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Unit 1, Week 3

Unit 1, Week 3. Rational & Irrational Numbers. Do Now – August 20 th , 2012. Solve for the variable. 3x – 12 = -24 -10x – 7 = 13 25 = - x -15 -40 = -7x - 5. Do Now – August 20 th , 2012. Please pick up your guided notes and sit down SILENTLY.

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Unit 1, Week 3

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  1. Unit 1, Week 3 Rational & Irrational Numbers

  2. Do Now – August 20th, 2012 Solve for the variable. 3x – 12 = -24 -10x – 7 = 13 25 = -x -15 -40 = -7x - 5

  3. Do Now – August 20th, 2012 • Please pick up your guided notes and sit down SILENTLY. • Respond to the following on your guided notes: • How did you prepare for your quiz? • What could you have done to better prepare your for your quiz? • What is your goal for this week’s quiz?

  4. Today’s Objective SWBAT review and track last week’s quiz. SWBAT obtain a class intern position if necessary. SWBAT define rational and irrational numbers and add to the number diagram.

  5. Today’s Agenda Do Now – 6 minutes Agenda Review – 2 minutes Review Quiz – 20 minutes Track quiz – 7 minutes Class Interns – 5 minutes Number Diagram INM – 8 minutes Close – 2 minutes

  6. Student of the Week! • Willie is… • Enthusiastic about learning! • Engaged in the material! • Positive in his thought! • Very kind! • A math rockstar! Willie White This could be you!

  7. Quiz Averages

  8. Class Interns Chief of Staff Supplies Distributor Document Filer Attendance Monitor Homework Distributor Whiteboard Distributor Expo Marker Distributor Time Keeper Line Leader (5th only) Calculator Manager

  9. Number Diagram Last week, we categorized numbers into our number diagram. Today, we will add more to the diagram. Integers Whole Natural

  10. Copy this onto your notes! Irrational Rational Integers Whole Natural

  11. Rational and Irrational Numbers • Rational Numbers • Any number that can be converted into a fraction. • Including: mixed numbers, percents, improper fractions, repeating decimals, and terminating decimals. • Example: 5 ½ , 10/5, 0.33333…, 0.515, 25% • Irrational Numbers • Any number that can’t be converted into a fraction. • Including: nonrepeating decimals, imperfect squares, and pi (π). • Example: √57, 0.521257392…,

  12. Academic Enrichment Do Now – August 21st • Please complete the following SILENTLY & INDEPENDENTLY: • Solve for the variable. • 12x – 60 = -24 • -5x + 10 = -50 • 0.5 = 0.5x + 3.5

  13. Do Now – August 21st, 2012 • Please respond to the following SILENTLY on your guided notes: • EXPLAIN the difference between rational and irrational numbers. • Is every whole number a rational number? • Name an integer that is not a whole number.

  14. Today’s Objective SWBAT identify numbers as rational and irrational.

  15. Agenda Do Now – 6 minutes Agenda Review – 2 minutes Foldable Review – 10 minutes Identifying Numbers as Rational or Irrational Numbers GP – 25 minutes Exit Ticket – 5 minutes

  16. Identifying Numbers as Rational or Irrational. Before we start to classify numbers, we will make a foldable and recall what we introduced yesterday. You must WATCH to make your foldable, I will not verbally give you directions!

  17. Identifying Numbers as Rational or Irrational Irrational Rational Types of Numbers

  18. Identifying Numbers as Rational or Irrational Rational Numbers Irrational Numbers

  19. Identifying Numbers as Rational or Irrational • In order to determine whether or not a number is rational or irrational, we must convert it into a decimal.

  20. Identifying Numbers as Rational or Irrational • Example 1: ¾ • Converted to a decimal it is 0.75 • Is this rational or irrational? • Why? • Example 2: 53% • Converted to a decimal it is 0.53 • Is this rational or irrational? • Why?

  21. Identifying Numbers as Rational or Irrational • Example 3: -5 ½ • Converted to a decimal it is -5.5 • Is this rational or irrational? • Why? • Example 4: √5 • Converted to a decimal it is 5 • Is this rational or irrational? • Why?

  22. Identifying Numbers as Rational or Irrational • Example 5: 2/3 • Converted to a decimal it is 0.6666666…. • Is this rational or irrational? • Why? • Example 6: √150 • Converted to a decimal it is 12.247448….. • Is this rational or irrational? • Why?

  23. Identifying Numbers as Rational or Irrational • Example 7: √100 • Converted to a decimal it is 10 • Is this rational or irrational? • Example 8: 0.71711711171111…. • Is this rational or irrational? • Example 9: -0.5% • Converted to a decimal it is -0.005 • Is this rational or irrational?

  24. Identifying Numbers as Rational or Irrational • Example 10: 152 • Converted to a decimal it is 225 • Is this rational or irrational?

