the number system

GRADE 7 MATHEMATICS: UNIT 1 - The Number System

STANDARDS:

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.

• 7.NS.A.1.A Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
• 7.NS.A.1.B Understand 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. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
• 7.NS.A.1.C 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.
• 7.NS.A.1.D Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

• 7.NS.A.2.A Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
• 7.NS.A.2.B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
• 7.NS.A.2.C Apply properties of operations as strategies to multiply and divide rational numbers.
• 7.NS.A.2.D Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers

lESSONS

Lesson 1: The Number System Review

Extra Practice:

• Khan Academy Fractions Boot Camp!
• Identify rational numbers and game

Lesson 2: Adding and Subtracting Integers with a Number Line

Extra Practice:

• Number line models
• more number line equation models
• movement on the number line

Lessons 3: Adding Rational Numbers

Extra Practice:

• Add positives and negative integers
• equivalent expressions
• Adding negatives: signs of sums and practice
• Adding and subtracting rational numbers - decimals and fractions

Lesson 4: Subtracting Rational Numbers

Extra Practice:

• Subtract positive and negative integers
• Subtraction: adding the opposite and practice

Lessons 5: Adding & Subtracting Rational Numbers in Real Life

Lesson 6: Multiplying & Dividing Integers

Lessons 7: Multiplying & Dividing Rational Numbers

Lesson 8: Multiplying & Dividing Rational Numbers in Real Life

Extra Practice:

• Multiply decimals and harder decimals
• Dividing decimals
• Multiply positive and negative fractions
• Multiply and divide positives and negatives and more practice; multiplying fractions; multiplying mixed numbers
• Dividing negative fractions; dividing by zero

Lesson 9: Applying Properties to Operations

Extra Practice:

• Distributive property
• Commutative property
• Associative property of multiplication

New or Recently Introduced Terms

• Rational number
• Irrational number
• Absolute value
• Additive Inverse
• Integer
• Improper fraction
• Mixed number
• Complex fraction
• Multiplicative inverse (reciprocal)
• Square Root
• Associative, Commutative, and Distributive Properties

more online practice problems

• Find absolute value and game
• Find additive inverse; identify negative numbers on number line; absolute value and opposites game
• Add and subtract fractions, more fractions (mathgames) negative fractions, mixed numbers, more mixed numbers (mathgames), positive and negative mixed numbers (mathgames) and decimals
• Word problems: adding and subtracting negatives and interpreting word problems
• Multi-step word problems
• Convert fraction to decimal