1 / 34

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

Download Presentation

Bell Work

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related