6.NS.5 - About the Math, Learning Targets, and Increasing Rigor

Grade 5 G/T The Number System

6.NS.5

About the Math

Full Standard 

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

5th Grade Students Learning 5 G/T Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

 

 

Learning Targets (I can)

  • Explain what integers are.
  • Use integers to describe quantities and/or real-world contexts.
  • Describe the relationship of integers to 0.
  • Represent integers on number lines with varied endpoints.

 

About the Math

  • Explain what integers are.

An integer is a number that can be written without a fractional component. They can be positive or negative. Zero is an integer. 

  • Use integers to describe quantities and/or real-world contexts.

Integers explain real-world situations. They can explain altitude, temperature, sea-level, profits, and much more. Students should be comfortable thinking about integers in these contexts. 

  • Describe the relationship of integers to 0.

Integers are related. Their distance from one another is one way to think about the relationship. "3" is one away from "2" and "4." But it is related to other integers as well. "3" is 7 way from "10" and "-4."

  • Represent integers on number lines with varied endpoints

Integers can be represented on number lines. When working with integers on number lines, it is important that the endpoints (and location of 0 - if present at all) change. Students should be able to place -10 on a number line with the endpoints of -20 and 20, -20 and 0, -50 and 0, or something different. Each time, studetns should be able to justify the location of integers. 

Essential vocabulary for this standard includes rational numbers, opposites, positive, negative, and integers.

 

The article linked below from NRICH provides a variety of contexts to help students understand how positive and negative numbers can be used to describe actions in real-life situations.

 

 

Making Sense of Positives and Negatives Links to an external site.

 

 

 

Progression of Standard within Grade 5 G/T

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Explain what integers are.
  • Use integers to describe quantities and/or real-world contexts.
  • Describe the relationship of integers to 0.
  • Represent integers on number lines with varied endpoints.
  

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade  Grade 7
  • This concept is not taught prior to Grade 6.
  • Add and subtract rational numbers (7.NS.1)

 

 

Back to Top

 

Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

  • When I woke up the temperature was 5 degrees below 0. By noon the temperature rose and then declined again by evening. The evening temperature ended up being 7 degrees. What could have been the temperature at noon? What was the difference between the noon temperature and the evening temperature? Explain your thinking.
  • What is an example of negative numbers in real life? (loss of yards in football, temperature, sea level, withdrawals from accounts)
  • A dolphin can swim up to 150 feet below sea level. Write a negative integer to represent the depth that a dolphin could possibly dive.
  • Aoki says that any negative integer can be greater than a positive integer. Justin disagrees. Who is correct? Explain your reasoning. (absolute value can be part of the discussion)
  • Katrina is playing a game. On her first turn she earns 5 points and on the second turn she loses 7 points. How many points does she have? Illustrate your answer using a number line.

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 6 • Positive & Negative Numbers

Identify and Represent Positive and Negative Numbers:

 

 

Additional Tasks

These links provide instructional ideas connected to this standard.  [NOTE: NCTM membership required for access to Illuminations lessons.] 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 6-8 What is Her Net Worth?, Activity 10.9, Page 181
(American) Football Statistics, Activity 10.10, Page 183
Find the Zero, Activity 10.11, Page 185

Hands-On Standards

 5-6 118-119 (Introduction to Integers)

Problem-Driven Math

 5 100 (Riding the Rail)

 

 

 

 

Back to Top

 

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

Performance Based Task

 

Back to Top

 

Assessment

Learning Targets

rubric

  • Explain what integers are.
  • Use integers to describe quantities and/or real-world contexts.
  • Describe the relationship of integers to 0.
  • Represent integers on number lines with varied endpoints.

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

 

 

 

Back to Top

 

 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.