Activities

1. What is the first term in each pattern?    3, 6, 9, 12           3, 6, 12, 24
   
   
2. How many terms are there in each pattern?    3, 7, 11, 15, 19                3, 6, 9, 12, 14
   
   
3. Are the fourth terms in each sequence equal?    1, 2, 4, 8, 16           2, 4, 6, 8, 10
   
   
4. Is the rule for both patterns the same?      1, 2, 4, 8, 16           1, 3, 9, 27, 81

5. Determine the relationship between corresponding terms in the two patterns.  Use this relationship to find the missing terms in the second pattern
   Pattern #1       1, 4, 8, 12, 16, 20, 24
   Pattern #2       1, 2, 4, _____, 8, _____, 12
   
   
6. Identify the correct relationship between the corresponding terms in the following patterns.                      Pattern 1:  7, 10, 13, 16, 19                Pattern 2:  7, 13, 19, 25, 31
   
   
   1. Pattern #1 is three less than the corresponding term is Pattern #2
   2. Pattern #1 is six less than the corresponding term is Pattern #2
   3. The difference between corresponding terms doubles for each successive term in the pattern.
   4. The difference between corresponding terms increases by three for each successive term in the pattern.
      
      
7. The first term in two patterns is 4. If pattern #1 has the rule “add four” and pattern #2 has the rule “add 9”, what statement below is correct with respect to the relationship between corresponding terms?
   
   
   1. Pattern #1 is five less than the corresponding term is Pattern #2
   2. Each term in Pattern #1 is at least ½ the corresponding term in Pattern #2
   3. The difference between corresponding terms doubles for each successive term in the pattern
   4. The difference between corresponding terms increases by five for each successive term in the pattern
      
      
8. Complete the following sentence regarding the corresponding terms in the two patterns.
   Pattern A:   1, 5, 9, 13, 17                   Pattern B:  1, 3, 7, 15, 31
   The corresponding terms in Pattern B are greater than those in Pattern A, starting with the _______ term.
   
   
9. Identify the true statement regarding the corresponding terms in the following patterns. 
   Pattern A:  3, 8, 13, 18, 23, 28, 33      Pattern B:  3, 13, 23, 33, 43, 53, 63
   
   
   1. Corresponding terms in Pattern B will always be double minus 3 the terms in Pattern A
   2. The corresponding terms will never be two odd numbers.
   3. Corresponding terms in Pattern A will always be 5 less than Pattern B
   4. The corresponding terms will be one odd and one even number.
      
      
10. Complete the true sentence regarding the corresponding terms in the two patterns.
    Pattern X:   2, 8, 14, 20, 26                 Pattern Y:  2, 5, 11, 23, 47
    The sum of the corresponding terms are always _____ numbers, starting with the second term in the patterns.

11. Two patterns with the same rule must have identical corresponding terms.  Determine if this statement is true or false.  Explain your reasoning and provide an example that justifies your reasoning.
    
    
12. List two true statements about the relationship between corresponding terms in the two patterns. Explain your reasoning for both.
    5, 9, 13, 17, 21                  5, 11, 17, 23, 29
    
    
13. Write two different rules for patterns where the difference between the corresponding terms is greater by 2 for each successive term in the pattern.  The first term in the pattern should be the same.  Justify your reasoning.
    
    
14. Identify one correct relationship between the corresponding terms in Kiera and David’s patterns, which have the same first term. Explain.
    Kiera’s Pattern:  7, 9, 11, 13, 15               David’s rule:  add 7
    
    
    1. The sum of the corresponding terms is always an even number.
    2. Kiera’s pattern is five less than the corresponding term in David’s pattern.
    3. The difference between corresponding terms is a multiple of 5 for each successive term in the pattern, after the first term.
    4. The sum of corresponding terms increases by nine for each successive term in the pattern.
       
       
15. Hallie’s pattern has a rule of “add 2” and Amber’s pattern has a rule of “add 8”, with both patterns starting with the same number.
    
    LaShawn’s pattern has a rule of “add 2” and Parker’s pattern has a rule of “add 8”, with both patterns starting with the same number.  Explain how it is possible for the terms in Hallie’s pattern to be 4 times the corresponding terms in Amber’s pattern, but this is not the case for LaShawn and Parker even though they have the same rules. Provide an example.
    
    
16. Write two patterns and their corresponding rules that meet the following conditions:
    
    Both patterns start with the same number.
    The terms in one pattern are 3 times the corresponding terms in the other pattern.
    Explain.

Answer Key/Rubric

1. 3
   
   
2. 5
   
   
3. Yes
   
   
4. No

5. The terms in Pattern #2 are half of the corresponding terms in Pattern #1.   6 and 10.
   
   
6. D
   
   
7. D
   
   
8. Fourth
   
   
9. A
   
   
10. Odd

11. False.  Example is the rule add two:  Pattern #1:  1, 3, 5, 7, 9, 11     Pattern #2:  2, 4, 6, 8, 10, 12.  The two patterns must also have the same first term. 
    
    
12. Answers will vary.  Example:  The sum of the corresponding terms of the two patterns is: 10, 20, 30, 40.  The statement:  The sum of the corresponding terms of the two patterns increases by ten for each consecutive term.   Example:  The difference between the corresponding terms of the two patterns is 2, 4, 6, 8.  The statement:  The difference between the corresponding terms of the two patterns is a multiple of two.
    
    
13. Answers will vary.  One example:  rule #1: add 4 and rule #2: multiply by 2 and add 1, with the first term of 5.  So the patterns are:  5, 9, 13, 17, 21 and 5, 11, 17, 23, 29.  The difference between the corresponding terms are 0, 2, 4, 6, 8 so the difference is two greater with each term.
    
    
14. Answers c and d are correct.  Explanations will vary. Example:  The difference between the terms in the patterns is as follows 0, 5, 10, 15, 20.  So it is true when it is stated that the successive terms are multiples of 5 because each number is divisible by 5.   Example:  The sum of the corresponding terms is as follows:  14, 23, 32, 41, 50.  Each successive term is 9 greater than the last, which makes the statement true.
    
    
15. Hallie: 0, 2, 4, 6, 8 and Amber: 0, 8, 16, 24, 32    

Each term in Hallie’s pattern is multiplied by 4 to get the corresponding term in Amber’s pattern.
LaShawn: 2, 4, 6, 8, 10 and Parker: 2, 10, 18, 26, 34 

Multiplying each term in LaShawn’s pattern by 4 will not give you the corresponding term in Parker’s pattern.  Starting with zero allows the pattern to be multiples of 2 and 8 respectively; however, starting with 2 does not allow for Parker’s pattern to be multiples of 8.

16. Answers will vary. 

Example:  Pattern #1: 0, 3, 6, 9, 12; Rule:  “add 3” and Pattern #2:  0, 9, 18, 27, 36; Rule: “add 9”
Students must explain that one rule must be three times the other, for example 3 and 9.  They must also explain that the first term must be zero in order for the multiples to work according to the conditions set forth.