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What are we going to do? What does represent mean? Represent means __________.

Learning Objective. 9.9.14. We will represent 1 quantities using positive and negative numbers. What are we going to do? What does represent mean? Represent means __________. CFU. Common Core Standard 7.NS.1

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What are we going to do? What does represent mean? Represent means __________.

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  1. Learning Objective 9.9.14 We will represent1 quantities using positive and negative numbers. What are we going to do? What does represent mean? Represent means __________. CFU Common Core Standard 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract integers (AND other rational numbers); represent addition and subtraction on a horizontal or vertical number line diagram. Activate Prior Knowledge A number lineshows the order of numbers based on their value. Locate the numberon the number line that represents 40 positive units from zero. Locate the numberon the number line that represents 20 negative units from zero. Students, you already know how to work with positive and negative numbers on a number line. Now, we will use this knowledge to represent quantities using positive and negative numbers. Make Connection -50 -40 -30 -20 -10 0 10 20 30 40 50 1 show Vocabulary

  2. Concept Development • A quantityis a measured amount. • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. CFU Which example can be represented using a positive number? How do you know? Which example can be represented using a negative number? How do you know? What quantity is shown by the third example? A Mt. George is 1200 feet above sea level. B A large fish was seen about 10 feet below sea level. C A boat is floating on the sea. Positive and Negative Numbers Juan is practicing diving. He dives from the 10-meter platform, and sinks to about 8 meters deep in the pool. +10 meters positive negative Water Level (0 meters) zero -8 meters Juan’s position before the dive is 10 meters. Juan’s position after the dive is -8 meters.

  3. Skill Development/Guided Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. How did I/you identify the quantities in the problem? How did I/you represent the quantity using positive or negative numbers? How did I/you explain why each number was positive or negative? How did I/you explain what zero meant? CFU 3 Represent quantities using positive or negative numbers. 2 Read the problem. Identify2 the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 4 2 3 5 4 • Last summer, the high temperature was 37 degrees Celsius. Today in winter, the low temperature is 7 degrees below zero Celsius. 5 The high temperature in summer is positive because it is hot in the summer. The low temperature is negative because it is labeled as below zero. 0 37 degrees C -7 degrees C Explain the value of the zero on the number line. 2 find (synonym) Vocabulary The zero on the number line represents 0 degrees Celsius (the freezing point of water).

  4. Skill Development/Guided Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. How did I/you identify the quantities in the problem? How did I/you represent the quantity using positive or negative numbers? How did I/you explain why each number was positive or negative? How did I/you explain what zero meant? CFU 3 Represent quantities using positive or negative numbers. 2 Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 4 2 3 5 4 The weatherman said today’s high temperature will be only 45 degrees Fahrenheit. Overnight, the temperature is expected to drop to 5 degrees below zero. 5 The high temperature in summer is positive because it is not labeled as negative. The low temperature is negative because it is labeled as below zero. 0 45 degrees -5 degrees Explain the value of the zero on the number line. 2 find (synonym) Vocabulary The zero on the number line represents 0 degrees Fahrenheit.

  5. Skill Development/Guided Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. How did I/you identify the quantities in the problem? How did I/you represent the quantity using positive or negative numbers? How did I/you explain why each number was positive or negative? How did I/you explain what zero meant? CFU 3 Represent quantities using positive or negative numbers. 2 Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 4 2 3 5 4 Death Valley, Calif., is the lowest area in the U.S. at 282 feet below sea level. Mt. Whitney is the highest area in the U.S. at 14,505 feet above sea level. 5 The lowest point is negative because it is below sea level. The highest area is positive because it is above sea level. Application T: Redraw the number line vertically. Explain why it makes sense to use a vertical number line for this question. 0 14,505 feet Explain the value of the zero on the number line. Height is measured vertically. The vertical number line is better at showing height. -282 feet 14,505 The zero on the number line represents sea level. -282 2 find (synonym) Vocabulary

  6. Skill Development/Guided Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. How did I/you identify the quantities in the problem? How did I/you represent the quantity using positive or negative numbers? How did I/you explain why each number was positive or negative? How did I/you explain what zero meant? CFU 3 Represent quantities using positive or negative numbers. 2 Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 4 2 3 5 4 The pilot radioed that his airplane was at 10,000 feet. The submarine captain said his ship was at a depth of 2,000 feet. 5 The height of the plane is positive because it is above the ground. The submarine’s depth is negative because submarines travel under the ocean. Application S: Redraw the number line vertically. Explain why it makes sense to use a vertical number line for this question. 0 10,000 feet -2,000 feet Explain the value of the zero on the number line. 2 find (synonym) Vocabulary The zero on the number line represents sea level (the altitude of planes is measured above sea level).