  25. Identifying Numbers as Rational or Irrational Work on examples 11 – 15 with your partner. DO NOT MOVE ON TO EXAMPLES 16-20! π √39 ⅙ ∞ -35%

  26. Identifying Numbers as Rational or Irrational Please work on the following on your own SILENTLY & INDEPENDENTLY. √49 -32 0.41423414341424… 7π -⅛ CHALLENGE: Name a rational number that is NOT an integer

  27. Exit Ticket Each of you will receive an exit ticket. The exit ticket has 10 problems on it. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY HOMEWORK – Worksheet! 

  28. Academic Enrichment – Do Now – August 22nd Simplify the following expressions: -6(-8m – 7) 3(2 – 5) -1(-m – 11) 4 ( 3 + 8) -5(x + 2) = 20

  29. Do Now - August 23rd, 2012 • Please respond to the following SILENTLY & INDEPENDENTLY on your guided notes: • What is the fundamental difference between a rational and irrational number? • Identify these numbers into their most specific subset: • -⅔ • π • 0 • 102 • √80

  30. Today’s Objective SWBAT simplify expressions and identify as rational or irrational.

  31. Agenda Do Now – 6 minutes Agenda – 2 minutes Simplifying Expression INM – 12 minutes Simplifying Expressions GP – 10 minutes Simplifying Expressions IP – 10 minutes Exit Ticket – 5 minutes

  32. Simplifying Expressions • Before we can identify expressions as rational or irrational, we must simplify them. • Depending on the number, we simplify in different ways.

  33. Simplifying Expressions • Example 1: • This problem is actually saying √100 divided by √25. • To solve, take the square root of the top number, take the square root of the top number, and then divide. • √100 = 10 • √25 = 5 • 10/5 = 2 • Is 2 rational or irrational? Rational

  34. Simplifying Expressions • Example 2: • This problem is actually saying √49 divided by √10. • To solve, take the square root of the top number, take the square root of the top number, and then divide. • √49 = 7 • √10 = 3.162… • 7/3.162… = 0.4517… • Is 0.4517… rational or irrational? irrational

  35. Simplifying Expressions • Is there an easier way to determine whether or not these type of expressions are rational or not? Write your rule below! • Think with your partner for 1 minute. • Easy rule to follow when determining rational or irrational:

  36. Simplifying Expressions Work on example 3 – 5 with your partner. DO NOT MOVE ON TO EXAMPLES 6 – 8.

  37. Simplifying Expressions Work on examples 6 – 8 ON YOUR OWN!

  38. Simplifying Expressions • Sometimes, you will see expressions like this: • Example 9: 3√25 • This problem is telling you to multiply the square root of 25 by 3. • In order to solve this, you do what was stated above √25 = 5 x 3 = 15 OR identify if the square is perfect or imperfect. • If the square is perfect, the answer will be rational. • If the square is imperfect, the answer will be irrational.

  39. Simplifying Expressions • Example 10: √3 + 2 • The same rule applies to any number that has a square root in it. • Based off of what we discovered earlier and applied in the previous example, is the answer to this expression rational or irrational? • Try example 11- 13 with your partner. • 4√100 • √39 + 7 • -7√16

  40. Simplifying Expressions Complete examples 14 – 18 on your own. √50 – 10 4√169 √144 + 6 ½ √5 -3√36

  41. Simplifying Expressions • The last type of expressions you might see include those with squares and π. • Example 19: (√15) 2 • According to PEMDAS, you take the square root of 15 and then square your answer. Determine if its rational or irrational. • However, there is an easier way to solve this. • Think with your partner for 1 minute. • Rule for solving these problems: Squaring and square root are opposite. So they simply cancel each other out so determine if the number in the radical is I or R! • Example 20: (√-10) 2 • Rational or irrational?

  42. Simplifying Expressions Work on examples 21 – 24 with your partner. DO NOT MOVE ON TO EXAMPLES 25 – 27. (√17) 2 (√100) 2 (√½) 2 (√π) 2 (√39) 2

  43. Simplifying Expressions • If you see a problem with π (pi), you must make sure it is not being cancelled out before you assume its irrational. • Example 26: • Pi on top cancels pi on bottom so your problem is √10/√15. • When you simplify your answer is irrational. • This will not always happen. • Example 27: • Rational or irrational?

  44. Simplifying Expressions Work on examples 28 – 29 with your partner and then do examples 30 – 31 on your own. 28. 29. 10π 30.½π 31.

  45. Exit Ticket Each of you will receive an exit ticket. The exit ticket has 4 problems on it. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY HOMEWORK – Worksheet! 

  46. Academic Enrichment Do Now – August 23rd Please work these on the back of your homework. -5x (3 – 10) 20(-x – 2) 7(-x-6) -10(-2x + 4)=-100

  47. Do Now - August 23rd,2012 Please respond to the following SILENTLY & INDEPENDENTLY on your guided notes: Identify as rational or irrational: (√-7π)2 4√37

  48. Today’s Objective SWBAT identify numbers as rational or irrational.

  49. Agenda Do Now – 6 minutes Agenda – 2 minutes Homework Review – 10 minutes Guided Practice – 30 Close – 3 minutes

  50. Homework Review Please get out your homework and we will go over it to check for your understanding.

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