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Mathematics 6 COMMON CORE Standards Plus ® S N O S S E L SAMPLE ® COMMON CORE Standards Plus MATHEMATICS GRADE 6 ts, n e m s s e s s A COMMON CORE o n s , 2 Plus s o n 8 L e s sStandards nce Les a m r o f r e P 1 and ® % = x c lu d e s : in m a r g o r te p ents, T h e c o m p le 34 Assessm s, 136 Lesson Lessons, e c n a m r o f r 12 Pe Projects d e t a r g e t a n d 3 In + 6 Mathematics rds Plus ® Available in GRADE 6 of Educators andardsplus.org • Fax: 909.484.6004 ay North, Suite 509 camonga, CA 91730 COMMON CORE Standards Plus ® PAPER & DIGITAL formats Wha t is Com mon Cor e Sta nda rds Plus ? Three Types of Lessons: (Available in Print and Interactive Digital Format) Daily Lessons and Weekly Assessments (Evaluations): (15-20 minutes daily) There are 34 weeks of daily lessons and assessments (evaluations) written directly to the standards. A week of instruction is comprised of four lessons and a corresponding assessment. The daily lessons are written to DOK Levels 1 and 2. Daily Lessons & Weekly Assessm ents Performance Lessons: (3-5 days 30 minutes each day) After one or more weeks of daily lessons written to a particular standard or topic, you will find a Performance Lesson. Performance Lessons are written to DOK Level 3. These lessons require that students apply what they have learned and use reasoning, planning, evidence, and a higher level of thinking than the daily lessons. Many standards are assessed at this level of rigor on state assessments. Performance Lessons Integrated Projects: (Multiple class sessions over several days or weeks) Three Integrated Projects are located immediately after the supporting daily lessons, assessments, and performance lessons. Integrated Projects require that students plan, synthesize information, produce high-quality products, and present their findings. Integrated Projects are written to DOK level 4. 2 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Integrated Projects 2 1 3 2 4 3 E1 4 5 E1 6 5 7 6 8 7 E2 8 Divide Multi‐digit Numbers Divide Multi‐digit Numbers Add and Subtract Decimals Divide Multi‐digit Numbers Add and Subtract Decimals Add and Subtract Decimals Evaluation – Divide Multi‐Digit Numbers / Add and Subtract Decimals Add and Subtract Decimals Evaluation – Divide Multi‐Digit Numbers / Multiplying Decimals Add and Subtract Decimals Multiplying Decimals Multiplying Decimals the standard algorithm. 6.NS.2: Fluently divide multi‐digit numbers using 6.NS.3: Fluently add, subtract, multiply, and the standard algorithm. divide multi‐digit decimals using the standard algorithm for each operation. 6.NS.3: Fluently add, subtract, multiply, and divide multi‐digit decimals using the standard 6.NS.2, 6.NS.3 algorithm for each operation. 4 3 5 4 1‐2 6 5 1‐2 6.NS.2, 6.NS.3 9 7 S am pl e Le ss on s In cl ud ed in th is Bo ok le t Dividing Decimals Multiplying Decimals Dividing Decimals Dividing Decimals 7 6 6.NS.3 10 9 11 10 1‐2 6.NS.3 12 11 1‐2 Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Evaluation – Multiplying and Dividing The Number System The Number System The Number System (Number System Standards: 6.NS.1‐6.NS.8) (Number System Standards: 6.NS.1‐6.NS.8) (Number System Standards: 6.NS.1‐6.NS.8) 13 Dividing Decimals 12 Decimals Student DOK Evaluation – Multiplying and Dividing Domain Lesson Focus Standard(s) 15 9 Common Factors 13 E2 Page Level Decimals Distributive Property and Greatest Common 6.NS.4: Find the greatest common factor of two Divide Multi‐digit Numbers 3 1 16 6.NS.2: Fluently divide multi‐digit numbers using 10 15 9 Common Factors whole numbers less than or equal to 100 and the Factor the standard algorithm. least common multiple of two whole numbers less 4 Distributive Property and Greatest Common 2 Divide Multi‐digit Numbers Distributive Property and Greatest Common 6.NS.4: Find the greatest common factor of two 16 than or equal to 12. Use the distributive property to 10 17 1‐2 whole numbers less than or equal to 100 and the 11 Factor Factor 6.NS.3: Fluently add, subtract, multiply, and express a sum of two whole numbers 1–100 with a 5 3 Add and Subtract Decimals least common multiple of two whole numbers less 1‐2 Distributive Property and Greatest Common divide multi‐digit decimals using the standard common factor as a multiple of a sum of two whole Distributive Property and Least Common than or equal to 12. Use the distributive property to 17 11 18 12 1‐2 6 Factor 4 Add and Subtract Decimals numbers with no common factor. For example, algorithm for each operation. Multiple express a sum of two whole numbers 1–100 with a express 36 + 8 as 4 (9 + 2). common factor as a multiple of a sum of two whole Distributive Property and Least Common Evaluation – Divide Multi‐Digit Numbers / Evaluation – Distributive Property and GCF 6.NS.2, 6.NS.3 18 12 7 E1 19 E3 Add and Subtract Decimals numbers with no common factor. For example, Multiple and LCM express 36 + 8 as 4 (9 + 2). Evaluation – Distributive Property and GCF 6.NS.1: Interpret and compute quotients of fractions, and solve 9 5 Multiplying Decimals 19 Dividing Fractions 21 E3 13 and LCM word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the 10 6 Multiplying Decimals 6.NS.1: Interpret and compute quotients of fractions, and solve Dividing Fractions 22 14 Dividing Fractions problem. For example, create a story context for (⅔) ÷ (¾) and 21 13 word problems involving division of fractions by fractions, e.g., use a visual fraction model to show the quotient; use the Dividing Decimals 11 7 by using visual fraction models and equations to represent the 6.NS.3 1‐2 relationship between multiplication and division to explain that Dividing Fractions 23 15 22 1‐2 14 Dividing Fractions problem. For example, create a story context for (⅔) ÷ (¾) and (⅔) ÷ (¾) = 8/9 because ¾ of 8/9 is ⅔. (In general, (a/b) ÷ (c/d) = 12 use a visual fraction model to show the quotient; use the 8 Dividing Decimals ad/bc.) How much chocolate will each person get if 3 people Dividing Fractions 24 16 relationship between multiplication and division to explain that Dividing Fractions 23 1‐2 15 Evaluation – Multiplying and Dividing share ½ lb of chocolate equally? How many ¾‐cup servings are in (⅔) ÷ (¾) = 8/9 because ¾ of 8/9 is ⅔. (In general, (a/b) ÷ (c/d) = ⅔ of a cup of yogurt? How wide is a rectangular strip of land 13 E2 Decimals ad/bc.) How much chocolate will each person get if 3 people 25 with length ¾ mi and area ½ square mi? E4 Evaluation – Dividing Fractions Dividing Fractions 24 16 share ½ lb of chocolate equally? How many ¾‐cup servings are in Common Factors 15 ⅔ of a cup of yogurt? How wide is a rectangular strip of land 9 Performance Lesson #1 – Compute with Fractions & Decimals (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4) 27‐32 3 P1 Evaluation – Dividing Fractions 25 with length ¾ mi and area ½ square mi? E4 Distributive Property and Greatest Common 6.NS.4: Find the greatest common factor of two 6.NS.6a: Recognize opposite signs of numbers as indicating 16 10 Factor whole numbers less than or equal to 100 and the locations on opposite sides of 0 on the number line; recognize (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4) 27‐32 3 P1 Opposite Numbers & the Number Line 33 17 Performance Lesson #1 – Compute with Fractions & Decimals least common multiple of two whole numbers less that the opposite of the opposite of a number is the number Distributive Property and Greatest Common than or equal to 12. Use the distributive property to 6.NS.6a: Recognize opposite signs of numbers as indicating itself, e.g., ‐(‐3) = 3, and that 0 is its own opposite. 17 1‐2 11 Factor locations on opposite sides of 0 on the number line; recognize 6.NS.5: Understand that positive and negative numbers are used express a sum of two whole numbers 1–100 with a 33 17 Opposite Numbers & the Number Line that the opposite of the opposite of a number is the number together to describe quantities having opposite directions or common factor as a multiple of a sum of two whole Distributive Property and Least Common itself, e.g., ‐(‐3) = 3, and that 0 is its own opposite. Positive and Negative Numbers/Number Line 34 values (e.g., temperature above/below zero, elevation 18 18 12 6.NS.5: Understand that positive and negative numbers are used numbers with no common factor. For example, Multiple above/below sea level, credits/debits, positive/negative electric together to describe quantities having opposite directions or express 36 + 8 as 4 (9 + 2). Positive and Negative Numbers/Number Line charge); use positive and negative numbers to represent 34 values (e.g., temperature above/below zero, elevation 18 Evaluation – Distributive Property and GCF quantities in real‐world contexts, explaining the meaning of 0 in 19 E3 1‐2 above/below sea level, credits/debits, positive/negative electric and LCM each situation. 