7.NS.1 - About the Math, Learning Targets, and Rigor

Grade 5 GT The Number System

7.NS.1

About the Math

Full Standard

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

1c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).  Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

1d. Apply properties of operations as strategies to add and subtract rational numbers.

 

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 addition and subtraction of different number types.

Report Card Measurement Topic: Demonstrates understanding of addition and subtraction of different number types.

 

 

Learning Targets (I can)

  • Explain subtraction using additive inverse representing it with two-sided counters, number lines, algebra tiles, and equations.
  • Represent the distance between two rational numbers on a horizontal or vertical number line.
  • Estimate the sum and difference between two rational numbers.
  • Apply the properties of operations to add and subtract rational numbers (e.g. The Associative Property can be used to reorder addends for efficiency, -13 + 27 - 7 can be thought of as -13 + -7 + 27 or -20 + 27).
  • Solve real-world and mathematical problems with rational numbers and absolute value.

 

About the Math

Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. Students previously learned about negative numbers and the kinds of quantities they can be used to represent; they also learned about absolute value and ordering of rational numbers, including in real-world contexts. With this standard, students will add, subtract, multiply, and divide within the system of rational numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in Grade 5 GT depends on rational number arithmetic, fluency with rational number arithmetic should be the goal for this standard.

 

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 subtraction using additive inverse representing it with two-sided counters, number lines, algebra tiles, and equations.
  • Represent the distance between two rational numbers on a horizontal or vertical number line.
  • Estimate the difference between two rational numbers (e.g. the difference of -33 and 10 is about 40 rather than about 20).
  • Apply the properties of operations to add and subtract rational numbers (e.g. The Associative Property can be used to reorder addends for efficiency, -13 + 27 - 7 can be thought of as -13 + -7 + 27 or -20 + 27).
  • Solve real-world and mathematical problems with rational numbers and absolute value.
  • Explain subtraction using additive inverse representing it with two-sided counters, number lines, algebra tiles, and equations.
  • Represent the distance between two rational numbers on a horizontal or vertical number line.
  • Estimate the difference between two rational numbers (e.g. the difference of -33 and 10 is about 40 rather than about 20).
  • Apply the properties of operations to add and subtract rational numbers (e.g. The Associative Property can be used to reorder addends for efficiency, -13 + 27 - 7 can be thought of as -13 + -7 + 27 or -20 + 27).
  • Solve real-world and mathematical problems with rational numbers and absolute value.

 

 

 

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 6 Grade 8
  • Understand a rational number as a point on the number line and as ordered pair (6.NS.6)
  • Understand ordering and absolute value of  rational numbers . (6.NS.7)
  • Understand positive and negative numbers (6.NS.5)
  • Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion (8.NS.1)
  • Use square root and cube root symbols to represent solutions to equations (8.EE.2)

 

 

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Instructional Tasks

TASKS

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

  • Checking Account: Your current checking account balance is $236. You bought an iPod for $299 and basketball shoes for $109. You deposited $352, which you received from your birthday and completing various chores, into the account. What is your account balance?
  • Temperature: You and a group of friends are scaling Mount Rushmore. When you begin your expedition the temperature was 12 degrees Fahrenheit. When you reached the top of Lincoln’s head the temperature was -6 degrees Fahrenheit, how much did the temperature drop while you were on your expedition?

 

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

Add and Subtract Fractions and Decimals:

Module 7 • Adding and Subtracting Rational Numbers

Add and Subtract Integers:

 

 

Additional Tasks

These links provide instructional ideas connected to this standard. 

CC Indicates colleague created HCPSS instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.

 

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

Find the Zero, Activity 10.11, p.185

Repeater or Terminator, Activity 10.1, p.193

Find the Zero, p.196-197 

Hands on Standards Common Core Edition Grade

 

 7 26-­29

30­-33

34­ 37

38­-41

Nimble with Numbers

 6-7 106-­107

108­-109

110­-111

122-­123

Groundworks Reasoning with Numbers

7 64­-71
Teaching Common Core Math Standards with Hands on Activities 6-8  90-91

 

 

 

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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 subtraction using additive inverse representing it with two-sided counters, number lines, algebra tiles, and equations.
  • Represent the distance between two rational numbers on a horizontal or vertical number line.
  • Estimate the difference between two rational numbers (e.g. the difference of -33 and 10 is about 40 rather than about 20).
  • Apply the properties of operations to add and subtract rational numbers (e.g. The Associative Property can be used to reorder addends for efficiency, -13 + 27 - 7 can be thought of as -13 + -7 + 27 or -20 + 27).
  • Solve real-world and mathematical problems with rational numbers and absolute value.

 

 

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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 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.