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Grade 6Grade 6 SAMPLER

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Sample Lessons Included in this Booklet

See the lesson index for the entire program on pages 31-38.

Common Core Standards Plus® ‐ Mathematics – Grade 6 – Lesson Index

Domain Lesson Focus Standard(s) Student Page

DOK Level

The

Num

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1 Divide Multi‐digit Numbers 6.NS.2: Fluently divide multi‐digit numbers using the standard algorithm.

3

1‐2

2 Divide Multi‐digit Numbers 4

3 Add and Subtract Decimals 6.NS.3: Fluently add, subtract, multiply, and divide multi‐digit decimals using the standard algorithm for each operation.

5

4 Add and Subtract Decimals 6

E1 Evaluation – Divide Multi‐Digit Numbers / Add and Subtract Decimals 6.NS.2, 6.NS.3 7

5 Multiplying Decimals

6.NS.3

9

1‐2

6 Multiplying Decimals 10

7 Dividing Decimals 11


E2 Evaluation – Multiplying and Dividing Decimals 13

9 Common Factors 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).

15

1‐2

10 Distributive Property and Greatest Common Factor 16


12 Distributive Property and Least Common Multiple 18

E3 Evaluation – Distributive Property and GCF and LCM 19

13 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?

21

1‐2

14 Dividing Fractions 22



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) 27‐32 3

17 Opposite Numbers & the 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.

33

1‐2

18 Positive and Negative Numbers/Number Line

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.

34

19 Positive and Negative Numbers/Number Line 35

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



DOK Level

The

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(Num

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ystem Stand



3

1‐2



5




6.NS.3

9

1‐2






15

1‐2






21

1‐2







33

1‐2



34






DOK Level

The

Num

ber S

ystem

(Num

ber S

ystem Stand



3

1‐2



5




6.NS.3

9

1‐2






15

1‐2






21

1‐2







33

1‐2



34




Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Common Factors Lesson: #9Standard: 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.” 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, 70

2. The greatest common factor: 14 3. The greatest common factor: 4


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Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Common Factors Lesson: #9Standard: 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

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

2. What is the greatest common factor of 28 and 70?


List all the factors of 30:





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- Student Response Page

Common Core Standards Plus® – Mathematics – Grade 6Domain: The Number System Focus: Distributive Property and Greatest Common Factor Lesson: #10Standard: 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.”

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: 1. Factor Pairs of 84: 1, 2, 3, 4, 6, 7, 12, 14Factor 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


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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

30 + 36 = 66Example: 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

Factor Pairs of 84:

Factor Pairs of 60:




2. 35 + 56

Factor Pairs of 35:

Factor Pairs of 56:





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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.”

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.”



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) = 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


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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:

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:


Remaining factors of the factor pairs:


Directions: Rewrite and solve using the Distributive Property.1. 12 + 72

Factor pairs of 12:

Factor pairs of 72:




2. 24 + 80 =

Factor pairs of 24:

Factor pairs of 80:





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Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Least Common Multiple Lesson: #12Standard: 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.”

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.”



Closure: “Today you found the least common multiple of two whole numbers.”

Answers: 1. 24 2. 20 3. 18 4. 30


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Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Distributive Property and Least Common Multiple Lesson: #12Standard: 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.

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


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Common Core Standards Plus® – Mathematics – Grade 6Domain: 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.

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) 24 2. (6.NS.4) 36 3. (6.NS.4) 5 4. (6.NS.4) 9 (3 + 7) 5. (6.NS.4) 6 (7 + 15)


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Common Core Standards Plus® – Mathematics – Grade 6Domain: 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?


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.


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Common Core Standards Plus® – Mathematics – Grade 6Domain: The Number System Focus: Dividing Fractions Lesson: #13Standard: 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.”

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÷ .5 2 You change the division sign to multiplication and invert

the divisor. You write 4 2 .5 1 You can’t simplify the numbers so multiply the numerators and

denominators and the product is 8 .5 This number is in simplest terms, but is still an improper

fraction.” Review the reminders before you release the students to work independently.



Closure: “Today you divided fractions using the rule of changing the division to multiplication and inverting the divisor.”

Answers: 1. 1514

2. 32


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Common Core Standards Plus® – Mathematics – Grade 6Domain: The Number System Focus: Dividing Fractions Lesson: #13Standard: 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:


the right of the sign.2 4 2 33 3 3 4

3. Multiply the numerators. 2 3 = 64. Multiply the denominators. 3 4 = 12

5. Re-write your answer in its simplified form, if needed. 6 1=12 2Why 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:

2343

2 4÷ = .3 3

Make the denominator equal to 1 by using the Multiplicative Inverse Property:

1 1

1 2

2 2 3 2 3 2 32 4 2 3 13 3 4 3 4 3 4

4 4 3 123 3 1 3 4 23 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


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Lesson Objective: Students will divide with fractions.