6.NS.6c: Find and position integers and other charge); use positive and negative numbers to represent 35 rational numbers on a horizontal or vertical number line 19 Positive and Negative Numbers/Number Line 6.NS.1: Interpret and compute quotients of fractions, and solve quantities in real‐world contexts, explaining the meaning of 0 in diagram; find and position pairs of integers and other rational 21 1‐2 13 Dividing Fractions word problems involving division of fractions by fractions, e.g., each situation. 6.NS.6c: Find and position integers and other numbers on a coordinate plane. Positive and Negative Numbers/Number Line 35 by using visual fraction models and equations to represent the rational numbers on a horizontal or vertical number line 19 Dividing Fractions 22 14 problem. For example, create a story context for (⅔) ÷ (¾) and diagram; find and position pairs of integers and other rational 6.NS.6c 36 20 Position Fractions on a Number Line use a visual fraction model to show the quotient; use the numbers on a coordinate plane. relationship between multiplication and division to explain that 1‐2 23 15 Dividing Fractions Evaluation – Numbers and Their Opposites, (⅔) ÷ (¾) = 8/9 because ¾ of 8/9 is ⅔. (In general, (a/b) ÷ (c/d) = 6.NS.6c 36 20 6.NS.5, 6.NS.6a, 6.NS.6c 37 E5 Position Fractions on a Number Line ad/bc.) How much chocolate will each person get if 3 people Position Rational Numbers 24 16 Dividing Fractions Evaluation – Numbers and Their Opposites, share ½ lb of chocolate equally? How many ¾‐cup servings are in ⅔ of a cup of yogurt? How wide is a rectangular strip of land 6.NS.5, 6.NS.6a, 6.NS.6c 37 E5 Position Rational Numbers 25 with length ¾ mi and area ½ square mi? E4 Evaluation – Dividing Fractions S e e th e le s s o n in d e x f o r th e e n ti re p ro g ra m o n p a g e s 3 1- 3 8 . P1 Performance Lesson #1 – Compute with Fractions & Decimals (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4) 27‐32 17 Opposite Numbers & the Number Line 18 Positive and Negative Numbers/Number Line 6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ‐(‐3) = 3, and that 0 is its own opposite. 6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts, explaining the meaning of 0 in each situation. 6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Learn more about our Digital Lessons at: http://standardsplus.org/about-our-digital-platform/ 19 Positive and Negative Numbers/Number Line 20 E5 Position Fractions on a Number Line 6.NS.6c www.standardsplus.org - 1.877.505.9152 Evaluation – Numbers and Their Opposites, © 2016 Learning Plus Associates 6.NS.5, 6.NS.6a, 6.NS.6c Position Rational Numbers 3 33 34 35 36 37 1‐2 3 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Common Factors Lesson: #9 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Lesson Objective: Students will find common factors and the greatest common factor of two whole numbers. Introduction: “Today you will find common factors and the greatest common factor of two whole numbers.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “A factor is a number that divides evenly into another number. For example the factors of 15 are 1, 3, 5, and 15. It makes the job of finding all the factors of a number easier by thinking of factor pairs. A factor pair are two numbers that are multiplied together to get a product. The factor pairs of 15 are 1 × 15 and 3 × 5. Today you will be using a Venn diagram to help illustrate the relationship between two whole numbers. The intersection of the circles of a Venn diagram represents what the two categories you are comparing have in common. Each circle of the Venn diagram is labeled. Use the label to guide what numbers you place in each circle.” Guided Practice: “Let’s look at the example together. (Model all the steps to find common factors of two numbers and the use of the Venn diagram to illustrate the relationship between the factors of the two numbers.) First I list the factors of each number. I will write the factors down in the box on the right of the Venn diagram. I will find factor pairs. The factor pairs of 30 are 1 × 30, 2 × 15, 3 × 10, 5 × 6. The factor pairs of 36 are 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6. Next I find what factors are in common between 30 and 36. From my list I see that 1, 2, 3, and 6 are on both lists. Next I write the common factors of 1, 2, 3, and 6 in the intersection of the circles. The remaining factors 5, 10, 15, and 30 I write in the left side of the left circle labeled The Factors of 30. The remaining factors 4, 9, 12, 18, and 36 I write in the right side of the right circle labeled The Factors of 36. I then answer the questions. What the numbers in the intersection of the circle have in common is that they are all factors of both 30 and 36. I use my completed diagram to find the greatest common factor by only focusing on the numbers located in the intersection of the Venn diagram. From those factors, I choose the greatest number. The greatest number is 6. Therefore the greatest common factor of 30 and 36 is 6.” Independent Practice: “Follow the same process to complete the problems. Number 3 does not provide you a Venn diagram. You may sketch one on your own. You may also list the factors of each number and find the greatest common factor from your lists.” Review: When the students are finished, go over the answers. Closure: “Today you found common factors and the greatest common factor of two numbers. You used a Venn diagram to illustrate the relationship between the two numbers’ factors.” Answers: 4 1. Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors in left circle (not in intersection): 4, 28 Factors in the intersection: 1, 2, 7, 14 Factors in the right circle (not in intersection): 5, 10, 35, 70 2. The greatest common factor: 14 3. The greatest common factor: 4 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Common Factors Lesson: #9 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Fill in the Venn diagram with the factors of 30 and 36. Factors of 30 Factors of 36 List all the factors of 30: List all the factors of 36: Sample Daily Lesson - Student Response Page What do the numbers in the intersection have in common? Explain how you can use your completed diagram to find the greatest common factor of 30 and 36. What is the greatest common factor of 30 and 36? Directions: Complete the problems below. 1. Fill in the Venn diagram with the factors of 28 and 70. Factors of 28 Factors of 70 List all the factors of 28: List all the factors of 70: 2. What is the greatest common factor of 28 and 70? 3. What is the greatest common factor of 8 and 36? www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 5 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Greatest Common Factor Lesson: #10 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Lesson Objective: Students will rewrite the sum of two whole numbers using the Distributive Property and the greatest common factor. Introduction: “Today we are going to rewrite expressions using the Distributive Property and the greatest common factor of two whole numbers.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “The general rule of the Distributive Property is a(b + c) = ab + ac. In today’s lesson we will apply the general rule of the distributive property to solve addition problems. To apply the distributive property, you must find the greatest common factor first. We practiced the skill of finding the greatest common factor of two numbers yesterday. Today you will also find the greatest common factor of two numbers as a step needed to rewrite an expression using the Distributive Property. You will be given a sum of two whole numbers and you will find the greatest common factor of the two numbers and write an expression that shows the Distributive Property.” Go over the example and the steps from the student page that shows how to rewrite an expression using the Distributive Property. Guided Practice: “Let’s look at the example together. (Model the process of finding greatest common factor of two numbers and rewrite the sum of two whole numbers using the Distributive Property.) I must rewrite the sum of 18 + 54. First I list the factor pairs of 18. The factors pairs are 1 × 18, 2 × 9, 3 × 6. Next I list the factor pairs of 54. The factor pairs are 1 × 54, 2 × 27, 3 × 18, 6 × 9. From the list of factor pairs I find the greatest common factor which is 18. The remaining factors from the factor pairs with 18 are 1 and 3. Finally I rewrite using the Distributive Property. 