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Math Grade 4

Math Grade 4. Mrs. Ennis Permutations and Combinations Lesson 40. 369 + 560 + D = 1321 9349 – 450 = M 30 x A = 180 275 x 20 = 42 ÷ D = 7 3 hours = _______ minutes. How many sides on a hexagon? 8. Write in standard form: 70,000 + 300,000 + 50 + 2.

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Math Grade 4

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  1. MathGrade 4 Mrs. Ennis Permutations and Combinations Lesson 40

  2. 369 + 560 + D = 1321 • 9349 – 450 = M • 30 x A = 180 • 275 x 20 = • 42 ÷ D = 7 • 3 hours = _______ minutes

  3. How many sides on a hexagon? 8. Write in standard form: 70,000 + 300,000 + 50 + 2 9. Jack gets $40 for each lawn he mows. The bike he is saving for costs $300. How many lawns does he have mow to have enough money to buy the bike?

  4. 10. There are 20 players on the soccer team. The coach is ordering pizzas for their team party. If each player can eat 1/3 of a pizza, how many pizzas should the coach order?

  5. 1. 392 2. 8,899 3. 6 4. 5,500 5. 6 6. 180 7. 6 8. 370,052 9. 8 10. 7

  6. Permutations and Combinations

  7. Vocabulary

  8. Combination: a collection of things, in which the order does not matter. Example: If you are making a sandwich, how many different combinations of 2 ingredients could you make with cheese, mayo, and turkey?

  9. Solution: (Turkey and Cheese) (Turkey and Mayo) (Mayo and Cheese) In this case, the order of the ingredients doesn’t matter. A turkey and cheese sandwich is the same as a cheese and turkey sandwich.

  10. Permutation: the arrangements of a set of things in a certain order. Example: You want to visit the homes of three friends, Alex(A), Betty(B), and Chris(C), but haven’t decided in what order. What are your choices?

  11. Solution: {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a} In this case order does matter, because you are deciding what order to visit your friends.

  12. Permutation or Combination? • My fruit salad contains grapes, pineapples, strawberries, and blueberries. • Does it matter what order I place the ingredients in the bowl? • Which one is it?

  13. It’s a combination!

  14. Permutation or Combination? • My locker combination is 23-5-17. • Does it matter what order I turn the numbers? • Which one is it?

  15. It’s a permutation!

  16. Permutation or Combination? • Coach needs to decide who receives a Gold, Silver, and Bronze medal for “Best Athlete in the World.” • Does it matter what order he places the names? • Which one is it?

  17. It’s a permutation.

  18. Permutation or Combination? • What if the Coach can’t afford separate Gold, Silver or Bronze medals. The top 3 athletes receive a certificate. • Does it matter what order he prints the awards? • Which one is it?

  19. It’s a combination.

  20. Solving Combinations Problems

  21. Problem: In your closet, there are three shirts and two pairs of pants. The shirts are red, green, and yellow. The pants are blue and tan. How many different outfits can you make?

  22. Solution: 6 Combinations

  23. Problem: Jill is planning her day. She can go for a walk, mow the lawn, or go to the beach. For lunch she can eat at a Mexican restaurant or at a sandwich shop. How many choices does she have for spending her day?

  24. 1 Mexican Sandwich 2 3 Mexican Sandwich 4 5 Mexican 6 Sandwich

  25. Problem: Jeff is makinga cake. He can make a chocolate, yellow, or white cake. It can have chocolate, butter cream, or vanilla icing. He can also add sprinkles or leave them off. How many combinations are there for his cake?

  26. Solution: C Y W C V C C B V V B B n n n n s s n s n n s s n s s s n s 18 combinations

  27. There is an easier way!!!

  28. In your closet, there are three shirts and two pairs of pants. The shirts are red, green, and yellow. The pants are blue and tan. How many different outfits can you make? 3 shirts 2 pants = 6 combinations x

  29. Jill is planning her day. She can go for a walk, mow the lawn, or go to the beach. For lunch she can eat at a Mexican restaurant or at a sandwich shop. How many choices does she have for spending her day? 3 activities 2 restaurants = x 6 combinations

  30. Jeff is makinga cake. He can make a chocolate, yellow, or white cake. It can have chocolate, butter cream, or vanilla icing. He can also add sprinkles or leave them off. How many combinations are there for his cake? 3 cakes 3 icings 2 toppings = x x 18 combinations

  31. You Try It: Janet was ordering breakfast. She had to choose scrambled, fried, or poached eggs. She also had to pick grits, fruit or potatoes. There was also a choice of bacon, ham, or sausage. How many different combinations including eggs, meat, and a side were there?

  32. Solution: 3 eggs x 3 sides x 3 meats = 27 combinations

  33. You Try It: Greta was making jewelry. She could use a silver or gold clasp, and amethyst, citrine, or peridot beads. The necklace could be 16, 18, or 20 inches long. How many different necklaces could she make?

  34. Solution: 2 clasps x 3 beads x 3 lengths = 18 combinations

  35. Solving Permutation Problems

  36. Permutation: all the possible arrangements of a collection of things where order matters. Example: How many ways can we arrange the letters A, E, and O?

  37. Solution: A E O E A O O E A A O E E O A O A E There are 6 permutations.

  38. Problem: Tony’s computer has a 4 digit security code containing the numbers 4, 5, 6, and 7. How many ways are there to arrange these 4 numbers?

  39. Solution: 4 5 6 7 5 4 6 7 6 5 7 4 7 5 6 4 4 5 7 6 5 4 7 6 6 5 4 7 7 5 4 6 4 6 5 7 5 6 4 7 6 4 5 7 7 6 5 4 4 6 7 5 5 6 7 4 6 4 7 5 7 6 4 5 4 7 6 5 5 7 6 4 6 7 4 5 7 4 6 5 4 7 5 6 5 7 4 6 6 7 5 4 7 4 5 6 There are 24 ways to arrange these four numbers.

  40. Problem: You have been commissioned to create a striped flag for your city. You have yellow red and gray cloth. How many different arrangements can you make?

  41. Solution: R Y G Y G R G R Y R G Y Y R G G Y R There are 6 ways to arrange the colors.

  42. There is an easier way!!!

  43. Example: How many ways can we arrange the letters A, E, and O? 3 x 2 x 1 = 6 There are 6 permutations.

  44. Example: Tony’s computer has a 4 digit security code containing the numbers 4, 5, 6, and 7. How many ways are there to arrange these 4 numbers? x 4 x 3 x 2 1 = There are 24 ways to arrange these four numbers.

  45. You Try It: On your Ipod, you have 5 songs to make a playlist from. Using each song only once, how many ways are there to order the 5 songs?

  46. Solution: On your Ipod, you have 5 songs to make a playlist from. Using each song only once, how many ways are there to order the 5 songs? x 5 4 x 3 x 2 1 x There are 120 ways to arrange these five songs.

  47. You Try It: You are signing up for classes at school. You must take math, science, reading, and social studies. How many different schedule combinations do you have to choose from?

  48. Solution: You are signing up for classes at school. You must take math, science, reading, and social studies. How many different schedule combinations do you have to choose from? x 4 x 3 x 2 1 = There are 24 ways to arrange these four classes.

  49. Online Practice Permutation Word Problems Combinations Word Problems Permutation Guessing Game

  50. Math Fun: Jack has 14 fruit trees. He has 1 apricot tree and 1 pear tree, and the rest are divided evenly among apple, peach, and plum trees. Jack picked 6 apples from each apple tree, 10 plums from each plum tree, 3 peaches from each peach tree, and 4 pears from the pear tree. How many pieces of fruit did Jack pick?

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