Grade 6 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

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1 Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 6 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers Minute Lessons Assessments Consistent with CA Testing Technology Standards PLUS Targeted Intervention Ready to Teach RTI Tier Materials PRINT + DIGITAL Writing Program EL Strategies Performance Lessons Integrated Projects Written directly to the CA Standards by CA Educators

2 Close the Achievement Gap EL STRATEGIES All Standards Plus lessons explicitly teach communication skills, strategies, and conventions that meet the goal of EL Instruction. Standards PLUS Includes: Standards PLUS is so much more READY TO TEACH RTI / TIER Standards Plus Lessons provide: Whole Class Instruction Targeted Intervention Intense Intervention Standards PLUS is Seven Programs in One: MINUTE LESSONS DOK 1-2 / RTI Tiers 1-2 Research-based, Direct Instruction, K-8, ELA and Math lessons. Written to the state standards. PERFORMANCE LESSONS DOK 3 Students deepen and apply their knowledge into new applications. ASSESSMENTS DOK 1-2 Weekly formative assessments monitor student progress. Online assessments help students master digital item types. INTEGRATED PROJECTS DOK 4 Students apply knowledge to real-world situations. STANDARDS PLUS DIGITAL DOK 1-3 / RTI Tiers 1-3 Lessons and assessments match the the digital format of the state test. Students transfer their knowledge into a digital learning environment. TARGETED INTERVENTION LESSONS DOK 1-2 / RTI Tiers 2-3 Scaffolded lessons assigned based on assessment results. Digital program automates this process. WRITING PROGRAM (ELA Only) DOK 1-4 / RTI Tiers 1-2 Includes lessons on every writing genre. Writing performance lessons include skills trace, prompts, and rubrics. HOMEWORK/ PARENT CONNECTION (COMING SOON)

3 Sample Lessons Included in this Booklet 9 Domain Lesson Focus Standard(s) The Number System (Number System Standards: 6.NS.1 6.NS.8) E3 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 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 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). 13 Dividing Fractions 6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., 14 Dividing Fractions 15 Dividing Fractions 16 Dividing Fractions E4 Evaluation Dividing Fractions 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? P1 Performance Lesson #1 Compute with Fractions & Decimals (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4) See the lesson index for the entire program on pages

4 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 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. Sample Daily Lesson- Teacher Lesson Plan Introduction: Today you will find common factors and the greatest common factor of two whole numbers. 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: 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, The greatest common factor: The greatest common factor:

5 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 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: 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: Sample Daily Lesson - Student Response Page 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?

6 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 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 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(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: 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) = 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) =

7 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 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: Steps to rewrite an equivalent expression using the Distributive Property: 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: = 6(5 + 6) = 6(11) = = 66 Example: Rewrite an equivalent expression using the Distributive Property and the greatest common factor of 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. Sample Daily Lesson - Student Response Page Factor Pairs of 84: Factor Pairs of 60: Greatest common factor of 84 and 60: Factors of the factor pairs: Rewrite using the Distributive Property: Factor Pairs of 35: Factor Pairs of 56: Greatest common factor of 35 and 56: Factors of the factor pairs: Rewrite using the Distributive Property:

8 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 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 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 = 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: 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) = 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) =

9 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 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: = = 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: Example: Rewrite as an equivalent expression using the Distributive Property and the greatest common factor of 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 = Sample Daily Lesson - Student Response Page Factor pairs of 12: Factor pairs of 72: Greatest common factor of 12 and 72: Remaining factors of the factor pairs: Rewrite using the Distributive Property: Factor pairs of 24: Factor pairs of 80: Greatest common factor of 24 and 80: Remaining factors of the factor pairs: Rewrite using the Distributive Property:

10 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 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:

11 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 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. 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 and and 10 Sample Daily Lesson - Student Response Page 3. 9 and and

12 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 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: 1. (6.NS.4) (6.NS.4) (6.NS.4) 5 4. (6.NS.4) 9 (3 + 7) 5. (6.NS.4) 6 (7 + 15)

13 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? 3. What is the greatest common factor of 35 and 65? 4. Rewrite the expression using the Distributive Property and the greatest common factor. Sample Assessment - Student Response Page 5. Rewrite the expression using the Distributive Property and the greatest common factor

