Download “When any two whole numbers are added we always get another

UNIT 5 1.
INTEGERS IES CASTILBLANCO DE LOS ARROYOS 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.
2.
3.
4.
5.
6.
7.
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Marta has got two euros. Marta owes two euros. It´s very cold outside. The temperature is two degrees below zero. It´s very hot outside. The temperature is twenty‐two degrees I spent two euros and a half on a ticket for the circus My uncle gave me two euros and a half to wash his car I am on the second floor at the shopping centre My car is parked on level two of the underground car park My team lost two points today I bought one half kilos of tomatoes 3.
LET´S WATCH AND LISTEN CAREFULLY FILLING THE GAPS WITH THE RIGHT WORD ( 0‐3.40)http://www.youtube.com/watch?v=8Y82JLMN_Fc 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 4. 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 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( 3.40‐) http://www.youtube.com/watch?v=8Y82JLMN_Fc 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 8. LET´S CONTINUE WATCHING AND LISTENING CAREFULLY( 5.49‐) http://www.youtube.com/watch?v=8Y82JLMN_Fc 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. 4 + 5 3 – 6 8 + (‐8) 2 ∙ (‐4) 3 ∙ 6 – 4 ‐8 : 2 12 :(‐3) 5 + 4 – 6 2 ∙ (‐8) + 5 (‐3)2 + 32 10.
Listen to your teacher and fill in the gaps NUMBERS | INTEGERS|1º Página 3 de 8 Create yyour own line
e number an
nd try to ansswer in pairss the following questionss: 11.
Whicch number do you think is smaller ‐3
3 or +1? Whicch number has got the grreatest abso
olute value ‐3
3 or +1? Whicch is the opposite numbe
er of ‐3? Whatt happen if I add 3 + (‐3)=??? Listen to
o THIS SONG http://www
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P14SA 12.
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must organizee all the num
mbers we kno
ow. Can you give an exam
mple of A NU
UMBER OF each set? ((a collection of items, things in thesee case numbe
ers which share something) NATU
URALS WHOLE INTEG
GERS RATIO
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Choose ”the smallest sett of numberss” the numbe
er 5 belongss to: 13. a) Rational b) Integer
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Páginaa 4 de 8 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. OPPOSITES Quick review LISTEN AND FILL THE GAPS WITH THE APPROPRIATE WORD NUMBER LINE POSITIVE SIGN ZERO NEGATIVE ABSOLUTE VALUE INFINITY 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 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 • ‐4 is less than 1 because … ‐4 lies to the left of 1 • 6 is greater than ‐2 because … 6 lies to the right of ‐2 17. TRAVEL GAME 18. Quick review Type these integers in order, from least to greatest and represent them in the number line ‐5 4 ‐6 ‐4 0 ‐10 1 19. Watch this video and answer the following questions with your partner http://www.youtube.com/watch?v=8Y82JLMN_Fc:(7:40) 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. 21. MENTAL CALCULATION Quick review Fill the gaps with the right word NUMBERS | INTEGERS|1º Página 6 de 8 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” 24. 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
http://www.sheppardsoftware.com/mathgames/fruitshoot/FS_Mixed_Integers.htm 26. 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 28. TOTAL NEGATIVE POSITIVE Quick review Type these numbers in order, from least to greatest ‐5 4 NUMBERS | INTEGERS|1º GREATER −3
4
‐4 0 1 3
4 1
2
Página 7 de 8 29. EXERCISE: Calculate a)
−3 1 −5
+ −
=
4 2 6 b)
−3 1 −4
· −
= 4 2 8
b)
−3 1 4
: − = 4 2 8
30. EXERCISES 1) Calculate a ) [ ( −2) 5 ∙ ( −3) 2 ] : ( −2) 2 =(− 32 ∙ 9) : 4 = −288 : 4 = −72. Ex ampl e b) (−2) 2 ∙(−2) 3 ∙(−2) 4 = c)
(−8) ∙ (−2) 2 ∙ (−2) 0 (−2) = d) (‐2) 5 : (‐2) 3 = e) (‐3) 6 : (‐3) 3 = f)
g)
[( −2 ) 2 ] 3 ∙ ( −2) 3 : (−2 ) 4 = [(− 2)
6
: (− 2) 3 ]
3
· (− 2) : (−2 )
4
= 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 ‐12o C. The high for the day was‐3o C . What was the difference between the two values? 3) Complete the table below DATE 01/13/2013 01/18/2013 01/23/2013 INCOMES 1200 euros ‐ 300 euros CHARGES
600 euros
1000 euros
500 euros
BALANCE 600 euros ‐400 euros ?
NUMBERS | INTEGERS|1º Página 8 de 8