18(1 + 3). So 18 + 54 = 18(1 + 3) = 72.” Independent Practice: “Follow the same process to complete the problems.” Review: When the students are finished, go over the answers. Closure: “Today you rewrote a sum of two whole numbers using the Distributive Property and the greatest common factor of the two whole numbers.” Answers: 6 1. Factor Pairs of 84: 1, 2, 3, 4, 6, 7, 12, 14 Factor Paris of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Greatest Common Factor: 12 12(7 + 5) = 144 2. Factor Pairs of 35: 1, 5, 7, 35 Factor Pairs of 56: 1, 2, 4, 7, 8, 14, 28, 56 Greatest Common Factor: 7 7(5 + 8) = 91 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Greatest Common Factor Lesson: #10 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. General Rule of the Distributive Property: a(b + c) = ab + ac Rewrite the sum of two whole numbers using the Distributive Property: 30 + 36 Steps to rewrite an equivalent expression using the Distributive Property: 30 + 36 Find the greatest common factor of the two given numbers. For 30 and 36, it is 6. Notice the other factor pairs with the greatest common factor: 6 × 5 and 6 × 6 Write the greatest common factor. Place the other factor pairs inside a set of parentheses separated by a plus sign: 6(5 + 6). The resulting equation is equivalent to the given problem: 30 + 36 = 6(5 + 6) = 6(11) = 66 Sample Daily Lesson - Student Response Page 30 + 36 = 66 Example: Rewrite an equivalent expression using the Distributive Property and the greatest common factor of 18 + 54. Factor Pairs of 18: Factor Pairs of 54: Greatest common factor of 18 and 54: Factors of the factor pairs: Rewrite using the Distributive Property: Directions: Rewrite and solve using the Distributive Property. Check your work to see if the answers match. 1. 84 + 60 2. 35 + 56 Factor Pairs of 84: Factor Pairs of 35: Factor Pairs of 60: Factor Pairs of 56: Greatest common factor of 84 and 60: Greatest common factor of 35 and 56: Factors of the factor pairs: Factors of the factor pairs: Rewrite using the Distributive Property: Rewrite using the Distributive Property: www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 7 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Greatest Common Factor Lesson: #11 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Lesson Objective: Students will rewrite the sum of two whole numbers using the Distributive Property and the greatest common factor. Introduction: “Today we are going to continue rewriting expressions using the Distributive Property and the greatest common factor of two whole numbers.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “As a reminder, the Distributive Property is ab + ac = a(b + c). To apply the Distributive Property you must find the greatest common factor first. We have been practicing the skill of finding the greatest common factor of two numbers for the last couple days. Today you will also find the greatest common factor of two numbers as a step needed to rewrite an expression using the Distributive Property. You will be given a sum of two whole numbers and you will find the greatest common factor of the two numbers and place it outside of the parentheses.” Go over the steps from the student page on how to rewrite an expression using the Distributive Property. Guided Practice: “Let’s look at the example together. (Model the process of finding greatest common factor of two numbers and rewrite the sum of two whole numbers using the Distributive Property.) I must rewrite the sum of 18 + 63. First I list the factor pairs of 18. The factors pairs are 1 × 18, 2 × 9, 3 × 6. Next I list the factor pairs of 63. The factor pairs are 1 × 63, 3 × 21, 7 × 9. From the list of factor pairs I find the greatest common factor which is 9. The remaining factors from the factor pairs with 9 are 2 and 7. Finally I rewrite using the Distributive Property. 9(2 + 7). So 18 + 63 = 9(2 + 7) = 81.” Independent Practice: “Follow the same process to complete the problems.” Review: When the students are finished, go over the answers. Closure: “Today you rewrote a sum of two whole numbers using the Distributive Property and the greatest common factor of the two whole numbers.” Answers: 8 1. Factor Pairs of 12: 1, 2, 3, 4, 6, 12 Factor Pairs of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Greatest Common Factor: 12 12(1 + 6) = 84 2. Factor Pairs of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factor Pairs of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Greatest Common Factor: 8 8(3 + 10) = 104 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Greatest Common Factor Lesson: #11 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. General Rule of the Distributive Property: ab + ac = a(b + c) Rewrite the sum of two whole numbers using the Distributive Property: 30 + 36 = 6 × 5 + 6 × 6 = 6(5 + 6) ab + ac = a(b + c) Steps to rewrite an equivalent expression using the Distributive Property. Find the greatest common factor of the two given numbers. Notice the other factor pairs with the greatest common factor. Write the greatest common factor. Place the other factor pairs inside a set of parentheses separated by a plus sign. The resulting equation is equivalent to the given problem: Sample Daily Lesson - Student Response Page Example: Rewrite as an equivalent expression using the Distributive Property and the greatest common factor of 18 + 63. Factor pairs of 18: Factor pairs of 63: Greatest common factor of 18 and 63: Remaining factors of the factor pairs: Rewrite using the Distributive Property: Directions: Rewrite and solve using the Distributive Property. 1. 12 + 72 2. 24 + 80 = Factor pairs of 12: Factor pairs of 24: Factor pairs of 72: Factor pairs of 80: Greatest common factor of 12 and 72: Greatest common factor of 24 and 80: Remaining factors of the factor pairs: Remaining factors of the factor pairs: Rewrite using the Distributive Property: Rewrite using the Distributive Property: www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 9 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Least Common Multiple Lesson: #12 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Lesson Objective: Students will find the least common multiple of two whole numbers. Introduction: “Today you will be finding the multiples of two whole numbers. Multiples are the products of factor pairs. From the ordered lists of multiples of each of the whole numbers, you will be finding the first common multiple. We call that the least common multiple.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “To find multiples of a number, you multiply the number by 1, 2, 3, etc. For example the first four multiples of 3 are 3 × 1 = 3, 3 × 2 = 6, 3 × 3 = 9, 3 × 4 = 12. The multiples of 3 in a list form are: 3, 6, 9, 12, etc. You can think of multiples as skip counting. You can also find the multiples of a number on a multiplication chart by reading the number’s column or the number’s row. It is easier to start with the greater number of the two numbers given since you will find the least common multiple faster. Find the first 3 or 4 multiples of the greater number. Then find the multiples of the lesser number. The first multiple of the lesser number that matches any of the multiples of the greater number is the least common multiple.” Guided Practice: “Let’s look at the example together. (Model the process of finding least common multiple of two whole numbers.) I must find the least common multiple of 3 and 4. 4 is the greater number. The first three multiples of 4 are 4, 8, 12. Next I list the multiples of the lesser number until I come across the first multiple that matches with a multiple from the list of multiples of 4. The multiples of 3 are 3, 6, 9, 12. I stop at 12 since 12 appears on the list of multiples of 4. Therefore 12 is the least common multiple of 3 and 4.” Independent Practice: “Follow the same process to complete the problems.” Review: When the students are finished, go over the answers. Closure: “Today you found the least common multiple of two whole numbers.” Answers: 10 1. 2. 3. 4. 24 20 18 30 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Least Common Multiple Lesson: #12 Standard: 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Steps to finding the least common multiple: Identify the greater number of the two numbers given. List the first multiples of the greater number in order. Then list the multiples of the lesser number in order until you find the number that appears in your list of multiples of the greater number. The common multiple is the least common multiple. Note: You could keep listing the multiples of both whole numbers and find other common multiples, but the first number that appears on both ordered lists is the least common multiple and the only one we are finding today. Example: Find the least common multiple of 3 and 4. Sample Daily Lesson - Student Response Page Multiples of 4: Multiples of 3: The first common multiple on both lists is the least common multiple: Directions: Find the least common multiple of the two whole numbers. 