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Bell Work

Bell Work. Explain why the location of point A(1, -2) is different than the location of point B(-2, 1). **Answer in complete thought sentences. Adding Integers. Using Counters to Add/Subtract Integers. Let represent our Positive Integers Let represent our Negative Integers

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Bell Work

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  1. Bell Work • Explain why the location of point A(1, -2) is different than the location of point B(-2, 1). **Answer in complete thought sentences.

  2. Adding Integers

  3. Using Counters to Add/Subtract Integers • Let represent our Positive Integers • Let represent our Negative Integers • Pair up with to create “ZERO pairs” since 1+(-1) = 0, the remaining counters will represent the left over amounts. • Example: -3 + 5 • Thus we have 2 positive tokens left, so the answer would be -3+5 = 2.

  4. Use counters to find the following sums: • 5+6 • -4+3 • -2+7 • -5+(-2) • -7+2 Check your answers with a number line

  5. Tricks: Adding same-sign numbers If you are adding integers with the same sign (ex: 5+5), you simply add their absolute values and keep the sign. 5+5 = 10 -6+(-2) = -8 -2+-3 = -5

  6. Practice • Give an example of an addition sentence containing at least four integers whose sum is zero. • Explain how you know whether a sum is positive, negative, or zero without actually adding.

  7. Using Counters to Subtract Integers • Let represent our Positive Integers • Let represent our Negative Integers Example: -3 –2 1) Begin with the counters of the first integer given (-3) 2) Add the zero pairs determined by the number of the second integer. 3)Then, remove the positive or negative chips determined by the 2nd integer (+2). Create zero pairs and count the remaining! Why can we add these zero pairs? -3 –2 = -5

  8. Using a number line • Show -3 -2 on a number line. Can we rewrite the expression to make it addition? • How could we show -3 –(-2)? Hint think of assets and debts.

  9. Use counters or a number line to solve the following expressions: • 5-6 • -4-(-3) • -2-7 • -5-(-2) • -7-2

  10. Trick: Subtracting Integers • Rewrite subtracting a positive as adding a negative: 5-7 = 5+(-7) • Taking away a debt is a good thing!9-(-5) = 9+5 • If the numbers have the same signs, add the absolute values and keep the sign. -5-15 = -5+(-15) = -20 • If the numbers have opposite signs, subtract the two numbers and keep the sign of the number with the highest absolute value! • 9-12 = 9+(-12) think: 12-9 =3, but 12 is larger so -3!

  11. Evaluate an Expression • Evaluate x-y if x=12 and y =7 • Replace x and y with the numbers above and solve: x-y 12-7 12+ (-7) 5

  12. Integer Video • http://www.teachertube.com/video/integers-121930

  13. 1-3B/C Multiply Integers

  14. How do I write 5+5+5 as multiplication?

  15. How do I write 6+6+6+6+6 as multiplication?

  16. How do I write (-6)+(-6)+(-6)+ (-6)+(-6)? as multiplication?

  17. Explore Multiplying with Counters • The number of students who bring their lunch to Phoenix middle School has been decreasing at a rate of 4 students per month. What integer represents the total change after three months? • So what do we need to find? • The integer -4 represents a decrease of 4 students each month. After 3 months, the total change will be 3(-4) Use counters to model 3 groups of 4 negative counters.

  18. Model 3 x (-4) Place 3 sets of 4 negative counters on the mat. How many negative counters do we have? What does this represent?

  19. Use counters to find -2 x (-4) If the first factor is negative, you will need to remove counters front the mat.

  20. Draw it! • With your partner, figure out how you could represent 4x2 on a number line. • Now try representing (-3)(2).

  21. Write it!! The RULES: • Ways to express multiplication: • x, parenthesis, ∙ • For even numbers of factors: • Same (like) signs = POSITIVE • Different (unlike) signs = NEGATIVE • Or draw a triangle… Example: 3(4) =12 (-2)x(-7) = 14 (3)(-4) = -12 2(-7) = -14

  22. Use the Triangle + − −

  23. But what about the EXPONENTS? • (8)2 = ? • (-8)2 = ? • Write the rule for powers of 2! • (2)3 = ? • (-2)3 = ? • Write the rule for powers of 3! • Try powers of 4 and 5. Is there a pattern?

  24. Explain Your Reasoning • Evaluate (-1)50. Explain your reasoning. • Explain when the product of three integers is positive.

  25. 1-3D Divide Integers

  26. Integers- Part 2! Division

  27. The Rules: Same as Multiplication! • Division can be written in two ways: ÷ or by a fraction (top divided by the bottom number) • We call the answer to a division problem a Quotient • For 2 factors: • Like signs = POSITIVE • Unlike signs = NEGATIVE

  28. Multiplication/Division ONLY • Try this: • (3)(-4)(4) ÷(-12) = # of negatives: 2 • (24 ÷(-3))(7) ÷ 2 = # of negatives: 1 • (-2)(-2)(4)(-2) ÷(-4)= # of negatives: 4 • (7)(-2)(16 ÷(-8))(-3)= # of negatives: 3 • If your problem has only multiplication or division (no addition or subtraction signs) what do you notice about even and odd number of negatives?

  29. Evaluating Expressions • Rewrite the equation using given numbers. Make sure to plug into variables using (), especially when the number is negative! • Ex: Let x = -8 and y = 5. xy ÷ (-10) = (-8)(5) ÷ (-10) = (-40) ÷ (-10) = 4

  30. Evaluating Expressions 2) = -9 Note: (10-x)/(-2)  notice you simplify the top first in order of operations, then divide last!

  31. Review of all Rules! Addition: Same sign: add and keep the sign Different sign: subtract and keep the sign of the number with the largest absolute value Subtraction: Change minus sign to a plus and flip the sign of the 2nd number: Ex: 5-2 become 5+(-2) or 6-(-2) becomes 6+2, then follow the addition rules. ____________________________________________________ Multiplication/Division: Like sign: Positive Unlinkesign: Negative If it is all multiplication/Division, even negatives= positive odd negatives = negative

  32. Check Your Understanding • Page 63 #1-9 Rally Coach * Remember: One sheet of paper for the pair. Take turns coaching and writing.

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