6.NS.7 - About the Math, Learning Targets, and Increasing Rigor

Grade 5 G/T The Number System

6.NS.7

About the Math

Full Standard

Understand ordering and absolute value of rational numbers.

  1. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
  2. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 > –7º C to express the fact that –3º C is warmer than –7º C.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. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
  3. 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. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
  4. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

 

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.

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

 

 

Learning Targets (I can)

  • Explain how integers compare using physical models and number lines.
  • Compare and order integers.
  • Use rational numbers to compare real-world contexts.
  • Explain absolute value.
  • Make statements of comparisons using absolute value (i.e. -30 dollars is a debt of  30 dollars.)

 

About the Math

  • Explain how integers compare using physical models and number lines.
  • Compare and order integers.

Integers increase as one progresses on a number line from left to right. Therefore, a number to the left of another number is less than that number. Comparisons should also be made with other models including integer chips and/or real-world contexts.

Students use inequalities to express the relationship between two rational numbers, understanding that the value of numbers is smaller moving to the left on a number line. Common models to represent and compare integers include number line models, temperature models and the profit- loss model. On a number line model, the number is represented by an arrow drawn from zero to the location of the number on the number line; the absolute value is the length of this arrow. The number line can also be viewed as a thermometer where each point of on the number line is a specific temperature.

In the profit-loss model, a positive number corresponds to profit and the negative number corresponds to a loss. In working with number line models, students internalize the order of the numbers; larger numbers on the right (horizontal) or top (vertical) of the number line and smaller numbers to the left (horizontal) or bottom (vertical) of the number line. They use the order to correctly locate integers and other rational numbers on the number line. By placing two numbers on the same number line, they are able to write inequalities and make statements about the relationships between two numbers.

  • Use rational numbers to compare real-world contexts.

Rational numbers (including integers, fractions, and decimals) can be used to compare real-world contexts. Profits and losses are popular examples. Examples relative to sea level and elevation are also common. Invite students to find other examples and explain how those numbers are compared in context. 

  • Explain absolute value.

Students understand absolute value as the distance from zero and recognize the symbols | | as representing absolute value.Students write statements using < or > to compare rational number in context. However, explanations should reference the context rather than “less than” or “greater than.”

When working with positive numbers, the absolute value (distance from zero) of the number and the value of the number is the same; therefore, ordering is not problematic. However, negative numbers have a distinction that students need to understand. As the negative number increases (moves to the left on a number line), the value of the number decreases.

For example, –24 is less than –14 because –24 is located to the left of –14 on the number line. However, the absolute value is the distance from zero. In terms of absolute value (or distance) the absolute value of –24 is greater than the absolute value of –14. For negative numbers, as the absolute value increases, the value of the negative number decreases.

  • Make statements of comparisons using absolute value (i.e. -30 dollars is a debt of more than 30 dollars.)

 Absolute value can be used to compare as well. As noted in the learning target, -30 is more of debt than -20 dollars as 30 is greater than 20 which are the absolute values of those two debts. 

 

Essential vocabulary for this standard includes rational numbers, absolute value, greater than, >, less than, <, greater than or equal to, ≥, less than or equal to, and≤. 

 

 

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 how integers compare using physical models and number lines.
  • Compare and order integers.
  • Use rational numbers to compare real-world contexts.
  • Explain absolute value.
  • Make statements of comparisons using absolute value (i.e. -30 dollars is a debt of more than 30 dollars.)
  

 

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 5 Grade 7
  • Add and subtract rational numbers; represent addition and subtraction of rational numbers on number line  (7.NS.1)

 

 

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Instructional Tasks

TASKS

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

  • Compare (-12) and (-3) using a real world example to support your comparison.
  • Dion was absent yesterday and he wants you to share your notes from math class with him. Explain what absolute value is.
  • What is the greatest negative number? (-1) 
  • Why is absolute value used when finding distance? (Distance is always positive.)
  • Write three numbers less than and three numbers greater than (-5)
  • Order the following numbers: 10, -2, -12, 5, 2, 20, -8. Use what you know about numbers and their distance from zero to help explain how you ordered the numbers.
  • The table shows the altitude (in meters) of select locations. Which location is closest to sea level and which is farthest from sea level?
  • Jordan researched the coldest winter temperatures in Alaska and Minnesota. Alaska’s lowest temperature was -15 degrees and Minnesota’s lowest temperature was -23 degrees. Jordan wrote: Alaska was colder than Minnesota because -15 < -23. Is Jordan correct? Explain your answer.

 

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 5 • Fractions and Decimals

Ordering Fractions and Decimals:

Module 6 • Positive and Negative Numbers

Ordering Positive and Negative Numbers and Absolute Value:

 

 

Additional Tasks

These links provide instructional ideas connected to this standard. 

 

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

Hands-On Standards

 5-6 118-119 (Introduction to Integers)

 

 

 

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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.

 

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Assessment

Learning Targets

rubric

  • Explain how integers compare using physical models and number lines.
  • Compare and order integers.
  • Use rational numbers to compare real-world contexts.
  • Explain absolute value.
  • Make statements of comparisons using absolute value (i.e. -30 dollars is a debt of more than 30 dollars).

 

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.

 

 

 

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