1. 8 and 12 2. 4 and 10 3. 9 and 6 4. 10 and 6 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 11 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and GCF and LCM Evaluation: #3 The weekly evaluation may be used in the following ways: As a formative assessment of the students’ progress. As an additional opportunity to reinforce the vocabulary, concepts, and knowledge presented during the week of instruction. Standard: 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Sample Assessment - Teacher Lesson Plan Procedure: Read the directions aloud and ensure that students understand how to respond to each item. If you are using the weekly evaluation as a formative assessment, have the students complete the evaluation independently. If you are using it to reinforce the week’s instruction, determine the items that will be completed as guided practice, and those that will be completed as independent practice. Review: Review the correct answers with students as soon as they are finished. Answers: 12 1. 2. 3. 4. 5. (6.NS.4) 24 (6.NS.4) 36 (6.NS.4) 5 (6.NS.4) 9 (3 + 7) (6.NS.4) 6 (7 + 15) www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and GCF and LCM Evaluation: #3 Directions: Complete the following problems independently. Show your work. 1. What is the least common multiple of 6 and 8? 2. What is the least common multiple of 9 and 12? Sample Assessment - Student Response Page 3. What is the greatest common factor of 35 and 65? 4. Rewrite the expression 27 + 63 using the Distributive Property and the greatest common factor. 5. Rewrite the expression 42 + 90 using the Distributive Property and the greatest common factor. www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 13 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #13 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Lesson Objective: Students will divide with fractions. Introduction: “Today you will divide with fractions. We will review the rule we use to divide with fractions and see where the rule comes from using the Multiplicative Inverse Property.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “First we will review the rule or process we use to divide with fractions. Process steps to divide with fractions. 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 3. Multiply the numerators. 4. Multiply the denominators. 5. Rewrite your answer in its simplified form if needed. Why does this rule work? Why do we multiply the reciprocal to divide? Let’s look at the same problem with all the steps written out. We rewrite a fraction division problem like as a complex fraction. When working with complex fractions, we want to get rid of the denominator or more specifically, we want to transform the denominator into one. The reason we want the denominator to be one is that we know any number divided by one is the number. From the Multiplicative Inverse Property, we know that if we multiply any number by its reciprocal, the product is one. Therefore if we multiply the denominator by its reciprocal, we will transform the denominator to one. We multiply the denominator by its reciprocal, we must also multiply the numerator by the same number so the value of the expression doesn’t change. Let’s see how this works. Notice that you can simplify the fractions before you multiply and after you converted, or you can simplify the quotient at the end. The rule is a short cut to dividing with fractions, so we don’t have to do this long process each time.” Guided Practice: “Let’s look at the example together. (Model the process of dividing with fractions.) You must find 4 ÷ 1 . You change the division sign to multiplication and invert 5 2 the divisor. You write 4 2 . You can’t simplify the numbers so multiply the numerators and 5 1 denominators and the product is 8 . This number is in simplest terms, but is still an improper 5 fraction.” Review the reminders before you release the students to work independently. Independent Practice: “Follow the same process to complete the problems.” Review: When the students are finished, go over the answers. Closure: “Today you divided fractions using the rule of changing the division to multiplication and inverting the divisor.” Answers: 14 15 14 3 2. 2 1. www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #13 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Sample Daily Lesson - Student Response Page Process to divide with fractions: 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 2 4 2 3 3 3 3 4 3. Multiply the numerators. 2 3 = 6 4. Multiply the denominators. 3 4 = 12 5. Re-write your answer in its simplified form, if needed. 6 = 1 12 2 Why does this rule work? Why do we multiply to divide? Let’s look at the same problem with all the steps written out. Rewrite as a complex fraction: 2 2 ÷ 4 = 3 . 4 3 3 3 Make the denominator equal to 1 by using the Multiplicative Inverse Property: 2 2 3 2 3 2 3 2 4 3 3 4 3 4 3 4 1 2 31 1 1 12 3 3 4 43 1 3 42 2 3 3 4 12 Simplify before you multiply as shown above, or simplify the quotient at the end. Example: Find 4 ÷ 1 . 5 2 Reminders: Invert only the divisor. The divisor's numerator or denominator cannot be "zero". Convert the operation to multiplication and invert the fraction before performing any cancellations. Directions: Divide. Show your work. 1. 6 ÷ 4 = 7 5 2. 7 ÷ 14 = 9 27 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 15 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #14 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Lesson Objective: Students will divide with fractions. Introduction: “Today you will continue to divide with fractions. You will apply the rule we reviewed yesterday.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “Let’s review the process we use to divide with fractions. 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 3. Multiply the numerators. 4. Multiply the denominators. 5. Rewrite your answer in its simplified form, if needed. Remember you only invert the divisor. The divisor’s numerator or denominator cannot be zero. And you must convert the operation to multiplication before performing any cancellations.” Guided Practice: “Let’s look at the example together. (Model the process of dividing with fractions.) You must find to a fraction. 5 6 41 = . 7 7 5 6 3 ÷ . 7 14 You change the mixed number You change the division sign to multiplication and invert the divisor. You write 41 14 . 7 3 simplification looks like this: 14 3 17 41 You can simplify before multiplying. The 2 = 82 . 3 Independent Practice: “Follow the same process to complete the problems.” Review: When the students are finished, go over the answers. Closure: “Today you divided fractions using the rule of changing the division to multiplication and inverting the divisor.” Answers: 16 1. 16 15 2. 19 12 55 9 25 4. 3 3. www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #14 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Process to divide with fractions: 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 2 4 2 3 3 3 3 4 3. Multiply the numerators. 2 3 = 6 4. Multiply the denominators. 3 4 = 12 5. Re-write your answer in its simplified form, if needed. 6 = 1 12 2 2 41 14 41 14 Example: Find 5 6 ÷ 3 = 7 14 7 3 7 3 1 Sample Daily Lesson - Student Response Page Directions: Divide. Keep quotients in fraction form. Simplify to lowest terms. Show your work. 1. 32 ÷ 2 = 75 5 2. 2 3 ÷ 1 1 = 8 2 3. 11 ÷ 3 = 12 20 4. 5 ÷ 3 = 8 40 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 17 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #15 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Lesson Objective: Students will divide with fractions set in word problems. Introduction: “Today you will continue to divide with fractions but today you will have to solve word problems.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “Let’s review the process we use to divide with fractions. We are adding one more step. 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 3. Multiply the numerators. 4. Multiply the denominators. 5. Rewrite your answer in its simplified form, if needed. 