Lesson 1: Positive And Negative Numbers On The Number Line .

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Lesson 1NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 1: Positive and Negative Numbers on the Number Lineβ€”Opposite Direction and ValueExit Ticket1.If zero lies between π‘Žπ‘Ž and 𝑑𝑑, give one set of possible values for π‘Žπ‘Ž, 𝑏𝑏, 𝑐𝑐, and 𝑑𝑑.π‘Žπ‘Ž2.𝑏𝑏𝑐𝑐𝑑𝑑Below is a list of numbers in order from least to greatest. Use what you know about the number line to completethe list of numbers by filling in the blanks with the missing integers. 6, 5, , 3, 2, 1, , 1, 2, , 4, , 63.Complete the number line scale. Explain and show how to find 2 and the opposite of 2 on a number line.0Lesson 1:Date:2Positive and Negative Numbers on the Number Lineβ€”Opposite Directionand Value8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 2NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 2: Real-World Positive and Negative Numbers and ZeroExit Ticket1.Write a story problem that includes both integers 8 and 12.2.What does zero represent in your story problem?3.Choose an appropriate scale to graph both integers on the vertical number line. Label the scale.4.Graph both points on the vertical number line.Lesson 2:Date:Real-World Positive and Negative Numbers and Zero8/10/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 3NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 3: Real-World Positive and Negative Numbers and ZeroExit Ticket1.Write a story problem using sea level that includes both integers 110 and 120.2.What does zero represent in your story problem?3.Choose an appropriate scale to graph both integers on the vertical number line.4.Graph and label both points on the vertical number line.Lesson 3:Date:Real-World Positive and Negative Numbers and Zero8/10/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 3NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateExploratory Challenge Station Record SheetPoster οΏ½πŸ“Number Line Scale:Poster #Integers:Number Line Scale:Poster #Integers:Number Line Scale:Poster #Integers:Number Line Scale:Poster #Integers:Number Line Scale:Lesson 3:Date:Real-World Positive and Negative Numbers and Zero8/10/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 4NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 4: The Opposite of a NumberExit TicketIn a recent survey, a magazine reported that the preferred room temperature in the summer is 68 F. Awall thermostat, like the ones shown below, tells a room’s temperature in degrees Fahrenheit.Sarah’s Upstairs BedroomDownstairs Bedroom72 64 a.Which bedroom is warmer than the recommended room temperature?b.Which bedroom is cooler than the recommended room temperature?c.Sarah notices that her room’s temperature is 4 F above the recommended temperature andthe downstairs bedroom’s temperature is 4 F below the recommended temperature. Shegraphs 72 and 64 on a vertical number line and determines they are opposites. Is Sarahcorrect? Explain.d.After determining the relationship between the temperatures, Sarah now decides to represent72 F as 4 and 64 F as 4 and graphs them on a vertical number line. Graph 4 and 4 on thevertical number line on the right. Explain what zero represents in this situation.Lesson 4:Date:0The Opposite of a Number8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 5NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 5: The Opposite of a Number’s OppositeExit Ticket1.Jane completes several example problems that ask her to the find the opposite of the opposite of a number, and foreach example, the result is a positive number. Jane concludes that when she takes the opposite of the opposite ofany number, the result will always be positive. Is Jane correct? Why or why not?2.To support your answer from the previous question, create an example, written as an equation. Illustrate yourexample on the number line below.Lesson 5:Date:The Opposite of a Number’s Opposite8/11/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 6NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 6: Rational Numbers on the Number LineExit TicketUse the number line diagram below to answer the following questions.