what are we going to do? what does represent mean? represent means __________

What are we going to do?

What does represent mean?Represent means __________.

CFU

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

A number line shows the order of numbers based on their value.

1 show

Vocabulary

We will represent1 quantities using positive and negative numbers.

Learning Objective

Activate Prior Knowledge

Locate the number on the number line that represents 40 positive units from zero. Locate the number on the number line that represents 20 negative units from zero.

-50 -40 -30 -20 -10 0 10 20 30 40 50

9.9.14Common 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.

A quantity is a measured amount.Quantities can be measured using positive or negative numbers.• Positive or negative value is determined by comparing the quantity to zero.

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.

CFU

Positive and Negative Numbers

Concept Development

Juan is practicing diving. He dives from the 10-meter platform, and sinks to about 8 meters deep in the pool.

Juan’s position before the dive is 10 meters.Juan’s position after the dive is -8 meters.

positive

negative

zero

+10 meters

Water Level (0 meters)

-8 meters

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 negativeExplain what zero means in the problem.

Represent quantities using positive or negative numbers.1

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2 find (synonym)

Vocabulary

Skill Development/Guided Practice

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

2

3

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Quantities can be measured using positive or negative numbers.• Positive or negative value is determined by comparing the

quantity to zero.

1. Last summer, the high temperature was 37 degrees Celsius. Today in winter, the low temperature is 7 degrees below zero Celsius.

Explain the value of the zero on the number line.

0

-7 degrees C

37 degrees C

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.

The zero on the number line represents 0 degrees Celsius (the freezing point of water).

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 negativeExplain what zero means in the problem.


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2 find (synonym)

Vocabulary



CFU

2

3

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quantity to zero.

2. 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.


0

-5 degrees

45 degrees

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.

The zero on the number line represents 0 degrees Fahrenheit.



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2 find (synonym)

Vocabulary



CFU

2

3

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quantity to zero.

3. 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.


0

-282 feet14,505

feet

The lowest point is negative because it is below sea level. The highest area is positive because it is above sea level.

The zero on the number line represents sea level.

ApplicationT: Redraw the number line vertically. Explain why it makes sense to use a vertical number line for this question.

14,505

-282

Height is measured vertically. The vertical number line is better at showing height.



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2 find (synonym)

Vocabulary



CFU

2

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5


quantity to zero.

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.


0

-2,000 feet10,000

feet

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.

The zero on the number line represents sea level (the altitude of planes is measured above sea level).

ApplicationS: Redraw the number line vertically. Explain why it makes sense to use a vertical number line for this question.

5. The check deposit is positive because ____________________________________________.

3 the act of obtaining and paying for an item or service

Vocabulary

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

2

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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.

BANK ACCOUNT STATEMENTDate

DescriptionQuantity10/16 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

6. The grocery purchase is negative because ________________________________________.

7. The pay car loan is negative because ____________________________________________.

8. The cash deposit is positive because _____________________________________________.

purchasing is spending money

paying is spending money

depositing is putting money into an account

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

2

1

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5

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.

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 length of something left over. Abdul does not have enough sandwiches for all of his guests to eat 6 inches each.

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.

Representing quantities using positive and negative numbers will help you manage your world better.

Representing quantities using positive and negative numbers will help you do well on tests.

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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

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.

Relevance

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.


quantity to zero.

0

Skill Closure


quantity to zero.



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1. The temperature in the grocery store was 70 degrees. But the temperature in the walk-in freezer was 15 degrees below zero.


-15 degrees

70 degrees

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.

The zero on the number line represents 0 degrees.

0

Skill Closure


quantity to zero.



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2. At the carnival, the Ferris wheel was 30 feet high. The water in the duck pond, however, was 4 feet below the ground.


-4 feet 30 feet

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.

The zero on the number line represents the level of the ground.

What did you learn today about representing quantities using positive or negative numbers? (Pair-Share) Use words from the word bank.

Access Common Core

Word Bankquantity

measuredpositive

negative numbers

zero

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.


quantity to zero.

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.

Summary Closure

Independent Practice


quantity to zero.

1. The refrigerator keeps food at about 4 degrees Celsius, while the freezer keeps them at about 18 degrees below zero Celsius.


0

-18 degrees C

4degrees C

The temperature in the refrigerator is positive because refrigerators are not kept below freezing. The temperature in the freezer is labeled as below zero.




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quantity to zero.

2. To make iced tea, you need to heat water to 100 degrees Celsius, and freeze ice cubes at 0 degrees Celsius.


0

0degrees C

100degrees C

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.




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quantity to zero.

3. The latest poll showed the presidential candidate was up 12 points in the East, but down 15 points in the West.


0

-15 points

12points

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.

The zero on the number line represents the values of the previous poll numbers.



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quantity to zero.

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%.


0

-10% 12%

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.

The zero on the number line represents the values in the previous poll.



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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? ____________________________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

- 50 dollars

+ 50 dollars

Access Common Core

BANK ACCOUNT STATEMENTDate

DescriptionQuantity06/14 Deposit

check

$268.00

06/16

Purchase new books $38.72

06/23 Pay

phone bill

$45.39

06/24 Deposit

cash

$120.00

Look at the quantities in this bank account statement. Represent each quantity as a positive or negative number. Explain your answers. (Pair-Share)

Representation

_________

_________

_________

_________

+ 268.00

- 38.72

- 45.39

+ 120.00

Zero is no change in the account.

Zero is the amount of grapes each field yielded last year.

Periodic Review 2

Access Common Core

Determine whether these statements correctly represent quantities as positive or negative numbers.

2. A 30-foot high oak tree was found to have 15-foot deep roots, giving it strength and stability.Tree: ____________________Roots: _________________


1. 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: ____________________


+ 2 feet- 3 feet

+ 30 feet

- 15 feet

Statement Represented as a Pos. or Neg. Number

Yes or No

1. The hot air balloon went 200 feet high. - 200 feet O Yes O No

2. The scuba diver explored a 300-foot depth. - 300 feet O Yes O No

3. The aluminum melted at 1220 degrees F. -1220 degrees O Yes O No

4. George missed 3 hours of work today. 3 hours O Yes O No

5. Construction of the tall building started with a 20-foot deep foundation.

- 20 feet O Yes O No

6. John got $1.00 off on his tickets for the movie.

$1.00 O Yes O No

Zero is the level of the ground.

Zero is the level of the ground.

Periodic Review 3

1. 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: __________________


+ 200 points

- 53 points

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.

+ 30 ft - 50 ft

+ 4 mi - 4 mi

+ 85 + 1 in

+ 44 days

- 7, -14, or -21

+ $1,000,000

- $5,000 + 396 people

Zero represents no change in the markets.

what are we going to do? what does represent mean? represent means __________

Documents

positive number

negative value

positive units

negative units

connectiona number line

order of numbers

rational numbers

vertical number line