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1. Generate two numerical sequences using the rules "Add 5" and "Add 20." Start at zero. Sequence 1: 0 , 5 , 10 , 15 , 20 , 25 Sequence 2: 0 , 20 , 40 , 60 , 80 , 100 Compare: What is the relationship? Why? The terms on the second list are 4 times as big. The rule "add 20" is adding 4 times as much each time as the rule "Add 5."

2. Generate two numerical sequences using the rules "Add 6 " and "Add 18." Start at zero. Sequence 1: 0 , 6 , 12 , 18 , 24 , 30 Sequence 2: 0 , 18 , 36 , 54 , 72 , 90 Compare: What is the relationship? Why? The terms on the second list are 3 times as big. The rule "add 18 " is adding 3 times as much each time as the rule "Add 6."

3. Generate two numerical sequences using the rules "Add 3 " and "Add 12." Start at zero. Sequence 1: 0 , 3 , 6 , 9 , 12 , 15 Sequence 2: 0 , 12 , 24 , 36 , 48 , 60 Compare: What is the relationship? Why? The terms on the second list are 4 times as big. The rule "add 12 " is adding 4 times as much each time as the rule "Add 3."

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The various resources listed below are aligned to the same standard, (5OA03) taken from the CCSM (Common Core Standards For Mathematics) as the Algebra Worksheet shown above.
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.