6. Convert improper fractions to mixed numbers. Remember you only invert the divisor. The divisor’s numerator or denominator cannot be zero. You must convert the operation to multiplication before performing any cancellations. You may perform cancellations before you multiply or after.” Refer students to the written steps on the previous lesson if they need to read it again for themselves as they work through the problems. Guided Practice: “Let’s look at the example together. (Model the process of dividing with fractions.) Tony is making1/4-pound turkey patties. He has 2 4/5 pounds of ground turkey. How many whole turkey patties can Tony make? When reading a word problem, you must first decide on the operation. Today that is easy since you know that we are working with division. The next thing you need to decide is which number is the dividend and which one is the divisor. The dividend is the total amount you are starting with. The divisor is the amount you are breaking the total into. The total for this problem is 2 4/5. The amount you are breaking the total into is 1/4. Remember that you set up the problem as dividend divided by the divisor. Therefore you set up the problem as 2 4/5 ÷ 1/4. Next you convert the mixed number to a fraction. 2 4/5 becomes 14/5. Next you change the division sign to a multiplication sign and invert the second fraction. You now have 14/5 4/1. Since you can’t cancel any factors, multiply across. You end up with 56/5. Convert the improper fraction to a mixed number. 56/5 = 11 1/5. Be sure to answer the question. Go back to the problem and read it again. It asks for whole patties. Therefore you don’t need the fractional part of the mixed number. Tony can make 11 whole turkey patties.” Independent Practice: “Follow the same process to complete the word problems.” Review: When the students are done, go over the projected answers. Closure: “Today you solved word problems with fractions.” Answers: 1. 2. 11 2 53 ÷ 15 4 11 = 11 • 4 = 22 = 1 7 1 bags (Almost 1 ) 15 2 2 15 15 53 4 106 7 ÷ = • = = 9 9 strips . Have a discussion with students about 2 4 2 11 11 11 why they can’t have a fractional answer for this problem. Students must understand the structure of the problem. They should understand why they also can’t round up. 3. 18 9 2 ÷ 3 2 = 9 2 • = 3 batches 2 3 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #15 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Example: Solve. 1 4 Tony is making pound turkey patties. He has 2 pounds of ground turkey. How many 4 5 whole turkey patties can Tony make? Directions: Solve. Show all work. Label answer with units. 1 3 bags of fertilizer to cover an area of 3 square yards. If she wants to 2 4 distribute the fertilizer evenly, how many bags of fertilizer will she need to use for each square yard? 1. Kathy has 5 Sample Daily Lesson - Student Response Page 2. How many 2 3 1 foot strips of wire can be cut from a wire that is 26 feet long? 4 2 1 1 cups of sugar to make cookies. The cookie recipe calls for 1 cup for 2 2 a single batch. How many batches can Amanda make? 3. Amanda has 4 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 19 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #16 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Lesson Objective: Students will divide with fractions set in word problems. Introduction: “Today you will continue to divide with fractions and solve word problems.” Sample Daily Lesson- Teacher Lesson Plan Instruction: “Let’s review the process we use to divide with fractions. 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 3. Multiply the numerators. 4. Multiply the denominators. 5. Rewrite your answer in its simplified form, if needed. 6. Convert improper fractions to mixed numbers. Remember you only invert the divisor. The divisor’s numerator or denominator cannot be zero. And you must convert the operation to multiplication before performing any cancellations. You may perform cancellations before you multiply or after.” Refer students to the written steps on the previous lesson if they need to read it again for themselves as they work through the problems. Guided Practice: “Let’s look at the example together. (Model the process of dividing with fractions.) Janis is serving 2/3 cup of ice cream in bowls at her party. She has 15 1/2 cups of ice cream. How many servings can Janis make? The dividend is the total amount you are starting with. The divisor is the amount you are breaking the total into. The total for this problem is 15 1/2. The amount you are breaking the total into is 2/3. Remember that you set up the problem as dividend divided by the divisor. Therefore you set up the problem as 15 1/2 ÷2/3. Next you convert the mixed number to a fraction. 15 1/2 becomes 31/2. Next you change the division sign to a multiplication sign and invert the second fraction. You now have 31/2 ÷ 3/2. Since you can’t cancel then simply multiply across. You end up with 93/4 = 23 1/4. Janis can make 23 1/4 servings.” Independent Practice: “Follow the same process to complete the word problems.” Review: When the students are done, go over the projected answers. Closure: “Today you solved word problems with fractions.” Answers: 1. 2. 529 4 3 ÷ 2 = 529 24 • 2 1 31 = 529 62 8 33 62 bags 3 50 25 1 • = = 4 times . (This answer is multiplicative not additive. 4 50 4 9 6 6 1 In other words, students are 4 times more likely to use the internet than 6 ÷ 9 31 = go to the library.) 3. 20 15 2 ÷ 5 6 = 15 6 • = 9 sections 2 5 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #16 Standard: 6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 2 1 cup of ice cream in bowls at her party. She has 15 cups of 3 2 ice cream. How many servings can Janis make? Example: Janis is serving Sample Daily Lesson - Student Response Page Directions: Solve. Show all work. Label answer with units. 1 1. John is filling sand bags. He has 132 pounds of sand. Each bag must be filled with 4 1 15 pounds of sand. How many bags can John fill? 2 2. The students at a local school were surveyed about how they find information for a 3 9 research project. of the students said they use the Internet. of the students 4 50 said they go to the library for books. How many more times do students use the Internet than go to the library? 1 5 foot sections. How many 3. Rick has a 7 -foot long wood plank. He is cutting it into 2 6 sections can he make? www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 21 Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Evaluation: #4 The weekly evaluation may be used in the following ways: As a formative assessment of the students’ progress. As an additional opportunity to reinforce the vocabulary, concepts, and knowledge presented during the week of instruction. Standard: 6.NS.1 Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Sample Assessment - Teacher Lesson Plan Procedure: Read the directions aloud and ensure that students understand how to respond to each item. If you are using the weekly evaluation as a formative assessment, have the students complete the evaluation independently. If you are using it to reinforce the week’s instruction, determine the items that will be completed as guided practice, and those that will be completed as independent practice. Review: Review the correct answers with students as soon as they are finished. Answers: 22 3 8 12 • = 2 7 7 19 12 76 • = 2. (6.NS.1) 3 7 7 11 10 22 3. (6.NS.1) • = 5 87 87 26 2 52 1 • = = 17 17 bottles 4. (6.NS.1) 3 1 3 3 1. (6.NS.1) www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Evaluation: #4 Directions: Complete the following problems independently. Simplify to lowest terms. Keep answers in fraction form. Show your work. 1. 3 7 ÷ = 2 8 Sample Assessment - Student Response Page 1 7 = 2. 6 ÷ 3 12 1 7 = 3. 2 ÷ 8 5 10 2 ounces remaining of a beauty product in a container. The 3 1 1 manufacturer fills ounce bottles with the product. How many ounce bottles 2 2 can they fill? 4. A manufacturer has 8 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 23 Teacher Lesson Plan Sample Performance Lesson - Teacher Lesson Plan Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System Standard Reference: 6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? 6.NS.2: Fluently divide multi-digit numbers using the standard algorithm. 