(7.NS.1-7.NS.3) Number System Fluency Syllabus

Posted: December 8, 2015 in Advance, Periods 3&4

Add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram (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. Describe situations in which opposite quantities combine to make 0.

Lessons

  • In this lesson you will learn how to make a 0 sum by using the additive inverse of a number.

  • In this lesson you will learn how to determine which quantities combine to make 0 by using an algebraic expression.

Describe situations in which opposite quantities combine to make 0 (7.NS.A.1a)

Describe situations in which opposite quantities combine to make 0.

Lessons

Describe situations in which opposite quantities combine to make 0, understand p + q as the number |q| from p

Describe situations in which opposite quantities combine to make 0. 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.

Lessons

Describe situations in which opposite quantities combine to make 0, understanding p + q as the number |q| from p (1)

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; and 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.

Lessons

  • Understand the additive inverse

    In this lesson, you will learn the additive inverse by combining opposite quantities.

  • In this lesson, you will learn how to add integers by using a number line.

  • In this lesson, you will learn how to add integers by using color counters.

  • In this lesson, you will learn how to add integers with the same sign by analyzing the rules using a number line.

  • In this lesson, you will learn how to add integers with different signs by analyzing the rules using a number line.

     

Isolation Drills:

  • None

TenMarks Assignments:

  • Understanding and Identifying Opposite Quantities

Adding and subtracting rational numbers using distance, absolute value, and opposites (7.NS.A.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.

Lessons

  • In this lesson you will learn to add integers by using integer chips.

  • In this lesson you will learn to solve word problems by finding key words, writing equations, and creating models.

     

Describe situations in which opposite quantities combine to make 0, understand p + q as the number |q| from p

Describe situations in which opposite quantities combine to make 0. 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.

Lessons

Describe situations in which opposite quantities combine to make 0, understanding p + q as the number |q| from p (1)

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; and 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.

Lessons

  • In this lesson, you will learn the additive inverse by combining opposite quantities.

  • In this lesson, you will learn how to add integers by using a number line.

  • In this lesson, you will learn how to add integers by using color counters.

  • In this lesson, you will learn how to add integers with the same sign by analyzing the rules using a number line.

  • In this lesson, you will learn how to add integers with different signs by analyzing the rules using a number line.

     

Isolation Drills :

TenMarks Assignments:

  • Understanding Addition of Rational Numbers

 

Understand subtraction as addition of additive inverses, and differences in terms of distance on the number line (7.NS.A.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.

Lessons

Understand subtraction of rational numbers as adding the additive inverse

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.

Lessons

Lessons

Isolation Drills :

TenMarks Assignments:

  • Understanding Subtraction of Rational Numbers

 

Apply properties of operations to add and subtract rational numbers and understanding subtraction of rational numbers as adding the additive inverse (7.NS.A.1d)

Apply properties of operations as strategies to add and subtract rational numbers and understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q).

Lessons

Add and subtract mixed numbers

Add and subtract mixed numbers by regrouping.

Lessons

Use a place value chart

Use a place value chart.

Lessons

Isolation Drills :

TenMarks Assignments:

  • Applying Addition and Subtraction to Rational Numbers
  • Adding and Subtracting Integers

Multiply and divide rational numbers (7.NS.A.2a, 7.NS.A.2b)

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. 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.

Lessons

  • In this lesson you will learn to compare the outcomes of fraction division with the outcomes of decimal division by computing with fraction/decimal equivalents.

Understand multiplication of rational numbers (1)

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.

Lessons

Understand multiplication of rational numbers (2)

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.

Lessons

 

Isolation Drills :

TenMarks Assignments:

  • Understanding Multiplication of Fractions
  • Applying Multiplication to Integers and Fractions

Multiply and divide rational numbers (7.NS.A.2a, 7.NS.A.2b)

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. 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.

Lessons

  • In this lesson you will learn to compare the outcomes of fraction division with the outcomes of decimal division by computing with fraction/decimal equivalents.

 

Understand division of rational numbers (2)

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.

Lessons

Isolation Drills :

TenMarks Assignments:

  • Understanding Division of Integers
  • Understanding Division of Fractions
  • Applying Division to Integers and Fractions

Apply properties of operations to multiply and divide rational numbers (7.NS.A.2c)

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

Lessons

Applying properties of operations to multiply and divide rational numbers (1)

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

Lessons

Isolation Drills :

TenMarks Assignments:

  • Applying Multiplication and Division to Rational Numbers

Convert rational numbers to decimals using divisions; understand rational numbers (7.NS.A.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.

Lessons

  • In this lesson you will learn how to convert fractions to decimals by connecting the meaning of fractions to the division algorithm.

     

Convert a rational number to a decimal using long division

Convert a rational number to a decimal using long division

Lessons

  • In this lesson you will learn to identify rational numbers by exploring their characteristics.

  • In this lesson you will learn how to convert a unit fraction to a terminating decimal by using the standard algorithm for division.

  • In this lesson you will learn how to convert a unit fraction to a repeating decimal by using the standard algorithm for division.

  • In this lesson you will learn how to find the decimal equivalent of any fraction or mixed number by using the standard algorithm for decimal division.

  • In this lesson you will learn how to solve real world problems by working with rational numbers.

     

Convert rational numbers to decimals

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.

Lessons

 

Isolation Drills :

TenMarks Assignments:

  • Converting Rational Numbers to Decimals

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

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

Lessons

Simplify expressions with order of operations

Simplify expressions with order of operations.

Lessons

Isolation Drills :

TenMarks Assignments:

  • Converting Rational Numbers to Decimals

 

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