14 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- Teacher Lesson Plan 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. 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:

15 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. 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 Multiply the numerators. 2 3 = 6 4. Multiply the denominators. 3 4 = Re-write your answer in its simplified form, if needed. 6 = 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: = Make the denominator equal to 1 by using the Multiplicative Inverse Property: Simplify before you multiply as shown above, or simplify the quotient at the end. Example: Find 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 = = Sample Daily Lesson - Student Response Page

16 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 You change the mixed number to a fraction =. 7 7 invert the divisor. You write simplification looks like this: You change the division sign to multiplication and = You can simplify before multiplying. The 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:

17 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 Multiply the numerators. 2 3 = 6 4. Multiply the denominators. 3 4 = Re-write your answer in its simplified form, if needed. 6 = Example: Find = Directions: Divide. Keep quotients in fraction form. Simplify to lowest terms. Show your work = = 8 2 Sample Daily Lesson - Student Response Page = =

18 Sample Daily Lesson- Teacher Lesson Plan 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. 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 bags (Almost 1 ) = = = 9 9 strips 3.. Have a discussion with students about 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 batches

19 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. Tony is making 1 4 pound turkey patties. He has pounds of ground turkey. How many whole turkey patties can Tony make? Directions: Solve. Show all work. Label answer with units. 1. Kathy has bags of fertilizer to cover an area of square yards. If she wants to distribute the fertilizer evenly, how many bags of fertilizer will she need to use for each square yard? 2. How many foot strips of wire can be cut from a wire that is feet long? Sample Daily Lesson - Student Response Page 3. Amanda has 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?

20 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: = = 8 bags = = = 4 times. (This answer is multiplicative not additive In other words, students are 4 times more likely to use the internet than 6 go to the library.) = = 9 sections

21 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. Example: Janis is serving 2 3 cup of ice cream in bowls at her party. She has cups of ice cream. How many servings can Janis make? Directions: Solve. Show all work. Label answer with units John is filling sand bags. He has 132 pounds of sand. Each bag must be filled with pounds of sand. How many bags can John fill? 2. The students at a local school were surveyed about how they find information for a 3 research project. 4 of the students said they use the Internet. 9 of the students 50 said they go to the library for books. How many more times do students use the Internet than go to the library? Sample Daily Lesson - Student Response Page 3. Rick has a foot long wood plank. He is cutting it into 5 6 foot sections. How many sections can he make?

22 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: 1. (6.NS.1) 3 8 = (6.NS.1) = (6.NS.1) = (6.NS.1) = = bottles

23 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 = = = 5 10 Sample Assessment - Student Response Page 4. A manufacturer has ounces remaining of a beauty product in a container. The manufacturer fills 1 2 ounce bottles with the product. How many 1 2 ounce bottles can they fill?

24 Teacher Lesson Plan Common Core Standards Plus Mathematics Grade 6 Performance Task #1 Domain: The Number System Sample Performance Lesson - Teacher Lesson Plan 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 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). Required Student Materials: Student Pages: St. Ed. Pg. 27 (Vocabulary), St. Ed. Pgs (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 ) 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

25 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., ). Factor: A number being multiplied in a multiplication equation. Product: The solution in a multiplication equation. 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 Sample Performance Lesoon - Student Repsone Page 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

26 Student Page 2 of 6 Common Core Standards Plus Mathematics Grade 6 Performance Task #1 Domain: The Number System How to use the Distributive Property to express the sum of two whole numbers: a(b + c) = ab + ac For = Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Sample Performance Lesson - Student Response Page Greatest Common Factor: = 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 7 %i% Multiply the numerators. 4 3 = Multiply the denominators. 7 2 = Re- write your answer in its simplified form, if needed = 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 4 problem like this: 4 2 = 7. This is 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 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 7 i i = 4 7 'i'3 2 1 = 2 4 ''7 'i' 3 '2 1 = 6 7

27 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 cups of sugar. She will divide the sugar evenly among batches of cookie dough. How many cups of sugar will Luisa add to each batch of cookie dough? Show how to solve this problem: Explain how to solve this problem: 2. Divide and write the quotient in remainder and decimal form: Sample Performance Lesoon - Student Repsone Page Explain how to solve this problem:

28 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: 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: 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?

