Intro to Module 3. Video. September 22, Intro to Module 3 and Lesson 3 1 General.notebook

Transcription

1 Intro to Module 3 EQ: How can you use rational numbers to solve real world problems? Video 1

2 Unit Scale: Through independent work beyond what was taught in class, students could (examples include, but are not limited to): 4.0 determine if two expressions that describe cellular phone plan rates are equivalent and write them as expressions. investigate relationships between numbersin a Fibonacci sequence, identify number patterns, represent the information in graphic chart form, and generalize the results of an investigation. The students will: 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. a.describe situations in which opposite quantities combine to make 0. 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 realworld contexts. 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. d.apply properties of operations as strategies to add and subtract rational numbers. 3.0 apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 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. 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. c.apply properties of operations as strategies to multiply and divide rational numbers. 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. solve real world and mathematical problems involving the four operations with rational numbers. solve multi step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tool strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. The students will: determine the meaning of symbols, key terms, and other number sense, expression and equation specific words and phrases as they are used in a specific technical context relevant to grades 6 8 texts and topics (see Academic Vocabulary below). recall rational numbers. distinguish between positive and negative integers. apply single operations to like rational numbers. identify and calculate equivalent fractions. distinguish between an expression and an equation classify rational numbers. determine the absolute value of rational numbers. perform operations using a number line. translate written expressions into numerical expressions. understand conversion of mixed numbers and improper fractions. understand conversion of fractions, decimals, and percents. solve one step and two step equations. multiply a rational number by a variable. apply order of operations when solving equations. perform all four operations on fractions. With help, the students will have partial success at level 2.0 and level 3.0 content and recognition of academic vocabulary 2

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5 Unit Scale: Through independent work beyond what was taught in class, students could (examples include, but are not limited to): 4.0 determine if two expressions that describe cellular phone plan rates are equivalent and write them as expressions. investigate relationships between numbersin a Fibonacci sequence, identify number patterns, represent the information in graphic chart form, and generalize the results of an investigation. The students will: 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. a.describe situations in which opposite quantities combine to make 0. 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 realworld contexts. 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. d.apply properties of operations as strategies to add and subtract rational numbers. 3.0 apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 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. 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. c.apply properties of operations as strategies to multiply and divide rational numbers. 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. solve real world and mathematical problems involving the four operations with rational numbers. solve multi step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tool strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. The students will: determine the meaning of symbols, key terms, and other number sense, expression and equation specific words and phrases as they are used in a specific technical context relevant to grades 6 8 texts and topics (see Academic Vocabulary below). recall rational numbers. distinguish between positive and negative integers. apply single operations to like rational numbers. identify and calculate equivalent fractions. distinguish between an expression and an equation classify rational numbers. determine the absolute value of rational numbers. perform operations using a number line. translate written expressions into numerical expressions. understand conversion of mixed numbers and improper fractions. understand conversion of fractions, decimals, and percents. solve one step and two step equations. multiply a rational number by a variable. apply order of operations when solving equations. perform all four operations on fractions. With help, the students will have partial success at level 2.0 and level 3.0 content and recognition of academic vocabulary 5

6 Lesson 3 1 Rational Numbers and Decimals EQ: How can you convert a rational number into a decimal? 6

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12 Unit Scale: Through independent work beyond what was taught in class, students could (examples include, but are not limited to): 4.0 determine if two expressions that describe cellular phone plan rates are equivalent and write them as expressions. investigate relationships between numbersin a Fibonacci sequence, identify number patterns, represent the information in graphic chart form, and generalize the results of an investigation. The students will: 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. a.describe situations in which opposite quantities combine to make 0. 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 realworld contexts. 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. d.apply properties of operations as strategies to add and subtract rational numbers. 3.0 apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 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. 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. c.apply properties of operations as strategies to multiply and divide rational numbers. 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. solve real world and mathematical problems involving the four operations with rational numbers. solve multi step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tool strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. The students will: determine the meaning of symbols, key terms, and other number sense, expression and equation specific words and phrases as they are used in a specific technical context relevant to grades 6 8 texts and topics (see Academic Vocabulary below). recall rational numbers. distinguish between positive and negative integers. apply single operations to like rational numbers. identify and calculate equivalent fractions. distinguish between an expression and an equation classify rational numbers. determine the absolute value of rational numbers. perform operations using a number line. translate written expressions into numerical expressions. understand conversion of mixed numbers and improper fractions. understand conversion of fractions, decimals, and percents. solve one step and two step equations. multiply a rational number by a variable. apply order of operations when solving equations. perform all four operations on fractions. With help, the students will have partial success at level 2.0 and level 3.0 content and recognition of academic vocabulary 12

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