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:
In the Grade 4 pattern square, circle, square, circle, the next shape is circle.
Corrected: In the Grade 4 pattern square, circle, square, circle, the next shape is square.
The pattern square, circle, square, circle alternates between two shapes. Since the 4th term is circle, the next shape goes back to square, not circle.
2. Fix the sentence:
The Grade 4 sequence 1, 4, 9, 16 has a function rule of add 3 each time.
Corrected: The Grade 4 sequence 1, 4, 9, 16 has a function rule based on square numbers.
Each term is a perfect square: 1, 4, 9, 16 equal 1 squared, 2 squared, 3 squared, 4 squared, so the rule is squares.
3. Fix the sentence:
In the Grade 4 sequence 2, 4, 6, 8, the next term is 9.
Corrected: In the Grade 4 sequence 2, 4, 6, 8, the next term is 10.
Each term increases by 2, so after 8 the next output is 8 plus 2, which equals 10 in this even number sequence.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In the Grade 4 shape pattern triangle, square, triangle, square, the next shape is triangle.
After square, the pattern repeats, so triangle is the next term in this Grade 4 alternating sequence.
2. The Grade 4 growing sequence 1, 4, 9, 16 lists square numbers, so the next term is 25.
Each term equals n times n. The fifth term is 5 times 5, which equals 25 in this Grade 4 pattern.
3. In the Grade 4 sequence 5, 10, 15, 20, the function rule adds 5 each time.
10 minus 5 is 5, and 15 minus 10 is 5, so the rule adds 5 to each input to get the next output term.
4. In the Grade 4 pattern star, moon, star, moon, star, the sixth shape is moon.
Star is in odd positions and moon is in even positions, so the sixth term in this Grade 4 sequence is moon.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Describe the function rule for the Grade 4 sequence 3, 6, 9, 12 and give the next term.
Sample answer: The rule adds 3 each time, so the next term in the Grade 4 sequence is 15.
Each term increases by 3, so 12 plus 3 equals 15, which becomes the next output in this skip-counting Grade 4 sequence.
2. In the Grade 4 pattern circle, circle, square, circle, circle, square, what is the seventh shape?
Sample answer: The seventh shape is circle because the unit circle, circle, square repeats every three terms.
Position 7 starts a new chunk after positions 4, 5, 6, so the seventh shape in this Grade 4 pattern is circle.