The Number System Progression Map

Common Core MathGrades 6 to 813 core standards · 58 related · 88 connections

Extending arithmetic to negative numbers, rational numbers, and irrationals in middle school.

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Core learning progression

Select a standard to see its exact path and cross-topic foundations.

Grade 6

8 standards

Grade 7

3 standards

Grade 8

2 standards

How to Read This Map

Start in the focused explorer, where standards are grouped into human-readable skill threads and placed in grade order. Select a standard to see what it builds on and what it unlocks. The full network preserves every verified connection: solid lines are essential prerequisites and dashed lines are supporting connections. Cross-topic foundations appear in a selected standard's details. Every standard links to a full breakdown with teaching ideas. How these connections are verified.

All standards on this map, as a list

The Number System

  • 6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.
  • 6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
  • 6.NS.B.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a...
  • 6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
  • 6.NS.C.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level,...
  • 6.NS.C.6Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with...
  • 6.NS.C.7Understand ordering and absolute value of rational numbers.
  • 6.NS.C.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the...
  • 7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  • 7.NS.A.1Apply 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.
  • 7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.
  • 8.NS.A.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²).
  • 8.NS.A.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats...

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