# Integers and Fractions: Grade 7 Number Operations Central concept: **Number Operations** ## Connections - Number Operations (includes) -> Integers - Number Operations (includes) -> Fractions - Number Operations (includes) -> Decimal Numbers - Number Operations (uses) -> Operations on Positive and Negative Numbers - Number Operations (applies) -> Equivalent Forms - Integers (has) -> Apply Operations to Positive and Negative Numbers - Integers (has) -> Apply Operations to Positive and Negative Numbers - Fractions (has) -> Multiply Fractions - Fractions (has) -> Divide Fractions - Divide Fractions (uses) -> Reciprocal - Decimal Numbers (has) -> Multiply and Divide Decimals - Equivalent Forms (facilitates) -> Multiply and Divide Decimals ## Notes - **Number Operations**: Systems for calculating with integers, fractions, and decimals [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20871) - **Integers**: Positive and negative whole numbers with operations [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20871), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873) - **Fractions**: Parts of a whole with numerators and denominators [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893) - **Decimal Numbers**: Numbers expressed using place value and decimal point [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20902) - **Add and Subtract Integers**: Combine or remove positive and negative quantities [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20875) - **Multiply and Divide Integers**: Rules for signs: same signs give positive, different signs give negative [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20877), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879) - **Multiply Fractions**: Multiply numerators and denominators; result is part of a part [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20894) - **Divide Fractions**: Multiply by the reciprocal; quotient is number of fraction-sized groups [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20898) - **Reciprocal**: Multiplicative inverse; fraction and reciprocal multiply to 1 [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897) - **Multiply and Divide Decimals**: Use equivalent expressions, algorithms, or area models [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20902), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20901) - **Order of Operations**: Conventional sequence for evaluating expressions [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20905), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20907) - **Equivalent Forms**: Different expressions that represent the same value [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20906), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20878) ![Integers and Fractions: Grade 7 Number Operations](https://goa-cc-uat-aili-app-001.azurewebsites.net/api/generate/47d4e303-0a7c-48dc-84f0-482794d0fc72/asset/1395) --- *AILI word map · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id 47d4e303-0a7c-48dc-84f0-482794d0fc72* ### Sources - node:n1: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891) - node:n2: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20871) - node:n3: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897) - node:n4: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20898) - node:n5: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20899) - node:n6: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20902) - node:n7: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20901) - node:n8: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20903) - node:n9: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20895) - node:n10: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893) - node:n11: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20894) - node:n12: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20905) - node:n13: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20906) - node:n14: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20907) - node:n15: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873) - node:n16: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20875) - node:n17: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20874) - node:n18: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879) - node:n19: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20878) - node:n20: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20877)