6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Required Student Materials: • Student Pages: St. Ed. Pg. 27 (Vocabulary), St. Ed. Pgs. 27-32 (Student Worksheet) Lesson Objective: The students will add, subtract, multiply, and divide with decimals and divide fractions. Overview: Students will use their knowledge of decimal operations and dividing fractions to compute with fractions and decimals as addressed in Common Core Standards Plus The Number System Lessons 1-16, E1-E4. Students will: • Solve fraction division problems using the Multiplicative Inverse Property to explain the computation. • Add, subtract, multiply, and divide with multi-digit decimals using the standard algorithm for each. Guided Practice: (Required Student Materials: St. Ed. Pg. 27) • Review vocabulary. • Review Greatest Common Factor, Least Common Multiple, and the Distributive Property. • Review the Multiplicative Inverse Property. Independent Practice: (Required Student Materials: St. Ed. Pgs. 27-32) Have students: • Solve fraction division problems. • Explain with words and models how to use the Multiplicative Inverse Property to divide fractions. • Add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. • Determine factors and multiples of pairs of numbers. • Identify the greatest common factor and the least common multiple of given numbers. Review & Evaluation: • Have students review their answers with their partners. • Check problems together. • Review student worksheets to check for understanding. 24 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Student Page 1 of 6 Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System Vocabulary: Dividend: The number being divided. Divisor: The number by which the dividend is being divided. Quotient: The solution to a division problem. Terminating decimal: A decimal which has digits that do not go on forever (e.g., 7.623). Repeating decimal: A decimal that has digits that repeat infinitely (e.g., 4.5353535353…). Factor: A number being multiplied in a multiplication equation. Product: The solution in a multiplication equation. Sample Performance Lesoon - Student Repsone Page Greatest Common Factor: The largest factor two numbers have in common. Distributive Property: A number can be decomposed and its parts multiplied and result in the same product if the number is not decomposed: a(b + c) = ab + ac. Least Common Multiple: The lowest number that is a common multiple of two different values. Fraction: Part of the whole or part of a group. Numerator: The top number in a fraction. Denominator: The bottom number in a fraction. Common: The same (e.g., common denominator means having the same denominator.). Multiplicative Inverse Property: Any number multiplied by its reciprocal equals 1. Convert: To create an equivalent fraction by multiplying or dividing to change the denominator. Equivalent: Having the same value; the same size. To find the Greatest Common Factor of two numbers: List the factors of each number: 18: 1, 2, 3, 6, 9, 18 36: 1, 2, 3, 4, 6, 9, 18, 36 Determine the greatest (largest) number common to both factor lists. The Greatest Common Factor of 18 and 36 is 18. To find the Least Common Multiple of two numbers: List the first several multiples of each number: 6: 6, 12, 18, 24, 30, 36 10: 10, 20, 30, 40, 50 Determine the least (smallest) number common to both factor lists. The Least Common Multiple of 6 and 10 is 30. www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 25 Student Page 2 of 6 Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System Sample Performance Lesson - Student Response Page How to use the Distributive Property to express the sum of two whole numbers: a(b + c) = ab + ac For 56 + 48 = _____ Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Greatest Common Factor: 8 56 + 48 = 8(7 + 6) = 8(13) = 104 Process steps to divide with fractions. 1. Change all mixed numbers to fractions. 2. Change the division sign to a multiplication sign and invert the fraction (reciprocal) to the right of the sign. 4 ÷ 2 = 4 %i%3 7 3 7 2 3. Multiply the numerators. 4 • 3 = 12 4. Multiply the denominators. 7 • 2 = 14 5. Re-‐write your answer in its simplified form, if needed. 12 = 6 14 7 But why does this rule work? Why do we multiply to divide? Let’s look at the same problem with all the in-‐between steps written out. We can rewrite a division problem like this: 4 ÷ 2 = 7 3 4 7 . This is a complex fraction. When working with complex 2 3 fractions, we want to get rid of the denominator, or more specifically, we want to transform the denominator into 1. The reason we want the denominator to be 1 is that we know any number divided by 1 is the number. From the Multiplicative Inverse Property, we know that if we multiply any number by its reciprocal, the product is 1. Therefore, if we multiply the denominator by its reciprocal, we will transform the denominator to 1. But if we multiply the denominator by its reciprocal, we must also multiply the numerator by the same number to not change the value of the expression. Let’s see how this works: 4 ÷ 2 = 3 7 26 4 4 i 3 4 'i' 3 2 7 =' 7 2 = 7 2 = 4 'i' 3 = 6 7 2 2 i 3 1 ''7 ' 2 1 3 3 2 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Student Page 3 of 6 Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System Directions: Solve each problem. Show each step used to solve the problem, and explain how to solve on the lines below. 1. Luisa has 14 1 cups of sugar. She will divide the sugar evenly among 3 3 batches of 4 8 cookie dough. How many cups of sugar will Luisa add to each batch of cookie dough? Show how to solve this problem: Sample Performance Lesoon - Student Repsone Page Explain how to solve this problem: ____________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 2. Divide and write the quotient in remainder and decimal form: 649 ÷ 33 Explain how to solve this problem: ____________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 27 Student Page 4 of 6 Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System 3. Rewrite the problem in vertical format and subtract: 89.014 – 97.993 Show how to solve the problem: Explain how to solve this problem: ____________________________________________ _________________________________________________________________________ Sample Performance Lesson - Student Response Page _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 4. Rewrite the problem in vertical format and add: 172.314 + 6.5827 Show how to solve the problem: Explain how to solve this problem: ____________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 5. How do you know where to place the decimal point in a multiplication problem with decimals? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 28 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Student Page 5 of 6 Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System 6. Rewrite the problem in vertical format and multiply: 4.18 × .92 Show how to solve the problem: Explain how to solve this problem: ____________________________________________ Sample Performance Lesoon - Student Repsone Page _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 7. How do you know where to place the decimal point in a division problem with decimals? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ 8. Why do you multiply the reciprocal of the divisor when dividing fractions? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates 29 Student Page 6 of 6 Common Core Standards Plus® – Mathematics – Grade 6 Performance Task #1 – Domain: The Number System 9. List the factors and determine the greatest common factor of 39 and 65. Sample Performance Lesson - Student Response Page 10. List the multiples and determine the least common multiple of 4 and 9. 11. Use the distributive property to add 33 + 78. 30 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Domain Lesson 1 2 3 4 E1 5 6 7 8 The Number System (Number System Standards: 6.NS.1‐6.NS.8) E2 9 Focus Divide Multi‐digit Numbers Divide Multi‐digit Numbers Add and Subtract Decimals Add and Subtract Decimals Evaluation – Divide Multi‐Digit Numbers / Add and Subtract Decimals Standard(s) 6.NS.2: Fluently divide multi‐digit numbers using the standard algorithm. 6.NS.2, 6.NS.3 7 9 Multiplying Decimals 10 Dividing Decimals 6.NS.3 1‐2 6 Multiplying Decimals 11 Dividing Decimals 12 Evaluation – Multiplying and Dividing Decimals 13 1‐2 15 Common Factors E3 13 Dividing Fractions 14 Dividing Fractions 15 Dividing Fractions 16 Dividing Fractions E4 P1 Evaluation – Dividing Fractions 6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (⅔) ÷ (¾) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (⅔) ÷ (¾) = 8/9 because ¾ of 8/9 is ⅔. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many ¾‐cup servings are in ⅔ of a cup of yogurt? How wide is a rectangular strip of land with length ¾ mi and area ½ square mi? 12 4 5 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). 