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Unit 1 Lesson 1:
Input & Outputs
Example 1) Find the Input to Output Pattern Rule:
2
?
?
13
Draw out the input/output machine
Put your first input term on the input side and your first output term on the output side
2
x6
?
12
13
Input
Output
2
13
4
25
6
37
8
49
Step 1:
Step 2: Use trial and error to solve the first operation (x6)
2
x6
+1
12
13
Step 3: Use trial and error to solve the second operation to reach the output (13)
Step 4: Then try with other inputs (4, 6, 8) to see if each one equates the correct outputs (25, 37, 49)
Step 5: Write the solution as the input to output pattern rule:
"Multiply the input by 6, then add 1"
6n+1
Practice
Practice PDFs available for download:
1.2:Variables
Example 1) Find the input to output pattern rule using variables
Input
Output
2
13
4
25
6
37
8
49
2
?
?
13
Step 1) Use trial and error method to solve the 2 step input to output machine
x6
+1
12
13
Step 2) Now translate the machine into an algebraic expression:
"Multiply the input by 6, then add 1"
6n+1
"n" represents any input value
Step 3) Input the other input terms to check if they produce the correct outputs
Input
Output
2
13
4
25
6
37
8
49
6n+1
6(2)+1
6x2=12 +1 = 13
6n+1
6(4)+1
6x4=12 +1 = 25
6n+1
6(6)+1
6x6=12 +1 = 37
6n+1
6(8)+1
6x8=12 +1 = 49
Practice
Practice PDFs available for download:
1.3:Equivalent Equations
Example 1) Is this scale balanced
3 x 7
10 + 10 +1
Step 1) Solve each side of the scale
21
3 x 7
21
10 + 10 +1
21
21
=
Step 2)
Determine whether each product are equal in value
If they are equal, the scale is balanced
If they are not equal, the scale is not balanced
Commutative Property: When add or multiply two numbers together, the order does not effect their sum or product
Equivalent Equations II
Example 1) Find a equivalent equation for the following equation:
Rule to preserve equality:
"Whatever you do to one side, do to the other."
~Mr. Ram's Mom
3n = 12
n = 4
3(4) = 12
12 = 12
Both sides equal each other, therefore equality is preserved
3n = 12
n = 4
3n -1 = 12 -1
3(4) -1 = 12 -1
12 -1 = 12 -1
11 = 11
After (-1) on each side of the equation, both sides are still equal therefore equality is preserved
Practice
Practice PDFs available for download:
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