When any two whole numbers are added we always get another whole number

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1 UNIT 5 INTEGERS IES CASTILBLANCO DE LOS ARROYOS 1. MENTAL CALCULATION INTRODUCING INTEGERS 2. HOW MANY DIFFERENTS NUMBERS CAN I REMEMBER? Please listen these ten different situations and decide with your partner which number could you use for each one and the name of every type of number. 1. Marta has got two euros. 2. Marta owes two euros. 3. It s very cold outside. The temperature is two degrees below zero.. It s very hot outside. The temperature is twenty two degrees 5. I spent two euros and a half on a ticket for the circus 6. My uncle gave me two euros and a half to wash his car 7. I am on the second floor at the shopping centre 8. My car is parked on level two of the underground car park 9. My team lost two points today 10. I bought one half kilos of tomatoes 3. LET S WATCH AND LISTEN CAREFULLY FILLING THE GAPS WITH THE RIGHT WORD ( 0 3.0) In mathematics counting numbers are called. ( )Natural numbers do not include the number.( ) For instance the number 2009 represents two plus zero plus zero plus nine.( )The natural numbers plus zero became known as the numbers.( )When you add to any number, the of that number is unchanged.( )Zero is known as the additive.( ) When any is multiplied by its value is unchanged.( )One is known as the multiplicative. If we think that are representing distances one point then we can arrange numbers on a line.( ) We must now choose distance for the number. This distance is called the. Every number then corresponds to a multiple of that unit. This way of representing numbers is called a line. Since there an infinite of whole numbers we place an arrow on the right of the number to show that it goes in that direction. QUESTION. Do you agree with this statement? : When any two whole numbers are added we always get another whole number NUMBERS INTEGERS 1º Página 1 de 8

2 Use this kind of expressions to talk with your partner. If we add plus we got a number so it could be true. Try adding and. Which is the result? What is the result of this addition? I disagree with you. Think about this example.. I agree with you. Think about this example.. Can you repeat that,please? thank you. Can you find...? I don t think so. What does this word mean? 5. QUESTION. Do you agree with this statement? : When any two whole numbers are subtracted we always get another whole number Use this kind of expressions to talk with your partner. If we add plus we got a number so it could be true. Try adding and. Which is the result? What is the result of this addition? I disagree with you. Think about this example.. I agree with you. Think about this example.. Can you repeat that,please? thank you. Can you find...? I don t think so. What does this word mean? 6. LET S CONTINUE WATCHING AND LISTENING CAREFULLY( 3.0 ) When any two whole numbers are added we always get another whole number. ( ) Are the whole numbers closed under substractin? If you substract a larger number from a smaller whole number, is no whole number which represent the. (.) This all numbers can be, or, are called INTEGERS. ( ) 7. QUESTION. What do you think now about these statements? : When any two whole numbers are added we always get another whole number When any two whole numbers are subtracted we always get another whole number NUMBERS INTEGERS 1º Página 2 de 8

3 8. LET S CONTINUE WATCHING AND LISTENING CAREFULLY( 5.9 ) You are maybe wondering what a number actually means. As recently as the th century, negatives numbers were not accepted as legitimated numbers by many mathematicians. It was thought that only numbers represented in the real.(.) Integers can be represented on a number line just like natural numbers and whole numbers. (.) With a positive or sign, a can be thought as representing not only a but also a direction. 9. Listen to your teacher reading the numbers and symbols in the green box above. Write a verbal phrase with all you have listened ( 8) 2 ( ) : 2 12 :( 3) ( 8) + 5 ( 3) Listen to your teacher and fill in the gaps NUMBERS INTEGERS 1º Página 3 de 8

4 11. Create your own line number and try to answer in pairs the following questions: Which number do you think is smaller 33 or +1? Which number has got the greatest absolute value 33 or +1? Which is the opposite number of 3? What happen if I add 3 + ( 3) =??? 12. Listen to THIS SONG We must organize all the numbers we know. Can you give an example of A NUMBER OF each set? (a collection of items, things in thesee case numbers which share something) NATURALS WHOLE INTEGERS RATIONALS 13. Choose the a) Rational smallest set b) Integer t of numbers s the number 5 belongs to: c) Natural 1. Choose the smallest set of numbers the number belo ongs to: a) Integer b) Natural c) Rational 15. Decide which of these statements is true: a) The number 7 is rational c) The number 6 is a whole number b) The number 77 is natural d) The number is integer NUMBERS INTEGERS 1º Página de 8

