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Understanding Improper and Mixed Fractions: Comparison, Representation, and Equivalents

This educational resource explores improper and mixed fractions, focusing on their comparison, representation, and equivalencies. Activities include drawing fractional models, solving fraction problems, and understanding key concepts such as equivalent fractions and percentages. Students will engage in practical examples, like sharing portions of a cake, to visualize and solve fraction-related challenges. By the end of the module, learners will have a solid grasp of fractions with like and unlike denominators, and be able to perform operations such as addition, subtraction, and comparison of fractions confidently.

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Understanding Improper and Mixed Fractions: Comparison, Representation, and Equivalents

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  1. Improper and Mixed Fractions and Comparing Representing Fractions +/- Fractions Like Denominators Equivalent Fractions $200 $200 $200 $200 $400 $400 $400 $400 $600 $600 $600 $600 $800 $800 $800 $800 $1000 $1000 $1000 $1000

  2. Category 1 $200 • Draw a fractional model (picture form) that shows this amount: • 7/10

  3. Category 1 $400 • What fraction does this model represent? Is it fraction of a region or a set? Show your answer in simplest form.

  4. Category 1 $600 • Draw a picture to answer this question: • What is 2/3 of 9?

  5. Category 1 $800 • Draw a picture to answer this problem: • Ms. Schustak, Ms. Maryose, and Ms. Eiseman were sharing a cake. They split it up into 6 slices. Two of them ate the same amount of cake. How much could each person have eaten? How much did Ms. Eiseman and Ms. Schustak eat with these amounts?

  6. Category 1 $1000 • Is 1/2 of region A is larger than 1/2 of region B? What is 3/4 of region A? 1/3 of region B? Region B Region A

  7. Category 1 $200-Answer

  8. Category 1 $400-Answer • 8/24; 1/3; Fraction of a Region

  9. Category 1 $600-Answer • 2/3 of 9 is 6.

  10. Category 1 $800-Answer • Answers will vary: • Must: draw a picture, have two amounts the same, and have added the fractions correctly!

  11. Category 1 $1000-Answer • No, 1/2 of both regions equals 12, they are the same because they have the same area. • 3/4 of 24=18 • 1/3 of 8 = 24.

  12. Category 2 $200 • What is 8/15-4/15. If possible, show your answer in simplest form.

  13. Category 2 $400 Jenny used 3/4 cup of orange juice, and ¼ cup of pineapple juice in a fruit punch. How much more organe juice did Jenny use than pineapple juice? Daily Double

  14. Category 2 $600 • Evaluate each expression for n=1/8 • 7/8 - n =

  15. Category 2 $800 William ate 1/12 of a Hershey bar. Tai ate 5/12 of a Hershey bar. Shane ate 1/2 of a Hershey bar. How much of the Hershey bar was left?

  16. Category 2 $1000 • Find the sum of these fractions. Write the final answer in simplest form. • 5/4, 2/4, 7/4

  17. Category 2 $200-Answer • 4/5

  18. Category 2 $400-Answer • ½

  19. Category 2 $600-Answer • 6/8= 3/4

  20. Category 2 $800-Answer • There is no more left!

  21. Category 2 $1000-Answer 3 ½

  22. Category 3 $200 • What is 3 7/8 as an improper fraction? • Is this greater than or less than 3 3/4?

  23. Category 3 $400 • What is 59/8 as a mixed number. Is this greater than or less than 7 2/8?

  24. Category 3 $600 • Write three different improper fractions that equal the whole number 3.

  25. Category 3 $800 • Draw a picture to show this mixed fraction: 3 2/3 • What is this mixed number as an improper fraction?

  26. Category 3 $1000 • Compare these three fractions, listing them in order from least to greatest: • 13/8, 45/6, 58/7, 85/9

  27. Category 3 $600-Answer • Answers will vary: Examples 12/4, 36/12, etc.

  28. Category 3 $200-Answer • 31/8, 3 7/8 is greater

  29. Category 3 $400-Answer • 7 3/8; greater than

  30. Category 3 $800-Answer • 3 2/3=11/3

  31. Category 3 $1000-Answer • 13/8 (1 5/8), 45/6 (7 3/6), 58/7 (8 2/7), 85/9 (9 4/9).

  32. Category 4 $200 • Write three equivalent fractions for 1/3.

  33. Category 4 $400 • Use multiplication to find an equivalent fraction for 8/12. • Use division to find an equivalent fraction for 8/12.

  34. Category 4 $600 • Write 5 equivalent fractions for 6/10.

  35. Category 4 $800 • Write 5 equivalent fractions for 12/48.

  36. Category 4 $1000 • A fraction with a denominator of 100 can be written as a percent. Percent means “per 100.” • Write each fraction as a percent: • 1/2 • 3/4 • 6/10 • 3/25

  37. Category 4 $200-Answer • Answers will vary.

  38. Category 4 $400-Answer • Answers will vary.

  39. Category 4 $600-Answer • Answers will vary.

  40. Category 4 $800-Answer • Answers will vary.

  41. Category 4 $1000-Answer • 50% • 75% • 60% • 12%

  42. Final Jeopardy

  43. Final Jeopardy You have 1 minute to consult…

  44. Final Jeopardy You have 30 seconds to consult…

  45. Final Jeopardy • What are three major things that the European’s demanded of the Lenape? You have 15 seconds to consult…

  46. Final Jeopardy • What are three major things that the European’s demanded of the Lenape? Time Is Up

  47. Final Jeopardy - Answer • Their land • Beaver/Otter fur • Firewood • Change their culture/religion

  48. Jeopardy • Thank you for playing another fine round of America’s favorite question and answer game.

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