11 3 6.NS.3: Fluently add, subtract, multiply, and divide multi‐digit decimals using the standard algorithm for each operation. Distributive Property and Greatest Common Factor Distributive Property and Greatest Common Factor Distributive Property and Least Common Multiple Evaluation – Distributive Property and GCF and LCM 10 Student DOK Page Level 16 17 18 19 21 22 23 25 17 Opposite Numbers & the Number Line 18 Positive and Negative Numbers/Number Line 19 Positive and Negative Numbers/Number Line 20 Position Fractions on a Number Line 6.NS.6c 36 E5 Evaluation – Numbers and Their Opposites, Position Rational Numbers 6.NS.5, 6.NS.6a, 6.NS.6c 37 www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates 1‐2 24 Performance Lesson #1 – Compute with Fractions & Decimals (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4) 27‐32 6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ‐(‐3) = 3, and that 0 is its own opposite. 6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts, explaining the meaning of 0 in each situation. 6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 1‐2 3 33 34 35 1‐2 31 Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index The Number System (Number System Standards: 6.NS.1‐6.NS.8) Domain Lesson Standard(s) Standard(s) 21 Position Rational Numbers on a Line 22 Position Rational Numbers on a Line 23 Interpret Inequality Statements 24 Interpret Inequality Statements E6 Evaluation – Position Rational Numbers and 6.NS.6c, 6.NS.7a Interpret Inequalities Student DOK Page Level 39 6.NS.6c 40 6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret ‐3 > ‐7 as a statement that ‐3 is located to the right of ‐7 on a number line oriented from left to right. 6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real‐world situation. For example, for an account balance of ‐30 dollars, write |‐30| = 30 to describe the size of the debt in dollars. 6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than ‐30 dollars represents a debt greater than 30 dollars. 6.NS.7b: Write, interpret, and explain statements of order for rational numbers in real‐world contexts. For example, write ‐3°C > ‐7°C to express the fact that ‐3°C is warmer than ‐7°C. 6.NS.6b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 25 Absolute Values 26 Absolute Values 27 Real World Statements of Order 28 Identify and Write Reflections of Ordered Pairs E7 Evaluation – Absolute Values and Order 29 Plotting Points 30 Plotting Points 31 Plotting Points 32 Plotting Points E8 Evaluation – Plotting Points P2 Performance Lesson #2 – Find It on the Number Line (6.NS.5, 6.NS.6, 6.NS.6a, 6.NS.6b, 6.NS.6c, 6.NS.7, 6.NS.7a, 6.NS.7b, 6.NS.7c, 6.NS.7d, 6.NS.8) 6.NS.6b, 6.NS.7b, 6.NS.7c, 6.NS.7d 41 1‐2 42 43 45 46 47 1‐2 48 49 51 6.NS.6c, 6.NS.8: Solve real‐world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 53 1‐2 54 55 Integrated Project #1: Researching Numbers (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4, 6.NS.5, 6.NS.6, 6.NS.6a, 6.NS.6b, 6.NS.6c, 6.NS.7, 6.NS.7a, 6.NS.7b, 6.NS.7c, 6.NS.7d, 6.NS.8) Prerequisite Common Core Standards Plus Domain: The Number System 52 57‐59 3 60‐61 4 Product: The students will write and present a short research project using a visual aid on a topic related to number systems. Overview: In this project the students will research a topic related to number systems and write a brief report on their findings. Each student will present his or her findings to the class. The students will create a visual aid to assist in their presentation of their findings. The students will include a strong sense of how their findings are related to or impact the number system we use. Since this is a learning activity, all components will be completed in class. 32 www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Ratios and Proportional Relationships (Ratio and Proportional Relationships Standards: 6.RP.1‐6.RP.3d) Domain Lesson Focus 1 2 3 4 E1 5 6 7 8 E2 Concept of a Ratio 9 Ratio as Unit Rate Part‐to‐Part and Part‐to‐Total Part‐to‐Part and Part‐to‐Total Standard(s) 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Student DOK Page Level 62 63 64 Equivalent Ratios 6.RP.3a 65 Evaluation – Ratios 6.RP.1, 6.RP.3a 66 1‐2 67 Equivalent Ratios Ratios in Tables and Graphs Ratios in Tables and Graphs Comparing Ratios in Tables 6.RP.3a: Make tables of equivalent ratios relating quantities with whole‐number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 68 69 70 71 Evaluation – Ratios in Tables 6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. 73 10 11 12 E3 13 14 15 16 E4 P3 Unit Rates 17 Find the Percent of a Number 18 Find the Percent of a Whole 19 Find the Percent of a Whole 20 Find the Percent of a Whole E5 Evaluation – Find the Percent of a Number/Whole 92 21 22 23 24 E6 Percent of a Number 93 Percent of a Number 94 74 6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed. Comparing Ratios 1‐2 75 1‐2 76 Unit Rates Evaluation – Unit Rates Solve Ratio Problems Solve Ratio Problems Solve Ratio Problems Solve Ratio Problems Evaluation – Solve Ratio Problems 6.RP.2, 6.RP.3b 6.RP.3: Use ratio and rate reasoning to solve real‐ world and mathematical problems... 6.RP.3b 6.RP.3 6.RP.3, 6.RP.3b Performance Lesson #3 – Real‐World Ratios (6.RP.1, 6.RP.2, 6.RP.3, 6.RP.3a, 6.RP.3b) Percent of a Number 77 79 80 81 1‐2 82 83 85‐87 3 88 6.RP.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.RP.3c 89 90 91 95 Percent of a Number 96 Evaluation – Percent of a Number 97 www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates 1‐2 1‐2 33 Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Student DOK Page Level Standard(s) 25 Measurement Conversions 26 Measurement Conversions 27 Measurement Conversions 28 Measurement Conversions E7 Evaluation – Measurement Conversions P4 Performance Lesson #4 – Percent and Measurement Conversions (6.RP.3c, 6.RP.3d) 1 Statistical Questions 2 Statistical Questions 3 Measures of Center 4 Measures of Center 99 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 100 101 103 105‐108 6.SP.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.5c (See below) 6.SP.3, 6.Sp.5c: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered 110 111 Range and Mean Absolute Deviation 6 Range and Mean Absolute Deviation 7 number line, including dot plots, histograms, and box Dot Plots, Mean, Median, & Range plots. Common Core Standards Plus® – Language Arts – Grade 3 117 6.SP.2, 6.SP.4, 6.SP.5c, 6.SP.5d: Relating the choice of TE St. Ed. DOK 118 8 Dot Plots and Distribution Standard(s) measures of center and variability to the shape of the Page Page Level Evaluation – Mean Absolute Deviation and data distribution and the context in which the data Parts of Stories 282 131 5 were gathered. Dot Plots RL.3.5: Refer to parts of stories, dramas, 284 132 6 Parts of Dramas and poems when writing or speaking 6.SP.4, 6.SP.5a: Reporting the number of 9 7 Histograms about a text, using terms such as chapter, Parts of a Poem 286 133 1‐2 observations. 6.SP.5b: Describing the nature of the scene, and stanza; describe how each attribute under investigation, including how it was Parts of a Poem 288 134 successive part builds on earlier sections. 10 8 Histograms measured and its units of measurement. 290 135 E2 Evaluation – Stories, Poems, and Dramas 6.SP.4 11 9 Histograms Illustration and Mood 292 137 E2 Illustration and Setting Frequency Tables and Histograms 12 10 RL.3.7: Explain how specific aspects of a text’s illustration contribute to what is 6.SP.2, 6.SP.4 conveyed by the words in the story (e.g., create mood, emphasize aspects of a character or setting.) 11 Illustration and Character Evaluation – Histograms E3 12 Illustrations Evaluation – Illustrations Box Plots, Median, Interquartile Range 13 E3 294 138 296 139 298 140 300 141 Performance – Reading Literature: Character Study and Comic Strip (RL.3.1, RL.3.3, 302‐303 143‐146 P5 RL.3.5, RL.3.7) 14 Box Plots 13 Fables, Folktales, Myths, and Word Meanings Box Plots 15 14 Fables, Folktales, and Myths Fables, Folktales, and Myths Box Plots 16 15 RL.3.2: Recount stories, including fables, 308 folktales, and myths from diverse cultures: 6.SP.4, 6.SP.5b, 6.SP.5c, 6.SP.5d 310 determine the central message, lesson, or moral, and explain how it is conveyed 312 through key details in the text. RL.3.4: Determine the meaning of words 314 and phrases as they are used in a text, distinguishing literal from nonliteral 316 language. 