29 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: Show how to solve the problem: Explain how to solve this problem: 7. How do you know where to place the decimal point in a division problem with decimals? Sample Performance Lesoon - Student Repsone Page 8. Why do you multiply the reciprocal of the divisor when dividing fractions?

30 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 Use the distributive property to add

31 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) The Number System (Number System Standards: 6.NS.1 6.NS.8) Student Page 1 2 Divide Multi digit Numbers Divide Multi digit Numbers 6.NS.2: Fluently divide multi digit numbers using the standard algorithm Add and Subtract Decimals 6.NS.3: Fluently add, subtract, multiply, and 5 divide multi digit decimals using the standard 4 Add and Subtract Decimals algorithm for each operation. 6 Evaluation Divide Multi Digit Numbers / Add and Subtract Decimals 6.NS.2, 6.NS Multiplying Decimals 9 6 Multiplying Decimals 10 7 Dividing Decimals 6.NS Dividing Decimals 12 Evaluation Multiplying and Dividing Decimals 13 9 Common Factors 15 Distributive Property and Greatest Common 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the 16 Factor least common multiple of two whole numbers less Distributive Property and Greatest Common than or equal to 12. Use the distributive property to 17 Factor express a sum of two whole numbers with a Distributive Property and Least Common common factor as a multiple of a sum of two whole numbers with no common factor. For example, 18 Multiple express as 4 (9 + 2). Evaluation Distributive Property and GCF 19 and LCM E1 E E3 13 Dividing Fractions 6.NS.1: Interpret and compute quotients of fractions, and solve 21 word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the 14 Dividing Fractions 22 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? 15 Dividing Fractions Dividing Fractions 24 E4 Evaluation Dividing Fractions 25 P1 Performance Lesson #1 Compute with Fractions & Decimals (6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4) 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. 19 Positive and Negative Numbers/Number Line Position Fractions on a Number Line 6.NS.6c 36 E5 Evaluation Numbers and Their Opposites, Position Rational Numbers NS.5, 6.NS.6a, 6.NS.6c 37 DOK Level Learning Plus Associates 31

32 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Standard(s) Standard(s) Student Page DOK Level 21 Position Rational Numbers on a Line 39 6.NS.6c 22 Position Rational Numbers on a Line Interpret Inequality Statements 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. 24 Interpret Inequality Statements The Number System (Number System Standards: 6.NS.1 6.NS.8) E6 Evaluation Position Rational Numbers and Interpret Inequalities 25 Absolute Values 6.NS.6c, 6.NS.7a 43 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. 26 Absolute Values Real World Statements of Order 28 Identify and Write Reflections of Ordered Pairs E7 Evaluation Absolute Values and Order 6.NS.6b, 6.NS.7b, 6.NS.7c, 6.NS.7d Plotting Points 30 Plotting Points 31 Plotting Points 32 Plotting Points 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 E8 Evaluation Plotting Points 55 Performance Lesson #2 Find It on the Number Line P2 (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) 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 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 Learning Plus Associates

33 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) Ratios and Proportional Relationships (Ratio and Proportional Relationships Standards: 6.RP.1 6.RP.3d) Student Page 1 Concept of a Ratio 62 6.RP.1: Understand the concept of a ratio and 2 Part to Part and Part to Total use ratio language to describe a ratio 63 relationship between two quantities. 3 Part to Part and Part to Total 64 4 Equivalent Ratios 6.RP.3a 65 E1 Evaluation Ratios 6.RP.1, 6.RP.3a 66 5 Equivalent Ratios 67 6 Ratios in Tables and Graphs 6.RP.3a: Make tables of equivalent ratios relating 68 quantities with whole number measurements, find 7 Ratios in Tables and Graphs missing values in the tables, and plot the pairs of 69 values on the coordinate plane. Use tables to 8 Comparing Ratios in Tables compare ratios. 70 E2 Evaluation Ratios in Tables 71 9 Ratio as Unit Rate 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. 10 Unit Rates Comparing Ratios 6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed Unit Rates 76 E3 Evaluation Unit Rates 6.RP.2, 6.RP.3b Solve Ratio Problems 14 Solve Ratio Problems 6.RP.3: Use ratio and rate reasoning to solve realworld and mathematical problems... 6.RP.3b Solve Ratio Problems 81 6.RP.3 16 Solve Ratio Problems 82 E4 Evaluation Solve Ratio Problems 6.RP.3, 6.RP.3b 83 P3 Performance Lesson #3 Real World Ratios (6.RP.1, 6.RP.2, 6.RP.3, 6.RP.3a, 6.RP.3b) Find the Percent of a Number 18 Find the Percent of a Whole 89 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. 19 Find the Percent of a Whole Find the Percent of a Whole 91 E5 Evaluation Find the Percent of a Number/Whole 21 Percent of a Number 22 Percent of a Number Percent of a Number 6.RP.3c Percent of a Number 96 E6 Evaluation Percent of a Number DOK Level Learning Plus Associates 33