𝐾𝐾 1011.What is the length of each segment on the number line?2.What number does point 𝐾𝐾 represent?3.What is the opposite of point 𝐾𝐾?4.Locate the opposite of point 𝐾𝐾 on the number line and label it point 𝐿𝐿.5.In the diagram above, zero represents the location of Martin Luther King Middle School. Point 𝐾𝐾 represents thelibrary, which is located to the east of the middle school. In words, create a real-world situation that couldrepresent point 𝐿𝐿, and describe its location in relation to 0 and point 𝐾𝐾.Lesson 6:Date:Rational Numbers on the Number Line10/1/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 7NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 7: Ordering Integers and Other Rational NumbersExit TicketIn math class, Christina and Brett are debating the relationship between two rational numbers. Read their claims below,and then write an explanation of who is correct. Use a number line model to support your answer.1212Christina’s Claim: β€œI know that 3 is greater than 2 . So, 3 must be greater than 2 .”12Brett’s Claim: β€œYes, 3 is greater than 2 , but when you look at their opposites, their order will be opposite. So that12means 2 is greater than 3.”Lesson 7:Date:Ordering Integers and Other Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 8NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 8: Ordering Integers and Other Rational NumbersExit TicketOrder the following set of rational numbers from least to greatest, and explain how you determined the order.1121 3, 0, , 1, 3 , 6, 5, 1,,4235Lesson 8:Date:Ordering Integers and Other Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 9NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 9: Comparing Integers and Other Rational NumbersExit Ticket1.Interpret the number line diagram shown below, and write a statement about the temperature for Tuesdaycompared to Monday at 11: 00 p.m.Monday’s Temperature ( F) at 11:00 p.m.Tuesday’s Temperature ( F) at 11:00 p.m.2.If the temperature at 11: 00 p.m. on Wednesday is warmer than Tuesday’s temperature, but still below zero, what isa possible value for the temperature at 11: 00 p.m. Wednesday?Lesson 9:Date:Comparing Integers and Other Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

6 3Lesson 9NYS COMMON CORE MATHEMATICS CURRICULUMActivity Cards ΜΆ Page 1The Navy Seals are practicingnew techniques. The bluesubmarine is 450 ft. belowsea level, while the redsubmarine is 375 ft. belowsea level.Colorado is known for drasticchanges in temperatures.Tuesday morning thetemperature was 32 F, butTuesday night thetemperature was 3 F.Holly sold lemonade two daysin a row. On Saturday, Hollyearned 5.75. On Sunday,Holly earned 3.25. πŸ“πŸ“πŸ“πŸ“πŸ“πŸ“ πŸ’πŸ’πŸ’πŸ’πŸ’πŸ’ πŸ‘πŸ‘πŸ‘πŸ‘πŸ‘πŸ‘ 𝟐𝟐𝟐𝟐𝟐𝟐 𝟏𝟏𝟏𝟏𝟏𝟏 πŸ’πŸ’ 𝟐𝟐 𝟏𝟏Lesson 9:Date:πŸŽπŸŽπŸ’πŸ’πŸ–πŸ–πŸŽπŸŽ 𝟏𝟏Dolphins love to jump out ofthe water. Dolly, the dolphin,can jump 5 meters above thewater and swim 450 metersbelow the surface of thewater.𝟎𝟎𝟏𝟏𝟏𝟏 𝟏𝟏𝟏𝟏 𝟐𝟐𝟐𝟐 𝟐𝟐𝟐𝟐 𝟐𝟐𝟐𝟐 πŸ‘πŸ‘πŸ‘πŸ‘πŸπŸπŸ‘πŸ‘ πŸ’πŸ’πŸ“πŸ“πŸ”πŸ”πŸ•πŸ•πŸ–πŸ–The high school football teamlost 8 yards on first down.On second down, the teamgained 2 yards.In golf, the lowest score wins.Pete’s final score was 2 andAndre’s final score was 5. πŸ’πŸ’πŸ’πŸ’πŸ’πŸ’ πŸ‘πŸ‘πŸ‘πŸ‘πŸ‘πŸ‘ 𝟐𝟐𝟐𝟐𝟐𝟐 𝟏𝟏𝟏𝟏𝟏𝟏 πŸ–πŸ– πŸ•πŸ•πŸŽπŸŽ πŸ”πŸ” πŸ’πŸ’ 𝟐𝟐𝟎𝟎𝟐𝟐 πŸ“πŸ“ πŸ‘πŸ‘ 𝟏𝟏𝟎𝟎 πŸπŸπŸ‘πŸ‘Comparing Integers and Other Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 9NYS COMMON CORE MATHEMATICS CURRICULUM6 3Activity Cards ΜΆ Page 2Jayden has earned 3 bonuspoints completing math extracredit assignments, whileShontelle has earned 32 bonuspoints.Teagon earned 450 lastmonth cutting grass. Xavierspent 375 on a newcomputer.Last month, the stock marketKim and her friend Stacey wentto the book store. Stacey spent 8 on notebooks. Kim spent 5on snacks and pencils.3dropped 5 points overall. So4far this month, the stock14market rose 3 points.At a beach in California, if aperson stands in the water, heBrittany went to an officesupply store twice last week.The first time she made2 copies that cost 0.20 each.The second time she did notbuy anything, but found 2dimes in the parking lot.1or she is ft. below sea level. If5the person walks onto the2beach, he or she is ft. abovesea level.5Lesson 9:Date:Comparing Integers and Other Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 10NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 10: Writing and Interpreting Inequality StatementsInvolving Rational NumbersExit TicketKendra collected data for her science project. She surveyed people asking them how many hours they sleep during atypical night. The chart below shows how each person’s response compares to 8 hours (which is the answer sheexpected most people to say).NameNumber of Hours(usually slept each night)Compared to 8 hours8.50.5FrankieMr. FieldsKarla7 1.0809.5LouisTiffany71.534 14a.Plot and label each of the numbers in the right-most column of the table above on the number line below.b.List the numbers from least to greatest.c.Using your answer from part (b) and inequality symbols, write one statement that shows the relationshipamong all of the numbers.Lesson 10:Date:Writing and Interpreting Inequality Statements Involving RationalNumbers8/13/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 10NYS COMMON CORE MATHEMATICS CURRICULUM6 3Number Correct:Rational Numbers: Inequality Statements – Round 1Directions: Work in numerical order to answer Problems 1–33. Arrange each set of numbers in order according to theinequality symbols.1.2.3. 12. 1 , 1 , 0 1 , 1 , 013. 14. 4.3 Β½ , 3 Β½ , 015.5.3 Β½ , 3 Β½ , 0 16.6. 1 , Β½ ,Β½17. 1 , Β½ ,Β½18. 3 , 4 , 519. 13 , 14 , 1520.7.8.9. 10. 13 , 14 , 1521.11. ΒΌ , 1 , 022. ΒΌ , 1 , 0Lesson 10:Date: 17 , 4 , 1625. 17 , 4 , 1626. 0 , 12 , 1127.0 , 12 , 1128. 1,ΒΌ ,Β½29. 0.5 , 1 , 0.6 1,ΒΌ ,Β½30. 0.5 , 1 , 0.6 Β½,Β½ ,031. 8 , 9 , 8 Β½ , Β½ , 032. 18 , 19 , 250 , 10 , 033. 2 , 3 , 1 24. 50 , 10 , 025 , ΒΎ , ΒΎ 25 , ΒΎ , ΒΎ 2.2 , 2.3 , 2.4 1.2 , 1.3 , 1.4 0.2 , 0.3 , 0.4 2 , 3 , 1Writing and Interpreting Inequality Statements Involving RationalNumbers8/13/14 2014 Common Core, Inc. Some rights reserved. commoncore.org 7 , 6 , 6 323.This work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 10NYS COMMON CORE MATHEMATICS CURRICULUM6 3Number Correct:Improvement:Rational Numbers: Inequality Statements – Round 2Directions: Work in numerical order to answer Problems 1–33. Arrange each set of numbers in order according to theinequality symbols.1. 12. 2.1/7 , 1/7 , 013.3.1/7 , 1/7 , 04. 23. 1ΒΌ , 1 , 1Β½24.14.11ΒΌ , 11 , 11Β½25.3/7 , 2/7 , 1/715.11ΒΌ , 11 , 11Β½26. 82 , 93 , 1045.3/7 , 2/7 , 1/716.0 , 0.2 , 0.127. 82 , 93 , 1046. 4/5 , 1/5 , 1/517.0 , 0.2 , 0.128.0.5 , 1 , 0.67. 4/5 , 1/5 , 1/518.1 , 0.7, 1/1029. 0.5 , 1 , 0.68. 8/9 , 5/9, 1/919.1 , 0.7, 1/1030. 0.5 , 1 , 0.69. 8/9 , 5/9, 1/920.0 , 12 , 12Β½31.1 ,8,910. 30 , 10 , 5021.0 , 12 , 12Β½32.11. 30 , 10 , 5022.5 , 1 , 033. 40 , 20 , 60Lesson 10:Date: 5 , 1 , 0 1 , 1ΒΎ , 1ΒΎ 1 , 8 , 9 2 , 3 , 5 2 ,3,5Writing and Interpreting Inequality Statements Involving RationalNumbers8/13/14 2014 Common Core, Inc. Some rights reserved. commoncore.org1 , 1ΒΎ , 1ΒΎThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 11NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 11: Absolute Valueβ€”Magnitude and DistanceExit TicketJessie and his family drove up to a picnic area on a mountain. In the morning, they followed a trail that led to themountain summit, which was 2,000 feet above the picnic area. They then returned to the picnic area for lunch. Afterlunch, they hiked on a trail that led to the mountain overlook, which was 3,500 feet below the picnic area.a.Locate and label the elevation of the mountain summit and mountain overlook on a vertical number line.The picnic area represents zero. Write a rational number to represent each location.Picnic area:Mountain summit:0Mountain overlook:b.Use absolute value to represent the distance on the number line of each location from thepicnic area.Distance from the picnic area to the mountain summit:Distance from the picnic area to the mountain overlook:c.What is the distance between the elevations of the summit and overlook? Use absolute value and yournumber line from part (a) to explain your answer.Lesson 11:Date:Absolute Valueβ€”Magnitude and Distance8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 12NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 12: The Relationship Between Absolute Value and OrderExit Ticket1.Bethany writes a set of rational numbers in increasing order. Her teacher asks her to write the absolute values ofthese numbers in increasing order. When her teacher checks Bethany’s work, she is pleased to see that Bethany hasnot changed the order of her numbers. Why is this?2.Mason was ordering the following rational numbers in math class: 3.3, 15, 8 .a.Order the numbers from least to greatest.b.List the order of their absolute values from least to greatest.c.Explain why the orderings in parts (a) and (b) are different.Lesson 12:Date:89The Relationship Between Absolute Value and Order8/14/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 13NYS COMMON CORE MATHEMATICS CURRICULUMName6 3DateLesson 13: Statements of Order in the Real WorldExit Ticket1.Loni and Daryl call each other from different sides of Watertown. Their locations are shown on the number linebelow using miles. Use absolute value to explain who is a further distance (in miles) from Watertown. How muchcloser is one than the other?2.Claude recently read that no one has ever scuba dived more than 330 meters below sea level. Describe what thismeans in terms of elevation using sea level as a reference point.Lesson 13:Date:Statements of Order in the Real World8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

NYS COMMON CORE MATHEMATICS CURRICULUMMid-Module Assessment TaskNameDate1. The picture below is a flood gauge that is used to measure how far (in feet) a river’s waterlevel is above or below its normal level.a.6 3Explain what the number 0 on the gauge represents, and explain what the numbersabove and below 0 represent.1.51.00.50 0.5 1.0 1.5River Water 2.0 2.5 3.0 3.5b.Describe what the picture indicates about the river’scurrent water level.c.What number represents the opposite of the water level shown in the picture, and where is itlocated on the gauge? What would it mean if the river water was at that level?d.If heavy rain is in the forecast for the area for the next 24 hours, what reading might you expect tosee on this gauge tomorrow? Explain your reasoning.Module 3:Date:Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Mid-Module Assessment TaskNYS COMMON CORE MATHEMATICS CURRICULUM6 32. Isaac made a mistake in his checkbook. He wrote a check for 8.98 to rent a video game but mistakenlyrecorded it in his checkbook as an 8.98 deposit.a.Represent each transaction with a rational number, and explain the difference between thetransactions.b.On the number line below, locate and label the points that represent the rational numbers listed inpart (a). Describe the relationship between these two numbers. Zero on the number line representsIsaac’s balance before the mistake was made.0c.Use absolute value to explain how a debit of 8.98 and a credit of 8.98 are similar.Module 3:Date:Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Mid-Module Assessment TaskNYS COMMON CORE MATHEMATICS CURRICULUM6 33. A local park’s programs committee is raising money by holding mountain bike races on a course throughthe park. During each race, a computer tracks the competitors’ locations on the course using GPStracking. The table shows how far each competitor is from a check point.NumberCompetitor NameDistance to Check Point223Florence0.1 mile beforeRebecca240Lita249a.2Mary231mile past0.5 mile before2Nancy25551210mile pastmile beforeThe check point is represented by 0 on the number line. Locate and label points on the number linefor the positions of each listed participant. Label the points using rational numbers.0Check Pointb.Which of the competitors is closest to the check point? Explain.c.Two competitors are the same distance from the check point. Are they in the same location?Explain.d.Who is closer to finishing the race, Nancy or Florence? Support your answer.Module 3:Date:Rational Numbers8/15/14 2014 Common Core, Inc. Some rights reserved. commoncore.orgThis work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Mid-Module Assessment TaskNYS COMMON CORE MATHEMATICS CURRICULUM6 34. AndrΓ©a and Marta are testing three different coolers to see which keeps the coldest temperature. Theyplaced a bag of ice in each cooler, closed the coolers, and then measured the air temperature inside eachafter 90 minutes. The temperatures are recorded in the table below:CoolerTemperature (α΅’C)A 2.91B5.7C 4.3Marta wrote the following inequality statement about the temperatures: 4.3 2.91 5.7.AndrΓ©a claims that Marta made a mistake in her statement and that the inequality statement should bewritten as 2.91 4.3 5.7.a.Is either student correct? Explain.b.The students want to find a cooler that keeps the temperature inside the cooler more than3 degrees below the freezing point of water (0α΅’C) after 90 minutes. Indicate which of the testedcoolers meets this goal and explain why.M

Lesson 3: Real-World Positive and Negative Numbers and Zero . Exit Ticket . 1. Write a story problem using sea level that includes both integers 110 and 120. 2. What does zero represent in your story problem? 3. Choose an appropriate scale to graph both integers on the vertical number

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