algebra 1 rules and robots. single machines processor input output imagine that we have a robot to...
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Algebra 1
Rules and Robots
Single machines
PROCESSORINPUT OUTPUT
Imagine that we have a robot to help us make patterns.
6
7
10+ 5
1
2
5
Single machines
PROCESSORINPUT OUTPUT
Imagine that we have a robot to help us make patterns
10
13
18− 7
17
20
25
Single Machines
PROCESSORINPUT OUTPUT
Imagine that we have a robot to help us make patterns
12
24
48× 4
3
6
12
Single machines
PROCESSORINPUT OUTPUT
Imagine that we have a robot to help us make patterns
4
11
9÷ 3
12
33
27
Exercises 1 Here are single number machines What is the output since we know the input?
+ 21
3
5
3
5
7
a
- 7 9
13
29
2
6
22
b
× 43
7
9
12
28
36
c
× 711
9
7
77
63
49
d
÷ 612
36
66
2
6
11
e
÷ 918
54
81
2
6
9
f
Exercises 2 Here are single number machines. What is the output since we know the input?
+ 91
3
5
10
12
14
a
- 1111
24
36
0
13
25
b
× 84
7
9
32
56
72
c
× 96
4
9
54
36
81
d
÷ 721
49
63
3
7
9
e
÷ 1111
33
66
1
3
6
f
Inverse machines
INVERSEPROCESSORINPUT OUTPUT
Can we calculate the input since we know the output?
12
14
23+ 6
6
8
17+ 6− 6
Inverse Machines
INVERSEPROCESSORINPUT OUTPUT
Can we calculate the input since we know the output?
32
15
7− 8
40
23
15− 8+ 8
Inverse Machines
INVERSEPROCESSORINPUT OUTPUT
Can we calculate the input since we know the output?
30
45
55× 5
6
9
11× 5÷ 5
Inverse Machines
INVERSEPROCESSORINPUT OUTPUT
Can we calculate the input since we know the output?
3
5
12÷ 4
12
20
48÷ 4× 4
Exercises 3 Here are single number machines What is the input since we know the output?
+ 37
11
34
4
8
31
a
- 66
8
12
12
14
18
b
× 642
66
72
7
11
12
c
× 1260
24
72
5
2
6
d
÷ 133
5
7
39
65
91
e
÷ 152
5
7
30
75
105
f
Exercises 4 Here are single number machines What is the input since we know the output?
+ 1319
16
25
6
3
12
a
- 175
9
11
22
26
28
b
× 1545
135
165
3
9
11
c
× 1428
56
84
2
4
6
d
÷ 162
5
7
32
80
112
e
÷ 194
2
6
76
38
114
f
A Broken Processor
??????????INPUT OUTPUT
Imagine that the processor has broken!!!!!
10
15
30???
5
10
25+ 5
A Broken Processor
???????????INPUT OUTPUT
Imagine that the processor has broken!!!!!
9
13
17???
17
21
25− 8
A Broken Processor
??????????INPUT OUTPUT
Imagine that the processor has broken!!!!!
21
42
49???
3
6
7× 7
A Broken Processor
??????????INPUT OUTPUT
Imagine that the processor has broken!!!!!
9
2
4???
81
18
36÷ 9
Exercises 5 Here are single number machines What is the action since we know what the input and output are?
+ 81
3
5
9
11
13
a
- 510
41
88
5
36
83
b
× 64
7
9
24
42
54
c
× 113
7
10
33
77
110
d
÷ 1010
30
120
1
3
12
e
÷ 1734
102
51
2
6
3
f
Exercises 6 Here are single number machines What is the action since we know what the input and output are?
+ 45
11
23
9
15
27
a
- 715
42
88
8
35
81
b
× 54
7
9
20
35
45
c
× 83
7
10
24
56
80
d
÷ 339
66
120
13
22
40
e
÷ 742
63
77
6
9
11
f
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
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
Exercises 7 Here are two stage machines What is the output since we know the input?
× 52
4
8
a
× 75
10
7
b
× 66
3
1
c
+ 616
26
46
- 1124
59
38
- 531
13
1
Exercises 8 Here are two stage machines What is the output since we know the input?
÷ 26
8
10
a
÷ 545
55
75
b
÷ 742
21
35
c
+ 25
6
7
- 54
6
10
+ 612
9
11