Introduction: “Today you will continue to divide with fractions. You will apply the rule we reviewed yesterday.”

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 6 35 ÷ .

7 14 You change the mixed number

to a fraction. 6 415 = .7 7 You change the division sign to multiplication and

invert the divisor. You write 41 14 .7 3 You can simplify before multiplying. The

simplification looks like this:1

417 14

282= .

3 3



Closure: “Today you divided fractions using the rule of changing the division to multiplication and inverting the divisor.”

Answers:1. 16

15

2. 1912

3. 559

4. 253


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Common Core Standards Plus® – Mathematics – Grade 6Domain: The Number System Focus: Dividing Fractions Lesson: #14Standard: 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:


the right of the sign.2 4 2 33 3 3 4

3. Multiply the numerators. 2 3 = 64. Multiply the denominators. 3 4 = 12

5. Re-write your answer in its simplified form, if needed. 6 1=12 2

Example: Find 6 35 ÷ =7 14

2

1

41 14 41 14 7 3 7 3

Directions: Divide. Keep quotients in fraction form. Simplify to lowest terms. Show your work.

1. 32 2÷ =75 5

2. 3 12 ÷ 1 =8 2

3. 11 3÷ =12 20

4. 5 3÷ =8 40


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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.


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.

11 15 11 4 22 7 1÷ = • = = 1 bags (Almost 1 )

2 4 2 15 15 15 2

2. 53 11 53 4 106 7

÷ = • = = 9 9 strips2 4 2 11 11 11

. 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.

3.9 3 9 2

÷ = • = 3 batches2 2 2 3


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Example: Solve.

Tony is making 14

pound turkey patties. He has 425

pounds of ground turkey. How many

whole turkey patties can Tony make?

Directions: Solve. Show all work. Label answer with units.

1. Kathy has 152

bags of fertilizer to cover an area of 334

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 324

foot strips of wire can be cut from a wire that is 1262

feet long?

3. Amanda has 142

cups of sugar to make cookies. The cookie recipe calls for 112

cup for

a single batch. How many batches can Amanda make?


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Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #16Standard: 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.”

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.

529 31 529 2 529 33÷ = • = 8 bags

4 2 4 31 62 62

1

2

2.3 9 3 50 25 1

÷ = • = = 4 times4 50 4 9 6 6

. (This answer is multiplicative not additive.

In other words, students are 14

6 times more likely to use the internet than

go to the library.)

3.15 5 15 6

÷ = • = 9 sections2 6 2 5


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Common Core Standards Plus® – Mathematics – Grade 6 Domain: The Number System Focus: Dividing Fractions Lesson: #16Standard: 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 23

cup of ice cream in bowls at her party. She has 1152

cups of

ice cream. How many servings can Janis make?

Directions: Solve. Show all work. Label answer with units.

1. John is filling sand bags. He has 11324

pounds of sand. Each bag must be filled with

1152

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

research project. 34

of the students said they use the Internet. 950

of the students

said they go to the library for books. How many more times do students use the Internet than go to the library?

3. Rick has a 172

-foot long wood plank. He is cutting it into 56

foot sections. How many

sections can he make?


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Common Core Standards Plus® – Mathematics – Grade 6Domain: 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.

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 12• =

2 7 7

2. (6.NS.1) 19 12 76• =3 7 7

3. (6.NS.1) 11 10 22• =5 87 87

4. (6.NS.1) 26 2 52 1• = =17 17 bottles3 1 3 3


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Common Core Standards Plus® – Mathematics – Grade 6Domain: 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

2. 1 76 ÷ =3 12

3. 1 72 ÷ 8 =5 10

4. A manufacturer has 283

ounces remaining of a beauty product in a container. The

manufacturer fills 12

ounce bottles with the product. How many 12

ounce bottles

can they fill?


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Common Core Standards Plus® – Mathematics – Grade 6Performance Task #1 – Domain: The Number System

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.

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 choco-late 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)

Teacher Lesson Plan


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- Student Repsone Page


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.

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.

Student Page 1 of 6


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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.

