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The solution shows answers to flow diagrams and tables, including sequence patterns and input-output relationships. What are the questions associated with these examples?

Mathematics

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Here are the answers to the flow diagrams and tables.

Top Section Example (Green Row):
Sequence: 5,10,15,20,25,30,35,40,455, 10, 15, 20, 25, 30, 35, 40, 45

  • What will the next number be? 45+5=5045 + 5 = \boxed{50}.
  • How did you work it out? Each number is 5 more than the previous number.
  • What would the rule be? Add 5 to the previous number.

1. Answer these questions.

Part a· 1 step

Input-Output Diagram

  1. Analyze the relationship between input and output.

    For each pair of input and output:

    1→8(1×8=8)1 \to 8 \quad (1 \times 8 = 8) 3→24(3×8=24)3 \to 24 \quad (3 \times 8 = 24) 5→40(5×8=40)5 \to 40 \quad (5 \times 8 = 40) 7→56(7×8=56)7 \to 56 \quad (7 \times 8 = 56) 9→72(9×8=72)9 \to 72 \quad (9 \times 8 = 72)

    The rule is to multiply the input by 8.

Part a(i)

What would you write in the empty box? ×8\boxed{\times 8}

Part a(ii)

What do we call it? *Rule

Part b· 2 steps

Input-Output Diagram

  1. Work backward from the output to find the value before the "+4" step.

    For each output, subtract 4:

    9−4=59 - 4 = 5 19−4=1519 - 4 = 15 29−4=2529 - 4 = 25 34−4=3034 - 4 = 30 44−4=4044 - 4 = 40 59−4=5559 - 4 = 55

  2. Analyze the relationship between the input and the value before the "+4" step.

    1→5(1×5=5)1 \to 5 \quad (1 \times 5 = 5) 3→15(3×5=15)3 \to 15 \quad (3 \times 5 = 15) 5→25(5×5=25)5 \to 25 \quad (5 \times 5 = 25) 6→30(6×5=30)6 \to 30 \quad (6 \times 5 = 30) 8→40(8×5=40)8 \to 40 \quad (8 \times 5 = 40) 11→55(11×5=55)11 \to 55 \quad (11 \times 5 = 55)

    The rule for the first empty box is to multiply the input by 5.

Part b(i)

What would you write in the empty box? ×5\boxed{\times 5}

Part b(ii)

What do we call it? *Rule

Part c· 1 step

Input-Output Diagram

  1. Analyze the relationship between input and output.

    For each pair of input and output:

    8→40(8×5=40)8 \to 40 \quad (8 \times 5 = 40) 5→25(5×5=25)5 \to 25 \quad (5 \times 5 = 25) 9→45(9×5=45)9 \to 45 \quad (9 \times 5 = 45) 4→20(4×5=20)4 \to 20 \quad (4 \times 5 = 20) 7→35(7×5=35)7 \to 35 \quad (7 \times 5 = 35)

    The rule is to multiply the input by 5.

Part c(i)

What would you write in the empty box? ×5\boxed{\times 5}

Part c(ii)

What do we call it? *Rule

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