Problem Analysis:
The task involves a sequence of movements described in steps, and the goal is to predict the final position after completing these steps. Let's break it down step by step.
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Step-by-Step Solution:
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1) Finish this sentence: My starting spot is by...
- This is an open-ended question where you need to describe your starting point. For example:
- "My starting spot is by the tree."
- "My starting spot is by the playground."
- "My starting spot is by the classroom door."
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2) Stay in your spot and read over these four steps:
The instructions are as follows:
1. Take 100 steps forward.
2. Take 100 steps to the right.
3. Take another 100 steps forward.
4. Take 100 steps to the left.
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3) Write a prediction on where you will be after taking these four steps.
To predict the final position, let's analyze the movement mathematically:
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Step 1: Moving 100 steps forward changes your position along the forward axis (let’s call it the y-axis).
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Step 2: Moving 100 steps to the right changes your position along the right axis (let’s call it the x-axis).
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Step 3: Moving another 100 steps forward again changes your position along the y-axis.
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Step 4: Moving 100 steps to the left changes your position along the x-axis, reversing the effect of Step 2.
Now, let’s summarize the net effect:
- Along the
x-axis (right-left direction):
- Step 2: +100 steps to the right.
- Step 4: -100 steps to the left.
- Net change: \( +100 - 100 = 0 \) steps.
- Along the
y-axis (forward-backward direction):
- Step 1: +100 steps forward.
- Step 3: +100 steps forward.
- Net change: \( +100 + 100 = +200 \) steps.
Thus, after completing all four steps, you will be
200 steps forward from your starting point but in the same horizontal position (no change in the x-axis).
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Prediction:
You will be
200 steps forward from your starting spot.
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4) Complete the steps.
This step involves physically or mentally following the instructions to verify your prediction. If you follow the steps as described, you should end up 200 steps forward from your starting point.
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5) Was your prediction right? Explain.
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Explanation: Based on the analysis above, the net movement along the x-axis is zero (steps to the right and left cancel each other out), and the net movement along the y-axis is +200 steps (two forward movements add up). Therefore, your final position is indeed 200 steps forward from your starting spot.
If your prediction matched this result, then it was correct. If not, you can compare your prediction with the analysis to understand any discrepancies.
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Final Answer:
\[
\boxed{\text{200 steps forward}}
\]
Parent Tip: Review the logic above to help your child master the concept of 100 steps worksheet.
