Patterns and Input/Output Tables — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The Grade 4 sequence 50, 45, 40, 35 increases by 5 each time.
Corrected: The Grade 4 sequence 50, 45, 40, 35 decreases by 5 each time.
Since 45 is less than 50, the sequence shrinks, so the rule is subtract 5, making this Grade 4 pattern a decreasing one.
2. Fix the sentence:
In the Grade 4 sequence 100, 90, 80, 70, the next term is 65.
Corrected: In the Grade 4 sequence 100, 90, 80, 70, the next term is 60.
Each term drops by 10, so 70 minus 10 equals 60, which is the next output in this Grade 4 sequence.
3. Fix the sentence:
The Grade 4 rule for 24, 21, 18, 15 is subtract 2 each time.
Corrected: The Grade 4 rule for 24, 21, 18, 15 is subtract 3 each time.
24 minus 21 equals 3 and 21 minus 18 equals 3, so the function rule subtracts 3 each step in this Grade 4 sequence.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The Grade 4 sequence 50, 45, 40, 35 has the rule subtract 5 each time.
50 minus 45 equals 5 and 45 minus 40 equals 5, so the rule subtracts 5 from each input in this Grade 4 sequence.
2. In the Grade 4 sequence 80, 70, 60, 50, the next term is fifty.
Each term decreases by 10, so after 60 the next output is 60 minus 10, which equals 50 in this Grade 4 pattern.
3. If a Grade 4 sequence starts at 36 and the rule is subtract 4, the second term is 32.
36 minus 4 equals 32, so the second term in this Grade 4 input/output sequence is 32 after one step.
4. The Grade 4 sequence 90, 81, 72, 63 has a function rule of subtract 9 each step.
90 minus 81 equals 9, and 81 minus 72 equals 9, so the rule subtracts 9 from each term in this Grade 4 sequence.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Write the next two terms in the Grade 4 sequence 64, 56, 48, 40 and name the rule.
Sample answer: The rule subtracts 8, so the next two terms in this Grade 4 sequence are 32 and 24.
64 minus 56 equals 8, so subtract 8 twice from 40 to get 32 and then 24 as the next outputs in the sequence.
2. Explain how to find the missing term in the Grade 4 sequence 75, 70, ___, 60, 55.
Sample answer: The rule subtracts 5, so the missing term in this Grade 4 sequence is 65.
70 minus 5 equals 65, which fits between 70 and 60 and matches the constant subtract 5 rule of this Grade 4 sequence.