(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 determine the values of opposite numbers by comparing their distances and directions from 0.

• In this lesson you will learn the meaning of the term additive inverse by combining opposite numbers to make 0.

• 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.

• In this lesson you will learn how to find the additive inverse of a number by using an equation.

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

• In this lesson you will learn to create zero pairs by using integer chips.

• In this lesson you will learn to make zero by combining opposite numbers on a number line

• In this lesson you will learn to make zero by combining opposite rational numbers on a number line.

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

• In this lesson you will learn how opposite quantities combine to make zero by using a number line.

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

• In this lesson you will learn how to add positive and negative numbers by using a number line.

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:

• 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 add integers with the same sign by using a number line.

• In this lesson you will learn to add integers with opposite signs by using a number line.

• In this lesson you will learn to add integers with opposite signs by using an algorithm.

• In this lesson you will learn to add rational numbers by using algorithms and number lines.

• 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

• In this lesson you will learn how opposite quantities combine to make zero by using a number line.

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

• In this lesson you will learn how to add positive and negative numbers by using a number line.

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

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

• In this lesson you will learn to subtract integers by using a number line.

• In this lesson you will learn to subtract integers by finding the difference on a number line.

• In this lesson you will learn to subtract rational numbers by using an algorithm.

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

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

• In this lesson you will learn to add two positive or two negative integers by using a number line.

• In this lesson you will learn to add positive and negative integers by using a number line.

• In this lesson you will learn to demonstrate the commutative property of addition by using a number line.

• In this lesson you will learn to rethink a subtraction problem as an addition problem by using the additive inverse.

• In this lesson you will learn to subtract integers by using the “take away” definition of subtraction on a number line.

• In this lesson you will learn to determine the distance between integers by examining absolute value and number lines.

• In this lesson you will learn to subtract integers by using the difference definition of subtraction on a number line.

Add and subtract mixed numbers by regrouping.

Lessons

• In this lesson you will learn how to add mixed fractions by regrouping.

• In this lesson you will learn how to subtract mixed fractions by regrouping their fractional parts.

• In this lesson you will learn how to add mixed fractions by using improper fractions.

Use a place value chart

Use a place value chart.

Lessons

• In this lesson, you will learn to rewrite decimal division problems by using powers of ten.

• In this lesson you will learn how to subtract decimals by using a place value chart.

Isolation Drills :

TenMarks Assignments:

• Applying Addition and Subtraction to Rational Numbers

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 multiplication with the outcomes of decimal multiplication by computing with fraction/decimal equivalents.

• 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.

• In this lesson you will learn how to multiply a positive integer by a negative integer by thinking about equal groups.

• In this lesson you will learn how to multiply a negative integer by a positive integer by thinking about equal groups.

• In this lesson you will learn how to multiply a negative integer by a negative integer by thinking about equal groups.

• In this lesson you will learn how to create and use a neutral field by thinking about the relationship between positive and negative integers.

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

• In this lesson you will learn about multiplication with positive and negative integers by noticing patterns.

• In this lesson you will learn about the rules for multiplying a positive integer by a negative integer by using the distributive property.

• In this lesson you will learn about the rules for multiplying a negative integer by a negative integer by using the distributive property.

• In this lesson you will learn about multiply rational numbers other than integers by extending what you know about multiplication with integers.

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

• In this lesson, you will learn how to multiply integers by using the money model.

• In this lesson, you will learn how to multiply integers by using patterns.

• In this lesson, you will learn how to prove that a negative times a negative equals a positive by using the distributive property.

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 multiplication with the outcomes of decimal multiplication by computing with fraction/decimal equivalents.

• 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.

• In this lesson you will learn how to multiply a positive integer by a negative integer by thinking about equal groups.

• In this lesson you will learn how to multiply a negative integer by a positive integer by thinking about equal groups.

• In this lesson you will learn how to multiply a negative integer by a negative integer by thinking about equal groups.

• In this lesson you will learn how to create and use a neutral field by thinking about the relationship between positive and negative integers.

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

• In this lesson, you will learn how to divide integers by doing the inverse of multiplication.

• In this lesson you will learn where to put the negative sign in a fraction by exploring division.

• In this lesson you will learn that you can not divide rational numbers by zero by dividing blocks into groups.

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

• In this lesson you will learn to rewrite multiplication of numbers by applying the commutative property of multiplication.

• In this lesson you will learn how to apply the commutative property by rewriting division problems as multiplication.

• In this lesson you will learn to rewrite multiplication problems with rational numbers by using the associative property of multiplication.

• In this lesson you will learn to rewrite multiplication problems with rational numbers by using the commutative and associative properties of multiplication.

• In this lesson you will learn to rewrite problems with rational numbers by using different properties of multiplication and division.

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

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

Lessons

• In this lesson you will learn to solve multiplication problems by using the associative property.

• In this lesson you will learn to solve multiplication problems by using the Commutative and Associative Properties.

• In this lesson you will learn to solve multiplication problems by using the Distributive Property.

• In this lesson you will learn about using properties of operations in division problems by rewriting the division as multiplication by the reciprocal.

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 a fraction to a terminating decimal with one digit (tenths) or two digits (hundredths) by using visual representations.

• In this lesson you will learn how to convert more challenging fractions to decimals by using visual representations.

• In this lesson you will learn how to determine which fractions will convert to repeating decimals and how to write them by using visual representations.

• In this lesson you will learn how to determine whether fractions convert to terminating or repeating decimals by using proportional reasoning and double tape diagrams.

• 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

• In this lesson you will learn to rewrite fractions as decimals by using long division.

• In this lesson you will learn to rewrite fractions as repeating decimals by using long division.

• In this lesson you will learn to rewrite mixed numbers and improper fractions as decimals by using long division.

• In this lesson you will look at the relationship between fractions and decimals by using multiplication.

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

• In this lesson you will learn to use addition and subtraction to solve real-world problems involving decimals by analyzing the situation described in the problem.

• In this lesson you will learn to use addition and subtraction to solve real-world problems involving fractions by analyzing the situation described in the problem.

• In this lesson you will learn to use addition and division to solve real-world problems with rational numbers by analyzing the situation described in the problem.

Simplify expressions with order of operations

Simplify expressions with order of operations.

Lessons

• In this lesson you will learn how to simplify whole number expressions by applying the rules of the order of operations.

Isolation Drills :

TenMarks Assignments:

• Converting Rational Numbers to Decimals