47÷ 23= 47%i%32

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: 4723

4 2÷ =7 3 . 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:

47

÷ 23

=4723

='47 i 3

223 i 3

2

=47'i'32

1=

24''7

'i' 3'2 1

= 67

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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 14 cups of sugar. She will divide the sugar evenly among 3 38 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: 649 ÷ 33


_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

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3. Rewrite the problem in vertical format and subtract: 89.014 – 97.993

Show how to solve the problem:


_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

4. Rewrite the problem in vertical format and add: 172.314 + 6.5827



_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

5. How do you know where to place the decimal point in a multiplication problem with

decimals?

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

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6. Rewrite the problem in vertical format and multiply: 4.18 × .92



_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

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?

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

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9. List the factors and determine the greatest common factor of 39 and 65.

10. List the multiples and determine the least common multiple of 4 and 9.

11. Use the distributive property to add 33 + 78.

Student Page 6 of 6



DOK Level

The

Num

ber S

ystem

(Num

ber S

ystem Stand



3

1‐2



5




6.NS.3

9

1‐2






15

1‐2






21

1‐2







33

1‐2



34




Common Core Standards Plus - Math Grade 6 Lesson Index

31www.standardsplus.org - 1.877.505.9152 © 2013 Learning Plus Associates


Domain Lesson Standard(s) Standard(s) Student Page

DOK Level

The Num

ber S

ystem

(Num

ber S

ystem Stand


21 Position Rational Numbers on a Line 6.NS.6c

39

1‐2

22 Position Rational Numbers on a Line 40

23 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.

41

24 Interpret Inequality Statements 42

E6 Evaluation – Position Rational Numbers and Interpret Inequalities 6.NS.6c, 6.NS.7a 43

25 Absolute Values

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.

45

1‐2

26 Absolute Values 46

27 Real World Statements of Order 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.

47

28 Identify and Write Reflections of Ordered Pairs

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.

48

E7 Evaluation – Absolute Values and Order 6.NS.6b, 6.NS.7b, 6.NS.7c, 6.NS.7d 49

29 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.

51

1‐2

30 Plotting Points 52



E8 Evaluation – Plotting Points 55

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) 57‐59 3

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)

60‐61 4

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.





DOK Level

Ratio

s and

Propo

rtiona

l Relationships

(Ratio and

Propo

rtiona

l Relationships Stand

ards: 6.RP

.1‐6.RP.3d

)

1 Concept of a Ratio 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

62

1‐2

2 Part‐to‐Part and Part‐to‐Total 63

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

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.

67

1‐2

6 Ratios in Tables and Graphs 68

7 Ratios in Tables and Graphs 69

8 Comparing Ratios in Tables 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.

73

1‐210 Unit Rates

6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed.

74

11 Comparing Ratios 75

12 Unit Rates 76

E3 Evaluation – Unit Rates 6.RP.2, 6.RP.3b 77

13 Solve Ratio Problems 6.RP.3: Use ratio and rate reasoning to solve real‐world and mathematical problems... 6.RP.3b

79

1‐2

14 Solve Ratio Problems 80

15 Solve Ratio Problems 6.RP.3

81

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) 85‐87 3

17 Find the Percent of a Number

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.

88

1‐2

18 Find the Percent of a Whole 89



E5 Evaluation – Find the Percent of aNumber/Whole 92

21 Percent of a Number

6.RP.3c

93

1‐2

22 Percent of a Number 94



E6 Evaluation – Percent of a Number 97





DOK Level

Ratio

s and

Propo

rtiona

l Re

latio

nships

(Stand

ards: 6.RP

.1‐6.RP.3d

)

25 Measurement Conversions

6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

99

1‐2

26 Measurement Conversions 100



E7 Evaluation – Measurement Conversions 103

P4 Performance Lesson #4 – Percent and Measurement Conversions (6.RP.3c, 6.RP.3d) 105‐108 3

Statistic

s and

Proba

bility

(Statis

tics a

nd Proba

bility Stan

dards: 6.SP.1‐6.SP

.5d)

1 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.

109

1‐2

2 Statistical Questions 110

3 Measures of Center 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)

111

4 Measures of Center 112

E1 Evaluation – Statistical Questions and Measures of Center 113

5 Range and Mean Absolute Deviation 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

115

1‐2

6 Range and Mean Absolute Deviation 116

7 Dot Plots, Mean, Median, & Range 6.SP.2, 6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

117

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 data distribution and the context in which the data were gathered.

118

E2 Evaluation – Mean Absolute Deviation and Dot Plots 119

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.

