Generate and Analyze Number Patterns - 4th Grade Math

1. Identify the missing number: $2, 6, 18, \square, 162$ (rule: multiply by the same number each time).

   $54$. The pattern multiplies by $3$: $2×3=6$, $6×3=18$, $18×3=54$.

2. Identify the rule that matches the pattern $3, 7, 11, 15$.

   Add $4$ each time. Each term increases by $4$: $7-3=4$, $11-7=4$, $15-11=4$.

3. What are the first $5$ terms starting at $3$ with rule "multiply by $2$"?

   $3, 6, 12, 24, 48$. Start at $3$ and repeatedly multiply by $2$ to get each next term.

4. What parity pattern occurs for start odd and rule "Add $4$"?

   All terms stay odd. Odd + even = odd, so odd starting values remain odd.

5. Identify whether a pattern with rule "add $2$" keeps the same odd/even type each step.

   Yes, odd stays odd and even stays even. Adding even to odd/even preserves the original parity.

6. What is the common ratio for the pattern $4, 12, 36, 108$?

   $3$. Divide consecutive terms: $12÷4=3$, $36÷12=3$, $108÷36=3$.

7. What is the missing term in $81, 27, \_, 3$ if the rule is "divide by $3$"?

   $9$. Apply the rule: $27 ÷ 3 = 9$.

8. What is the rule for the pattern $4, 8, 12, 16, 20$?

   Start at $4$; add $4$ each time. Each term increases by $4$: $4, 8, 12, 16, 20$.

9. What is the number of squares in step $5$ if a shape pattern starts with $2$ squares and adds $3$ squares each step?

   $14$ squares. Start with $2$, add $3$ four times: $2 + 3(4) = 14$.

10. What is the rule for the pattern $81, 27, 9, 3, 1$?

    Start at $81$; divide by $3$ each time. Each term is one-third of the previous: $81÷3=27$, $27÷3=9$, etc.

11. What are the first $5$ terms for start $2$ and rule "Add $4$"?

    $2, 6, 10, 14, 18$. Starting at $2$, add $4$ repeatedly: $2+4=6$, $6+4=10$, etc.

12. Identify the feature: start at $2$ and "add $4$". Are all terms odd, even, or alternating?

    All even. Terms are $2, 6, 10, 14, 18$... (all divisible by $2$).

13. What is the $5$th term when starting at $3$ and using the rule "multiply by $2$"?

    $48$. Start at $3$, double four times: $3 × 2^4 = 48$.

14. What is the number of squares in term $4$ if a shape pattern adds $3$ squares each term starting from $2$?

    $11$. Term $4$: $2 + (3 × 3) = 11$ squares.

15. Identify the missing number in $5, 10, 15, \square, 25$ with the rule "add $5$".

    $20$. Pattern increases by $5$ each time: $15 + 5 = 20$.

16. Identify the missing number: $5, 9, 13, \square, 21$ (rule: add the same number each time).

    $17$. The pattern adds $4$ each time: $5+4=9$, $9+4=13$, $13+4=17$.

17. What is the next number after $4$ when the rule is "add $6$"?

    $10$. Apply the rule once: $4 + 6 = 10$.

18. What is the common difference for the pattern $7, 12, 17, 22$?

    $5$. Subtract consecutive terms: $12-7=5$, $17-12=5$, $22-17=5$.

19. What does the rule "Add $3$" mean for each next term in a number pattern?

    Add $3$ to the previous term each time. Each term increases by a constant difference of $3$.

20. What is the $5$th term if the start is $20$ and the rule is "subtract $5$"?

    $0$. Subtract $5$ four times: $20 - (4 × 5) = 0$.

21. What are the first $5$ terms starting at $1$ with rule "add $3$"?

    $1, 4, 7, 10, 13$. Start at $1$ and repeatedly add $3$ to get each next term.

22. What is the output when the rule is "multiply by $2$" and the input is $7$?

    $14$. Multiply input by $2$: $7 × 2 = 14$.

23. Identify the parity feature: starting at $6$ and adding $4$ each time, are all terms odd or even?

    All terms stay even. Even + even = even, so $6$ (even) + $4$ (even) stays even.

