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:
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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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. |
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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.
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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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.
Grade 6 | Grade 8 |
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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
Additional Tasks
These links provide instructional ideas connected to this standard.
- Lesson 5.3 -Changing Elevations Links to an external site. (Open-Up Resources - Illustrative Math )
- Lesson 5.4 -Money and Debts Links to an external site. (Open-Up Resources -Illustrative Math )
- Lesson 5.5 - Representing Subtraction Links to an external site. (Open-Up Resources -Illustrative Math)
- Lesson 5.6 - Subtracting Rational Numbers (Open-Up Resources -Illustrative Math)
- Differences of Integers Links to an external site. (Illustrative Math)
- Distances on Number Line 2 Links to an external site. (Illustrative Math)
- Operations on the Number Line Links to an external site. (Illustrative Math)
- Rounding and Subtracting Links to an external site. (Illustrative Math)
- Differences and Distances Links to an external site. (Illustrative Math: fractions)
- Lesson 5.1 -Interpreting Negative Numbers Links to an external site. (Illustrative Math )
- Lesson 5.2 -Changing Temperatures Links to an external site. (Illustrative Math )
- Lesson 5.7 - Adding and Subtracting to Solve Problems Links to an external site. (Illustrative Math )
- Bookstore Account Links to an external site. Links to an external site.(Illustrative Math)
- Rational Number Computation Links to an external site. (Open Middle)
- Creating Zero Links to an external site. (Open Middle)
- How Much Did the Temperature Drop? Links to an external site. (Robert Kaplinksy)
- Rational Numbers Links to an external site. (Engage NY)
- Cake Weighing Links to an external site. (Common Core Toolbox)
- Anne's Family Trip Links to an external site. (Common Core Toolbox)
- School Supplies Links to an external site.(Common Core Toolbox)
- Oscars Links to an external site. (Yummy Math)
- Opposite Quantities Combine to Make Zero Links to an external site. (Engage NY)
- Understanding Subtraction of Integers and other Rational Numbers Links to an external site. (Engage NY)
- James' Bank Account Links to an external site. (CC= colleague created)
- Creating -2 Links to an external site. ( CC=colleague created)
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.
Book Thumbnail | Book Title | Grade | Pages |
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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 |
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Hands on Standards Common Core Edition Grade |
7 | 26-29 30-33 34 37 38-41 |
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Nimble with Numbers |
6-7 | 106-107 108-109 110-111 122-123 |
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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.
- Add and Subtract Decimals Links to an external site.
- Add and Subtract Integers a Links to an external site.
- Add and Subtract Integers b Links to an external site.
- Problem Solving Add and Subtract Integers a Links to an external site.
- Problem Solving Add and Subtract Integers b Links to an external site.
- Represent And Explain Integer Expressions Using Models Links to an external site.
- Represent Integer Relationships Using Models and Expressions Links to an external site.
- Represent Real-World Situations Using Equations and Number Lines Links to an external site.
- Reason About Integers on a Number Line Links to an external site.
- Write and Solve Integer Expressions in a Real-World Context Links to an external site.
- Apply the Properties of Operations to Add and Subtract Integers Links to an external site.
- Solve Problems Involving Integers Links to an external site. Links to an external site.
- Generalize about Addition and Subtraction of Integers Links to an external site.
- Write and Solve Expressions Involving Addition and Subtraction of Integers Links to an external site.
- Solve Problems Involving Whole Numbers Links to an external site.
- Solve Problems Involving Whole Numbers_2 Links to an external site.
- Represent and Solve Problems Involving Whole Numbers Links to an external site.
- Solve Problems Involving Addition and Subtraction of Integers Links to an external site. Links to an external site.
- Solve Problems Involving Rational Numbers Links to an external site.
- Estimate and Solve Problems Involving Rational Numbers Links to an external site. Links to an external site.
- Solve Problems Involving Integers Links to an external site. Links to an external site.
- Solve and Create Problems Involving Integers Links to an external site. Links to an external site.
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Assessment
Learning Targets
- 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.
Rubric for Tasks Links to an external site.
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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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.