121

1‐2

10 Histograms 122

11 Histograms 6.SP.4 123

12 Frequency Tables and Histograms 6.SP.2, 6.SP.4

124‐125

E3 Evaluation – Histograms 126‐127

13 Box Plots, Median, Interquartile Range

6.SP.4, 6.SP.5b, 6.SP.5c, 6.SP.5d

129‐130

1‐2

14 Box Plots 131

15 Box Plots 132

16 Box Plots 133‐134

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)

137‐142 3

Common Core Standards Plus® – Language Arts – Grade 3

Strand Lesson Focus Standard(s) TE Page

St. Ed.Page

DOK Level

Read

ing L

iterature

(Reading

Lite

rature Stand

ards: RL.3.1, R

L.3.2, RL.3.3, RL.3.4, RL.3.5, RL.3.6, RL.3.7)

5 Parts of Stories

RL.3.5: Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections.

282 131

1‐2

6 Parts of Dramas 284 132

7 Parts of a Poem 286 133

8 Parts of a Poem 288 134

E2 Evaluation – Stories, Poems, and Dramas 290 135

9 Illustration and Mood

RL.3.7: Explain how specific aspects of a text’s illustration contribute to what is conveyed by the words in the story (e.g., create mood, emphasize aspects of a character or setting.)

292 137

1‐2

10 Illustration and Setting 294 138

11 Illustration and Character 296 139

12 Illustrations 298 140

E3 Evaluation – Illustrations 300 141

P5 Performance – Reading Literature: Character Study and Comic Strip (RL.3.1, RL.3.3, RL.3.5, RL.3.7)

302‐303 143‐146 3

13 Fables, Folktales, Myths, and Word Meanings RL.3.2: Recount stories, including fables, folktales, and myths from diverse cultures: determine the central message, lesson, or moral, and explain how it is conveyed through key details in the text. RL.3.4: Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.

308 147

1‐2

14 Fables, Folktales, and Myths 310 148



E4 Evaluation – Fables, Folktales, Myths, and Vocabulary 316 151

17 Point of View

RL.3.6: Distinguish their own point of view from that of the narrator or those of the characters.

318 153

1‐2

18 Point of View 320 154



E5 Evaluation – Point of View 326 157

P6 Performance – Reading Literature: Point of View Movie Poster (RL.3.2, RL.3.4, RL.3.6) 328‐329 159‐162 3

Integrated Project # 2: The Play’s the Thing (RL.3.1, RL.3.2, RL.3.3 RL.3.4, RL.3.5, RL.3.6, RL.3.10, L.3.1, L.3.2, L.3.3, L.3.3a, L.3.3b, L.3.4, L.3.4a, L.3.4b, L.3.4c, L.3.5, L.3.5a, L.3.5b, L.3.5c, L.3.6, SL.3.1, SL.3.1b, SL.3.1c, SL.3.4, SL.3.6, W.3.3, W.3.3a, W.3.3b, W.3.3c, W.3.4, W.3.5, W.3.6, W.3.10)

337‐342 163‐169 4

Prerequisite Common Core Standards Plus Strands: Knowledge of Language, Vocabulary Acquisition and Use, and Reading Literature

Product: Writing and performing an original play.

Overview: In this project, the students will choose one of the following tales to rewrite as a play: The Three Little Pigs, Jack and the Beanstalk, Goldilocks and the Three Bears, Town Mouse and Country Mouse, Little

Red Riding Hood, or The Tortoise and the Hare The students will work in groups to re‐write, stage, and present the tale as a play. If they choose a tale with just two characters, they will need to add more characters and/or a narrator to provide each group member with a role. The group size must match the number of roles in the play. Since this is a learning activity, all components will be completed in class.





DOK Level

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)

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.





DOK Level

Expression

s and

Equ

ations

(Expressions and

Equ

ations Stand

ards: 6.EE.1 – 6.EE.9)

1 Exponents 6.EE.1: Write and evaluate numerical expressions involving whole‐number exponents. 145

1‐2

2 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

3 Order of Operations 147

4 Order of Operations 148

E1 Evaluation – Order of Operations 149

5 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.

151

1‐26 Writing Algebraic Expressions 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.

152

7 Writing Algebraic Expressions 153

8 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.

154

E2 Evaluation – Math Terminology and Writing Algebraic Expressions

6.EE.2a, 6.EE.2b, 6.EE.6 155

9 Writing Algebraic Expressions 6.EE.2a, 6.EE.6 157

1‐2

10 Evaluate Expressions

6.EE.2c

158

11 Evaluate Expressions 159

12 Evaluate Expressions 160

E3 Evaluation – Write and Evaluate Algebraic Expressions 6.EE.2a, 6.EE.2c, 6.EE.6 161

13 Distributive Property 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.

163

1‐2

14 Distributive Property 164



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) 169‐172 3

17 Identifying Equivalent Expressions

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.

