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Algebra Unit One: Assignment #1 Numbers and Operations BASIC Evaluate each of the following without the use of a calculator. 1. 234 + 782 7. 2 7 9 3 2. 982 – 649 8. 4 9 3 5 3. 23 × 236 9. 4.17 + 1.35 4. 5537 ÷ 7 10. 14.35 – 9.68 5. 3 2 5 3 11. 1.4 × 3.8 6. 7 3 6 4 12. 24.4 ÷ 2.1 13. 36 15. 4 38 14. 43 16. 7 142 Evaluate each of the following using a calculator. 17. Describe what 54 means. 18. Describe what 3 16 means. 19. Give an example of a rational number. 20. Give an example of an irrational number. 21. Give an example of a whole number. 22. Given an example of an integer. Algebra Unit One: Assignment #1 Numbers and Operations Proficient Evaluate each of the following without using a calculator. 23. 23,567 + 87, 952 24. 12,368 ÷ 124 25. 62,134 – 38, 976 26. 432 × 184 1 7 27. 2 3 4 10 28. 1 3 2 1 6 4 3 2 29. 2 1 5 3 30. 1 2 6 1 3 5 31. 12.376 + 14.198 32. 11.87 – 4.562 33. 3.87 × 1.64 34. 12.456 ÷ 4.12 35. Describe what the expression 65 means, and evaluate this expression using a calculator. 36. Describe what the expression calculator. 7 40 represents, and evaluate this expression using a 37. Why is the number 6 considered a rational number? 38. What operation typically results in an irrational answer? 39. Why isn’t 16 an irrational number? Advanced 40. [Connect concepts and procedures in a verbal explanation] Provide a written explanation of how to add two fractions. Keep in mind the Six Traits as they apply to mathematical writing. 41. [Apply knowledge and skills in an unfamiliar context] In an alphametic puzzle, each letter of the puzzle stands for a different numerical digit. No two letters stand for the same digit, and each letter represents the same digit throughout the problem. To solve the alphametic, you must determine which digit is represented by each letter. Solve the following alphametic. Provide a written explanation of the reasoning that you used to come up with your answer. SEND +M O R E MONEY Algebra Unit One: Assignment #1 42. Numbers and Operations [Learn a new concept above and beyond what you have been taught] Read the handout on the “Closure Property” and complete the following tasks. Task One Determine if the following sets are closed under the given operations. Explain why you think the set is or is not closed. a. b. c. d. e. The set of Whole Numbers under addition. The set of Natural Numbers under subtraction. The set of Integers under subtraction. The set of Integers under multiplication. The set of Integers under division. Task Two Provide a written explanation that describes what you learned about closure. Your audience is another student in this class who has yet to learn about closure. Keep in mind the Six Traits as they apply to mathematical writing. 43. [Analyze and critique the work of others] The following work was shown by a student trying to add the following fractions: 3 2 4 5 Provide a written explanation that can be used to correct the student’s error and help the student understand how to do the problem correctly. Your explanation should describe what the student did wrong, why it is wrong, and what the student needs to do to get the problem right. 44. [Apply what you have learned in a real life situation] Determine the dimensions A, B, C, D, E, and F of the profile gage shown in the picture to the right. [Mathematics For Machine Technology, pg.43]