1. Algebra 1 Rules and Robots

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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