LFS Unit 1: the Number System with Rational Numbers

Standards: Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers. MCC6.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? MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm

MCC6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

MCC6.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).

Transition Standard for 2012-2013: MCC5.NF.6 (DOK 2)– Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 6th Grade– CCGPS Math LFS Unit 1: The Number System with Rational Numbers

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 1 K-U-D Unit 1: Number System Fluency

UNDERSTAND… By the end of the unit, I want my students to understand… how to extend and fluently apply the concept of part(s) of a whole to manipulate numbers (fractions, decimals, multiples, factors, etc.) to solve real world problems.

Know Do Vocabulary: Evaluate; Quotient; Dividend;  Divide (NS.1) & multiply fractions. (NS.6) DOK1 Minuend; Subtrahend; Fraction; Multiple; Factor;  Fluently add, subtract, divide and multiply multi- Factorization; Prime Number; Composite digit decimals. (NS.3) DOK1 Number; Exponent; Exponential; Distribution  Fluently divide multi-digit numbers. (NS.2) Property; Decompose; Greatest Common Factor (GCF); Least Common Multiple (LCM); Relatively DOK1 Prime; Array; Model; Sum; Difference; Algorithm  Divide whole numbers and fractions with  Multiple strategies and models to solve various fractions. (NS.1) DOK1 problems with fractions and decimals. (NS1; NS3)  Interpret real world situations in expressions  The standard algorithm for addition, subtraction, and equations – by determining if multiplication or multiplication and division of multi-digit numbers division of whole and partial numbers is and decimals. (NS3; NS4) necessary. (NF.6) DOK2  The relationship between multiplication and  Model visually multiplication (NF.6) and division. (NS1; NS4) division of fractions to represent real world  Which operation(s) to apply to a word problem situations/word problems. (NS.1) DOK2 and/or real world situation. (NS1)  Find common multiples of two whole numbers  What dividing by a fraction means. (NS1) less than or equal to 12. (NS.4) DOK1 Ex: ( 3 ÷ is asking  Find common factors of two whole numbers "how many 2/5are in 3?) less than or equal to 100. (NS.4) DOK1  A number divided by a fraction has a higher  Find the greatest common factor (GCF) and quotient than the dividend. (NS1; NS2) least common multiple (LCM). (NS.4) DOK1  The relationship between the distribution property  Factor numbers with prime factorization and and factors and multiples. (NS4) write numbers in exponential form. (NS.4) DOK1  The relationship between multiples and factors.  Use the distributive property to express a sum (NS4) of two whole numbers 1 – 100 (with a common  The value of using properties of multiples and factor) as a multiple of a sum of two whole factors in real world situations/word problems. numbers (with no common factor). (NS.4) DOK1 (NS1) Ex: Whole numbers (36 & 8) have a common factor  Divisibility rules. (NS2) of 4. Whole numbers (9 & 2) have no common factor. Use the distributive property to express 36 + 8 as 4 (9 + 2).Notice: 36+8 = 44 & 4(9+2) =44.

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 2 SLM Unit 1: Number System Fluency Key Learning Extend and fluently apply the uses of the four basic operations (addition, subtraction, multiplication and division) to manipulate numbers (fractions, decimals, multiples, factors, etc.) to solve real world problems.

Unit EQ

How can I effectively use the properties of numbers to understand and solve real world problems?

Concept Concept Concept Fluent addition, subtraction, Identification and application of Division of whole numbers and of multiplication and division of multi- properties of numbers. fractions by fractions. digit decimals and whole numbers.

Lesson EQ’s Lesson EQ’s Lesson EQ’s 1. How does the answer of 1. What is the composition of 1. How can I visually model multiplying a whole number by numbers? division by fractions? a whole number compare with 2. What is the relationship 2. How does the quotient of the answer of multiplying a between factors and multiples? dividing a whole number by a whole number by a decimal? 3. How can I express the fraction differ from dividing a 2. How does the quotient of composition of a number? whole number by a whole dividing a decimal by a whole 4. How do I decompose numbers? number? Why? number compare with the How can I express the 3. When do I need to divide by quotient of dividing a decimal 5. decomposition of a number? fractions in everyday life? by a decimal? 4. How does the quotient from 3. What strategies can I use to 6. When would I use factors and multiples in everyday life? dividing by a fraction compare become fluent in adding, to the quotient from dividing by subtracting, multiplying and a decimal? dividing whole numbers and decimals? 4. How can the divisibility rules help me become fluent in adding, subtracting, multiplying and dividing whole numbers and decimals?

Vocabulary Vocabulary Vocabulary Quotient; Dividend; Fraction; Sum; Multiple; Factor; Factorization; Array; Model; Mixed Decimals; Difference Prime Number; Composite Number; Mixed Numbers; Improper Fraction; Exponent; Distribution Property; Numerator; Denominator Decompose; Greatest Common Factor (GCF); Least Common Multiple (LCM); Relatively Prime; Factor Tree

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 3 Domain: Cluster: Apply and extend previous understandings of multiplication and division to divide Number Systems fractions by fractions. MCC6.NS.1 What does this standard mean? 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) In this standard contexts and visual models can help students to understand quotients of fractions and begin and use a visual fraction model to show the to develop the relationship between multiplication and division. Model development can be facilitated by quotient; use the relationship between building from familiar scenarios with whole or friendly number dividends or divisors. Computing quotients of multiplication and division to explain that (2/3) ÷ fractions build upon and extends student understandings developed in Grade 5. (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, whole numbers by unit fractions. Students continue this understanding by using visual models and equations (a/b) ÷ (c/d) = ad/bc.) How much chocolate will to divide whole numbers by fractions and fractions by fractions to solve word problems. 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?

Examples and Explanations

Students understand that a division problem such as is asking, “how many are in 3?” One possible visual model 6.MP.1. Make sense of problems would begin with three whole and divide each into fifths. There are 7 groups of two-fifths in the three wholes. and persevere in solving them. However, one-fifth remains. Since one-fifth is half of a two-fifths group, there is a remainder of Therefore, , meaning there are groups of two-fifths. Students interpret the solution, explaining how division by fifths can result 6.MP.2. Reason abstractly and in an answer with halves. quantitatively.

6.MP.3. Construct viable arguments and critique the reasoning of others.

6.MP.4. Model with mathematics. Students also write contextual problems for fraction division problems. For example, the problem, can be illustrated with the following word problem: 6.MP.7. Look for and make use of structure. Susan has of an hour left to make cards. It takes her about of an hour to make each card. About how many cards can she make? 6.MP.8. Look for and express regularity in repeated reasoning. This problem can be modeled using a number line. 1. Start with a number line divided into thirds.

2. The problem wants to know how many sixths are in two-thirds. Divide each third in half to create sixths.

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 4 Each circled part represents . There are four sixths in two-thirds; therefore, Susan can make 4 cards.

Examples:  3 people sharepound of chocolate. How much of a pound of chocolate does each person get? Solution: Each person getslb of chocolate.

 Manny has yard of fabric to make book covers. Each book is made from yard of fabric. How many book covers can Manny make? Solution: Manny can make 4 book covers.

 Represent in a problem context and draw a model to show your solution. Context: You are making a recipe that calls for cup of yogurt. You have cup of yogurt from a snack pack. How much of the recipe can you make?

Explanation of Model: The first model showscup. The shaded squares in all three models show cup. The second model shows cup and also shows cups horizontally. The third model shows cup moved to fit in only the area shown by of the model. is the new referent unit (whole) . 3 out of the 4 squares in the portion are shaded. A cup is only of a cup portion, so you can only make ¾ of the recipe.

Suggested Instructional Strategy

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 5 Use this problem: How many servings of popcorn are in 4½ cups if each person receives 3/4 cup of popcorn The teacher provides 4½ cups of popcorn. Students use a 3/4 cup measuring cup to solve the problem. Record solutions as a group. 1. Think-Pair-Draw-Share: Put students in pairs. Have one solve the problem using a picture/diagram and the other solve using the algorithm. Then they get together and compare. 2. Think-Pair-Share: Students solve the problem on their own, then get together and discuss how their solutions are the same and how they are different. 3. Four Corners: Give students a problem and the quotient. Give each corner in your room a label and have students go to the corner they think would be the correct label for the quotient.

Skill Based Task Problem Task Use representations to show that 1/4 divided by ½ is ½ that 2/3 divided by  You have 5/8 pound of Skittles. You want to give your friends 2/5 is 5/3, that 2/3 divided by 3/4 is 8/9, and that 1½ divided by 6/4 is 1. 1/4 lb. each. How many friends can you give Skittles to? Explain your answer.  You have a 3/4-acre lot. You want to divide it into 3/8-acre lots. How many lots will you have? Draw a diagram to justify your solution.  You have a 3/4-acre lot. You want to divide it into 2 sections. How many acres in each section will you have? Draw a diagram to justify your solution.  How wide is a rectangular strip of land with length 3/4 mi. and area 1/2 square mi.? Models and Algorithms Instructional TEACHER CONTENT . Math Forum - Teacher Tutorial - http://mathforum.org/dr.math/faq/faq.divide.fractions.html Resources/Tools . Dividing Fractions - Teacher Tutorial - http://www.tpub.com/math1/5g.htm

STUDENT ACTIVITIES/LESSONS  NLVM - Fraction Number Line Bars- Interactive Applet - http://nlvm.usu.edu/en/nav/frames_asid_265_g_3_t_1.html? open=activities&from=category_g_3_t_1.html . Visual Fractions - “Divide Fractions” - Interactive Applets and Game - http://www.visualfractions.com/divide.htm . UEN - “Modeling Multiplication and Division of Fractions” Lesson - http://www.uen.org/Lessonplan/preview.cgi?LPid=23394

Mixed Numbers and Improper Fractions STUDENT ACTIVITIES/LESSONS . LearnAlberta - “Improper Fractions and Mixed Numbers” Video Lesson - http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell02.swf Lessons STUDENT ACTIVITIES/LESSONS . Illuminations “Feeding Frenzy” - Unit Rates; Multiply/Divide Fractions - http://illuminations.nctm.org/LessonDetail.aspx?id=L781 . UEN - “Sticky Note Math” Lesson - http://www.uen.org/Lessonplan/preview?LPid=15443 UEN - “Dividing Fractions” Lesson - http://www.uen.org/Lessonplan/preview?LPid=530 1

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 6 Baking Cookies: http://illustrativemathematics.org/illustrations/50 Drinking Juice, Variation 2: http://illustrativemathematics.org/illustrations/412 Drinking Juice, Variation 3: http://illustrativemathematics.org/illustrations/413 How many containers are in one cup/one container: http://illustrativemathematics.org/illustrations/408 Making Hot Cocoa, Variation 1: http://illustrativemathematics.org/illustrations/407 Making Hot Cocoa, Variation 2: http://illustrativemathematics.org/illustrations/411 Running to School, Variation 2: http://illustrativemathematics.org/illustrations/410 Traffic Jam: http://illustrativemathematics.org/illustrations/464 Video Game Credits: http://illustrativemathematics.org/illustrations/267

Literature Connections: The Doorbell Rang by Pat Hutchins Full House: An Invitation to Fractions by Dayle Ann Dodds.

CCGPS Internet Resources: https://ccgps.org/6.NS.html

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 7 Domain: Cluster: Number Systems Compute fluently with multi-digit numbers and find common factors and multiples. MCC6.NS.2 What does this standard mean?

Fluently divide multi-digit numbers using the Procedural fluency is defined by the Common Core as “skill in carrying out procedures flexibly, accurately, efficiently and appropriately.” In the elementary grades, students were introduced to division through concrete standard algorithm. models and various strategies to develop an understanding of this mathematical operation (limited to 4-digit numbers divided by 2-digit numbers). In 6th grade, students become fluent in the use of the standard division algorithm. This understanding is foundational for work with fractions and decimals in 7

Examples and Explanations Students are expected to fluently and accurately divide multi-digit whole numbers. Divisors can be any number of digits at this grade level. As students divide they should continue to use their understanding of place value to describe what they are doing. When using the standard algorithm, students’ language should reference place value. For example, when dividing 32 into 8456, as they write a 2 in the quotient they should say, “there are 200 thirty-twos in 8456 ” and could write 6400 beneath the 8456 rather than only writing 64.

There are 200 thirty twos in 8456.

200 times 32 is 6400. 8456 minus 6400 is 2056.

There are 60 thirty twos in 2056.

60 times 32 is 1920. 2056 minus 1920 is 136.

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 8 There are 4 thirty twos in 136. 4 times 32 is 128.

The remainder is 8. There is not a full thirty two in 8; there is only part of a thirty two in 8.

This can also be written as or. There is ¼ of a thirty two in 8. 8456 = 264 * 32 + 8

Suggested Instructional Strategy

1. Think Aloud: Do the problem with a partner while explaining and telling what you are thinking and doing. 2. Have students identify in a problem set when they would use mental math and when they would use the standard algorithm. 3. Connect students’ existing strategies for division with the standard algorithm. 4. As a starter activity, use division problems that can reasonably be solved by using mental math (e.g., 105/25), estimation (e.g., 150 ÷ 12, 227 ÷ 30), and reasoning (e.g., when I think of 105 divided by 25, I think of 4 sets of 25 with 5 left over, the 5 left over is 5/25 which is 1/5, so the answer is 4 1/5). Model for the students your thinking as you work through the problem. (Note: This strategy would not apply to complex division problems for which the algorithm is most appropriate [e.g., 4567 ÷ 192]). Skill Based Task Problem Task

248 divided by 18. I spent $504 on 28 tickets for a rock concert. How much did I spend on each ticket?

th Instructional Elementary & Middle School Mathematics (VanDeWalle, 7 Ed.) . TEACHER CONTENT o Division of Whole Numbers: p. 232-237 Resources/Tools . STUDENT ACTIVITIES o Division of Whole Numbers: p. 232-237 Figures 12.23-12.27 & problems in bold print Elementary & Middle School Mathematics (VanDeWalle, 6th Ed.) . TEACHER CONTENT o Division of Whole Numbers: p. 236-241 . STUDENT ACTIVITIES o Division of Whole Numbers: p. 236-241 Figures 13.24-13.28 & problems in bold print

Internet: Division of Whole Numbers TEACHER CONTENT

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 9 . LearnAlberta - “Division of Whole Numbers” - Video Tutorial – http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=9 STUDENT ACTIVITIES/LESSONS . BBC - Division Strategy Practice - http://www.bbc.co.uk/skillswise/numbers/wholenumbers/division/written/game.shtml . Division by a 2-Digit Number - Algorithm Applet - http://www.doubledivision.org/ http://nlvm.usu.edu/en/nav/frames_asid_197_g_2_t_1.html?open=activities&from=search.html?qt=division

Literature Connection: The Phantom Tollbooth by Norton Juster

CCGPS Internet Resources: https://ccgps.org/6.NS_41B6.html

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 10 Domain: Cluster: Number Systems Compute fluently with multi-digit numbers and find common factors and multiples. MCC6.NS.3 What does this standard mean? Fluently add, subtract, multiply, Procedural fluency is defined by the Common Core as “skill in carrying out procedures flexibly, accurately, efficiently and appropriately.” In 4th and 5th grades, students added and subtracted decimals. Multiplication and division of decimals was and divide multi-digit decimals th using the standard algorithm for introduced in 5 grade (decimals to the hundredth place). At the elementary level, these operations were based on concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition each operation. and subtraction. In 6th grade, students become fluent in the use of the standard algorithms of each of these operations. Examples and Explanations Mathematical Practice Standards The use of estimation strategies supports student understanding of operating on decimals. 6.MP.2. Reason abstractly and quantitatively. Example:  First, students estimate the sum and then find the exact sum of 14.4 and 8.75. An 6.MP.7. Look for and make use of structure. estimate of the sum might be 14 + 9 or 23. Students may also state if their estimate is 6.MP.8. Look for and express regularity in repeated low or high. They would expect their answer to be greater than 23. They can use their reasoning. estimates to self-correct.

Answers of 10.19 or 101.9 indicate that students are not considering the concept of place value when adding (adding tenths to tenths or hundredths to hundredths) whereas answers like 22.125 or 22.79 indicate that students are having difficulty understanding how the four-tenths and seventy-five hundredths fit together to make one whole and 25 hundredths.

Students use the understanding they developed in 5th grade related to the patterns involved when multiplying and dividing by powers of ten to develop fluency with operations with multi- digit decimals. Suggested Instructional Strategy Have students look at student work that contains a common misconception and look at errors and discuss how to correct the error.

Skill Based Task Problem Task Skill-based Task: The school had a bake sale and raised $75.55. If each cookie cost $0.05, how many cookies were sold? Explain how you got your answer. 1. 242.134 + 308.02 2. 38.9 – 14.334 3. 11.82 x 2.81 4. 341.8 ÷ 1.2

Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.) Instructional . TEACHER CONTENT o Computation with Decimals: p. 342-345 . STUDENT ACTIVITIES Resources/Tools o Computation with Decimals: p. 342-345 Activity 17.11-17.13 & problems in bold print Elementary & Middle School Mathematics (VanDeWalle, 6th Ed.) . TEACHER CONTENT

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 11 o Computation with Decimals: p. 346-350 . STUDENT ACTIVITIES o Computation with Decimals: p. 346-350 Activity 18.12-18.14 & problems in bold print Internet: Addition/Subtraction of Decimals STUDENT ACTIVITIES/LESSONS . NLVM - Base Block Decimals - http://nlvm.usu.edu/en/nav/frames_asid_264_g_3_t_1.html?from=category . NLVM - Circle 3 - Adding Decimals - Puzzle - http://nlvm.usu.edu/en/nav/frames_asid_187_g_3_t_1.html?open=instructions&from=category_g_3_t_1.html . LearnAlberta - “Solving Problems with Decimals” Video Lesson - http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell05.swf . LearnAlberta - “Addition and Subtraction of Decimals” Video Lesson - http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=7 . Math Play - Jeopardy - Computation Game - http://www.math-play.com/Decimals-Jeopardy/decimals-jeopardy.html

Multiplication/Division of Decimals TEACHER CONTENT . LearnAlberta - Multiplication and Division of Decimals - Video Tutorial - h ttp://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10

CCGPS Internet Resources: https://ccgps.org/6.NS_8KH5.html

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 12 Domain: Cluster: Number Systems Compute fluently with multi-digit numbers and find common factors and multiples. MCC6.NS.4 What does this standard mean? 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 Students will find the greatest common factor of two whole numbers less than or equal to 100. Students sum of two whole numbers 1–100 with a also understand that the greatest common factor of two prime numbers will be 1 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). Examples and Explanations Mathematical Practice Standards Students will find the greatest common factor of two whole numbers less than or equal to 100. 6.MP.7. Look for and make use of structure. For example, the greatest common factor of 40 and 16 can be found by 1) listing the factors of 40 (1, 2, 4, 5, 8, 10, 20, 40) and 16 (1, 2, 4, 8, 16), then taking the greatest common factor (8). Eight (8) is also the largest number such that the other factors are relatively prime (two numbers with no common factors other than one). For example, 8 would be multiplied by 5 to get 40; 8 would be multiplied by 2 to get 16. Since the 5 and 2 are relatively prime, then 8 is the greatest common factor. If students think 4 is the greatest, then show that 4 would be multiplied by 10 to get 40, while 16 would be 4 times 4. Since the 10 and 4 are not relatively prime (have 2 in common), the 4 cannot be the greatest common factor. 2) listing the prime factors of 40 (2 • 2 • 2 • 5) and 16 (2 • 2 • 2 • 2) and then multiplying the common factors (2 • 2 • 2 = 8). Students also understand that the greatest common factor of two prime numbers will be 1. Students use the greatest common factor and the distributive property to find the sum of two whole numbers. For example, 36 + 8 can be expressed as 4 (9 + 2) = 4 (11). Students find the least common multiple of two whole numbers less than or equal to twelve. For example, the least common multiple of 6 and 8 can be found by 1) listing the multiples of 6 (6, 12, 18, 24, 30, …) and 8 (8, 26, 24, 32, 40…), then taking the least in common from the list (24); or 2) using the prime factorization. Step 1: find the prime factors of 6 and 8. 6 = 2 • 3 8 = 2 • 2 • 2 Step 2: Find the common factors between 6 and 8. In this example, the common factor is 2 Step 3: Multiply the common factors and any extra factors: 2 • 2 • 2 • 3 or 24 (one of the 2s is in common; the other 2 and the 3 are the extra factors. Suggested Instructional Strategy Solve for LCM and/or GCF using factor towers, Venn diagrams, and factor trees. Use a model to show that 4(9 + 2) is four groups of 9 and four groups of 2. Skill Based Task Problem Task Hot dogs come in packs of 8. Buns come in packs of 12. How many packs of Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 13 Find the greatest common factor of 24 and 60. hot dogs and bags of buns would you have to buy to have an equal number of Find the least common multiple of 6 and 10. hot dogs and buns? Use the distributive property to show 15 + 75. You need to make gift bags for a party with the same number of balloons and candy in each bag. One package of candy has 24 pieces. One package of balloons has 20 balloons. You need to use all the candy and all the balloons. What is the greatest number of gift bags that you can make containing an equal number of items? Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.) . TEACHER CONTENT o Properties of Multiplication and Division: p. 160-161

Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.) . TEACHER CONTENT o Properties of Multiplication and Division: p. 157-158

Web: Greatest Common Factor and Least Common Multiple TEACHER CONTENT . Amby - Teacher Tutorial - http://amby.com/educate/math/

STUDENT ACTIVITIES/LESSONS . Illuminations - “The Venn Factor” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L859 . Illuminations - “Factor Findings” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L872 Instructional . Illuminations - “Factor Trail Game” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L719 . NLVM - Factor Tree - Interactive Applet - http://nlvm.usu.edu/en/nav/frames_asid_202_g_2_t_1.html?from Resources/Tools . LearnAlberta Spy Guys - “Factors, Multiples, and Prime Factorization” Video Lesson - http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell07.swf . IXL - GCF and LCM Word Problems - Assessment - http://www.ixl.com/math/grade-6/greatest-common-factor-word- problems . Greatest Common Factor Lesson http://www.math.com/school/subject1/lessons/S1U3L2GL.html This lesson is a resource for teachers or for students after participating in lessons exploring GCF.

Distributive Property STUDENT ACTIVITIES/LESSONS . Study Stack - Matching Game - http://www.studystack.com/matching-1870 . Illuminations - “Distributing and Factoring Using Area” Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L744

CCGPS Internet Resources: https://ccgps.org/6.NS_B3VJ.html

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 14 More Resources – Misconceptions – Take Note Resources: Lesson Websites: Visually model word problems with fractions - www.thinkingblocks.com *Great with the SmartBoard! Factors & Multiples: http://www.math.com/school/subject1/lessons/S1U3L1GL.html Greatest Common Factor: http://www.math.com/school/subject1/lessons/S1U3L2GL.html Factoring: http://www.purplemath.com/modules/factnumb.htm Divisibility Rules: http://mathforum.org/dr.math/faq/faq.divisibility.html Game Websites: Higher order fraction addition: http://fen.com/studentactivities/MathSplat/mathsplat.htm Factor & Multiple Jeopardy: http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and- Multiples-Jeopardy.html *Up to four teams – keeps score for you! Factors/Divisibility Rules: http://www.aaamath.com/g57f-findafactor.html Prime Factorization/Multiples/Factors Jeopardy: http://www.quia.com/cb/8436.html Least Common Multiple: http://www.aaamath.com/g57i-lcm.html Add/Subtract/Multiply/Divide Fractions: http://www.funbrain.com/fractop/index.html Literature: My Full Moon is Square by Elinor J. Pinczes The Doorbell Rang by Pat Hutchins Spaghetti and Meatballs for All by Marilyn Burns Dad’s Diet by Barbara Comer One Riddle, One Answer by Laura Thompson “Beasts of Burden” in the Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

Douglas County School System 6th Grade Math 4/8/2018 Number System Fluency Page 15 Misconceptions/Suggestions: Dividing a number by a fraction does not produce a smaller quotient than the dividend. Instead, dividing a number by a fraction produces a quotient larger than the dividend. Why? Dividing by a fraction is solving how many parts are in the whole. When dividing decimals, students tend to focus on the algorithm and not consider the actual values of the numbers. Start division of decimals with estimation.

Take Note: A strong focus is on fluency and on real world application this year! Please visit the corestandards.org Mathematics standards page 4 to read more about how we must shift the students’ way of thinking and their approach to mathematics. Addition, subtraction and multiplication of fractions and mixed numbers have been moved from this unit! Division by fraction is the primary focus. Students should already know, but you may have to review: Decimal place values to the 10thousandths place; The standard algorithm for addition, subtraction, multiplication and division; How to use estimation to predict and assess whether a solution is reasonable; How to add, subtract and multiply fractions and mixed numbers; A simplified fraction regardless of the value of the numerator and/or the denominator is always between 0 & 1. (Later this year, they will learn the value of a fraction is also between 0 & -1); Fractions are just a representation of division. Just as multiplication is repeated addition, division is repeated subtraction.

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