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12.07 Iterations

Worksheet
Iterations
1

Nadia follows an algorithm to eat her breakfast.

  1. Place bowl and spoon on the table.

  2. Pour cereal into the bowl.

  3. Pour milk into the bowl.

  4. Spoon a mouth of cereal into your mouth.

  5. Repeat step 4 until the cereal is finished.

  6. Place bowl and spoon in the sink.

Which two steps form the loop?

2

Determine the shape that has been mapped out if the following algorithms are followed:

a
  1. Stand in the middle of a room.

  2. Take five steps forward.

  3. Turn left.

  4. Repeat steps 2 and 3 three more times.

b
  1. Stand in the middle of a room.

  2. Take three steps forward.

  3. Turn right.

  4. Take six steps forward.

  5. Turn right.

  6. Repeat steps 2,3,4, and 5 one more time.

3

Complete the following tables by writing the results of each the algorithm:

a
StepInstructionResult
1\text{Start with the number } 7
2\text{Add } 4 \text{ to this number}
3\text{Repeat step } 2 \text { three more times}
b
StepInstructionResult
1\text{Start with the number } 29
2\text{Subtract } 1 \text{ from this number}
3\text{Repeat step } 2 \text { three more times}
c
StepInstructionResult
1\text{Start with the number } 8
2\text{Multiply this number by } 6
3\text{Repeat step } 2 \text { three more times}
d
StepInstructionResult
1\text{Start with the number } 54
2\text{Add } 6 \text{ to this number}
3\text{Repeat step } 2 \text { three more times}
4\text{Round this number to the nearest } 10
e
StepInstructionResult
1\text{Start with the number } 29
2\text{Subtract } 1 \text{ from this number}
3\text{Repeat step } 2 \text { three more times}
4\text{Double the number}
f
StepInstructionResult
1\text{Start with the number } 40\,000
2\text{Divide this number by } 10
3\text{Repeat step } 2 \text { three more times}
g
StepInstructionResult
1\text{Start with the number } 5
2\text{Double this number}
3\text{Repeat step } 2 \text { three more times}
4

Consider the given algorithm.

  1. Start with the number 7.

  2. Add 7 to this number.

  3. Repeat step 2 three more times.

a

How many 7's have been added together?

b

Write this algorithm as a sum.

c

What is the final answer?

d

Calculate 7 \times 5.

5

For each of the following algorithm:

i

What is the final answer?

ii

How many times was step 2 performed?

a
  1. Start with the number 2.

  2. Add 5 to the number.

  3. Repeat step 2 until the answer is greater than 30.

b
  1. Start with the number 37.

  2. Subtract 4 from the number.

  3. Repeat step 2 until the answer is less than 20.

6

For each of the following:

i

Complete the table by writing the results of the algorithm.

ii

Write the multiplication that represents the problem in the table.

a
StepInstructionResult
1\text{Start with the number } 6
2\text{Add } 6 \text{ to this number}
3\text{Repeat step } 2 \text { three more times}
b
StepInstructionResult
1\text{Start with the number } 13
2\text{Add } 13 \text{ to this number}
3\text{Repeat step } 2 \text { three more times}
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