24. What is the output when the rule is "multiply by $3$" and the input is $4$?

    $12$. Multiply input by $3$: $4 × 3 = 12$.

25. What is the odd/even pattern feature for starting at $6$ with rule "add $4$"?

    All terms are even. Even start plus even rule keeps all terms even.

26. What is the output when the rule is "Multiply by $3$, then add $1$" and the input is $4$?

    $13$. Apply operations in order: $4×3 = 12$, then $12+1 = 13$.

27. Identify the parity feature: starting odd and adding $2$ each time, are all terms odd or even?

    All terms stay odd. Odd + even = odd, so starting odd keeps all terms odd.

28. Which option is the next term after $7$ for "Start $1$, add $3$ each time"?

    $10$. Following the pattern: $1, 4, 7, 10$ (adding $3$ each time).

29. What are the first $5$ terms starting at $20$ with the rule "Subtract $5$"?

    $20, 15, 10, 5, 0$. Starting at $20$: $20-5=15$, $15-5=10$, $10-5=5$, $5-5=0$.

30. What are the first $5$ terms starting at $2$ with the rule "add $4$"?

    $2, 6, 10, 14, 18$. Start at $2$ and add $4$ repeatedly: $2, 6, 10, 14, 18$.

31. What does the rule "Multiply by $2$" mean for each next term in a number pattern?

    Multiply the previous term by $2$ each time. Each term doubles the previous value.

32. What are the first $5$ terms starting at $81$ with rule "divide by $3$"?

    $81, 27, 9, 3, 1$. Start at $81$ and repeatedly divide by $3$ to get each next term.

33. Identify the rule: $2, 5, 8, 11, 14$.

    Start $2$, then add $3$ each time. Each term increases by $3$ from the previous term.

34. What are the first $4$ terms starting at $20$ with rule "subtract $4$"?

    $20, 16, 12, 8$. Start at $20$ and repeatedly subtract $4$ to get each next term.

35. Identify the next term: $1, 3, 6, 10, 15, \square$ (rule: add $2, 3, 4, 5, \dots$).

    $21$. Next difference is $+6$: $15+6=21$.

36. Identify the rule that matches the pattern $2, 4, 8, 16$.

    Multiply by $2$ each time. Each term doubles: $2×2=4$, $4×2=8$, $8×2=16$.

37. Which statement is true for start even and rule "Add $2$": odd/even pattern?

    All terms stay even. Even + even = even, so even numbers stay even when adding $2$.

38. What is the next term after $12$ if the rule is "add $3$" and the start was $1$?

    $15$. Continue the pattern: $12 + 3 = 15$.

39. Identify the rule that matches the pattern $18, 15, 12, 9$.

    Subtract $3$ each time. Each term decreases by $3$: $18-15=3$, $15-12=3$, $12-9=3$.

40. What is the rule for the shape pattern: $1$ square, then $2$ squares, then $3$ squares in a row?

    Add $1$ square each step. Each step increases the number of squares by $1$.

41. Identify the parity feature: starting even and adding $2$ each time, are all terms odd or even?

    All terms stay even. Even + even = even, so starting even keeps all terms even.

42. Identify the rule that changes $2, 6, 18, 54$ into the next term each time.

    Multiply by $3$ each time. Each term is $3$ times the previous term.

43. What is the $6$th term when starting at $2$ and using the rule "add $4$"?

    $22$. Start at $2$, add $4$ five times: $2 + 4(5) = 22$.

44. What are the first $5$ terms starting at $15$ with the rule "subtract $3$"?

    $15, 12, 9, 6, 3$. Start at $15$ and subtract $3$ repeatedly: $15, 12, 9, 6, 3$.

45. Identify whether a pattern with rule "add $3$" alternates odd and even numbers.

    Yes, it alternates odd and even. Adding odd changes parity: odd becomes even, even becomes odd.

46. What is the next shape count if a pattern adds $2$ squares each step: $3, 5, 7, 9, \square$?

    $11$ squares. Pattern adds $2$ each time: $9+2=11$.

47. What are the first $5$ terms starting at $1$ with the rule "Add $3$"?

    $1, 4, 7, 10, 13$. Starting at $1$: $1+3=4$, $4+3=7$, $7+3=10$, $10+3=13$.