16 Fables, Folktales, and Myths E4 Evaluation – Box Plots Evaluation – Fables, Folktales, Myths, and E4 Vocabulary Performance Lesson #5 – Data Displays and Analysis Point of View P5 17 (6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.5a, 6.SP.5b, 6.SP.5c, 6.SP.5d) 18 Point of View RL.3.6: Distinguish their own point of view from that of the narrator or those of the 19 Point of View www.standardsplus.org - 1.877.505.9152 characters. © 2013 Learning Plus Associates 20 Point of View E5 Evaluation – Point of View 1‐2 154 322 155 324 156 326 157 1‐2 119 121 122 123 1‐2 126‐127 131 1‐2 133‐134 135 151 320 116 132 150 153 115 129‐130 3 148 318 113 124‐125 1‐2 147 149 1‐2 112 5 6.SP.2, 6.SP.4: Display numerical data in plots on a 3 109 Evaluation – Statistical Questions and Measures of Center 1‐2 102 E1 (Reading Literature Standards: RL.3.1, RL.3.2, RL.3.3, RL.3.4, RL.3.5, RL.3.6, RL.3.7) 34 Focus Strand Lesson Focus Reading Literature Statistics and Probability (Statistics and Probability Standards: 6.SP.1‐6.SP.5d) (Standards: 6.RP.1‐6.RP.3d) Ratios and Proportional Relationships Domain Lesson 137‐142 1‐2 3 Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Domain Lesson Focus Standard(s) Integrated Project #2 – Survey Says… (6.RP.3, 6.RP.3c, 6.RP.3d, 6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.5a, 6.SP.5b, 6.SP.5c, 6.SP.5d) Student DOK Page Level 143‐144 4 Prerequisite Common Core Standards Plus Domain: Ratios and Proportional Relationships and Statistics & Probability Product: The students will write statistical questions, conduct a survey, collect and represent the data, and analyze the data using measures of center and percent. The students will provide a very brief oral report on the statistical question asked, number of participants in the survey, and conclusions drawn from the survey. Overview: In this project, the students will work in groups to write statistical questions. They will each conduct a survey on a single question and collect data from at least 40 participants. They will represent the data with at least two plots. They will use percent to analyze the responses to the survey and determine the measures of center for the data collected. The students will provide a written report for the survey. Each student will report briefly and orally on the statistical question, number of participants, and conclusions drawn from the experience. Since this is a learning activity, all components will be completed in class. www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates 35 Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Domain Lesson Expressions and Equations (Expressions and Equations Standards: 6.EE.1 – 6.EE.9) 1 2 3 4 E1 36 Focus 6.EE.1: Write and evaluate numerical expressions involving whole‐number exponents. 145 Order of Operations 6.EE.1, 6.EE.2c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real‐world problems. Perform arithmetic operations, including those involving whole‐number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. 146 Order of Operations Order of Operations Evaluation – Order of Operations Math Terminology 6 7 Writing Algebraic Expressions E2 9 Student DOK Page Level Exponents 5 8 Standard(s) Writing Algebraic Expressions Writing Algebraic Expressions 6.EE.2b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. 6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. 6.EE.2a, 6.EE.6: Use variables to represent numbers and write expressions when solving a real‐world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 147 148 149 151 152 153 155 Writing Algebraic Expressions 157 10 Evaluate Expressions 11 Evaluate Expressions 12 Evaluate Expressions E3 Evaluation – Write and Evaluate Algebraic Expressions 13 Distributive Property 14 Distributive Property 15 Distributive Property 16 Distributive Property E4 Evaluation – Distributive Property P6 Performance Lesson #6 – All About Expressions (6.EE.1, 6.EE.2a, 6.EE.2b, 6.EE.2c, 6.EE.6) 17 Identifying Equivalent Expressions 18 Dependent and Independent Variables 19 Dependent and Independent Variables 20 Dependent and Independent Variables E5 Evaluation – Equivalent Expressions / Dependent & Independent Variables 1‐2 154 Evaluation – Math Terminology and Writing 6.EE.2a, 6.EE.2b, 6.EE.6 Algebraic Expressions 6.EE.2a, 6.EE.6 1‐2 158 6.EE.2c 159 1‐2 160 6.EE.2a, 6.EE.2c, 6.EE.6 6.EE.3: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. 6.EE.9: Use variables to represent two quantities in a real‐world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. 6.EE.4, 6.EE.9 www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates 161 163 164 165 1‐2 166 167 169‐172 3 173 174 175 176 177 1‐2 Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Expressions and Equations (Expressions and Equations Standards: 6.EE.1 – 6.EE.9) Domain Lesson Focus Standard(s) Student DOK Page Level 21 Writing Algebraic Equations 179 22 Writing Algebraic Equations 180 23 Writing Algebraic Equations 24 Writing Algebraic Equations 182 E6 Evaluation – Writing Algebraic Equations 183 25 Writing Algebraic Equations 185‐186 26 Writing Algebraic Equations 187‐188 27 Writing Algebraic Equations 28 Writing Algebraic Equations E7 Evaluation – Writing Algebraic Equations P7 Performance Lesson #7 – Writing Algebraic Equations (6.EE.4, 6.EE.9) 29 Finding a Number that Makes an Equation True 30 Finding Values that Make Inequalities True 31 6.EE.7: Solve real‐world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 200 1‐2 32 Understanding Properties to Solve Equations Understanding Properties to Solve Equations E8 Evaluation – Solving Algebraic Equations 6.EE.5, 6.EE.7 202 33 34 Understanding Properties to Solve Equations Understanding Properties to Solve Equations 35 Solve Equations 36 Solve Equations 206 E9 Evaluation – Solving Algebraic Equations 207 37 Graph Inequalities 209 38 Translate Inequality Phrases 39 Translate Inequality Phrases 40 Write and Graph Inequalities from Real‐ world Scenarios 6.EE.9 6.EE.9 189‐190 1‐2 191‐192 193 6.EE.5: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 195‐197 3 198 199 201 203 204 6.EE.7 6.EE.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real‐world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. E10 Evaluation – Working with Inequalities P8 181 1‐2 Performance Lesson – Equations and Inequalities (6.EE.5, 6.EE.7, 6.EE.8) www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates 205 1‐2 210 211 1‐2 212 213 215‐218 3 37 Comm on Core Stand ards Plus - Math Grade 6 Lesso n Index Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index Domain Lesson 1 2 3 Areas of Special Quadrilaterals 4 Find Missing Dimensions Using Area Formulas Evaluation – Areas of Triangles and Quadrilaterals (Geometry Standards: 6.G. 1‐6.G.4) E1 Geometry Focus Areas of Special Quadrilaterals Areas of Triangles Standard(s) Student DOK Page Level 219 6.G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real‐world and mathematical problems. 5 Areas of Triangles and Quadrilaterals 6 Areas of Rectangular Composite Figures 6.G.1 7 Solving Area Problems 8 Solving Area Problems E2 Evaluation – Solving Area Problems 9 Nets 6.G.4: Represent three‐dimensional figures using nets made up of rectangles and triangles, 10 Surface Area of Prisms and use the nets to find the surface area of 11 Surface Area of Pyramids these figures. Apply these techniques in the context of solving real‐world and mathematical 12 Surface Area in Real‐world Problems problems. E3 Evaluation – Surface Area and Nets 13 Volume 6.G.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the 14 Volume appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the 15 Volume edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with Volume 16 fractional edge lengths in the context of solving real‐world and mathematical problems. E4 Evaluation – Volume P9 Performance Lesson #9 – Area, Surface Area, and Volume (6.G.1, 6.G.2, 6.G.4) 6.G.3: Draw polygons in the coordinate plane 17 Coordinate Geometry given coordinates for the vertices; use 18 Coordinate Geometry coordinates to find the length of a side joining points with the same first coordinate or the Coordinate Geometry 19 same second coordinate. Apply these 20 Coordinate Geometry techniques in the context of solving real‐world and mathematical problems. E5 Evaluation – Coordinate Geometry P10 Performance Lesson #10 – Graphic Display (6.G.3) Integrated Project #3: Sweet Wheat Surprise (6.EE.1, 6.EE.2, 6.EE.2a, 6.EE.2b, 6.EE.2c, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.9, 6.G.3, 6.G.4) 220 221 222 1‐2 223 225 226 227 1‐2 228 229 231 232‐233 234 1‐2 235 236 237 238 239 1‐2 240 241 243‐245 3 246 247 248 1‐2 249‐250 251 253‐255 3 256 4 Prerequisite Common Core Standards Plus Domain: Expressions and Equations and Geometry Product: The students will develop the plan for producing and packaging a new cereal. They will present their plans to the class. Overview: In this project the students will design the dimensions for three different sized cereal boxes, production requirements for the new cereal, and determine a favorable price structure for the new cereal. They will present their plans to the class. Since this is a learning activity, all components will be completed in class. 38 www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates
