more efficiently.
  • In the equation 3 + −3 = 0, 3 and −3 are additive inverses of each other.
  • Students should represent a variety of types of rational numbers on a number line diagram presented both horizontally and vertically.

Teaching Strategies

  • Represent operations with rational numbers both visually and numerically, including number line diagrams.
  • Students should be allowed to explore the signs of integers and what they really mean to discover integer rules.
  • It is common to use colored chips to represent integers, with one color representing positive integers and another representing negative integers, subject to the rule that chips of different colors cancel each other out; thus, a number is not changed if you take away or add such a pair. Also implicit in the use of chips is that the commutative and associative properties extend to addition of integers, since combining chips can be done in any order.

Progressions

  • A fundamental fact about addition of rational numbers is that p + (-p) = 0 for any rational number p; in fact, this is a new property of operations tha comes into play when negative numbers are introduced. (Please reference pages 9 and 10 in the Progression document).

Examples

2021 Oregon Math Guidance: 7.NS.A.2

 ODE and Oregon Math Project Logo

Cluster: 7.NS.A - Apply and extend previous understandings of operations with fractions.

STANDARD: 7.NS.A.2

 Standards Statement (2021):

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Interpret operations of rational numbers solving problems in authentic contexts.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.NS.A.1, 7.NS.A.1

8.NS.A.1

5.NF.B.4, 7.AEE.B.3

7.NS.A.2

7.NS.A Crosswalk

 Standards Guidance:

Clarifications

  • Students should be allowed to explore the signs of integers and what they really mean to discover integer rules.
  • If p and q are integers (q ≠ 0), then –(p/q)=(-p)/q= p/(-q)
  • Students should be able to reason about direction on a number line when representing multiplication and division using the tool.

Boundaries

  • Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.
  • Apply properties of operations as strategies to multiply and divide rational numbers.
  • Convert a rational number to a decimal using division; know that the decimal form of a rational number terminates or eventually repeats.

Teaching Strategies

  • Represent operations with rational numbers both visually and numerically,
  • Apply properties of operations such as identity, inverse, distributive, associative and commutative properties.
  • Student should have opportunities to use concepts of repeated addition and the meaning of a negative sign as the “opposite of,” with both models and representations, leading to deriving the rules for multiplying signed numbers.

Progressions

  • Just as the relationship between addition and subtraction helps students understand subtraction of rational numbers, so the relationship between multiplication and division helps them understand division.To calculate -8 divided by 4, students recall that (-2) x 4 = -8, and so -8 divided by 4 = -2. By the same reasoning, -8 divided by 5 = -8/5 because -8/5 x 5 = -8. (Please reference page 11 in the Progression document).

Examples

2021 Oregon Math Guidance: 7.NS.A.3

 ODE and Oregon Math Project Logo

Cluster: 7.NS.A - Apply and extend previous understandings of operations with fractions.

STANDARD: 7.NS.A.3

 Standards Statement (2021):

Understand that equivalent rational numbers can be written as fractions, decimals and percents.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.NS.B.3, 7.NS.A.1

8.NS.A.1

7.AEE.B.3, 8.AEE.A.2

7.NS.A.3

7.NS.A Crosswalk

 Standards Guidance:

Clarifications

  • Students should build upon their understanding of percents as a ratio comparison to 100.
  • This is an extension of previous understanding from 6th grade of writing common fractions as decimal numbers and percents.

Boundaries

  • Use long division to convert fractions to decimals.
  • Students should know that every rational number can be written as the ratio of two integers, terminating decimal numbers, or repeating decimal numbers.

Examples

  • A water well drilling rig has dug to a height of −60 feet after one full day of continuous use. If the rig has been running constantly and is currently at a height of −143.6 feet, for how long has the rig been running? (Modified from Illustrative Mathematics)
  • Identify whether the decimal form of a rational number is a terminating or repeating decimal.
  • Convert terminating decimals to fractions.
  • If Sara makes $25 an hour gets a 10% raise, she will make an additional 110 of her salary an hour, or $2.50, for a new salary of $27.50.
  • Illustrative Mathematics:
  • Student Achievement Partners: