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UNIT 1: Number Sense

Total Number of Days: 16 days Grade/Course: 6th Grade

ESSENTIAL QUESTIONS ENDURING UNDERSTANDINGS

How is multiplying and dividing used in real life? What are exponents and how can they help me to learn further

concepts? How does the order of operations affect the value of an

expression? How are exponents, factors, and factor trees used to calculate

the prime factorization of a number? What are the different methods for calculating the GCF and

LCM of a set of numbers?

Operations create relationships between numbers. The order of operations affects the value of an expression. The prime factorization of a number is an equivalent expression to the original

number. The GCF and LCM of numbers are used to solve real world problems as well as in

fraction operations.

PACING CONTENT SKILLS STANDARDS (CCCS/MP)

RESOURCES LEARNING ACTIVITIES/ASSESSMENTS

Math in Focus

OTHER (e.g., tech)

3 days Pre-requisite from grade 5

*Fluently multiply multi-digit numbers *Fluently find whole number quotients of whole numbers of up to 4 digit dividends and 2 digit divisors

5.NBT.B.5 – Fluently multiply multi-digit whole numbers using the standard algorism. 5.NBT.B.6 – Find whole-number quotients of whole numbers of up to 4-digit dividends and 2-digit divisors, using strategies based on place value, the properties of operations, and/or the

Sample Problems: http://www.ixl.com/math/grade-6/multiply-whole-numbers-with-four-or-more-digits http://www.ixl.com/math/grade-6/multiply-whole-numbers-word-problems http://www.ixl.com/math/grade-6/divisibility-

*Multiplying Multi-Digit Number Quiz *Study Island *Number Sense Math Menu

http://www.ixl.com/math/grade-6/multiply-whole-numbers-with-four-or-more-digits








http://www.ixl.com/math/grade-6/multiply-whole-numbers-word-problems








http://www.ixl.com/math/grade-6/divisibility-rules




2

relationship between multiplication and division.

rules http://www.ixl.com/math/grade-6/divide-whole-numbers-2-digit-divisors Methods: *Standard Algorithm *Lattice Method *Parital Product *Grid Paper Multiplication

2 days

Division of multi-digit whole numbers

*Fluently multiply multi-digit whole numbers

6.NS.B.2 – Fluently divide multi-digit numbers using the standard algorithm

Math in Focus pg. 16 – 18 Basic- Reteach pg. 15 - 16 Core- Book A pg. 18 Advanced- Enrichment pg. 5

Sample Problems: http://www.ixl.com/math/grade-6 http://www.ixl.com/math/grade-6/divide-whole-numbers-3-digit-divisors

*http://www.quia.com/mathjourney.html (click on division of 4 digit divisors) *Dividing Multi-Digit Number Quiz *Study Island

4 days

Exponents and Order of Operations

*Write exponential expressions in expanded form as well as exponential form *Simplify numerical expressions with exponents using the order of operations

6.EE.A.3 – Apply the properties of operations to generate equivalent expressions. 6.EE.A.1 – Write and evaluate

Math in Focus pg. 19 – 28 Basic- Reteach pg. 17 - 27 Core- Book A pg. 27 - 28 Advanced- Enrichment

Videos: http://www.brainpop.com/math/numbersandoperations/exponents/preview.weml http://www.brainpop.com/math/number

*“A Grain of Rice” Story (read APPENDIX Teacher resource extensions #1 for activity) *Manipulatives- Students get a bag

of beans or something similar, have

the students model a problem using

beans(i.e. 2+4*5). Emphasize that if

they do not use the correct order of

http://www.ixl.com/math/grade-6/divide-whole-numbers-2-digit-divisors







http://www.ixl.com/math/grade-6










http://www.quia.com/mathjourney.html

http://www.quia.com/mathjourney.html

http://www.brainpop.com/math/numbersandoperations/exponents/preview.weml






http://www.brainpop.com/math/numbersandoperations/orderofoperations/



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numerical expressions involving whole number exponents.

pg. 2 - 4 sandoperations/orderofoperations/ http://www.teac

hertube.com/vie

wVideo.php?vid

eo_id=79967&ti

tle=PEMDAS_

Rap

Sample Problems: http://www.ixl.com/math/grade-6 *Manipulatives – unifix cubes to demonstrate exponential relationships

operations, they will not get the

correct answer *Order of Operations Treasure Hunt Project *Fill – In PEMDAS puzzle *Order of Operations Encrypted Puzzle *Order of Operations Practice Cards Pair Activity *http://shodor.com/interactivate/activities/OrderOfOperationsFou/?version=1.5.0_16&browser=safari *http://www.math-play.com/Order-

of-Operations-Millionaire/order-of-

operations-millionaire.html *http://www.mrnussbaum.com/orde

rops.htm

*http://www.aplusmath.com/cgi-

bin/Flashcards/Order_Of_Operation

s

*http://www.mathgoodies.com/lesso

ns/vol7/operations_exponents.html

*http://www.quia.com/cm/16544.ht

ml?AP_rand=564405241

*http://www.funbrain.com/cgi-

bin/alg.cgi?A1=s&A2=3

*http://www.shodor.org/interactivate

/activities/OrderOfOperationsFou/

*http://www.coolmath-

games.com/0-make24/index.html *Exponents and PEMDAS Quiz *Study Island

2 days

Prime Numbers and Prime Factorization

*Differentiate between prime and composite numbers based on its prime factorization and rules of divisibility *Express a whole number as a product of its prime factors using exponents

6.NS.B.4 - Find the greatest common factor of two whole numbers less than or equal to 100 and the least common

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 54-58

Brain Pop Video: http://www.brainpop.com/math/numbersandoperations/factoring/preview.weml

*Extra Practice pg. 5 – 6 *Factor Trees Graphic Organizer http://www.softschools.com/math/factors/factor_tree/ http://www.mathplayground.com/factortrees.html http://www.mathgoodies.com/factors/prime_factors.html

http://www.teachertube.com/viewVideo.php?video_id=79967&title=PEMDAS_Rap









http://shodor.com/interactivate/activities/OrderOfOperationsFou/?version=1.5.0_16&browser=safari




http://www.math-play.com/Order-of-Operations-Millionaire/order-of-operations-millionaire.html



http://www.mrnussbaum.com/orderops.htm

http://www.mrnussbaum.com/orderops.htm

http://www.aplusmath.com/cgi-bin/Flashcards/Order_Of_Operations



http://www.mathgoodies.com/lessons/vol7/operations_exponents.html

http://www.mathgoodies.com/lessons/vol7/operations_exponents.html

http://www.quia.com/cm/16544.html?AP_rand=564405241

http://www.quia.com/cm/16544.html?AP_rand=564405241

http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=3

http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=3

http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/

http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/

http://www.coolmath-games.com/0-make24/index.html

http://www.coolmath-games.com/0-make24/index.html

http://www.brainpop.com/math/numbersandoperations/factoring/preview.weml






http://www.softschools.com/math/factors/factor_tree/

http://www.softschools.com/math/factors/factor_tree/

http://www.mathplayground.com/factortrees.html

http://www.mathplayground.com/factortrees.html

http://www.mathgoodies.com/factors/prime_factors.html

http://www.mathgoodies.com/factors/prime_factors.html

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multiple of two whole numbers less than or equal to 12.

Basic: Reteach-6A: pp.41-42 ELL: TE-4A: pp. Advanced: Enrichment-6A: pp. 10

Sample Problems: http://www.ixl.com/math/grade-6/prime-or-composite http://www.ixl.com/math/grade-6/prime-factorization http://www.ixl.com/math/grade-6/prime-factorization-with-exponents Illuminations Resource: http://illuminations.nctm.org/ActivityDetail.aspx?ID=64 * Manipulatives – unifix cubes to demonstrate prime factorization of numbers

*Math Boxes introduced for Unit 1 http://www.quia.com/rr/323715.html *Prime Factorization Quiz *Study Island

3 days

Factors and Multiples *Find the common factors and the greatest common factors of two whole numbers *Find the common multiples and the least common multiple of two whole numbers

6.NS.B.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

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 58-61 Basic: Reteach-6A:

Sample Problems: http://www.ixl.com/math/grade-6/identify-factors http://www.ixl.com/math/grade-

*http://illuminations.nctm.org/ActivityDetail.aspx?ID=12 *http://illuminations.nctm.org/ActivityDetail.aspx?ID=29 *Factor Captor Pair Game *Multiples “Down by the Banks” Hand Game *Extra Practice pg. 7 – 8 *Unit 1 Museum Walk *Math Games:

http://www.ixl.com/math/grade-6/prime-or-composite




http://www.ixl.com/math/grade-6/prime-factorization




http://www.ixl.com/math/grade-6/prime-factorization-with-exponents






http://illuminations.nctm.org/ActivityDetail.aspx?ID=64




http://www.quia.com/rr/323715.html

http://www.quia.com/rr/323715.html

http://www.ixl.com/math/grade-6/identify-factors





http://www.ixl.com/math/grade-6/greatest-common-factor







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less than or equal to 12.

pp.43-44 ELL: TE-4A: pp. Advanced: Enrichment-6A: pp. 11

6/greatest-common-factor http://www.ixl.com/math/grade-6/least-common-multiple http://www.ixl.com/math/grade-6/greatest-common-factor-word-problems

http://media.emgames.com/emgames/demosite/playdemo.html?activity=M2A070&activitytype=dcr

http://hotmath.com/hotmath_help/games/factortris/factortris_hotmath_sound.swf

http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples-Jeopardy.html

http://www.jamit.com.au/htmlFolder/app1004.html

http://www.toonuniversity.com/flash.asp?err=499&engine=14

http://www.theproblemsite.com/games/sidebyside.asp

http://illuminations.nctm.org/activitydetail.aspx?id=12

*GCF Quiz *LCM Quiz *Study Island

Square and Square Roots Cubes and Cube Roots

*Find the square root of a number *Find the square root of a perfect square *Find the cube root of a number *Find the cube root of a perfect cube *Evaluate numerical expressions involving whole number exponents

NOT ALIGNED WITH THE NJCCCS

Math in Focus pg. 29 - 38 Basic- Reteach pg. 17 - 27 Core- Book A pg. 32 and 37 - 38 Advanced- Enrichment pg. 6

*Extra Practice pg. 9 - 12

http://www.ixl.com/math/grade-6/least-common-multiple





http://www.ixl.com/math/grade-6/greatest-common-factor-word-problems



























6

2 days Chapter Wrap Up Assessment

1. Reinforce, consolidate, and extend chapter skills and concepts

CCSS: 5.NBT.B.5 5.NBT.B.6 6.NS.B.2 6.NS.B.4 6.EE.A.3 6.EE.A.1


*Whole Class Jeopardy

Volcabulary Review: TE pp. 39 Chapter Wrap Up: pp. 39 Chapter Review: pp. 40-41 Chapter Test: Number Sense *Study Island

INSTRUCTIONAL FOCUS OF UNIT

A single number can be represented in many ways. Every integer greater than 1 can be expressed as a product of prime factors in only one way, regardless of how you start to factor the number. The greatest common factor is the product of the common prime factors and can be found using the tree diagram, listing the factors, or the upside down

cake method. The order of operations is a set of rules for evaluating expressions to ensure that the solution is always the same.

PARCC FRAMEWORK/ASSESSMENT Karen has a red ribbon that is 18 feet long and a blue ribbon that is

12 feet long. She wants to cut both ribbons into pieces that are all the same length, and she wants to have no ribbon left over when she is done. What is the greatest length, in feet, of each piece of ribbon that she can cut?

a. 3 b. 6 c. 36 d. 72 Find the greatest common factor of 14 and 42. Show your work. Bridget’s Bakery sells cupcakes in packages of 6. Perry’s Pastries sells cupcakes in packages of 10. Sheldon wants to buy the same number of cupcakes from each

bakery for a party, and he can only buy cupcakes in packages. Which of the following could be the number of cupcakes he buys from each bakery? a. 2 b. 16 c. 20 d. 30 Write a pair of whole numbers that satisfy the following conditions.

Both numbers are less than 13.

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The least common multiple of the numbers is 36. http://www.state.nj.us/education/modelcurriculum/math/6u2.shtml (please see appendix)

21ST CENTURY SKILLS (4Cs & CTE Standards)

9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.2.8.C.4: Calculate the cost of borrowing various amounts of money using different types of credit 9.4.12.A.4: Select and emply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.

MODIFICATIONS/ACCOMMODATIONS

Grid paper for multiplication and long division Math drills given by math coach Factor tree graphic organizer for prime factorization Additional Support (ELL , Struggling Learners): TE pp.2F Advanced Learners: TE pp.2F

APPENDIX (Teacher resource extensions)

1) Activity: Have students break into pairs, and give each pair a set of two dice. One player should roll the dice, and that player gets to choose which of these two numbers to add to or subtract from her score--whether "A^B" or "B^A." For example, if she rolls a "2" and a "5," she gets to choose whether to use "2^5" or "5^2." The other player is forced to add or subtract the other value to his score. On the next turn, they switch roles and continue accordingly. The goal of the game is to have the score closest to zero by the end of the sixth round.

2) http://www.quia.com/cb/8436.html ,

http://www.state.nj.us/education/modelcurriculum/math/6u2.shtml Model Curriculum Assessment Unit 2 #5-8MP.7- Look for and make use of structure TE = Teacher’s Edition http://www.state.nj.us/education/modelcurriculum/math/6u1.shtml Model Curriculum Assessment Unit 1 #16-17 http://www.state.nj.us/education/modelcurriculum/math/6u4.shtml Model Curriculum Assessment Unit 4 #1-8, 14-16,

http://www.state.nj.us/education/modelcurriculum/math/6u2.shtml

http://www.ehow.com/list_5895141_middle-school-exponent-activities.html

http://www.quia.com/cb/8436.html




8

Chapter 2: Negative Numbers and the Number Line

Total Number of Days:8 Grade/Course: 6


How can positive and negative numbers be used to describe opposites?

How can we find and position rational numbers on a number line?

How can we order negative numbers and the absolute value of negative numbers?

Negative numbers can be represented by quantities in the real world. The distance of a number is called the absolute value and it can only be positive. Read, compare, and order negative numbers according to their quantities



Math in Focus

OTHER (e.g., tech)

1 day Recall Prior Knowledge:

Negative Numbers and the Number Line

1. Infer that negative numbers are the opposites of positive numbers 2. Recognize that for every positive number, there is a corresponding negative number

CCSS: 6.NS.7a 6.NS.7b Foundational for: 6.NS.6 6.NS.6a MP: MP.4 MP.7

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 42-44 Basic: Reteach-6A: pp.33-37 Advanced: Enrichment-6A: pp. 7-8

*Math Menu Activity *Integer Balloon Project *Integer Timeline Project

Chapter Opener:TE pp.42 -Do you know what an ice berg is? -Where can you find icebergs? -Can anyone guess what is the temperature of an iceberg? Quick Check: Draw a horizontal number line to represent each set of numbers: 1) Odd numbers from 20 to 30 2) Mixed numbers from 3 to 5, with an interval of 1/6 between each pair of mixed numbers 3) Decimals between 8.0 And 10.0, with an interval of 0.25 between each pair of decimals ExtraP-6A: pp.14-15 Pre-Test: Chapter 2 Test Prep

Assessment Bk. pp. 10 *Study Island

9

2 days

Rational Numbers on the Number Line

*Represent whole numbers, fractions, and decimals on a number line *Interpret and write statements of inequalities for two given positive numbers using symbols > and <.

6.NS.C.6c – Find and position rational numbers on a horizontal or vertical number line diagram 6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Math in Focus pg. 2-15 Basic- Reteach pg. 1 - 14 Core- Book A pg. 14 - 15 Advanced- Enrichment pg. 1

Practice Questions: http://www.ixl.com/math/grade-6/compare-rational-numbers http://www.ixl.com/math/grade-6/put-rational-numbers-in-order http://www.ixl.com/math/grade-6/decimal-number-lines

*Human Number Line (manipulatives) *Estimating Dumbbell Activity on Communicators *Extra Practice pg. 1 – 4 *Number Line Quiz *Study Island

2 days 2.1 Negative Numbers

1. Create a signed integer to represent real world quantities 2. Represent, compare, and order positive and negative numbers on a number line

CCSS: 6.NS.6 6.NS.6a 6.NS.7a 6.NS.7b MP: MP.4 MP.7

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 45-53 Basic: Reteach-6A: pp.38-40 ELL: TE-4A: pp. 48 Advanced: Enrichment-6A: pp. 9

*Human number line created on the ground with tape *Horizontal and Vertical number lines in communicators

5-minute Warm Up: pp. 45 Model: remind students that

negative numbers can also be represented on a number line. Use human number line.

Guided Practice: pp. 48-51 Hands-On Activity pp.50:

Represent negative number on a number line and compare two negative numbers using > and <.

Problem of the Lesson: pp. 46 #5-9

Day 1: pp. 52 #1-18 Day 2: pp. 52 #19-42 ExtraP-6A: pp.16

Exit Ticket: List two numbers that are greater than -10 and two

http://www.ixl.com/math/grade-6/compare-rational-numbers






http://www.ixl.com/math/grade-6/put-rational-numbers-in-order






http://www.ixl.com/math/grade-6/decimal-number-lines





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numbers that are less than -10. Then list the numbers (including -10) in order from least to greatest and explain how you can use a number line to help you compare the numbers. *Comparing and Ordering Integers Quiz *Study Island

1 day 2.2 Absolute Value

1. Demonstrate the absolute value of a number is its distance from 0 on the number line 2. Interpret absolute value as magnitude for a positive or negative quantity in a real world situation

CCSS: 6.NS.7c 6.NS.7d MP: MP.2 MP.4

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 54-58 Basic: Reteach-6A: pp.41-42 ELL: TE-4A: pp. Advanced: Enrichment-6A: pp. 10

*Horizontal and vertical number lines in communicators

5-minute Warm Up: pp. 54 Model: Use human number

line to demonstrate distance from zero and absolute value.

Guided Practice: pp. 55-56 Brain at Work: pp.58 #1-2 Problem of the Lesson: pp. 56

#14 Day 1: pp. 57-58 #1-15 ExtraP-6A: pp.17 Exit Ticket: Explain the difference between the absolute value of a number and the opposite of a number. *Absolute Value Quiz *Study Island

2 days Chapter Wrap Up Assessment

1. Describe quantities in the real world using negative numbers 2. Compare and order negative numbers, absolute values, and opposites of numbers 3. Reinforce, consolidate, and

CCSS: 6.NS.6 6.NS.6a 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 58-61 Basic: Reteach-6A:

*Whole Class Jeopardy

Volcabulary Review: TE pp. 59 ExtraP-6A: pp.18-19 Chapter Wrap Up: pp. 59 Chapter Review: pp. 60-61 Chapter Test: Negative Number and the Number Line

11

extend chapter skills and concepts

pp.43-44 ELL: TE-4A: pp. Advanced: Enrichment-6A: pp. 11

*Study Island


A number line can help students to compare positive whole numbers and that on a horizontal number line, numbers increase in value from left to right, whereas on a vertical number line, numbers increase from the bottom to the top.

The distance between any two whole numbers on a number line can be divided into fractional parts to represent and compare decimals and fractions. Students explore negative numbers and representing them on a number line. Each number on the number line has an opposite, the number that is the same distance away from 0. Number lines can help students to compare and order negative and positive numbers by visualizing the relationship among the number’s position. Negative numbers are used to record temperatures, elevations, money owed, and many other quantities. The absolute value of a number is its distance from 0 on a number line. Absolute value bars are used to show absolute value. Absolute values can be used

to interpret real world situations involving positive and negative numbers.

PARCC FRAMEWORK/ASSESSMENT

Example 1:

a.Use an integer to represent 25 feet below sea level

b.Use an integer to represent 25 feet above sea level.

c.What would 0 (zero) represent in the scenario above?

Example 2:

Using the number line, what is the opposite of 2 ½? Explain your answer.

Example 3:

Write a statement to compare – 4 ½ and –2. Explain your answer.

Example 4:

One of the thermometers shows -3°C and the other shows -7°C. Which thermometer shows which temperature? Which is the colder temperature? How much colder? Write an inequality to show the relationship between the temperatures and explain how the model shows this relationship.

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Example 4: The Great Barrier Reef is the world’s largest reef system and is located off the coast of Australia. It reaches from the surface of the ocean to a depth of 150 meters. http://www.state.nj.us/education/modelcurriculum/math/6u1.shtml (please see appendix) http://www.state.nj.us/education/modelcurriculum/math/6u4.shtml (please see appendix)


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.2.8.C.4: Calculate the cost of borrowing various amounts of money using different types of credit 9.4.12.A.4: Select and emply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


Communicators or Whiteboards Responders Integer counter manipulatives Human number line, integer number line on communicators (vertical and horizontal) Additional Support (ELL , Struggling Learners): TE pp.42D Advanced Learners: TE pp.42D



13


6.NS.6- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.6a- Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. 6.NS.7a- Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. 6.NS.7b- Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC. 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. MP = Mathematical Practices MP.2- Reason abstractly and quantiatively MP.4- Model with mathematics MP.7- Look for and make use of structure TE = Teacher’s Edition http://www.state.nj.us/education/modelcurriculum/math/6u1.shtml Model Curriculum Assessment Unit 1 #16-17 http://www.state.nj.us/education/modelcurriculum/math/6u4.shtml Model Curriculum Assessment Unit 4 #1-8, 14-16,

Chapter 3 (Part 1): Fractions and Decimals



How do we perform operations on fractions and decimals? How is multiplying fractions related to the division of fractions? How can we use knowledge of place value to add and subtract

decimals? How do we use the standard algorithm to multiply and divide

decimals?

Fractions and decimals can be used to represent real world situations and problems

Fractions and decimals can be equal to each other and are interchangeable Operations with decimals are related to the operations of whole numbers and the

standard algorithm can be used to solve operations with decimals


RESOURCES LEARNING ACTIVITIES/ASSESSMENT

S Math in Focus

OTHER (e.g., tech)



14

4 days Recall Prior Knowledge:

Review of Fractions (adding, subtracting,

and multiplying) Converting mixed

numbers to improper fractions and vice

versa.

1. Create connections between whole number concepts to fractions and decimals when more precise calculations are needed 2. Apply calculations of addition, subtraction, and multiplication of fractions appropriately in real world applications

CCSS: 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.6 5.NF.7 MP: MP.6 MP.7

TE-5A: pp.

*Math Menu Activity *Fraction and Decimals Recipe Project

Pre-Test: Chapter 3 Test Prep Assessment Bk. pp. 17

*Adding and Subtracting Fractions Quiz *Multiplying Fractions Quiz *Study Island

3 days 3.1: Dividing Fractions

1. Calculate the division of a fraction, whole number, or mixed number by a fraction or a mixed number

CCSS: 6.NS.1 MP: MP.3 MP.4

TE-6A: pp. 42-61 Core: Student Book 6A: pp. 76-77 Basic: Reteach-6A: pp.45-54 ELL: TE-6A: pp. 66 Advanced: Enrichment-6A: pp. 12-14 #1,3,5,6

*Fraction Bars/strips *Bar model drawing

5-minute Warm Up: pp. 65 Model: Dividing a whole

number by a fraction using fraction bars or circles (day 1)

Guided Practice: pp. 66-69 (day 1)

Hands-On Activity pp.67: Dividing whole numbers by a fraction (day 1)

Problem of the Lesson: pp. 68 part b (day 1)

Guided Practice: pp. 71 (day 2)

Hands-On Activity pp.70: Dividing Fractions (day 2)

Guided Practice: pp. 73-75 (day 3)

Hands-On Activity pp.72 or pp. 75 : Dividing Fractions with a remainder/Division involving whole numbers and fractions (day 3)

Day 1: pp. 76-77 #1,2,5,9,10,27

Day 2: pp. 76-77 #3,4,6,11,12,28

Day 3: pp. 76-77 #7,8,13,26,29-31

15

ExtraP-6A: pp.21-23

Exit Ticket: In your own words, explain how to use multiplication to divide any number by a fraction. *Dividing Fractions Quiz *Study Island

1 day Recall Prior Knowledge: Adding and

Subtracting Decimals

1. Calculate the addition and subtraction of a decimal by a decimal or a decimal by a whole number

CCSS: 6.NS.3 MP:

TE-5A: pp. Core: Student Book 5A: pp. Basic: Reteach-5A: pp. ELL: TE-5A: pp. Advanced: Enrichment-5A: pp.

*Decimal Checkbook Project *Math Boxes Activity

*Adding and Subtracting Decimals Quiz *Study Island

1 day 3.2: Multiplying Decimals

1. Compute the multiplication of a decimal by a decimal

CCSS: 6.NS.3 MP: MP.2 MP.3 MP.4

TE-6A: pp. 78-86 Core: Student Book 6A: pp. 86 Basic: Reteach-6A: pp.55-61

*Grid Paper graphic organizer

5-minute Warm Up: pp. 78 Model: Use a number line to

show 3 x 0.4 using the concept of repeated addition

Guided Practice: pp. 80-84 Hands-On Activity pp.85:

Finding the factors of a decimal

Problem of the Lesson: pp. 79 Day 1: pp. 86 #1-28 Day 2: pp. 86 #29-38

16

Advanced: Enrichment-6A: pp. 12-16 #2,4,9

ExtraP-6A: pp.24-25

Exit Ticket: In your own

words, explain how multiplication of whole numbers compares to multiplication with decimals

*Multiplying Decimals Quiz *Study Island

2 days

3.3 Dividing Decimals 1. Compute the division a whole number or a decimal by a decimal

CCSS: 6.NS.2 6.NS.3 MP: MP.4 MP.8

TE-6A: pp. 87-93 Core: Student Book 6A: pp. 93 Basic: Reteach-6A: pp.62-68 ELL: TE-6A: pp. 89 Advanced: Enrichment-6A: pp. 16#8,10

*Bar model 5-minute Warm Up: pp. 87 Model: Draw one bar model

of 1 mile divided into five equal parts of 0.2 mile. Lead students to see that there are five 0.2s in 1 whole.

Guided Practice: pp. 87-92 Problem of the Lesson: pp. 87 Day 1: pp. 93 #1-22 Day 2: pp. 93 #23-40 ExtraP-6A: pp.24-25

Exit Ticket: Briefly describe two methods for dividing decimals. *Dividing Decimals Quiz *Study Island

2 days

Cumulative Review and Assessment

CCSS: 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.6 5.NF.7 6.NS.1 6.NS.2 6.NS.3

*Fraction and Decimal Unit Post-Test *Review Stations

17


In order to add and subtract fractions, you must calculate the least common denominator, which requires you to find the least common multiple of the denominators. Simplifying fractions requires you to find the greatest common factor of the numerator and the denominator.

Dividing a whole number by a fraction can be easily modeled using the bar model. Adding and subtracting decimals requires you to line up the place values to ensure the correct answer. Students apply multiplication and division skills to real world problems involving fractions and decimals.

PARCC FRAMEWORK/ASSESSMENT Examples:

3 people share2

1pound of chocolate. How much of a pound of chocolate does each person get?

Solution: Each person gets6

1lb. of chocolate.

Manny has 2

1 yard of fabric to make book covers. Each book is made from

8

1 yard of fabric. How many book covers can Manny make? Solution: Manny can

make 4 book covers.

http://www.state.nj.us/education/modelcurriculum/math/6u1.shtml (please see appendix)


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.2.8.B.1: Construct a simple personal savings and spending plan based on various sources of income 9.2.8.B.9: Create debit and credit balance sheets and income and cash statements


18

9.2.8.C.3: Demonstrate an understanding of the terminology associated with difference types of credit 9.2.8.E.1: Prioritize personal wants and needs when making purchases 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


Communicators or Whiteboards Responders Fraction Circles or Bars Bar Model Fractions Additional Support (ELL , Struggling Learners): TE pp.62D Advanced Learners: TE pp.62D


5.NF.1- Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. 5.NF.3- Interpret a fractions as a division of the numerator by the denominator. Solve word problems involving the division of whole numbers leading to answers in the form of fractions or mixed numbers. 5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.6- Solve real world problems involving multiplication of fractions and mixed numbers. 5.NF.7- Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 6.NS.1- Interpret and comput quotients of fractions, and solve word problems involving the division of fractions by fractions. 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 MP- Mathematical Practices MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u1.shtml Model Curriculum Assessment Unit 1 #1-11 on fractions #12-15 on decimals

Chapter 3 (part b): Converting Fractions and Decimals



19


How can I convert fractions into decimals and decimals into fractions?

Why do we need to convert fractions and decimals? How can I use a number line to compare fractions and

decimals?

Numbers can be represented in different ways and still equal each other. Fractions and decimals are interchangeable and can be converted back and forth.



Math in Focus

OTHER (e.g., tech)

1 days Recall Prior Knowledge:

Comparing rational numbers on a number

line

1. Comparing rational numbers using a vertical or horizontal number line

CCSS: 6.NS.6.a MP: MP.4 MP.8

*Smart Shopping- students must convert fractions and decimals to calculate the discount. For example, if a store says 1/3 off the original price, they must convert 1/3 to a decimal before multiplying to find the discount.

*Study Island *Converting fractions and decimals quiz *Communicator boards

1 day Converting Decimals to Simplified or Equivalent Fractions

1. Converting decimals to fractions using knowledge of place value

CCSS: 5.NF.3 Foundational for: 6.RP.3c MP: MP.4 MP.8

*Smart Shopping- students must convert fractions and decimals to calculate the discount. For example, if a store says 1/3 off the original price, they must convert 1/3 to a decimal before multiplying to

20

find the discount.

1 days Converting Fractions to Decimals using division

1. Converting fractions to decimals using knowledge of decimal division

CCSS: 6.NS.2 6.NS.3 Foundational for: 6.RP.3c MP: MP.4 MP.8

*Converting fractions and decimals jeopardy

*Converting fractions and decimals test


You can use place value concepts to convert a decimal into a fraction. Division of the numerator and denominator can convert a fraction into a decimal.

PARCC FRAMEWORK/ASSESSMENT Example:

A baseball player’s batting average is 0.625. What does the batting average mean? Explain the batting average in terms of a fraction, ratio, and percent.

Solution:

o The player hit the ball 8

5 of the time he was at bat;

o The player hit the ball 62.5% of the time; or

o The player has a ratio of 5 hits to 8 batting attempts (5:8).


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


21

Communicators or Whiteboards Responders Fraction, Decimal, Percent Flip Chart Organizer Bar Models


5.NF.3- Interpret a fractions as a division of the numerator by the denominator. Solve word problems involving the division of whole numbers leading to answers in the form of fractions or mixed numbers. 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.6.c- Find and position integers and other rational numbers on a horizontal or vertical number line diagram. 6.RP.3c- Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent MP- Mathematical Practices MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition

Benchmark 1: Cumulative Review of Chapters 1-3

Total Number of Days: 4 Grade/Course: 6


How can I demonstrate my knowledge of math content from chapters 1 through 3?

How can I communicate my knowledge of math to others, both orally and in written form?

All of the chapters are interconnected and math builds upon itself.



Math in Focus

OTHER (e.g., tech)

22

2 days Cumulative Review: Chapters 1-3

1. Demonstrate knowledge of learned math content from units 1-3 2. Communicate knowledge of learned math content from units 1-3 verbally and written

CCSS: 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.6 5.NF.7 5.NBT.B.5 5.NBT.B.6 5.NF.3 6.NS.1 6.NS.2 6.NS.3 6.NS.4b 6.NS.6 6.NS.6a 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d 6.EE.A.3 6.EE.A.1

MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8

TE-6A: pp. 111-113

2 days

Assessment: Benchmark 1: Chapters 1-3


CCCS: 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.6 5.NF.7 5.NBT.B.5 5.NBT.B.6 5.NF.3 6.NS.1

Assessment Book 6: pp. 24-33

Formal Benchmark Given Online (Study Island Assessment with multiple choice and open-ended questions)

23

6.NS.2 6.NS.3 6.NS.4b 6.NS.6 6.NS.6a 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d 6.EE.A.3 6.EE.A.1

MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8


All of the content we learn in math is connected and math builds upon itself. Math is used in many different ways in real life.


Study Island Created Assessment- questions chosen from study island question bank




24

Modified Test Extended time provided Chunking the units


6.NS.6- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.6a- Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. 6.NS.7a- Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. 6.NS.7b- Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC. 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. 5.NF.1- Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. 5.NF.3- Interpret a fractions as a division of the numerator by the denominator. Solve word problems involving the division of whole numbers leading to answers in the form of fractions or mixed numbers. 5.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.6- Solve real world problems involving multiplication of fractions and mixed numbers. 5.NF.7- Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 6.NS.1- Interpret and comput quotients of fractions, and solve word problems involving the division of fractions by fractions. 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

5.NF.3- Interpret a fractions as a division of the numerator by the denominator. Solve word problems involving the division of whole numbers leading to answers in the form of fractions or mixed numbers. 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.6.c- Find and position integers and other rational numbers on a horizontal or vertical number line diagram. 6.RP.3c- Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent MP- Mathematical Practices MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning

25

Chapter 4 & 5: Ratios and Unit Rates



How can we use ratios to compare two quantities? How can we create equivalent ratios by using our knowledge

of equivalent fractions? How can we interpret a ratio that’s in fraction, ratio, or word

form? How can we use ratios to solve real-world problems? What is a unit rate and how is it used in real life? How can we calculate a unit rate and use it to compare

quantities?

Ratios are commonly seen in real life and in real-world problems By using a ratio we can compare two different quantities Ratios can be used to solve multi-step problems Rates are commonly seen in real life and in real-world problems By calculating the unit rate, we can compare different units. For example, we can

compare who ran faster, which item costs less, etc.



Math in Focus

OTHER (e.g., tech)

1 day Chapter Opener: Recall Prior Knowledge

1. You can use a ratio to compare two quantities, and you can use ratios to solve problems.

CCSS: Foundational for: 6.RP.1 6.RP.3d MP: MP.6 MP.7

TE-6A: pp. 115-117

*Ratios and Rates Math Menu Activity *Scale Model Engineering Project -Engineering -Technology -Math Google sketchup *STEAM PROJECT (see appendix)

Chapter Opener:TE pp.114 -Has anyone ever seen a recipe for a loaf of bread? Quick Check: Express each fraction as two equivalent fractions using multiplication: 1) ¾ 2) 7/9 3) 6/11 Express each fraction as two equivalent fractions using division: 1) 16/56 2) 21/63 3) 35/140 ExtraP-6A: pp. 116-117 Pre-Test: Chapter 4 Test Prep Assessment Bk. pp. 34-35 *Ratios Quiz

26

*Study Island

1 day

4.1 Comparing Two Quantities

1. Create ratios to compare two quantities. 2. Interpret ratios given in fraction or ratio form.

CCSS: 6.RP.1 6.RP.3d MP: MP.3 MP.4 MP.8

TE-6A: pp. 118-126 Core: Student Book 6A: pp. 125-126 Basic: Reteach-6A: pp. 85-91 ELL: TE-6A: pp. 119 Advanced: Enrichment-6A: pp. 18

*Bar Model Drawing

5-minute Warm Up: pp. 118 Model: Use five bars of the

same length to represent a red rod of 5 centimeters and nine bars of the same length to represent a blue rod of nine centimeters. (pp.118-119)

Guided Practice: pp. 119-124 Problem of the Lesson: pp.

124 Day 1: pp. 125 #1-10 Day 2: pp. 126 #11-16 ExtraP-6A: pp. 39-40

Exit Ticket: A tree is 15 meters tall. A seedling next to it is 7 centimeters tall. What is the ratio of the height of the seedling to the height of the tree? Show your work. *Study Island

8 days

4.2 Equivalent Ratios

1. Create equivalent ratios using bar models, data tables, and similar figures 2. Create equivalent ratios by writing them in simplest form 3. Compare ratios 4. Create equivalent ratios

CCSS: 6.RP.3a MP: MP.2 MP.4

TE-6A: pp. 127-139 Core: Student Book 6A: pp. 138-139 Basic: Reteach-6A: pp. 92-104

*Bar Model Drawing

5-minute Warm Up: TE pp. 127

Model: Use eight shaded circles to represent 8 red marbles and twelve unshaded circles to represent 12 blue marbles (TE pp. 127)


131 Day 1: pp. 138 #1-15, 24, 35

27

with measurement ELL: TE-6A: pp. 130 Advanced: Enrichment-6A: pp. 19-20

Day 2: pp. 138 #16-23, 25-34, 36

ExtraP-6A: pp. 41-42

Exit Ticket: Find the missing term in the pair of equivalent ratios 6:5 = 24: ____. Should you use multiplication or division? Explain. *Comparing and creating ratios quiz *Study Island

2 days

4.3 Real World Problem Ratios

1. Solve real world problems involving ratios

CCSS: 6.RP.3 MP: MP.1 MP.2 MP.6

TE-6A: pp. 140-149 Core: Student Book 6A: pp. 148-149 Basic: Reteach-6A: pp. 105-116 ELL: TE-6A: pp. 89 Advanced: Enrichment-6A: pp. 21-23

*Bar Model Drawing


Model: Use bar models to represent the scenario in part a) on pp. 140


141 #1 Day 1: pp. 148 #1-3 Day 2: pp. 148 #4-10 (#11-15

are challenge questions) ExtraP-6A: pp. 43-47

Exit Ticket: A number of baseball cards were shared among Ray, Serge, and Tony in the ratio Ray:Serge:Tony = 2:4:9. If Serge got 55 fewer cards than Tony, how many cards did Tony get? Explain how to solve this problem. *Real world problems ratios quiz *Study Island

28


1. Recognize that you can use a rate to compare one quantity to another quantity, and use rates to solve problems

CCSS: 6.NS.1 6.NS.2 6.RP.1 6.RP.3d MP: MP.6 MP.7

TE-6A: pp. 155-158

Chapter Opener:TE pp.154 -Has anyone played in a soccer match? What makes a player the best goal scorer? -Suppose player 29 scored 15 goals in 10 matches and Player 11 scored 25 goals in 20 matches. Who scored more goals? Can you conclude that Player 11 is a better scorer? Explain. Quick Check: Multiply: 1. 75 x 698 2. Find the product of 7/12 x 36 3. Find the product of 11/18 x 3/44 4. Find the quotient of 56 and 8/11 5. Find the quotient of 77/92 and 11/42 6. If 7 units represent 98 liters, find the value of 15 units. ExtraP-6A: pp.155-158 Pre-Test: Chapter 5 Test Prep Assessment Bk. pp. 42-43 *Study Island

2 days

5.1 Rates and Unit Rates

1. Solve unit rate problems including unit pricing and constant speed

CCSS: 6.RP.2 6.RP.3 MP: MP.4 MP.8



Model: Use 8 bars of the same legth to represent 24 bottles being filled in 8 minutes. Use 1 bar of the same length to represent the unknown number of bottles being filled in 1 minute. (TE pp.160)


29

ELL: TE-6A: pp. 160, 164 Advanced: Enrichment-6A: pp. 24-26

162 Day 1: pp. 166 #1,3,4,7,8 Day 2: pp. 166 #2,5,6,9-11 ExtraP-6A: pp. 48-50

Exit Ticket: In your own words, explain how a rate differs from a ratio and how a unit rate differs from a rate. *Unit Rate Quiz #1 *Study Island

2 days

5.2 Real-World Problems: Rates and Unit Rates

1. Solve problems involving rates and unit rates

CCSS: 6.RP.3 6.RP.3b MP: MP.1 MP.2 MP.3

TE-6A: pp. 168-178 Core: Student Book 6A: pp. 177-178 Basic: Reteach-6A: pp. 127-141 ELL: TE-6A: pp. Advanced: Enrichment-6A: pp. 27-29


Model: Use a bar model to represent a multiplication or division sentence (TE pp. 168)


171 Day 1: pp. 177 #1-4, 9 Day 2: pp. 177 #5-8, 10 (#11-

12 for challenge questions) ExtraP-6A: pp. 51-54

Exit Ticket: A factort produces 161 cars in 7 hours. At this rate, how many cars will the factory produce in 1 week? Assume the factory runs 24 hours a day, 7 days a week. Show your work. *Unit Rate Quiz #2 *Study Island

30

2 days

Chapter Wrap Up/Review


CCSS: 6.NS.1 6.NS.2 6.RP.1 6.RP.2 6.RP.3 6.RP.3a 6.RP.3b 6.RP.3d MP: MP.1 MP.2 MP.5 MP.7

TE-6A: pp. 151-153 Core: Student Book 6A: pp. 152-153 TE-6A: pp. 179-182 Core: Student Book 6A: pp. 180-181

Bar Model Vocabulary Review pp.151 Brain At Work: pp. 150 Chapter Wrap Up: pp. 151 Chapter Review: pp. 152-153 Vocabulary Review pp.179 Brain At Work: pp. 178 Chapter Wrap Up: pp. 179 Chapter Review: pp. 180-181 Chapter Test: Ratios and Unit Rates


Students extend concepts learned with fractions to ratios. Ratios can be represented in multiple ways and like fractions, you can create equivalent ratios and they can be simplified. The bar model can be used to represent ratios and help students to solve real world problems. Students extend their knowledge of ratios to the concept of a rate. The bar model can be used to help calculate the unit rate and to solve real world problems. Bar models help students visualize more complex ratio and

rate problems.

PARCC FRAMEWORK/ASSESSMENT Compare the number of black to white circles. If the ratio remains the same, how many black circles will you have if you have 60 white circles?

Black 4 40 20 60 ?

White 3 30 15 45 60

Using the information in the table, find the number of yards in 24 feet.

Feet 3 6 9 15 24

Yards 1 2 3 5 ?


On a bicycle you can travel 20 miles in 4 hours. What are the unit rates in this situation, (the distance you can travel in 1 hour and the amount of time required to


31

travel 1 mile)?

A simple modeling clay recipe calls for 1 cup corn starch, 2 cups salt, and 2 cups boiling water. How many cups of corn starch are needed to mix with each cup of salt? http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml (please see appendix)


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.17: Employ critical thinking and interpersonal skills to resolve conflicts 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


Communicators or Whiteboards Responders Bar Model Ratios Additional Support (ELL , Struggling Learners): TE pp.114D Advanced Learners: TE pp.114D Additional Support (ELL , Struggling Learners): TE pp.154D Advanced Learners: TE pp.154D


6.NS.1- Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions 6.NS.2- Fluently divide multi-digit numbers using the standard algorithm 6.RP.1- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2- Understand the concept of a unit rate and use rate language in the context of a ratio relationship 6.RP.3- Use ratio and rate reasoning to solve real-world and mathematical problems.


32

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. 6.RP.3b- Solve unit rate problems including those involving unit pricing and constant speed 6.RP.3d- Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml Model Curriculum Assessment Unit 5 #1-3 http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml Model Curriculum Assessment Unit 5 #4-7, 9-12 http://www.knowitall.org/nasa/pdf/connect/Right_Ratio_Connect_Guide.pdf (STEAM PROJECT)

Chapter 6: Percent



How can we use our knowledge of percent to calculate the percent of a number?

How is percent related to tax, interest, store markups, and store discounts?

How is percent used in real-world situations? How can we convert fractions, decimals, and percents?

Percents are used to solve real-world problems involving tax, interest, store markups, and store discounts.

The percent of a number can be found by multiplying by its decimal form Percent, fractions, and decimals can be equal and are interchangeable



Math in Focus

OTHER (e.g., tech)


1. Define percent as a concept used to compare quantities expressed per hundred

CCSS: Foundational for: 6.RP.3 6.RP.3c

TE-6A: pp. 182-184

*Shopping Project *Gas Elements

Chapter Opener: TE pp.182 -Have you ever wondered how an author or a cartoonist earns money from the sales of their books and comic books?



http://www.knowitall.org/nasa/pdf/connect/Right_Ratio_Connect_Guide.pdf

33

MP: MP.6 MP.7

Project (% of water in gas) -Science -Technology -Math *STEAM PROJECT continuation (see appendix)

-How do you think they earn money from their book sales? Quick Check: Multiply: 1. Find the missing numberators and denominators: a) 4/5 = 8/? = ?/100 2. Express the fraction 180/240 in simplest form. 3. Express the fractions 7/20 and 39/300 as a decimal. 4. Find the product of 7/9 x 30. Pre-Test: Chapter 6 Test Prep Assessment Bk. pp. 50

1 day

6.1 Rates and Unit Rates

1. Express certain quantities percent notation

CCSS: 6.RP.3 6.RP.3c MP: MP.3 MP.4

TE-6A: pp. 185-188 Core: Student Book 6A: pp. 188 Basic: Reteach-6A: pp. 142-147 ELL: TE-6A: pp. 182F, 186 Advanced: Enrichment-


Model: Shade 45 units on a 100s grid. Explain that you can write 45 out of 100 as a percent by writing 45%. (TE pp.185)


186 part c Day 1: pp. 188 #1-18 ExtraP-6A: pp. 55-56

Exit Ticket: of the 640 students at Jay’s school, 80 are fluent in a language other than English. Find the percent of students who are fluent in another language. Then

34

6A: pp. 30 express the percent as both a fraction in simplest form and as a decimal. Finally, find the percent of students who are NOT fluent in another language.

1 day

6.2 Fractions, Decimals, and Percents

1. Create more equivalent fractions, decimals, and percents

CCSS: 6.RP.3c MP: MP.3 MP.4 MP.7

TE-6A: pp. 189-192 Core: Student Book 6A: pp. 192 Basic: Reteach-6A: pp. 148-151 ELL: TE-6A: pp. Advanced: Enrichment-6A: pp. 31


Hands-On Activity: pp.189 Expressing Fractions or Mixed Numbers as Percents


191 part a and b Day 1: pp. 192 #1-21 (22-23

are challenge problems) ExtraP-6A: pp. 57-58

Exit Ticket: Explain how 35% and the equivalent fraction and decimal are related to each other.

1 day

6.3 Percent of a Quantity

1. Calculate the percent of a number

CCSS: 6.RP.3c MP: MP.2 MP.3

TE-6A: pp. 193-197 Core: Student Book 6A: pp. 196-197 Basic: Reteach-6A: pp. 152-155 ELL: TE-6A: pp. 194 Advanced: Enrichment-


Model: Use a bar model to represent a whole quantity (100%). Shade a small part of the bar model to represent 5%. Point out that 100% refers to the whole quantity or base (TE pp. 193)


195 (“Learn”) Day 1: pp. 196 #1-17 (18-20

are challenge problems) ExtraP-6A: pp. 59-62

35

6A: pp. 32 Exit Ticket: In your own words, explain how to use the unitary method to find the percent of a whole.

4 days

6.4 Real-World Problems: Percent

1. Solve problems involving percent

CCSS: 6.RP.3c 7.RP.3 MP: MP.1 MP.4

TE-6A: pp. 198-203 Core: Student Book 6A: pp. 203 Basic: Reteach-6A: pp. 156-164 ELL: TE-6A: pp. 199, 201 Advanced: Enrichment-6A: pp. 33


Model: Use a bar model to represent the scenario in part a (pp. 198). Lead students to see that 48 points 100%


199 “Learn” Day 1: pp. 203 #1-6 Day 2: pp. 203 #7-9 ExtraP-6A: pp. 63-65

Exit Ticket: Create and solve

a real-world percent problem that involves a royalty, sales tax, interest, or commission.

2 days

6.5 Percent of Change

1. Solve problems involving percent increase and decrease

CCSS: 6.RP.3c 7.RP.3 MP: MP.1 MP.2 MP.3 MP.5

TE-6A: pp. 204-213 Core: Student Book 6A: pp. 212-213 Basic: Reteach-6A: pp. 165-179 ELL: TE-6A: pp. 204, 208 Advanced: Enrichment-


Model: Draw a bar model to represent the amount Mr. Sato paid for the haddock. Show that this amount is $3.75, which is represented by 100%. (TE pp. 204)


204 “Learn” Day 1: pp. 212 #1-3, 5 Day 2: pp. 212 #4,6,7 (#8-11 are challenge problems) ExtraP-6A: pp. 66-69

36

6A: pp. 34 Exit Ticket: Create and solve a real-world problem that involves percent increase or percent decrease.

2 days

Chapter Wrap Up/Review/Test


CCSS: 6.RP.3 6.RP.3c 7.RP.3 MP: MP.1 MP.5 MP.6 MP.7


Vocabulary Review pp.215 Brain At Work: pp. 214 Chapter Wrap Up: pp. 215 Chapter Review: pp. 216-217 Chapter Test: Percents


Students use bar models to visualize percents, and solve problems using both the unitary method and traditional methods. Students learn the concept of base, and that percent has a base of 100. Students will connect percent to concepts they have already encountered when working with fractions and decimals. Percent of increase or decrease can be found using the bar model.


If 6 is 30% of a value, what is that value? (Solution: 20)

A credit card company charges 17% interest on any charges not paid at the end of the month. Make a ratio table to show how much the interest would be for several amounts. If your bill totals $450 for this month, how much interest would you have to pay if you let the balance carry to the next month? Show the relationship on a graph and use the graph to predict the interest charges for a $300 balance.

Charges $1 $50 $100 $200 $450

Interest $0.17 $8.50 $17 $34 ? http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml (please see appendix)


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.2.8.B.1: Construct a simple personal savings and spending plan based on various sources of income 9.2.8.B.9: Create debit and credit balance sheets and income and cash statements 9.2.8.C.3: Demonstrate an understanding of the terminology associated with difference types of credit


37

9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


Communicators or Whiteboards Responders Bar Model Percents Fraction, Decimal, Percents Flip Chart Organizer Additional Support (ELL , Struggling Learners): TE pp.182F Advanced Learners: TE pp.182F


6.RP.3- Use ratio and rate reasoning to solve real world and mathematical problems 6.RP.3c- Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent 7.RP.3- Use proportional relationships to solve multistep ratio and percent problems MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml Model Curriculum Assessment Unit 5 #8 http://www.knowitall.org/nasa/pdf/connect/Right_Ratio_Connect_Guide.pdf (STEAM PROJECT)

Chapter 7: Algebraic Expressions



How are algebraic expressions used to represent real-world problems?

What is an algebraic expression and how can we create

Algebraic expressions can be used to represent real-world scenarios and problems An algebraic expression can not be solved unless the value of the variable is given The distributive property and combining like terms can be used to simplify an


http://www.knowitall.org/nasa/pdf/connect/Right_Ratio_Connect_Guide.pdf

38

algebraic expressions when given a verbal sentence? How can we evaluate expressions when given the value of the

variable? How can we simplify an algebraic expression using the

distributive property and by combining like terms?

algebraic expression and the resulting expression is equal to the original expression



Math in Focus

OTHER (e.g., tech)


1. Recognize that algebraic expressions can be used to describe situations and solve real-world problems

CCSS: Foundational for: 6.EE.2a 6.EE.2b 6.EE.2c 6.EE.3 MP: MP.4 MP.7

TE-6A: pp. 218-220 ELL: TE 6A pp. 218F

*Expressions Math Menu

Chapter Opener: TE pp. 218 -Has anyone ever watched bungee jumping? -What makes the cord stretch when a person jumps? Quick Check: Draw a bar model to show each operation:

a) 15 + 4 b) 17 – 9 c) 6 x 5 d) 28/4

Find the common factors and greatest common factor of each pair of numbers:

a) 6 and 9 b) 4 and 12 c) 8 and 28

Complete with quotient, sum, difference, product, dividend, or divisor.

a) The ___ “5 less than 7 is 7-5

b) The ___ of 5 and 7 is 5/7. 7 is the ___ and 5 is the ___.

c) The ___of 5 and 7 is 7 x 5 d) The ___of 5 and 7 is 5 + 7

Pre-Test: Chapter 7 Test Prep Assessment Bk. pp. 57-58

39

3 days

7.1 Writing Algebraic Expressions

1. Use variables to write algebraic expressions

CCSS: 6.EE.2a 6.EE.2b 6.EE.6 MP: MP.2 MP.4

TE-6A: pp. 221-225 Core: Student Book 6A: pp. 225 Basic: Reteach-6A: pp. 180-184 ELL: TE-6A: pp. 218F Advanced: Enrichment-6A: pp. 35


Model: Remind students that a bar model can be used to represent the addition sentence in the example problems


221 “Learn” Day 1: pp. 225 #1-2 Day 2: pp. 225 #3-9 (#10-11 are challenge problems) ExtraP-6A: pp. 70-71

Exit Ticket: Ben is 3 times as old as Kyra. Dilip is 4 years younger than Kyra. If Kyra is x years old, how old is Ben? How old is Dilip? Write an algebraic expression for each boy’s age.

2 days

7.2 Evaluating Algebraic Expressions

1. Evaluate algebraic expression for given values of the variable

CCSS: 6.EE.2 6.EE.2c MP: MP.4 MP.8

TE-6A: pp. 226-228 Core: Student Book 6A: pp. 228 Basic: Reteach-6A: pp. 185-186 ELL: TE-6A:


Model: Use a bar model to show that Simon has (x-3) more marbles than Cynthia. Explain that, in order to know exactly how many more marbles, they need the exact value of x.

Guided Practice: pp. 227 Problem of the Lesson: pp.

226 “Learn” Day 1: pp. 228 #1-20 (#21-27 are challenge problems)

40

pp. Advanced: Enrichment-6A: pp. 36


Exit Ticket: Write two algebraic expressions using x that when evaluated for x=3 give the same value. Show your work.

3 days

7.3 Simplifying Algebraic Expressions

1. Create equivalent expressions by simplifying algebraic expressions in one variable 2. Recognize that the expression obtained after simplifying is equivalent to the original expression

CCSS: 6.EE.3 6.EE.4 6.EE.6 MP: MP.3 MP.4

TE-6A: pp. 229-238 Core: Student Book 6A: pp. 237-238 Basic: Reteach-6A: pp. 187-193 ELL: TE-6A: pp. Advanced: Enrichment-6A: pp. 37


Model: Use two bars of the same length to represent the addition of two straws of length y inches. Remind students that a variable represents a number. Here, the variable y represents a number that is unknown (TE pp. 229)

Hands-On Activity (TE 6A pp. 232) Recognize that simplified expressions are equivalent)


229(“Learn”) Day 1: pp. 237 #1-3 Day 2: pp.237 #4-6 Day 3: pp. 237 #7-23, 26 (#24-25 are challenge problems) ExtraP-6A: pp. 74-76

Exit Ticket: Write an

algebraic expression for the perimeter of a rectangle garden with a width of 3 feet and a length of 2y feet. Simplify your expression and find the perimeter of the garden if y=6. Show your work.

41

3 days

7.4 Expanding and Factoring Algebraic Expressions

1. Create equivalent expressions by expanding simple algebraic expressions 2. Create equivalent expressions by factoring simple algebraic expressions

CCSS: 6.EE.2 6.EE.3 6.EE.4 MP: MP.3 MP.4 MP.6

TE-6A: pp. 239-245 Core: Student Book 6A: pp. 244-245 Basic: Reteach-6A: pp. 194-197 ELL: TE-6A: pp. 240 Advanced: Enrichment-6A: pp. 38


Model: Use a bar model to show 2 groups of (r+8). Then rearrange the model such that the two bars of “r” are put together and the two bars of “8” are put together. (TE 6A pp.239)

Hands-On Activity (TE 6A pp. 241) Recognize that expanded expressions are equivalent


239 “Learn” Day 1: pp. 244 #1-6, 17-19 Day 2: pp. 244 #7-16, 20-22 (#23-27 are challenge problems) ExtraP-6A: pp. 77-80


algebraic expression and expand it by multiplying by a factor. Evaluate both expressions for the same value of the variable. Check that the answers to the evaluations are the same.

2 days

7.5 Real World Problems: Algebraic Expressions

1. Solve real-world problems involving algebraic expressions

CCSS: 6.EE.6 MP: MP.1 MP.2 MP.4



Model: Work through part a) with students to demonstrate the problem solving (TE pp. 246)


246 “Learn” Day 1: pp. 251 #1-2 Day 2: pp. 251 #3-4 (#5-6 are challenge problems)

42

ELL: TE-6A: pp. Advanced: Enrichment-6A: pp. 39-40


Exit Ticket: Briefly describe a

situation in your classroom that can be described algebraically. Then, write an algebraic expression for it. Finally, evaluate the expression by substituting a realistic number for the variable.

2 days



CCSS: 6.EE.2 6.EE.2a 6.EE.2b 6.EE.2c 6.EE.3 6.EE.4 6.EE.6 MP: MP.1 MP.5 MP.7

TE-6A: pp. 253-255A Core: Student Book 6A: pp. 254-255

Vocabulary Review pp.253 Brain At Work: pp. 252 Chapter Wrap Up: pp. 253 Chapter Review: pp. 254-255 Chapter Test: Algebraic Expressions


Algebraic expressions can be written to represent situations in the world and the variables are used to represent unknown quantities You can substitute a variable with a given value and then simplify the expression to evaluate that expression. Students use bar models to represent algebraic expressions and to recognize equivalent expressions.


Write the following as a numerical expressions using exponential notation.

o The area of a square with a side length of 8 m (Solution: 228 m )

o The volume of a cube with a side length of 5 ft.: (Solution: 335 ft )

o Yu-Lee has a pair of mice. The mice each have 2 babies. The babies grow up and have two babies of their own: (Solution: 32 mice)

Evaluate:

43

o 34 (Solution: 64)

o 625 4 ·+ (Solution: 101)

o 2632472 +¸- (Solution: 67)

Examples:

7 more than 3 times a number (Solution: 73 +x )

3 times the sum of a number and 5 (Solution: )5(3 +x

7 less than the product of 2 and a number (Solution: 72 -x )

Twice the difference between a number and 5 (Solution: )5(2 -z )

Evaluate 5(n + 3) – 7n, when n =1

2.

The expression c + 0.07c can be used to find the total cost of an item with 7% sales tax, where c is the pre-tax cost of the item. Use the expression to find the total cost of an item that cost $25.

The perimeter of a parallelogram is found using the formula p = 2l + 2w. What is the perimeter of a rectangular picture frame with dimensions of 8.5 inches by 11 inches.

Students use their understanding of multiplication to interpret 3 (2 + x). For example, 3 groups of (2 + x). They use a model to represent x, and make an array to show the meaning of 3(2 + x). They can explain why it makes sense that 3(2 + x) is equal to 6 + 3x.

Example:

Are the expressions equivalent? How do you know?

4m + 8 4(m+2) 3m + 8 + m 2 + 2m + m + 6 + m Solution:

Expression Simplifying the Expression Explanation

4m + 8 4m + 8 Already in simplest form

4(m+2) 4(m+2) 4m + 8

Distributive property

3m + 8 + m 3m + 8 + m 3m + m + 8 (3m + m) + 8

Combined like terms

44

4m + 8

2 + 2m + m + 6 + m 2 + 2m + m + 6 + m 2 + 6 + 2m + m + m (2 + 6) + (2m + m + m) 8 + 4m 4m + 8

Combined like terms

Examples:

Maria has three more than twice as many crayons as Elizabeth. Write an algebraic expression to represent the number of crayons that Maria has. (Solution: 2c + 3 where c represents the number of crayons that Elizabeth has.)

An amusement park charges $28 to enter and $0.35 per ticket. Write an algebraic expression to represent the total amount spent. (Solution: 28 + 0.35t where t represents the number of tickets purchased)




9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.1: Employ appropriate conflict resolution strategies. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


Communicators or Whiteboards Responders Algebra Tiles or Hands-On Equations manipulatives Bar Model Expressions Additional Support (ELL , Struggling Learners): TE pp.218F Advanced Learners: TE pp.218F


CCSS:



45

6.EE.2- Write, read, and evaluate expressions in which letters stand for numbers 6.EE.2a- Write expression that record operations with numbers and with letter standing for numbers. 6.EE.2b- Identify parts of an expression using mathematical terms; view one or more parts of an expression as a single entity. 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 6.EE.3- Apply the properties of operations to generate equivalent expressions 6.EE.4- Identify when two expressions are equivalent 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 MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u2.shtml – Model Curriculum Assessment Unit 2 #1-4, 9-21 http://www.state.nj.us/education/modelcurriculum/math/6u3.shtml Model Curriculum Assessment Unit 3 #1-5









Math in Focus

OTHER (e.g., tech)



46



CCSS: 6.NS.1 6.NS.2 6.RP.1 6.RP.2 6.RP.3 6.RP.3a 6.RP.3b 6.RP.3c 6.RP.3d 7.RP.3 6.EE.2 6.EE.2a 6.EE.2b 6.EE.2c 6.EE.3 6.EE.4 6.EE.6 MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8

TE-6A: pp. 256 #256-259

Extra Practice 6A: pp. 85-90

2 days



CCSS: 6.NS.1 6.NS.2 6.RP.1 6.RP.2 6.RP.3 6.RP.3a 6.RP.3b 6.RP.3c 6.RP.3d 7.RP.3 6.EE.2 6.EE.2a 6.EE.2b

Assessment Book 6: pp. 65-72 or pp. 73-80

47

6.EE.2c 6.EE.3 6.EE.4 6.EE.6 MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8










6.NS.1- Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions 6.NS.2- Fluently divide multi-digit numbers using the standard algorithm

48

6.RP.1- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2- Understand the concept of a unit rate and use rate language in the context of a ratio relationship 6.RP.3- Use ratio and rate reasoning to solve real-world and mathematical problems. 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. 6.RP.3b- Solve unit rate problems including those involving unit pricing and constant speed 6.RP.3c- Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent 6.RP.3d- Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 7.RP.3- Use proportional relationships to solve multistep ratio and percent problems 6.EE.2- Write, read, and evaluate expressions in which letters stand for numbers 6.EE.2a- Write expression that record operations with numbers and with letter standing for numbers. 6.EE.2b- Identify parts of an expression using mathematical terms; view one or more parts of an expression as a single entity. 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 6.EE.3- Apply the properties of operations to generate equivalent expressions 6.EE.4- Identify when two expressions are equivalent 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 MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning

Chapter 8: Equations and Inequalities



What are equations and inequalities and how are they used in real life?

How can we create an equation or an inequality to represent a real-world problem?

How can we solve equations and inequalities using inverse operations?

Equations and inequalities can be created and used to describe situations and solve real-world problems

Solving equations can be accomplished using inverse operations Equations and inequalities can be represented on a graph

49

How can we represent an equation or an inequality on a number line?



Math in Focus

OTHER (e.g., tech)


1. Recognize that equations and inequalities can be used to describe situations and solve real-world problems

CCSS: 6.EE.2a Foundational for: 6.EE.5 6.EE.8 6.EE.9 MP: MP.4 MP.6

TE-6B: pp. 2 - 4 ELL: TE 6B pp.2d

*STEAM PROJECT (see appendix)

Chapter Opener: TE 6B pp. 2 -Has anyone ever visited another country? -How much money does a person need when he or she goes to another country? Quick Check: Complete with =,>, or<. 1. 25 _____ -26 2. 12+12+12____3x12 3. -16___-7 4. 40/8 ___8/40 Write an algebraic expression for the following: 1. The sum of 15 and p 2. The difference “q less than 10” 3. The product of r and 23 4. Divide s by 11 Evaluate each expression for the given value: 1. 3x + 5 when x=9 and x = 12 2. 28 – 4x when x=4 and x=7 Plot the points in a coordinate plane: K(2,1), L(3,3), M(0,6), and N(7,5) Pre-Test: Chapter 8 Test Prep Assessment Bk. pp. 81-82

50

4 days

8.1 Solving Algebraic Equations

1. Solve equations in one variable 2. Solve equations by combining like terms 3. Solve equations by using the distributive property

CCSS: 6.EE.2c 6.EE.5 MP: MP.3 MP.4 MP.8

TE-6B: pp. 5-12 Core: Student Book 6B: pp. 188 Basic: Reteach-6B: pp. 1-15 ELL: TE-6B: pp. 6 Advanced: Enrichment-6B: pp. 41

5-minute Warm Up: TE 6B pp. 5

Model: Use manipulatives to show solving equations and have students use manipulatives to solve simple equations.

Guided Practice: pp. 6-11 Problem of the Lesson: pp. 11

#18 Day 1: pp. 12 #1-19 Day 2: pp. 12 #20-33 (#34-35 are challenge problems) ExtraP-6B: pp. 1-3

Exit Ticket: Explain how inverse operations are used to solve equations in one variable. Include at least 1 example.

3 days

8.2 Writing Linear Equations

1. Express the relationship between two quantities as a linear equation 2. Use a table or graph to represent a linear equation

CCSS: 6.EE.7 6.EE.9 MP: MP.4 MP.6 MP.7

TE-6B: pp. 13-21 Core: Student Book 6B: pp. 20-21 Basic: Reteach-6B: pp. 16-26 ELL: TE-6B: pp. 14, 16


Model TE 6B: pp. 13 Remind students that a bar model can be used to represent the scenario


“Learn” Day 1: pp. 20 #1-4 Day 2: pp. 20 #5-8 (#9 is a challenge problem) ExtraP-6B: pp. 4-8

Exit Ticket: In your own words,

51

Advanced: Enrichment-6B: pp. 42-43

describe a real-world math situation that involve two variables. Write a linear equation to describe the situation.

2 days

8.3 Solving Simple Inequalities

1. Use substitution to determine whether a given number is a solution of an inequality 2. Represent the solutions of an inequality on a number line

CCSS: 6.EE.5 6.EE.7 MP: MP.2 MP.3 MP.4

TE-6B: pp. 22-28 Core: Student Book 6B: pp. 27-28 Basic: Reteach-6B: pp. 27-32 ELL: TE-6B: pp. 23 Advanced: Enrichment-6B: pp. 44


Hands-On Activity: Writing Inequalities (TE 6B pp. 24)


“Learn” Day 1: pp. 27 #1-10 Day 2: pp. 27 #11-20 (#21-30 are challenge problems) ExtraP-6B: pp. 9-11


inequality for the number line below. Then give 4 possible solutions of the inequality: one whole number, one fraction, one mixed number, and one decimal.

2 days

8.4 Real-World Problems: Equations and Inequalities

1. Solve real-world problems by writing equations 2. Solve real-world problems by writing inequalities

CCSS: 6.EE.7 6.EE.8 MP: MP.1 MP.4

TE-6B: pp. 29-34 Core: Student Book 6B: pp. 203 Basic: Reteach-6B: pp. 33-39 ELL: TE-6B: pp.


Model: Solve the equation or, if preferred, ask a student to do it. Solve example b) using the same process applied to sample a). (TE 6B pp. 29)


“Learn” Day 1: pp. 33 #1-4, 9, 11 Day 2: pp. 33 #5-8,10 (#12-13 are challenge problems) ExtraP-6B: pp. 12-15

52

Advanced: Enrichment-6B: pp. 45-46

Exit Ticket: In your own words, describe a simple real-world math situation that involves one variable. Write an inequality to correctly describe the situation. Then draw a number line to represent the inequality.

2 days



CCSS: 6.EE.2a 6.EE.2c 6.EE.5 6.EE.7 6.EE.8 6.EE.9 MP: MP.1 MP.5

TE-6B: pp. 35-37A Core: Student Book 6B: pp. 36-37

Vocabulary Review pp.35 Brain At Work: pp. 34 Chapter Wrap Up: pp. 35 Chapter Review: pp. 36-37 Chapter Test: Equations and Inequalities


Students use inverse operations to isolate the variable on one side of an equal sign to solve an equation. Students extend their use of substitution to determine whether a given number is a solution to an inequality. The graphed solution to a simple equation is a line Students use number lines to represent solutions to inequalities Inequalities have infinite solutions and are, therefore, represented using rays In real-world problems, students learn that solutions to linear equations and inequalities may not be infinite.

PARCC FRAMEWORK/ASSESSMENT http://www.state.nj.us/education/modelcurriculum/math/6u3.shtml (Please see appendix) http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml (please see appendix)


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.1: Employ appropriate conflict resolution strategies. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information



53

9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.


Communicators or Whiteboards Responders Algebra Tiles or Hands-On Equations Manipulatives Bar Model Equations Horizontal number line Additional Support (ELL , Struggling Learners): TE 6B pp.2D Advanced Learners: TE 6B pp. 2D


CCSS: 6.EE.2a- Write expressions that record operations with numbers and with letters standing for numbers 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 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. 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 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 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. MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u3.shtml Model Curriculum Assessment Unit 3 #6-20 http://www.state.nj.us/education/modelcurriculum/math/6u5.shtml Model Curriculum Assessment Unit 5 #13-18 http://www.knowitall.org/nasa/pdf/connect/Breaking_Barriers.pdf (STEAM PROJECT)



http://www.knowitall.org/nasa/pdf/connect/Breaking_Barriers.pdf

54

Chapter 9: The Coordinate Plane



How are ordered pairs represented on a coordinate plane? How can we graph a polygon on the coordinate plane and use

the graphing to calculate the area? How can we calculate the length of a segment on the

coordinate plane? How is the coordinate plane used in real life?

The coordinate plane is used to represent real-world problems such as maps and blueprints

The length of a line segment on a coordinate plane can be found by counting the distance between the two ordered pairs

We can use the coordinate plane to calculate the area of a polygon



Math in Focus

OTHER (e.g., tech)


1. Recognize that every point in the coordinate plane can be represented by a pair of coordinates

CCSS: 6.NS.6 6.NS.7c Foundational for: 6.NS.6c 6.G.3 6.NS.8 MP: MP.5 MP.7

TE-6B: pp. 38-41 ELL: TE 6B pp.38D

*Mystery Picture Project

Chapter Opener: TE 6B pp. 38 -Has anyone seen a street directory? -Do you know what it is for? Quick Check (pp. 39): 1. Give the coordinates of points B,c, and D. 2. Use graph paper and plot the points on a coordinate plane: P(3,2) Q(2,3) R(0,4) 3. Identify the number that each indicated point represents on the number line. 4. Draw a horizontal number line to represent the numbers -15,-11,-9,-7,-2 5. Use the symbol II to write the absolute values of the following

55

numbers: 11, -16, and -21 Pre-Test: Chapter 9 Test Prep Assessment Bk. pp. 87-88

3 days

9.1 Points on the Coordinate Plane

1. Describe, name, and locate points on the coordinate plane 2. Draw and identify polygons on the coordinate plane

CCSS: 6.NS.6 6.NS.6c 6.G.3 MP: MP.4 MP.6 MP.7

TE-6B: pp. 42-49 Core: Student Book 6B: pp. 48-49 Basic: Reteach-6B: pp. 40-47 ELL: TE-6B: pp. 43, 47 Advanced: Enrichment-6B: pp. 47-49


Guided Practice: pp. 44-46 Hands-On Activity (TE 6B

pp.47) Problem of the Lesson: pp.

42”Learn” Day 1: pp. 48 #1-10 Day 2: pp. 48 #11-15 (#16-17 are challenge problems) ExtraP-6B: pp. 16-20

Exit Ticket: Rectangle EFGH has each of its four vertices in a different quadrant. Name one possible set of coordinates for the vertices of EFGH. Identify the quadrant in which each vertex is located.

2 days

9.2 Length of Line Segments

1. Calculate lengths of horizontal and vertical line segments on the coordinate plane as well as the perimeter 2. Solve real-world problems involving coordinates and a coordinate plane

CCSS: 6.NS.8 6.EE.2c 6.G.3 MP: MP.2 MP.4 MP.5

TE-6B: pp. 50-61 Core: Student Book 6B: pp. 58-61 Basic: Reteach-6B:


Model TE 6B: pp. 50 Mark points c(3,0) and D(7,0) on the coordinate plane. Then draw a line between C and D to form line segment CD.


“Learn”

56

pp. 48-63 ELL: TE-6B: pp. Advanced: Enrichment-6B: pp. 50-51

Day 1: pp. 58 #1-6 Day 2: pp. 58 #7-14 (#15-22 is a challenge problem) ExtraP-6B: pp. 21-24

Exit Ticket: A line segment has endpoints W(-1,1) and X(6,1). Line segment WX is one side of rectangle WXYZ, which has vertices in all four quadrants. The perimeter of WXYZ is 20 units. Name the locations of points Y and Z. Identify the lengths of YZ and WX. Find the area of the rectangle.

1 day

9.3 Real-World Problems: Graphing

1. Solve real-world problems involving equations, mapping, and a coordinate plane

CCSS: 6.RP.3a 6.RP.3b 6.NS.8 6.G.3 MP: MP.1 MP.2 MP.4

TE-6B: pp. 62-66 Core: Student Book 6B: pp. 65-66 Basic: Reteach-6B: pp. 64-67 ELL: TE-6B: pp. 62 Advanced: Enrichment-6B: pp. 52-53


Model (TE 6B pp. 62): Plot the points given in the tables on a coordinate plane.


“Learn” Day 1: pp. 65 #1-3 ExtraP-6B: pp. 25-28

Exit Ticket: A water tank has

10 gal of water in it. A hose is placed in the tank. Every min, 20 gal of water flowa out of the hose and into the tank. The number of gal of water g in the tank after m min is given by g = 20m +10. Graph the relationship between m and g. Use 1 unit on the horizontal axis to represent 1 min and 1 unit of the vertical axis to represent 20 gal. How

57

much water is in the tank at 1 min, 3 min, and 5 min?

2 days



CCSS: 6.NS.6 6.NS.6c 6.NS.7c 6.NS.8 6.EE.2c 6.G.3 6.RP.3a 6.RP.3b MP: MP.1 MP.5


Vocabulary Review pp.67 Brain At Work: pp. 66 Chapter Wrap Up: pp. 67 Chapter Review: pp. 68-71 Chapter Test: The Coordinate Plane


Students identify and plot points on a coordinate plane and identify their quadrants.. Students plot and connect points to form polygons, which they identify, as well as using properties of polygons to locate unknown vertices Students use the absolute value to calculate the lengths of segments on a coordinate plane, as well as calculate the perimeter of polygons on the

coordinate plane Students are introduced to linear graphs as a tool for visualizing the relationship between two variables. Students relate variables by graphing and using linear graphs to solve real-world problems


Twelve is less than 3 times another number can be shown by the inequality n312 < . What numbers could possibly make this a true statement?

The equation 1144.0 =s where s represents the number of stamps in a booklet. The booklet of stamps costs 11 dollars and each stamp costs 44 cents. How many stamps are in the booklet? Explain the strategies you used to determine your answer. Show that your solution is correct using substitution.

Andrew has a summer job doing yard work. He is paid $15 per hour and a $20 bonus when he completes the yard. He was paid $85 for completing one yard. Write an equation to represent the amount of money he earned. (Solution: 15h + 20 = 85 where h is the number of hours worked)

Describe a problem situation that can be solved using the equation 2c + 3 = 15; where c represents the cost of an item

Bill earned $5.00 mowing the lawn on Saturday. He earned more money on Sunday. Write an expression that shows the amount of money Bill has earned. (Solution: $5.00 + n)

58

Examples:

Meagan spent $56.58 on three pairs of jeans. If each pair of jeans costs the same amount, write an algebraic equation that represents this situation and solve to determine how much one pair of jeans cost.

Sample Solution: Students might say: “I created the bar model to show the cost of the three pairs of jeans. Each bar labeled J is the same size because each pair of jeans costs the same amount of money. The bar model represents the equation 3J = $56.58. To solve the problem, I need to divide the total cost of 56.58 between the three pairs of jeans. I know that it will be more than $10 each because 10 x 3 is only 30 but less than $20 each because 20 x 3 is 60. If I start with $15 each, I am up to $45. I have $11.58 left. I then give each pair of jeans $3. That’s $9 more dollars. I only have $2.58 left. I continue until all the money is divided. I ended up giving each pair of jeans another $0.86. Each pair of jeans costs $18.86 (15+3+0.86). I double check that the jeans cost $18.86 each because $18.86 x 3 is $56.58.”

Julio gets paid $20 for babysitting. He spends $1.99 on a package of trading cards and $6.50 on lunch. Write and solve an equation to show how much money Julio has left.

(Solution: 20 = 1.99 + 6.50 + x, x = $11.51)

Examples:

Graph x ≤ 4.

Jonas spent more than $50 at an amusement park. Write an inequality to represent the amount of money Jonas spent. What are some possible amounts of money Jonas could have spent? Represent the situation on a number line.

Less than $200.00 was spent by the Flores family on groceries last month. Write an inequality to represent this amount and graph this inequality on a number line.

Solution: 200 > x

Examples:

59

What is the relationship between the two variables? Write an expression that illustrates the relationship.

X 1 2 3 4

Y 2.5 5 7.5 10

Use the graph below to describe the change in y as x increases by 1.

Susan started with $1 in her savings. She plans to add $4 per week to her savings. Use an equation, table and graph to demonstrate the relationship between the numbers of weeks that pass and the amount in her savings account.

o Language: Susan has $1 in her savings account. She is going to save $4 each week.

o Equation: y = 4x + 1

o Table:

x y

0 1

1 5

2 9

o Graph:

60





Communicators or Whiteboards Responders Additional Support (ELL , Struggling Learners): TE 6B pp.38D Advanced Learners: TE 6B pp. 38D


6.NS.6- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates 6.NS.6c- Find and position integers and other rational number on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane 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 solve situation 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. 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 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 ot the same second coordinate. Apply these techniques in the context of solving real world and mathematical problems 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. 6.RP.3b- Solve unit rate problems including those involving unit pricing and constant speed MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.4- Model with mathematics


61

MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u4.shtml Model Curriculum Assessment Unit 4 #9-14, 17-23

Chapter 10: Area of Polygons



How is the area of polygons used in real life? How is using the formula for calculating the area of polygons

related to evaluating expressions? How can we calculate the area of a triangle, parallelogram, and

trapezoid by using the formulas? How can we calculate the area of composite figures?

Calculating the area of a polygon is related to evaluating expressions when using the formulas

The area of polygons is used in real-world applications such as construction, engineering, etc.

Composite figures can be broken into polygons and the area of the composite figure is equal to the sum of the areas of the polygons



Math in Focus

OTHER (e.g., tech)


1. Recognize that the area of a polygon can be found by dividing it into smaller shapes, and then adding the areas of those shapes

CCSS: 6.EE.2c Foundational for: 6.G.1 6.G.3 MP: MP.6 MP.7

TE-6B: pp. 72-74 ELL: TE 6B pp.72D

Chapter Opener: TE 6B pp. 72 -Have you ever seen a quilt? -What is it made of? How much fabric is needed to make the quilt? Quick Check (pp. 73): 1. Solve: The length of a rectangle is 15 meters and its width is 8 meters. Find the area of the rectangle.


62

2. Solve: A side length of a square is 10 centimeters. Find the area of the square. 3. Name each figure and identify the pairs of parallel lines. Pre-Test: Chapter 10 Test Prep Assessment Bk. pp. 95

2 days

10.1 Area of Triangles

1. Use a formula to find the area of a triangle

CCSS: 6.EE.2c 6.G.1 MP: MP.4 MP.7 MP.8




pp.76): Prove the formula for finding the area of a triangle

Problem of the Lesson: pp. 75 “Learn”

Day 1: pp. 83 #1-8, 15-17 Day 2: pp. 84 #9-14, 18-23 (#24-29 are challenge problems) ExtraP-6B: pp. 29-36

Exit Ticket: What is the base of a triangle with an area of 72 sq ft and a height of 12 ft? Show your work.

3 days

10.2 Area of Parallelograms and Trapezoids

1. Use a formula to find the area of a parallelogram, given its base and height 2. Use a formula to find the area of a trapezoid, given its base and height

CCSS: 6.G.1 6.G.3 MP: MP.4 MP.7 MP.8

TE-6B: pp. 88-98 Core: Student Book 6B: pp. 96-98 Basic: Reteach-6B: pp. 76-83 ELL:


Model TE 6B: pp. 88: Use the illustration in the text to demonstrate how to find the area of a parallelogram


“Learn” Day 1: pp. 96 #1-6, 19, 20 Day 2: pp. 96 #7-12, 21, 22 (#13-18 and 23 are challenge

63

TE-6B: pp. Advanced: Enrichment-6B: pp. 55

problems) ExtraP-6B: pp. 37-41

Exit Ticket: A trapezoid has an area of 84 square inches, a height of 7 inches, and one base that is 9 inches. What is the length of the other base? Show your work.

3 days

10.3 Area of Other Polygons

1. Express a polygon as a sum of its parts by dividing the polygon into triangles 2. Calculate the area of a regular polygon by dividing it into smaller shapes 3. Calculate the area and circumference of a circle using the formulas

CCSS: 6.G.1 MP: MP.1 MP.3 MP.6



Model (TE 6B pp. 99): Use the problem to illustrate how to find the area of regular polygons


“Learn” Day 1: pp. 102 #1-8 (#9-10 are challenge problems) ExtraP-6B: pp. 42-44

Exit Ticket: A regular

pentagon has sides that are 8 inches long. A line drawn from the center of the pentagon perpendicular to one of its sides measures 5.5 inches. What is the area of the pentagon? Show your work.

2 days

10.4 Area of Composite Figures

1. Recognize that a plane figure is made up of polygons 2. Solve problems involving areas of composite figures


TE-6B: pp. 104-112 Core: Student Book 6B: pp. 109-112 Basic: Reteach-6B:


Model (TE 6B pp. 104): Use the illustration of the trapezoid to discuss that a plane figure can be divided into other polygons. You may also want to have a trapezoid cut-out that can be folded

Guided Practice: pp. 104-108

64

pp. 88-95 ELL: TE-6B: pp. Advanced: Enrichment-6B: pp. 57-58

Problem of the Lesson: pp. 106 #3

Day 1: pp. 109 #1-4 Day 2: pp. 109 #6-9 (#10-14 are challenge problems) ExtraP-6B: pp. 45-53

Exit Ticket: Identify three possible combinations of polygons that the figure below can be divided into in order to find its area.

1 day



CCSS: 6.EE.2c 6.G.1 6.G.3 MP: MP.1 MP.6 MP.7


Vocabulary Review pp.114 Brain At Work: pp. 113 Chapter Wrap Up: pp. 114 Chapter Review: pp. 115-117 Chapter Test: Area of Polygons


Students use a diagonal to divide a rectangle into two right triangles, devising the formula to calculate the area of a triangle. Students will use their knowledge of rectangles and triangles to break down other polygons into familiar shapes. For example, a trapezoid can be broken

down into multiple triangles. Students learn that plane figures are made up of polygons, and composite figures can be divided into triangles, rectangles, and squares.


Find the area of a triangle with a base length of three units and a height of four units.

Find the area of the trapezoid shown below using the formulas for rectangles and triangles.

A rectangle measures 3 inches by 4 inches. If the lengths of each side double, what is the effect on the area?

65

The area of the rectangular school garden is 24 square units. The length of the garden is 8 units. What is the length of the fence needed to enclose the entire garden?

The sixth grade class at Hernandez School is building a giant wooden H for their school. The H will be 10 feet tall and 10 feet wide and the thickness of the block letter will be 2.5 feet.

o How large will the H be if measured in square feet?

o The truck that will be used to bring the wood from the lumber yard to the school can only hold a piece of wood that is 60 inches by 60 inches. What pieces of wood (how many pieces and what dimensions) are needed to complete the project?

On a map, the library is located at (-2, 2), the city hall building is located at (0,2), and the high school is located at (0,0). Represent the locations as points on a coordinate grid with a unit of 1 mile.

o What is the distance from the library to the city hall building? The distance from the city hall building to the high school? How do you know?

What shape is formed by connecting the three locations? The city council is planning to place a city park in this area. How large is the area of the planned park? http://www.state.nj.us/education/modelcurriculum/math/6u3.shtml (please see appendix)




Communicators or Whiteboards Responders Connections to evaluating expressions Additional Support (ELL , Struggling Learners): TE 6B pp.72D Advanced Learners: TE 6B pp. 72D



66

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. 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 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 MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition

http://www.state.nj.us/education/modelcurriculum/math/6u3.shtml Model Curriculum Assessment Unit 3 #21-23

DELETE THIS SECTION! NOT IN COMMON CORE STANDARDS! Chapter 11: Circumference and Area of a Circle



How are circles, circumference, and area used in real-world problems?

What are the parts of a circle and how is the radius related to the diameter of a circle?

What is circumference and how is it related to the perimeter of a polygon?

How can we calculate the circumference and area of a circle using the formulas given?

The circumference and area of a circle have real-world applications The parts of a circle are needed to calculate the circumference and area of a circle Calculating the circumference and area of a circle using the formulas is related to

evaluating expressions



Math in Focus

OTHER (e.g., tech)


67


1. Recall that a circle is a geometric figure that has many useful applications in the real world

CCSS: 6.NS.3 MP: MP.6 MP.7

TE-6B: pp. 118-121 ELL: TE 6B pp. 118D

Chapter Opener: TE 6B pp. 118 -Have you ever seen a rainbow? Quick Check (pp. 119): 1. Add: a) 0.451+3.12 b) 0.861+6.95 2. Subtract: a) 5.45 – 1.78 b) 42.781 – 36.19 3. Multiply: a) 1.34 x 9 b) 4.246 x 2 4. Divide: a) 2.56/5 b) 0.867/3 5. Round to the nearest whole number: a) 12.05 b) 46.59 6. Round to the nearest tenth: a) 7.68 b) 23.73 Pre-Test: Chapter 11 Test Prep Assessment Bk. pp. 102-103

68

2 days

11.1 Radius, Diameter, and Circumference of a Circle

1. Identify parts of a circle 2. Recognize that a circle’s diameter is twice its radius 3. Use the formula for the circumference of a circle 4. Identify semicircles and quarter circles and calculate the distance around them


TE-6B: pp. 122-135 Core: Student Book 6B: pp. 132-135 Basic: Reteach-6B: pp. 96-106 ELL: TE-6B: pp. 123, 128 Advanced: Enrichment-6B: pp. 59


Guided Practice: pp. 123-130 Model (TE 6B pp.122): With a

pair of compasses, draw a circle of radius 8 inches on the board. Label the center of the circle O and any 3 points on the circumference P,Q, and R. Draw segments OP, OQ, and OR.

Hands-On Activity (TE 6B pp.124): Drawing circles using a compass

Hands-On Activity (TE 6B pp.125): Investigating the relationship between the circumference and diameter of a circle

Hands-On Activity (TE 6B pp.131): Drawing semi-circles and quadrants

Problem of the Lesson: pp. 129 “Learn”


Exit Ticket: In your own words, define radius, diameter, and circumference. Then explain how radius, diameter, and circumference are mathematically related.

2 days

11.2 Area of a Circle

1. Use the formula to calculate the areas of circles, semicircles, and quadrants

CCSS: 6.EE.1 7.G.4 MP:

TE-6B: pp. 136-142 Core: Student


Model TE 6B: pp. 136 Show the circle cut-out and the one cut into 16 equal pieces.

69

MP.3 MP.4 MP.8

Book 6B: pp. 141-142 Basic: Reteach-6B: pp. 107-112 ELL: TE-6B: pp. 137 Advanced: Enrichment-6B: pp. 60-61

Rearrange the cut circle to match the figure shown in the text.


138 “Learn” Day 1: pp. 141 #1,2,7,10 Day 2: pp. 141 #3-6, 8,9,11 (#12 is a challenge problem) ExtraP-6B: pp. 58-61

Exit Ticket: Trina’s class plans to make a banner. The banner will be a semicircle with a diameter of 4 yards. Is 6 square yards of fabric enough to make the banner? Explain your answer.

2 days

11.3 Real-World Problems: Circles

1. Solve real-world problems involving area and circumference of circles 2. Solve real-world problems involving semicircles, quadrants, and composite figures

CCSS: 6.EE.2a 7.G.4 MP: MP.1 MP.2 MP.6

TE-6B: pp. 143-158 Core: Student Book 6B: pp. 154-158 Basic: Reteach-6B: pp. 113-126 ELL: TE-6B: pp. Advanced: Enrichment-6B: pp. 62-64


Model (TE 6B pp. 143): use the example to demonstrate the process of solving problems involving the circumference of circles


145 #2 Day 1: pp. 154 #1-4 Day 2: pp. 154 #5-9 (#10-14 are challenge problems) ExtraP-6B: pp. 62-67

Exit Ticket: A semicircular

window has a diameter of 56 inches. To insulate the window for winter, Avi wants to cut out a piece of plastic and tape it over the window. How much plastic does he

70

need? What length of tape does he need to tape along its edge? Show your work. Use 3.14 for pi.

1 day



CCSS: 6.NS.3 6.EE.1 6.EE.2c 6.G.1 6.G.4 MP: MP.1 MP.5 MP.7


Vocabulary Review pp.160 Brain At Work: pp. 158 Chapter Wrap Up: pp. 160 Chapter Review: pp. 161-163 Chapter Test: Circumference and Area of a Circle






Communicators or Whiteboards Responders Compass Additional Support (ELL , Struggling Learners): TE 6B pp.118D Advanced Learners: TE 6B pp. 118D

71


6.NS.3- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.EE.1- Write and evaluate numerical expressions involving whole-number exponents. 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 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 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. MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition









Math in Focus

OTHER (e.g., tech)

72



CCSS: 6.EE.2a 6.EE.2c 6.EE.5 6.EE.7 6.EE.8 6.EE.9 6.NS.6 6.NS.6c 6.NS.7c 6.NS.8 6.EE.2c 6.G.3 6.RP.3a 6.RP.3b 6.G.1 MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8

TE-6B: pp. 164-167

Extra Practice 6B: pp. 68-79

2 days



CCSS: 6.EE.2a 6.EE.2c 6.EE.5 6.EE.7 6.EE.8 6.EE.9 6.NS.6 6.NS.6c 6.NS.7c 6.NS.8 6.G.3 6.RP.3a 6.RP.3b


73

6.G.1 MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8










CCSS: 6.EE.2a- Write expressions that record operations with numbers and with letters standing for numbers 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

74

order 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. 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 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 6.EE.9- Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. 6.NS.6- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates 6.NS.6c- Find and position integers and other rational number on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane 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 solve situation 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. 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 ot the same second coordinate. Apply these techniques in the context of solving real world and mathematical problems 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. 6.RP.3b- Solve unit rate problems including those involving unit pricing and constant speed 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 MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning

75

Chapter 12: Surface Area and Volume of Solids



How is surface area and volume used in real life? How can we draw the net of a solid figure by looking at the

shape of each face? How is volume related to the area of the solid’s base? How can we calculate the volume and surface area of a solid

using the given formulas?

Surface area and volume are used to solve real-world problems The net of a solid is the result of taking the solid apart and flattening the faces The volume of any figure is the area of its base multiplied by its height Calculating the volume and surface area of a solid using the formulas is related to

evaluating expressions



Math in Focus

OTHER (e.g., tech)


1. Recall that area is measured in square units, and the surface area of a prism or pyramid is the sum of the areas of its faces. 2. Recall that volume is measured in cubic units, and the volume of a prism is the area of its base times its height

CCSS: 6.EE.1 6.EE.2c 6.G.2 Foundational for: 6.G.4 MP: MP.4 MP.7

TE-6B: pp. 168-171 ELL: TE 6B pp.168D

Chapter Opener: TE 6B pp. 168 -When you light a candle, have you ever though about how it was made? -How can you find how much wax is used to make a candle? -How can you find the surface area of a candle? Quick Check (pp. 169): 1. Name each prism shown below. 2. Find the area of each figure. 3. Find the volume of each solid. Pre-Test: Chapter 12 Test Prep Assessment Bk. pp. 124-125

76

2 days

12.1 Nets of Solids

1. Identify the net of a prism and pyramid 2. Identify the solid formed by a given net


TE-6B: pp. 172-180 Core: Student Book 6B: pp. 179-180 Basic: Reteach-6B: pp. 127-132 ELL: TE-6B: pp. 174,175 Advanced: Enrichment-6B: pp. 65-66

See appendix for interactive activity


Guided Practice: pp. 176-178 Model (TE 6B pp. 172): Show

students a paper cube made from a net of a cube. Open up the cube so that students can visualize how the cube can be cut along the red edges and laid flat as shown in the text.

Hands-On Activity (TE 6B pp.173): Identifying a cube from a net.

Hands-On Activity (TE 6B pp.175): Identifying a prism from a net.

Hands-On Activity (TE 6B pp.178): Classifying pyramids


Day 1: pp. 179 #3,6,9-14 Day 2: pp. 179 #1,2,4,5,7,8 (#15-19 are challenge problems) ExtraP-6B: pp. 80-82

Exit Ticket: Work with a partner. Write down the name of one of the solids discussed in the lesson. Without showing the name, tell your partner which shape or shapes make up the faces of the solid (including the bases) and how many of each type. Then your partner should identify the solid and draw an example of a net that will form it.

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3 days

12.2 Surface Area of Solids

1. Calculate the surface area of a prism and a pyramid

CCSS: 6.EE.1 6.G.4 MP: MP.2 MP.8



Model TE 6B: pp. 181 Use the example in the text to demonstrate how to find the surface area of a cube


184 “Learn” Day 1: pp. 187 #1-5 Day 2: pp. 187 #6-9 (#10-11 is a challenge problem) ExtraP-6B: pp. 83-85

Exit Ticket: In your own words, explain how to find the surface area of a cube, prism, or pyramid.

3 days

12.3 Volume of Prisms

1. Calculate the volume of a prism

CCSS: 6.EE.1 6.G.2 MP: MP.4 MP.6 MP.8




Model (TE 6B pp. 189): Use the example in the text to demonstrate how to find the volume of a rectangular prism whose edges are not all whole numbers

Hands-on Activity (TE 6B pp. 195): Determining the relationship between volume and surface area of prisms


193 Day 1: pp. 196 #1-7 Day 2: pp.197 #8-16 (#17-20 are challenge problems) ExtraP-6B: pp. 86-88

78

Exit Ticket: A triangular prism and a rectangular prism are the same height and have the same volume. Identify a set of possible dimensions for the bases of the prisms. The area of the bases must be equal.

2 days

12.4 Real World Problems: Surface Area of Volume

1. Solve problems involving surface area and volume of prisms

CCSS: 6.EE.2c 6.G.2 MP: MP.1 MP.2 MP.5



Model (TE 6B pp. 200): Use the example in the text to demonstrate how to find the volume of water needed to fill a tank that is partially full


200 #1 Day 1: pp. 207 #1-3 Day 2: pp.200 #4-6 (#7 is a challenge problem) ExtraP-6B: pp. 89-94

Exit Ticket: A triangular

prism is 20 inches high. Its triangular bases have a base of 30 inches and a height of 10 inches. Write a real-world problem involving this triangular prism. Find the surface area and volume of this prism.

2 days



CCSS: 6.EE.1 6.EE.2c 6.G.2 6.G.4 MP: MP.1


Vocabulary Review pp.209 Brain At Work: pp. 208 Chapter Wrap Up: pp. 209 Chapter Review: pp. 210-213

79

MP.7 Chapter Test: Surface Area and Volume of Solids


Students use formulas and algebraic thinking to solve surface area and volume problems Students need to use formulas thoughtfully. For example, in the formula S=6e², the exponent only applies to e, not to 6e. Students solve real world problems involving the surface area and volume of prisms


The model shows a cubic foot filled with cubic inches. The cubic inches can also be labeled as a fractional cubic unit with dimensions of 12

1ft

3.

The models show a rectangular prism with dimensions 3/2 inches, 5/2 inches, and 5/2 inches. Each of the cubic units in the model is 8

1in

3. Students work

with the model to illustrate 3/2 x 5/2 x 5/2 = (3 x 5 x 5) x 1/8. Students reason that a small cube has volume 1/8 because 8 of them fit in a unit cube.

80

Examples:

Describe the shapes of the faces needed to construct a rectangular pyramid. Cut out the shapes and create a model. Did your faces work? Why or why not?

Create the net for a given prism or pyramid, and then use the net to calculate the surface area.





81


Communicators or Whiteboards Responders Geometrical Shapes and Nets Additional Support (ELL , Struggling Learners): TE 6B pp.168D Advanced Learners: TE 6B pp. 168D


6.EE.1- Write and evaluate numerical expressions involving whole-number exponents. 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 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. 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. MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition


Interactive Activities:






82

Chapter 13: Introduction to Statistics



How are statistics used in the real world? How can we collect, organize, and tabulate data? What different ways can we represent data visually and what

is the best way to display a given set of data?

Data can be used to solve real-world problems and to help make decisions for future events

Data can be collected and organized into data tables, frequency charts, and/or other displays

Different displays are used to convey different trends in the data. For example, a line graph is used to show trends over a given period of time whereas a histogram is used to show frequency in a range of data



Math in Focus

OTHER (e.g., tech)


1. Recognize that statistics summarizes data so that information or decisions can be gathered from the data

CCSS: Foundational for: 6.SP.4 MP: MP.3 MP.6

TE-6B: pp. 214-216 ELL: TE 6B pp.214D

Chapter Opener: TE 6B pp. 214 -How does the cafeteria manager decide how many pancakes to prepare each day? -How might this help him or her? -What kind of patterns might they look for? Quick Check (pp. 216): 1. Use the data in the line plot to answer questions 1-10 Pre-Test: Chapter 13 Test Prep Assessment Bk. pp. 134

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1 day

13.1 Collecting and Tabulating Data

1. Collect, organize, and tabulate data

CCSS: 6.SP.1 6.SP.2 6.SP.5 6.SP.5a 6.SP.5b MP: MP.4 MP.5

TE-6B: pp. 217-221 Core: Student Book 6B: pp. 220-221 Basic: Reteach-6B: pp. 157-163 ELL: TE-6B: pp. 218 Advanced: Enrichment-6B: pp.



pp.219): Collect, Tabulate, and Interpret Data


Day 1: pp. 220 #1-4 ExtraP-6B: pp. 95-98

Exit Ticket: Describe a context that might produce the following data set. 1,3,4,4,6,5,3,2,2,7,9,11,8. Then, organize the data into three intervals and make a frequency table to display the data.

1 day

13.2 Dot Plots 1. Display and analyze data using a dot plot

CCSS: 6.SP.4 6.SP.5d MP: MP.2 MP.3 MP.4




Model TE 6B: pp. 222 Use the scenario in the text to show students how to display and analyze numerical data using a dot plot

Hands-On Activity (TE 6B pp. 225): Constructing a Distribution


223 #1 Day 1: pp. 226 #1-8 ExtraP-6B: pp. 99-103

Exit Ticket: In your own words, compare frequency tables and dot plots as methods of displaying a data set. Describe how the data is displayed in each and the advantages of each.

84

5 days

13.3 Histograms 1. Display and analyze data using a histogram 2. Display and analyze data using a box and whiskers plot

CCSS: 6.SP.4 6.SP.5d MP: MP.4 MP.5





229 “Learn” Day 1: pp. 234 #1-4 Day 2: pp. 235 #5-10 (#11-12 are challenge problems) ExtraP-6B: pp. 104-113


words, compare how a data set might be displayed in a dot plot and in a histogram.

2 days



CCSS: 6.SP.1 6.SP.2 6.SP.4 6.SP.5 6.SP.5a 6.SP.5b 6.SP.5d MP: MP.1 MP.8


Vocabulary Review pp.238 Brain At Work: pp. 237 Chapter Wrap Up: pp. 238 Chapter Review: pp. 239-241 Chapter Test: Introduction to Statistics


Students collect, organize, and tabulate data, and then display data using dot plots and histograms, as well as analyze data. A normal data distribution is symmetrical about a vertical line. Students display data using various forms of graphs


Consider the data shown in the dot plot of the six trait scores for organization for a group of students.

o How many students are represented in the data set?

85

o What are the mean, median, and mode of the data set? What do these values mean? How do they compare?

o What is the range of the data? What does this value mean?

Examples:

Nineteen students completed a writing sample that was scored using the six traits rubric. The scores for the trait of organization were

0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6. Create a data display.

What are some observations that can be made from the data display?

Grade 6 students were collecting data for a math class project. They decided they would survey the other two grade 6 classes to determine how many DVDs

each student owns. A total of 48 students were surveyed. The data are shown in the table below in no specific order. Create a data display. What are some observations that can be made from the data display?

11 21 5 12 10 31 19 13 23 33

10 11 25 14 34 15 14 29 8 5

22 26 23 12 27 4 25 15 7

2 19 12 39 17 16 15 28 16

A histogram using 5 ranges (0-9, 10-19, …30-39) to organize the data is displayed below.

86

Ms. Wheeler asked each student in her class to write their age in months on a sticky note. The 28 students in the class brought their sticky note to the front

of the room and posted them in order on the white board. The data set is listed below in order from least to greatest. Create a data display. What are some observations that can be made from the data display?

130 130 131 131 132 132 132 133 134 136

137 137 138 139 139 139 140 141 142 142

142 143 143 144 145 147 149 150

Five number summary

Minimum – 130 months

Quartile 1 (Q1) – (132 + 133) ÷ 2 = 132.5 months

Median (Q2) – 139 months

Quartile 3 (Q3) – (142 + 143) ÷ 2 = 142.5 months

Maximum – 150 months

This box plot shows that:

o ¼ of the students in the class are from 130 to 132.5 months old

o ¼ of the students in the class are from 142.5 months to 150 months old

o ½ of the class are from 132.5 to 142.5 months old

o the median class age is 139 months.



87


9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.B.2: Assess data gathered to solve a problem for which there are varying perspectives and determine how the data can best be used to design

multiple solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.12: Develop and interpret tables, charts, and figures to support written and oral communications. 9.4.12.A.26: Employ spreadsheet applications to organize and manipulate data. 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.




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 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.4- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5- Summarize numerical data sets in relation to their context 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. 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 MP- Mathematical Practices MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition



88

Interactive Activities:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=77 http://illuminations.nctm.org/ActivityDetail.aspx?ID=78

Chapter 14: Measures of Central Tendency



How can measures of central tendency be used to make decisions in real life?

What are the mean, median, and mode and how can we calculate them when given a set of data?

Which measure of central tendency is the most accurate in a given set of data?

The mean, median, and mode of a set of data can be used to show trends in data and to help make predictions for future events

Different measures of central tendency are more accurate in difference scenarios



Math in Focus

OTHER (e.g., tech)


1. Recognize that measures of central tendency can be used to summarize data distributions, and help you make decisions in real-world problems

CCSS: Foundational for: 6.SP.2 6.SP.3 6.SP.5 MP: MP.6 MP.7

TE-6B: pp. 242-243 ELL: TE 6B pp.242D

Chapter Opener: TE 6B pp. 242 -How do manufacturers know which sizes of jeans are the most popular? Quick Check (pp. 243): 1. Divide: 48.09/7 2. Find the average of the following data set: 25ft, 32ft, 46ft, 55ft, 78ft Pre-Test: Chapter 14 Test Prep Assessment Bk. pp. 143



89

2 days

14.1 Mean

1. Calculate the mean of a set of data 2. Use the mean of a set of data to solve problems

CCSS: 6.SP.2 6.SP.5 6.SP.5a 6.SP.5c 6.SP.5d MP: MP.1 MP.2 MP.3 MP.4

TE-6B: pp. 244-250 Core: Student Book 6B: pp. 249-250 Basic: Reteach-6B: pp. 181-189 ELL: TE-6B: pp. Advanced: Enrichment-6B: pp.



pp.248): Finding mean and using the mean to solve problems

Problem of the Lesson: pp. 246 ”Learn”


Exit Ticket: In your own words, describe how to find the mean of a set of values.

2 days

14.2 Median 1. Calculate the median of a set of data 2. Use the median of a set of data to solve problems

CCSS: 6.SP.3 6.SP.5d MP: MP.2 MP.4 MP.5 MP.8

TE-6B: pp. 251-257 Core: Student Book 6B: pp. 256-257 Basic: Reteach-6B: pp. 190-197 ELL: TE-6B: pp. 252 Advanced: Enrichment-


Model TE 6B: pp. 5251 Use the example to show students how to find the median of a set of data

Hands-On Activity (TE 6B pp. 255): Collecting and Tabulating Data to Find the Mean


253 “Learn” Day 1: pp. 256 #1-8 Day 2: pp. 256 #9-13 (#14-16 are challenge problems)

90

6B: pp. ExtraP-6B: pp. 118-121

Exit Ticket: In your own words, describe how to find the median of a set of values.

2 days

14.3 Mode 1. Calculate the mode of a set of data 2. Use the mode of a set of data to solve problems

CCSS: 6.SP.4 6.SP.5d MP: MP.3 MP.4 MP.5

TE-6B: pp. 258-263 Core: Student Book 6B: pp. 262-263 Basic: Reteach-6B: pp. 198-202 ELL: TE-6B: pp. Advanced: Enrichment-6B: pp.


Model (TE 6B pp. 258): Use the table and dot plot to help students understand the concept of mode

Hands-On Activity (TE 6B pp. 261): Finding mean, median, and mode


260 “Learn” Day 1: pp. 262 #1-6 Day 2: pp. 262 #7-9 (#10-11 are challenge problems) ExtraP-6B: pp. 122-124


words, describe how to find the mode of a set of data.

2 days

14.4 Real-World Problems: Mean, Median, and Mode

1. Solve problems that are related to the concepts of mean, median, and mode, including selection of the measure of central tendency to be used for problems

CCSS: 6.SP.3 6.SP.5d MP: MP.1 MP.5 MP.7 MP.8

TE-6B: pp. 264-271 Core: Student Book 6B: pp. 269-271 Basic: Reteach-6B: pp. 203-210 ELL: TE-6B: pp. 265


Model (TE 6B pp. 264): Use the example in the text to show students how to decide which measure of central tendency must be used

Hands-On Activity (TE 6B pp. 268): Finding possible values of mean, median, and mode

Guided Practice: pp. 265-268 Brain At Work: pp.271 Problem of the Lesson: pp.

266 “Learn” Day 1: pp. 269 #1-8

91

Advanced: Enrichment-6B: pp.

Day 2: pp. 269 #9-16 (#17-21 are challenge problems) ExtraP-6B: pp. 125-129

Exit Ticket: Explain how the

measures of a center in a skewed distribution and in a symmetrical distribution differ.

2 days



CCSS: 6.SP.2 6.SP.3 6.SP.4 6.SP.5 6.SP.5a 6.SP.5c 6.SP.5d MP: MP.1 MP.7


Vocabulary Review pp.272 Brain At Work: pp. 271 Chapter Wrap Up: pp. 272 Chapter Review: pp. 273-274 Chapter Test: Measures of Central Tendency


Students will learn to calculate the mean, median, mode, and range of a data set, and how to solve real world problems involving them. Students will relate mean, median, and mode to the distribution of a data set


A baseball player’s batting average is 0.625. What does the batting average mean? Explain the batting average in terms of a fraction, ratio, and percent.

Solution:

o The player hit the ball 8

5 of the time he was at bat;

o The player hit the ball 62.5% of the time; or

o The player has a ratio of 5 hits to 8 batting attempts (5:8).




92

9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.B.2: Assess data gathered to solve a problem for which there are varying perspectives and determine how the data can best be used to design

multiple solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information 9.4.12.A.12: Develop and interpret tables, charts, and figures to support written and oral communications. 9.4.12.A.26: Employ spreadsheet applications to organize and manipulate data. 9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.




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.4- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5- Summarize numerical data sets in relation to their context 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. 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 MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning TE- Teacher’s Edition



93









Math in Focus

OTHER (e.g., tech)



CCSS: 6.EE.1 6.EE.2c 6.G.2 6.G.4 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 MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8

TE-6B: pp. 275-279

Extra Practice 6B: pp. 130-138

94

2 days



CCSS: 6.EE.1 6.EE.2c 6.G.2 6.G.4 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 MP: MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8







9.1.8.A.1: Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem solving skills. 9.1.8.B.1: Use multiple points of view to create alternative solutions. 9.1.8.C.3: Model leadership skills during classroom and extra-curricular activities. 9.1.8.D.2: Demonstrate the ability to understand inferences. 9.4.12.A.4: Select and apply appropriate reading and communication strategies to learn and use technical concepts and vocabulary in practice. 9.4.12.A.8: Use correct grammar, punctuation, and terminology to write and edit documents. 9.4.12.A.11: Apply active listening skills to obtain and clarify information

95

9.4.12.A.46: Employ organizational skills to foster positive working relationships and accomplish organizational goals. 9.4.12.A.47: Employ teamwork skills to achieve collective goals and use team members’ talents effectively.




6.EE.1- Write and evaluate numerical expressions involving whole-number exponents. 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 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. 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. 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 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.4- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5- Summarize numerical data sets in relation to their context 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. 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 MP- Mathematical Practices MP.1-Make sense of problems and persevere in solving them MP.2- Reason abstractly and quantitatively MP.3- Construct viable arguments and critique the reasoning of others MP.4- Model with mathematics MP.5- Use appropriate tools strategically MP.6- Attend to precision MP.7- Look for and make use of structure MP.8- Look for and express regularity in repeated reasoning

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