34 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) Ratios and Proportional Relationships (Standards: 6.RP.1 6.RP.3d) Statistics and Probability (Statistics and Probability Standards: 6.SP.1 6.SP.5d) 25 Measurement Conversions 6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Student Page 26 Measurement Conversions Measurement Conversions Measurement Conversions 102 E7 Evaluation Measurement Conversions 103 P4 Performance Lesson #4 Percent and Measurement Conversions (6.RP.3c, 6.RP.3d) Statistical Questions 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 6.SP.2, 6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 2 Statistical Questions Measures of Center 4 Measures of Center 112 E1 Evaluation Statistical Questions and Measures of Center 5 Range and Mean Absolute Deviation 6 Range and Mean Absolute Deviation Dot Plots, Mean, Median, & Range 8 Dot Plots and Distribution 6.SP.2, 6.SP.4, 6.SP.5c, 6.SP.5d: Relating the choice of measures of center and variability to the shape of the Evaluation Mean Absolute Deviation and data distribution and the context in which the data Dot Plots were gathered. E2 9 Histograms 6.SP.4, 6.SP.5a: Reporting the number of observations. 6.SP.5b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. 10 Histograms Histograms 6.SP Frequency Tables and Histograms SP.2, 6.SP.4 E3 Evaluation Histograms DOK Level 13 Box Plots, Median, Interquartile Range Box Plots Box Plots 6.SP.4, 6.SP.5b, 6.SP.5c, 6.SP.5d Box Plots E4 Evaluation Box Plots 135 P5 Performance Lesson #5 Data Displays and Analysis (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) Learning Plus Associates

35 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) Student Page 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) 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. DOK Level Learning Plus Associates 35

36 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) Student Page 6.EE.1: Write and evaluate numerical expressions involving 1 Exponents whole number exponents 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 Order of Operations real world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional Order of Operations order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = 148 s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Expressions and Equations (Expressions and Equations Standards: 6.EE.1 6.EE.9) E1 Evaluation Order of Operations Math Terminology 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 Writing Algebraic Expressions 6.EE.2a: Write expressions that record operations with Writing Algebraic Expressions numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y Writing Algebraic Expressions E2 Evaluation Math Terminology and Writing Algebraic Expressions 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 EE.2a, 6.EE.2b, 6.EE Writing Algebraic Expressions 6.EE.2a, 6.EE Evaluate Expressions 11 Evaluate Expressions 6.EE.2c Evaluate Expressions 160 E3 Evaluation Write and Evaluate Algebraic Expressions 13 Distributive Property EE.2a, 6.EE.2c, 6.EE 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. 14 Distributive Property Distributive Property Distributive Property 166 E4 Evaluation Distributive Property 167 P6 Performance Lesson #6 All About Expressions (6.EE.1, 6.EE.2a, 6.EE.2b, 6.EE.2c, 6.EE.6) Identifying Equivalent Expressions 18 Dependent and Independent Variables 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. 19 Dependent and Independent Variables Dependent and Independent Variables 176 E5 Evaluation Equivalent Expressions / Dependent & Independent Variables EE.4, 6.EE DOK Level Learning Plus Associates