173

1‐218 Dependent and Independent Variables 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.

174

19 Dependent and Independent Variables 175

20 Dependent and Independent Variables 176

E5 Evaluation – Equivalent Expressions / Dependent & Independent Variables 6.EE.4, 6.EE.9 177





DOK Level

Expression

s and

Equ

ations

(Expressions and

Equ

ations Stand

ards: 6.EE.1 – 6.EE.9)

21 Writing Algebraic Equations

6.EE.9

179

1‐2

22 Writing Algebraic Equations 180



E6 Evaluation – Writing Algebraic Equations 183

25 Writing Algebraic Equations

6.EE.9

185‐186

1‐2

26 Writing Algebraic Equations 187‐188



E7 Evaluation – Writing Algebraic Equations 193

P7 Performance Lesson #7 – Writing Algebraic Equations (6.EE.4, 6.EE.9) 195‐197 3

29 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.

198

1‐2

30 Finding Values that Make Inequalities True 199

31 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.

200

32 Understanding Properties to Solve Equations 201

E8 Evaluation – Solving Algebraic Equations 6.EE.5, 6.EE.7 202

33 Understanding Properties to Solve Equations

6.EE.7

203

1‐2

34 Understanding Properties to SolveEquations 204

35 Solve Equations 205

36 Solve Equations 206

E9 Evaluation – Solving Algebraic Equations 207

37 Graph Inequalities

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.

209

1‐2

38 Translate Inequality Phrases 210

39 Translate Inequality Phrases 211

40 Write and Graph Inequalities from Real‐world Scenarios 212

E10 Evaluation – Working with Inequalities 213

P8 Performance Lesson – Equations and Inequalities (6.EE.5, 6.EE.7, 6.EE.8) 215‐218 3





DOK Level

Geom

etry

(Geo

metry Stand

ards: 6.G. 1‐6.G.4)

1 Areas of Special Quadrilaterals 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.

219

1‐2

2 Areas of Special Quadrilaterals 220 3 Areas of Triangles 221

4 Find Missing Dimensions Using Area Formulas 222

E1 Evaluation – Areas of Triangles and Quadrilaterals 223

5 Areas of Triangles and Quadrilaterals

6.G.1

225

1‐26 Areas of Rectangular Composite Figures 226

7 Solving Area Problems 227

8 Solving Area Problems 228

E2 Evaluation – Solving Area Problems 229

9 Nets 6.G.4: Represent three‐dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real‐world and mathematical problems.

231

1‐210 Surface Area of Prisms 232‐233

11 Surface Area of Pyramids 234 12 Surface Area in Real‐world Problems 235 E3 Evaluation – Surface Area and Nets 236

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 appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real‐world and mathematical problems.

237

1‐214 Volume 238 15 Volume 239 16 Volume 240 E4 Evaluation – Volume 241

P9 Performance Lesson #9 – Area, Surface Area, and Volume (6.G.1, 6.G.2, 6.G.4) 243‐245 3

17 Coordinate Geometry 6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real‐world and mathematical problems.

246

1‐218 Coordinate Geometry 247 19 Coordinate Geometry 248 20 Coordinate Geometry 249‐250

E5 Evaluation – Coordinate Geometry 251

P10 Performance Lesson #10 – Graphic Display (6.G.3) 253‐255 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)

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.



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to the California Standards by learninglist.com.

Standards Plus is a perfect fit for California Schools

Standards Plus has a proven record of closing achievement gaps in districts throughout California.

Standards Plus Materials Benefit English Learners:

• By explicitly targeting the standards

• Emphasizing academic vocabulary

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Using Standards Plus instruction

across grade levels ensures

all students are given equal

access to grade level,

standards-based instruction.

Over 190+ Schools in California implemented

Standards Plus in 2016 and exceeded the

State Test average in one or more grade levels.

OVER 83% of Schools that implemented Standards Plus

in 2015-2016 more than doubled the California SBAC

growth rate in one or more grade level.

www.standardsplus.org | 1•877•505•9152

Standards Plus Closes the Achievement Gapwith 7 Di�erent Programs in One

Standards Plus includes:

Standards Plus is Proven E�ective in California Schools

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Lessons in Print

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with Equity

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