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.

describe situations in which opposite quantities combine to make 0.

understand as the number located a distance from, in the positive or negative direction depending on whether 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.

understand subtraction of rational numbers as adding the additive inverse, .

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.

apply properties of operations as strategies to add and subtract rational numbers.

apply and extend previous understandings of multiplication and division to multiply and divide rational numbers.

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 and the rules for multiplying signed numbers.

interpret products of rational numbers by describing real-world contexts.

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.

understand if and are integers then .

interpret quotients of rational numbers within real-world contexts.

apply properties of operations as strategies to multiply and divide rational numbers.

convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.

solve real-world and mathematical problems involving the four operations with rational numbers.

Vocabulary* Additive Inverse: The sum of a number and its additive inverse is zero.

Multiplicative Inverse: Numbers are multiplicative inverses of each other if they multiply to equal the identity, 1.

Absolute Value: The distance between a number and zero on the number line. The symbol for absolute value is shown in this equation: |-8| = 8

Integers: The set of whole numbers and their opposites {…-3, -2, -1, 0, 1, 2, 3…}

Long Division: Standard procedure suitable for dividing simple or complex multi-digit numbers. It breaks down a division problem into a series of easier steps.

Natural Numbers: The set of numbers {1, 2, 3, 4,…}. Natural numbers can also be called counting numbers.

Negative Numbers: The set of numbers less than zero.

Opposite Numbers: Two different numbers that have the same absolute value. Example: 4 and -4 are opposite numbers because both have an absolute value of 4.

Positive Numbers: The set of numbers greater than zero.

Rational Numbers: The set of numbers that can be written in the form a/b where a and b are integers and b does not equal 0.

Repeating Decimal: A decimal number in which a digit or group of digits repeats without end.

Terminating Decimal: A decimal that contains a finite number of digits.

Zero Pair: Pair of numbers whose sum is zero.

August-September Lessons 7.NS.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. Video: Determine the values of opposite numbers using a number line Video: Understand the concept of additive inverse Video: Using additive inverses Video: Determine which values combine to make zero

7.NS.1a. Describe situations in which opposite quantities combine to make 0. Video: Create zero pairs using integer chips Video:Combine opposite numbers on a number line Video: Combine opposite rational numbers on a number line

7.NS.1b. 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. Video: Add integers using chips Video: Add integers with the same sign using number lines Video: Add integers with opposite signs using a number line Video:Adding integers with opposite signs using an algorithm Video: Add rational numbers using algorithms and number lines Video: Solve word problems with rational numbers

7.NS.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. Video: Subtract integers using integer chips Video: Subtract integers using number lines Video:Subtract integers using distance on a number line

7.NS.2a. 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. Video: Multiply a positive integer by a negative integer Video:Multiply a negative integer by a positive integer

7.NS.2b. 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. Video: Compare fraction and decimal division

7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers. Video: Rewrite multiplication problems using the commutative property Video: Rewrite division problems using the commutative property Video: Rewrite multiplication problems with rational numbers using the associative property Video: Rewrite multiplication problems with rational numbers using the commutative and associative properties Video:Rewrite problems with rational numbers using different properties of multiplication and division

7.NS.2d. 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. Video: Convert unit fractions to terminating decimals Video: Convert unit fractions into repeating decimals Video: Convert fractions and mixed numbers to decimals

7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. Video: Use addition and subtraction to solve real-world problems involving decimals Video:Use addition and subtraction to solve real-world problems involving fractions Video: Use addition and multiplication to solve real-world problems with rational numbers Video: Use addition and division to solve real-world problems with rational numbers

15minute-math-integers.ppt

15minute-math-decimals.ppt

HomeworkHomework 9/30 textbook pg, 168, ch 2 cumulative test 1-22 + Castlelearning

: The sum of a number and its additive inverse is zero.Additive Inverse: Numbers are multiplicative inverses of each other if they multiply to equal the identity, 1.Multiplicative Inverse: The distance between a number and zero on the number line. The symbol for absolute value is shown in this equation: |-8| = 8Absolute Value: The set of whole numbers and their opposites {…-3, -2, -1, 0, 1, 2, 3…}Integers: Standard procedure suitable for dividing simple or complex multi-digit numbers. It breaks down a division problem into a series of easier steps.Long DivisionThe set of numbers {1, 2, 3, 4,…}. Natural numbers can also be called counting numbers.Natural Numbers:The set of numbers less than zero.Negative Numbers:: Two different numbers that have the same absolute value. Example: 4 and -4 are opposite numbers because both have an absolute value of 4.Opposite NumbersThe set of numbers greater than zero.Positive Numbers:The set of numbers that can be written in the form a/b where a and b are integers and b does not equal 0.Rational Numbers:A decimal number in which a digit or group of digits repeats without end.Repeating Decimal:A decimal that contains a finite number of digits.Terminating Decimal:: Pair of numbers whose sum is zero.Zero PairAugust-September Lessons7.NS.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.Video: Determine the values of opposite numbers using a number line

Video: Understand the concept of additive inverse

Video: Using additive inverses

Video: Determine which values combine to make zero

7.NS.1a. Describe situations in which opposite quantities combine to make 0.Video: Create zero pairs using integer chips

Video: Combine opposite numbers on a number line

Video: Combine opposite rational numbers on a number line

7.NS.1b.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.Video: Add integers using chips

Video: Add integers with the same sign using number lines

Video: Add integers with opposite signs using a number line

Video: Adding integers with opposite signs using an algorithm

Video: Add rational numbers using algorithms and number lines

Video: Solve word problems with rational numbers

7.NS.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.Video: Subtract integers using integer chips

Video: Subtract integers using number lines

Video: Subtract integers using distance on a number line

7.NS.2a.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.Video: Multiply a positive integer by a negative integer

Video: Multiply a negative integer by a positive integer

7.NS.2b.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.Video: Compare fraction and decimal division

7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.Video: Rewrite multiplication problems using the commutative property

Video: Rewrite division problems using the commutative property Video: Rewrite multiplication problems with rational numbers using the associative property

Video: Rewrite multiplication problems with rational numbers using the commutative and associative properties

Video: Rewrite problems with rational numbers using different properties of multiplication and division

7.NS.2d.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.Video: Convert unit fractions to terminating decimals

Video: Convert unit fractions into repeating decimals

Video: Convert fractions and mixed numbers to decimals

7.NS.3.Solve real-world and mathematical problems involving the four operations with rational numbers.Video: Use addition and subtraction to solve real-world problems involving decimals

Video: Use addition and subtraction to solve real-world problems involving fractions

Video: Use addition and multiplication to solve real-world problems with rational numbers

Video: Use addition and division to solve real-world problems with rational numbers