--- title: "7.NR.1: Rational Number Operations (Georgia Mathematics standard)" code: 7.NR.1 cite_as: Georgia Standards of Excellence, Mathematics, 7.NR.1 subject: math grades: - grade-7 language: en canonical_url: https://georgiahomeroom.org/standards/code/7.NR.1 md_url: https://georgiahomeroom.org/standards/code/7.NR.1.md alternate_language_url: https://georgiahomeroom.org/es/standards/code/7.NR.1.md source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180 source_last_changed: 2024-10-09 data_built: 2026-09-18 publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district. up: https://georgiahomeroom.org/standards/math/grade-7.md index: https://georgiahomeroom.org/standards/index.md --- # 7.NR.1: Rational Number Operations Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers). - Subject: Mathematics - Appears in: Grade 7, https://georgiahomeroom.org/standards/math/grade-7.md ## Expectations - **7.NR.1.1**: Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. - **7.NR.1.2**: Show and explain $p + q$ as the number located a distance $|q|$ from $p$, in the positive or negative direction, depending on whether $q$ is positive or negative. Interpret sums of rational numbers by describing applicable situations. - **7.NR.1.3**: Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems. - **7.NR.1.4**: Show and explain 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 contextual situations. - **7.NR.1.5**: Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers. - **7.NR.1.6**: Make sense of multiplication of rational numbers using realistic applications. - **7.NR.1.7**: Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number. - **7.NR.1.8**: Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation. - **7.NR.1.9**: Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario. - **7.NR.1.10**: Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats. - **7.NR.1.11**: Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. ## Georgia Milestones coverage - Mathematics Grade 7 (EOG). Numerical Reasoning. Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers). (about 21% of the test; 12 points) ## What mastery looks like Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level. - **Beginning**: Identify that the sum of a number and its opposite is 0. Identify the absolute value of a rational number. Given a horizontal or vertical number line, solve a problem involving the addition of two rational numbers. Identify that the subtraction of two rational numbers is equivalent to adding the additive inverse. Identify equivalent expressions involving the addition of rational numbers by using the properties of operations. Identify repeating decimal numbers as rational numbers. - **Developing**: Solve relevant problems involving the sum of a number and its opposite. Solve problems involving the sum of two rational numbers. Given a horizontal or vertical number line, solve a problem involving the subtraction of two rational numbers. Given a number line, demonstrate the subtraction of two rational numbers as the absolute value of their difference to represent a situation. Identify equivalent expressions involving the addition, subtraction, multiplication, and division of rational numbers by using the properties of operations. Match fractional forms of rational numbers to the decimal and/or percentage forms. - **Proficient**: Solve relevant problems involving the addition, subtraction, multiplication, and division of two rational numbers and interpret the solution. Apply the properties of operations to add, subtract, multiply, and divide rational numbers. Solve multi-step contextual problems involving rational numbers, converting between forms as appropriate and assessing the reasonableness of answers. - **Distinguished**: Solve complex, multi-step contextual problems involving rational numbers, converting between forms as appropriate and assessing the reasonableness of answers by using mental computation and estimation strategies. ## The same standard across grades - Kindergarten, K.NR.1: Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the last number counted represents the total quantity in a set). https://georgiahomeroom.org/standards/code/K.NR.1.md - Grade 1, 1.NR.1: Extend the count sequence to 120. Read, write, and represent numerical values to 120 and compare numerical values to 100. https://georgiahomeroom.org/standards/code/1.NR.1.md - Grade 2, 2.NR.1: Using the place value structure, explore the count sequences to represent, read, write, and compare numerical values to 1000 and describe basic place-value relationships and structures. https://georgiahomeroom.org/standards/code/2.NR.1.md - Grade 3, 3.NR.1: Use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers up to 1,000. https://georgiahomeroom.org/standards/code/3.NR.1.md - Grade 4, 4.NR.1: Recognize patterns within the base ten place value system with quantities presented in real-life situations to compare and round multi-digit whole numbers through the hundred-thousands place and compare decimal numbers to the hundredths place. https://georgiahomeroom.org/standards/code/4.NR.1.md - Grade 5, 5.NR.1: Use place value understanding to solve real-life, mathematical problems. https://georgiahomeroom.org/standards/code/5.NR.1.md - Grade 6, 6.NR.1: Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. https://georgiahomeroom.org/standards/code/6.NR.1.md - **Grade 7, 7.NR.1 (this standard)**: Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers). - Grade 8, 8.NR.1: Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications. https://georgiahomeroom.org/standards/code/8.NR.1.md Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.