5 Use this kind of expressions to talk with your partner. I think that must be a..number because its sign is (+ or negative) I think that must be a..number because it is a fraction I agree with you. Think about this example.. I disagree with you. Think about this example.. Can you repeat that, ºplease? Thank you. Can you find...? I don t think so. 16. Quick review LISTEN AND FILL THE GAPS WITH THE APPROPRIATE WORD OPPOSITES NUMBER LINE NEGATIVE ABSOLUTE VALUE INFINITY POSITIVE SIGN ZERO ORIGIN NEGATIVE SIGN POSITIVE You can visualize positive and negative integers using the. It s important to understand the number line because it shows you that every number has an opposite. An integer is a whole number that can be either greater than 0, called, or less than 0, called. Zero is neither positive nor negative. Two integers that are the same distance from the origin in opposite directions are called opposites. The arrows on each end of the number line show us that the line stretches to in both the negative and positive direction. We don t have to include a (+) when we write positive numbers. However, we do have to include the ( ) when we write negative numbers. Zero is called the, and it s neither negative nor positive. For every positive integer, there s a negative integer an equal distance from the origin. Two integers that lie the same distance from the origin in opposite directions are called. For example, negative 5 is the opposite of positive 5. Every number on the number line also has an, which simply means how far that number is from zero. The symbol for absolute value is two vertical lines. Since opposites are the same distance from the origin, they have the same absolute value. For example, the absolute value of negative 10 is ten, and the absolute value of positive 10 is also 10. The absolute value of zero is. NUMBERS INTEGERS 1º Página 5 de 8

6 Examples 2 is less than 5 because 2 lies to the left of 5 1 is greater than 3 because 1 lies to the right of 3 is less than 1 because lies to the left of 1 6 is greater than 2 because 6 lies to the right of TRAVEL GAME 18. Quick review Type these integers in order, from least to greatest and represent them in the number line Watch this video and answer the following questions with your partner If I add a positive number I must move in the number line to the. If I add a negative number I must move in the number line to the. If I subtract a positive number I must move in the number line to the. If I subtract a negative number I must move in the number line to the. So subtracting a negative number is the same that. So adding a negative number is the same that. 20. MENTAL CALCULATION 21. Quick review Fill the gaps with the right word NUMBERS INTEGERS 1º Página 6 de 8

7 22. Can you give me an example of every rule? 23. QUESTION. Do you agree with this statement? : When any two whole numbers are multiplied we always get another whole number 2. QUESTION. Do you agree with this statement? : When any two whole numbers are divided we always get another whole number 25. A GAME TO PRACTICE WITH INTEGERS OPERATIONS TRAVEL GAME 27. Quick review. Fill the gaps with the right word ADDING AND SUBTRACTING INTEGERS To integers with the same sign, add their absolute values. Give the result the same as the integers. To add integers with signs, subtract their. Give the result the same sign as the integer with the absolute value ADD SIGN DIFFERENT ABSOLUTE VALUES ADDING AND SUBTRACTING SEVERAL POSITIVE AND NEGATIVE INTEGERS To perform with several addends, you should: First add the numbers Next add the numbers Then subtract the negative amount from the total amount and give the result the same sign as the integer with the absolute value OPERATIONS POSITIVE GREATER TOTAL NEGATIVE POSITIVE 28. Quick review Type these numbers in order, from least to greatest NUMBERS INTEGERS 1º Página 7 de 8

8 29. EXERCISE: Calculate 3 a) + b ) b ) : 2 5 = 6 = 8 8 = 30. EXERCISES 1) Calculate a) [( 2) 5 ( 3) 2 ] : ( 2) 2 =( 32 9) : = 288 : = 72. Example b) ( 2) 2 ( 2) 3 ( 2) = c) ( 8) ( 2) 2 ( 2) 0 ( 2) = d) ( 2) 5 : ( 2) 3 = e) ( 3) 6 : ( 3) 3 = f) [( 2 ) 2 ] 3 ( 2) 3 :( 2) = g) [( 2) 6 : ( 2) 3 ] 3 ( 2) : ( 2) = 2) Express with an operation with integers numbers the following situations a) The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. What is the distance from the top of Mt. McKinley to the bottom of Death Valley? b) The temperature outside when I got up yesterday morning was 12 o C. The high for the day was 3 o C. What was the difference between the two values? 3) Complete the table below DATE INCOMES CHARGES BALANCE 01/13/ euros 600 euros 600 euros 01/18/ euros 00 euros 01/23/ euros 500 euros? NUMBERS INTEGERS 1º Página 8 de 8

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