48. What is the next term after $27$ if the rule is "divide by $3$"?

    $9$. Divide by $3$: $27 ÷ 3 = 9$.

49. Identify the rule that changes $100, 50, 25, 12.5$ into the next term each time.

    Divide by $2$ each time. Each term is half of the previous term.

50. Identify the rule that changes $5, 9, 13, 17$ into the next term each time.

    Add $4$ each time. Each term increases by $4$ from the previous term.

51. What is the odd/even pattern feature for starting at $7$ with rule "add $4$"?

    All terms are odd. Odd start plus even rule keeps all terms odd.

52. Identify the parity feature: starting at $5$ and adding $4$ each time, are all terms odd or even?

    All terms stay odd. Odd + even = odd, so $5$ (odd) + $4$ (even) stays odd.

53. What are the first $5$ terms for start $3$ and rule "Multiply by $2$"?

    $3, 6, 12, 24, 48$. Starting at $3$, multiply by $2$ repeatedly: $3×2=6$, $6×2=12$, etc.

54. What is the missing term: start $1$, rule "Add $3$": $1, 4, 7, \square, 13$?

    $10$. Pattern increases by $3$ each time: $7+3=10$.

55. Identify the feature not stated: start at $10$ and subtract $2$ each time; do terms stay even?

    Yes; all terms stay even. Even - even = even, so $10$ (even) - $2$ (even) stays even.

56. Identify the feature: start at $1$ and "add $3$". Are the terms odd, even, or alternating?

    Alternating odd and even. Terms are $1, 4, 7, 10, 13$... (odd, even, odd, even, odd).

57. Identify the missing number in $30, 24, 18, \square, 6$ with the rule "subtract $6$".

    $12$. Pattern decreases by $6$ each time: $18 - 6 = 12$.

58. Which statement is true for "Start at $3$ and multiply by $2$ each time" after the first term?

    All later terms are even. Odd × even = even, so $3×2=6$ (even), then all stay even.

59. Identify the feature: start at $7$ and "add $6$". Are all terms odd, even, or alternating?

    All odd. Terms are $7, 13, 19, 25$... (odd + even = odd always).

60. What are the first $5$ terms starting at $3$ with the rule "Multiply by $2$"?

    $3, 6, 12, 24, 48$. Starting at $3$: $3×2=6$, $6×2=12$, $12×2=24$, $24×2=48$.

61. Identify whether $1, 4, 7, 10, 13$ alternates odd and even numbers.

    Yes, it alternates odd and even. Adding $3$ to odd gives even, adding $3$ to even gives odd.

62. What is the $6$th term if the start is $1$ and the rule is "add $3$"?

    $16$. Add $3$ five times: $1 + (5 × 3) = 16$.

63. What is the number of triangles in term $5$ if a shape pattern adds $2$ triangles each term starting from $1$?

    $9$. Term $5$: $1 + (4 × 2) = 9$ triangles.

64. Identify the feature not in the rule: start $5$, rule "multiply by $10$"; $5, 50, 500$ all end with what digit?

    They all end with $0$ (after the first term). Multiplying by $10$ adds a zero to the end of each term.

65. Which option is the rule for $1, 3, 6, 10, 15$ (increasing differences)?

    Add $2, 3, 4, 5, \dots$ each time. Differences increase by $1$: $+2$, $+3$, $+4$, $+5$.

66. What is the missing term in $4, 7, \_, 13$ if the rule is "add $3$"?

    $10$. Apply the rule: $7 + 3 = 10$.

67. What is the next number in the pattern starting at $2$ with rule "add $5$" after $2, 7, 12$?

    $17$. Continue the pattern by adding $5$ to the last term: $12 + 5 = 17$.

68. Identify the parity pattern: start at $1$ and add $3$ each time; do terms alternate odd and even?

    Yes; the terms alternate odd and even. Odd + odd = even, even + odd = odd, creating alternation.

69. Which statement is true for start odd and rule "Add $2$": odd/even pattern?

    All terms stay odd. Odd + even = odd, so odd numbers stay odd when adding $2$.

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