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Robot Rules and Algebraic Machines: Solve Patterns with Single and Inverse Processors

Explore the world of algebraic machines and robots to solve pattern problems using input-output processors, single machines, and inverse processors. Practice with exercises to determine outputs and inputs of single number machines and broken processors. Challenge yourself with two-stage machines and double vision scenarios to enhance your algebraic skills.

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Robot Rules and Algebraic Machines: Solve Patterns with Single and Inverse Processors

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  1. Algebra 1 Rules and Robots

  2. Single machines • Imagine that we have a robot to help us make patterns. INPUT OUTPUT PROCESSOR 1 6 7 2 10 5 + 5

  3. Single machines • Imagine that we have a robot to help us make patterns INPUT OUTPUT PROCESSOR 17 10 13 20 18 25 − 7

  4. Single Machines • Imagine that we have a robot to help us make patterns INPUT OUTPUT PROCESSOR 3 12 24 6 48 12 × 4

  5. Single machines • Imagine that we have a robot to help us make patterns INPUT OUTPUT PROCESSOR 12 4 11 33 9 27 ÷ 3

  6. Exercises 1 • Here are single number machines • What is the output since we know the input? a d 3 77 1 11 + 2 × 7 5 63 3 9 7 49 5 7 b e 2 2 9 12 - 7 ÷ 6 6 6 13 36 22 11 29 66 c f 12 2 3 18 × 4 ÷ 9 28 6 7 54 36 9 9 81

  7. Exercises 2 • Here are single number machines. • What is the output since we know the input? a d 10 54 1 6 + 9 × 9 12 36 3 4 14 81 5 9 b e 0 3 11 21 - 11 ÷ 7 13 7 24 49 25 9 36 63 c f 32 1 4 11 × 8 ÷ 11 56 3 7 33 72 6 9 66

  8. Inverse machines • Can we calculate the input since we know the output? INVERSE PROCESSOR INPUT OUTPUT 6 12 14 8 23 17 − 6 + 6 + 6

  9. Inverse Machines • Can we calculate the input since we know the output? INVERSE PROCESSOR INPUT OUTPUT 40 32 15 23 7 15 + 8 − 8 − 8

  10. Inverse Machines • Can we calculate the input since we know the output? INVERSE PROCESSOR INPUT OUTPUT 6 30 45 9 55 11 ÷ 5 × 5 × 5

  11. Inverse Machines • Can we calculate the input since we know the output? INVERSE PROCESSOR INPUT OUTPUT 12 3 5 20 12 48 × 4 ÷ 4 ÷ 4

  12. Exercises 3 • Here are single number machines • What is the input since we know the output? a d 4 5 7 60 + 3 × 12 8 2 11 24 31 6 34 72 b e 12 39 6 3 - 6 ÷ 13 14 65 8 5 18 91 12 7 c f 7 30 42 2 × 6 ÷ 15 11 75 66 5 12 105 72 7

  13. Exercises 4 • Here are single number machines • What is the input since we know the output? a d 6 2 19 28 + 13 × 14 3 4 16 56 12 6 25 84 b e 22 32 5 2 - 17 ÷ 16 26 80 9 5 28 112 11 7 c f 3 76 45 4 × 15 ÷ 19 9 38 135 2 11 114 165 6

  14. A Broken Processor • Imagine that the processor has broken!!!!! INPUT OUTPUT ?????????? 5 10 15 10 30 25 + 5 ???

  15. A Broken Processor • Imagine that the processor has broken!!!!! INPUT OUTPUT ??????????? 17 9 13 21 17 25 − 8 ???

  16. A Broken Processor • Imagine that the processor has broken!!!!! INPUT OUTPUT ?????????? 3 21 42 6 49 7 × 7 ???

  17. A Broken Processor • Imagine that the processor has broken!!!!! INPUT OUTPUT ?????????? 81 9 2 18 4 36 ÷ 9 ???

  18. Exercises 5 • Here are single number machines • What is the action since we know what the input and output are? a d 9 33 1 3 + 8 × 11 11 77 3 7 13 110 5 10 b e 5 1 10 10 - 5 ÷ 10 36 3 41 30 83 12 88 120 c f 24 2 4 34 × 6 ÷ 17 42 6 7 102 54 3 9 51

  19. Exercises 6 • Here are single number machines • What is the action since we know what the input and output are? a d 9 24 5 3 + 4 × 8 15 56 11 7 27 80 23 10 b e 8 13 15 39 - 7 ÷ 3 35 22 42 66 81 40 88 120 c f 20 6 4 42 × 5 ÷ 7 35 9 7 63 45 11 9 77

  20. Double vision • Imagine that we have two robots to help us make patterns • The output of machine 1 is input to machine 2 4 12 13 7 21 22 25 8 24 × 3 + 1 Machine 2 Machine 1

  21. Double Vision • Imagine that we have two robots to help us make patterns • The output of machine 1 is input to machine 2 4 16 11 3 12 7 39 11 44 × 4 − 5 Machine 2 Machine 1

  22. Exercises 7 • Here are two stage machines • What is the output since we know the input? a 16 2 × 5 + 6 26 4 46 8 b 24 5 × 7 - 11 59 10 38 7 c 31 6 × 6 - 5 13 3 1 1

  23. Exercises 8 • Here are two stage machines • What is the output since we know the input? a 5 6 ÷ 2 + 2 6 8 7 10 b 4 45 ÷ 5 - 5 6 55 10 75 c 12 42 ÷ 7 + 6 9 21 11 35

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