37 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) 21 Writing Algebraic Equations Student Page 179 DOK Level 22 Writing Algebraic Equations Writing Algebraic Equations 6.EE Writing Algebraic Equations 182 E6 Evaluation Writing Algebraic Equations Writing Algebraic Equations Writing Algebraic Equations Writing Algebraic Equations 6.EE Expressions and Equations (Expressions and Equations Standards: 6.EE.1 6.EE.9) 28 Writing Algebraic Equations E7 Evaluation Writing Algebraic Equations 193 P7 Performance Lesson #7 Writing Algebraic Equations (6.EE.4, 6.EE.9) Finding a Number that Makes an Equation True 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. 30 Finding Values that Make Inequalities True Understanding Properties to Solve Equations Understanding Properties to Solve Equations 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. E8 Evaluation Solving Algebraic Equations 6.EE.5, 6.EE Understanding Properties to Solve Equations Understanding Properties to Solve Equations 35 Solve Equations 6.EE Solve Equations 206 E9 Evaluation Solving Algebraic Equations Graph Inequalities Translate Inequality Phrases 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. 39 Translate Inequality Phrases Write and Graph Inequalities from Realworld Scenarios E10 Evaluation Working with Inequalities P8 Performance Lesson Equations and Inequalities (6.EE.5, 6.EE.7, 6.EE.8) Learning Plus Associates 37

38 Common Core Standards Plus - Math Grade 6 Lesson Index Domain Lesson Focus Standard(s) Geometry (Geometry Standards: 6.G. 1 6.G.4) Student Page 1 Areas of Special Quadrilaterals G.1: Find the area of right triangles, other 2 Areas of Special Quadrilaterals 220 triangles, special quadrilaterals, and polygons 3 Areas of Triangles by composing into rectangles or decomposing 221 Find Missing Dimensions Using Area into triangles and other shapes; apply these 4 techniques in the context of solving real world 222 Formulas Evaluation Areas of Triangles and and mathematical problems. E1 223 Quadrilaterals 5 Areas of Triangles and Quadrilaterals Areas of Rectangular Composite Figures Solving Area Problems 6.G Solving Area Problems 228 E2 Evaluation Solving Area Problems Nets G.4: Represent three dimensional figures 10 Surface Area of Prisms using nets made up of rectangles and triangles, and use the nets to find the surface area of 11 Surface Area of Pyramids 234 these figures. Apply these techniques in the 12 Surface Area in Real world Problems context of solving real world and mathematical 235 E3 Evaluation Surface Area and Nets problems Volume 6.G.2: Find the volume of a right rectangular prism with Volume fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the Volume volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and Volume V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real world 240 E4 Evaluation Volume and mathematical problems. 241 P9 Performance Lesson #9 Area, Surface Area, and Volume (6.G.1, 6.G.2, 6.G.4) Coordinate Geometry 6.G.3: Draw polygons in the coordinate plane 246 given coordinates for the vertices; use 18 Coordinate Geometry 247 coordinates to find the length of a side joining 19 Coordinate Geometry points with the same first coordinate or the 248 same second coordinate. Apply these 20 Coordinate Geometry techniques in the context of solving real world E5 Evaluation Coordinate Geometry and mathematical problems. 251 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) 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. DOK Level Learning Plus Associates

39 Standards Plus is a perfect fit for California Schools Standards Plus has a proven record of closing achievement gaps in districts throughout California. Over 190+ Schools in California implemented Standards Plus in 2016 and exceeded the State Test average in one or more grade levels. Standards Plus Materials Benefit English Learners: Using Standards Plus instruction across grade levels ensures all students are given equal access to grade level, standards-based instruction. By explicitly targeting the standards Emphasizing academic vocabulary Accelerating language development Providing immediate feedback to students Improving student confidence Standards Plus Supplemental Materials have been independently reviewed and verified for alignment to the California Standards by learninglist.com

40 Standards Plus is Proven Effective in California Schools CALIFORNIA SBAC GROWTH RATE STANDARDS PLUS SCHOOLS SBAC GROWTH RATE* more than doubled OVER 83% of Schools that implemented Standards Plus in more than doubled the California SBAC growth rate in one or more grade level. Standards Plus Closes the Achievement Gap with 7 Different Programs in One Standards Plus includes: Today s Lesson Performance Lessons Integrated Projects Minute Direct Instruction Lessons in Print and Online Increase EL Performance with Equity ELA & Math in Grades K-8 Transfer of Knowledge to a Digital Learning Environment Intervention Materials Built-In Students Experience SBAC-Like Technology Fits into Every Budget starting at $ a Student