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

Grade 5 GT The Number System

7.NS.1

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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