  7. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 Maria looked at her bank statement for the last few days. She saw the transactions3 below. Explain why each value is shown as a positive or negative number. 4 5 BANK ACCOUNT STATEMENT Date Description Quantity 10/16 Deposit check +$67.00 10/20 Purchase groceries -$182.46 10/22 Pay car loan -$112.48 10/22 Deposit cash +$121.83 depositing is putting money into an account 5. The check deposit is positive because ____________________________________________. 3 the act of obtaining and paying for an item or service Vocabulary purchasing is spending money 6. The grocery purchase is negative because ________________________________________. paying is spending money 7. The pay car loan is negative because ____________________________________________. depositing is putting money into an account 8. The cash deposit is positive because _____________________________________________.

  8. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 Abdul was calculating how much of the large sub sandwiches he would have left over after a party. He found that if every guest ate 6 inches of sandwich, he would have -4 inches of sandwich left over. Explain why this cannot happen. 4 5 It is not possible to have a negative length of something left over. Abdul does not have enough sandwiches for all of his guests to eat 6 inches each. Milena wants to give apples from her apple tree away to all her friends. She calculated that if she gave each friend ten apples, she would have -15 apples left. Explain why she cannot have -15 apples. It is not possible to have a negative amount of something left over. Milena does not have enough apples to give all of her friends ten each.

  9. Relevance • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Representing quantities using positive and negative numbers will help you manage your world better. 1 You will be able to adjust your clothing for temperature, adjust your direction up or down, balance your bank account, and understand how electricity works. Representing quantities using positive and negative numbers will help you do well on tests. 2 Sample Test Question: 32. The Cake Factory bakes cakes for a grocery chain. All cakes must be within 3 ounces of the target weight of 30 ounces. Cakes were assigned a negative number if they were below 30 ounces and a positive number if above 30 ounces. Which cake weights below would be accepted? A A cake with a reading of -1.2 oz. B A cake with a reading of 2.7 oz. C A cake with a reading of -5.3 oz. D A cake with a reading of 3.1 oz. Does anyone else have another reason why it is relevant to represent quantities using positive and negative numbers? (Pair-Share) Why is it relevant to represent quantities using positive and negative numbers? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU

  10. Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Skill Closure Represent quantities using positive or negative numbers. Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 2 3 4 5 Word Bank • The temperature in the grocery store was 70 degrees. But the temperature in the walk-in freezer was 15 degrees below zero. The high temperature in the store is positive because stores are usually kept comfortably warm. The temperature in the freezer is negative because it is labeled as below zero. 0 70 degrees -15 degrees Explain the value of the zero on the number line. The zero on the number line represents 0 degrees.

  11. Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Skill Closure Represent quantities using positive or negative numbers. Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 2 3 4 5 Word Bank At the carnival, the Ferris wheel was 30 feet high. The water in the duck pond, however, was 4 feet below the ground. The height of the Ferris wheel is a positive number because it is a height above the ground. The depth of the duck pond is negative because it is below the ground. 0 30 feet -4 feet Explain the value of the zero on the number line. The zero on the number line represents the level of the ground.

  12. Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Access Common Core The school’s swimming pool was 14 feet deep and the diving board was 3 feet above the water. Charles said these quantities could be represented with positive and negative numbers as 14 and -3. Do you agree? Explain. No. The depth of the pool should be negative, as it is below the surface, and the diving board is above, so it should be positive. Word Bank quantity measured positive negative numbers zero Summary Closure What did you learn today about representing quantities using positive or negative numbers? (Pair-Share) Use words from the word bank.

  13. Independent Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Represent quantities using positive or negative numbers. Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 2 3 4 • The refrigerator keeps food at about 4 degrees Celsius, while the freezer keeps them at about 18 degrees below zero Celsius. 5 The temperature in the refrigerator is positive because refrigerators are not kept below freezing. The temperature in the freezer is labeled as below zero. 0 4 degrees C -18 degrees C Explain the value of the zero on the number line. The zero on the number line represents 0 degrees Celsius (the freezing point of water).

  14. Independent Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Represent quantities using positive or negative numbers. Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 2 3 4 To make iced tea, you need to heat water to 100 degrees Celsius, and freeze ice cubes at 0 degrees Celsius. 5 The temperature that water boils at is positive because boiling water is hot. The temperature that water freezes at is neither negative nor positive because it is 0 degrees Celsius. 0 100 degrees C 0 degrees C Explain the value of the zero on the number line. The zero on the number line represents 0 degrees Celsius (the freezing point of water).

  15. Independent Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Represent quantities using positive or negative numbers. Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 2 3 4 The latest poll showed the presidential candidate was up 12 points in the East, but down 15 points in the West. 5 The amount that the presidential candidate was up is a positive number because his poll numbers were higher in the East in the new poll. The amount that his poll numbers were down is a negative number because his poll numbers were below what they were in the West in the previous poll. 0 12 points -15 points Explain the value of the zero on the number line. The zero on the number line represents the values of the previous poll numbers.

  16. Independent Practice • Quantities can be measured using positive or negativenumbers. • Positive or negative value is determined by comparing the quantity to zero. Represent quantities using positive or negative numbers. Read the problem. Identify the quantities in the word problem. (underline) Represent the quantity using positive or negative numbers. Hint: Compare the numbers to zero. Explain why each number is positive or negative Explain what zero means in the problem. 1 2 3 4 Polls showed that the number of people favoring the new immigration law went up 12% this month, and the number against the law went down 10%. 5 The change in the number of people favoring the new immigration law is positive because the number of people for it went up. The change in the number of people against the law is negative because the number of people against it went down. 0 -10% 12% Explain the value of the zero on the number line. The zero on the number line represents the values in the previous poll.

  17. Periodic Review 1 1. To save for a new bike, Amandeep transferred $50 from her checking to her savings account. How would you describe the values below? The change in her checking account: ____________________ The change in her savings account: _________________ What is the value of zero in these examples? ____________________________ - 50 dollars + 50 dollars Zero is no change in the account. 2. Juan is looking at his grape vines this year. His first field yielded 110 more pounds of grapes than last year. The second field yielded 68 fewer pounds than last year. How would you describe these changes? 1st field: ___________________ 2nd field: ____________________ What is the value of zero in this example? ____________________________ + 110 pounds - 68 pounds Zero is the amount of grapes each field yielded last year. Access Common Core Look at the quantities in this bank account statement. Represent each quantity as a positive or negative number. Explain your answers. (Pair-Share) BANK ACCOUNT STATEMENT Representation Date Description Quantity _________ _________ _________ _________ 06/14 Deposit check $268.00 06/16 Purchase new books $38.72 06/23 Pay phone bill $45.39 06/24 Deposit cash $120.00 + 268.00 - 38.72 - 45.39 + 120.00

  18. Periodic Review 2 • When building a house, the plumbing pipes are set 3 feet deep in the ground, and allowed to rise up in the air about 2 feet. • Above ground: ____________________ • Below ground: ____________________ • What is the value of zero in this example? ____________________________ + 2 feet - 3 feet Zero is the level of the ground. 2. A 30-foot high oak tree was found to have 15-foot deep roots, giving it strength and stability. Tree: ____________________ Roots: _________________ What is the value of zero in this example? ____________________________ + 30 feet - 15 feet Zero is the level of the ground. Access Common Core Determine whether these statements correctly represent quantities as positive or negative numbers.

  19. Periodic Review 3 • The radio reported that the Dow Jones Average of the stock market was up 200 points today after being down 53 points yesterday. • Today: ________________ • Yesterday: __________________ • What is the value of zero in this example? ____________________________ + 200 points - 53 points Zero represents no change in the markets. Access Common Core Read the paragraph and represent all quantities as positive or negative numbers. Contestants on the reality show Survivor had to participate in many challenges. They had to climb 30-foot trees, dive into 50-foot deep lakes, hike four miles one way, then come back and hike four miles the opposite way. The temperature averaged 85 degrees above zero, plus they had 1 inch of rain per day. Each participant had to commit to a maximum of 44 days for the adventure, but if he or she got voted off, their time could be shortened by 7, 14, or 21 days. The winner would receive $1 million dollars, but had to spend $5000 to go to the interviews. A total of 396 people have competed so far. - 50 ft + 30 ft + 4 mi - 4 mi + 1 in + 85 + 44 days - 7, -14, or -21 + $1,000,000 - $5,000 + 396 people

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