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Chapter 3: Problem 3

Match these walking instructions with their graph sketches. a. The walker stands still. b. The walker takes a few steps toward the 0 -mark, then walks away. c. The walker steps away from the 0 -mark, stops, then continues more slowly in the same direction.

Short Answer

Expert verified
a: flat line; b: V-shape; c: gradual increase, pause, then slow.

Step by step solution

01

Understand the Walking Instructions

Examine each walking instruction carefully: - Instruction (a): The walker stands still, implying a flat horizontal line on the graph, as there is no change in position over time. - Instruction (b): The walker initially moves towards the 0-mark, then away, suggesting a movement towards a specific point and then away from it, possibly creating a V-shaped graph. - Instruction (c): The walker moves away from the 0-mark, stops, and then continues at a slower pace. This indicates an increasing slope that decreases.
02

Analyze Graph Sketches

Identify possible graph sketches that could represent the above descriptions: - Sketch for instruction (a) should be a flat line indicating no movement. - Sketch for instruction (b) should show a decrease in distance followed by an increase, such as a V-shape or a line moving toward and then away from a point. - Sketch for instruction (c) should show an increase in distance, a stop (horizontal line), and a continuation with a gentler slope.
03

Match Instructions With Graphs

Match each instruction with the graph based on the analysis: - Instruction (a) corresponds to any graph showing a flat horizontal line. - Instruction (b) matches a graph with a movement toward and then away from a point, typically represented by a V-shape or similar. - Instruction (c) corresponds to a graph with an initial upward slope, a pause, and then a continuation with a reduced slope.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Walking Instructions
Walking instructions are detailed descriptions of movements that a person may take. In the context of graphs, these instructions are interpreted as changes in position over time. Each detail in the walking instruction correlates to a specific feature in a graph.
  • Standing still is shown by a horizontal line, representing no movement or change in position.
  • Movement towards a point or zero mark is reflected by a line moving closer to the origin or a decrease in distance on the graph.
  • Stopping and then moving again at a different pace is illustrated by a shift in the slope of the line, indicating a change in speed.
When interpreting walking instructions for graphs, the key is to identify how the movement starts, any changes in direction, and any pauses or shifts in speed.
Understanding Graphs
Graphs are visual representations that show how a value changes over time. They are particularly useful in illustrating scenarios described by walking instructions. Each part of a graph corresponds to an action or a lack of action by the walker. Understanding a graph involves:
  • Identifying Zero Mark: The zero mark on a graph signifies the starting point or origin. Movements toward or away from this mark denote changes in position relative to the starting point.
  • Slopes: The slope of a line in a graph signifies the speed of movement. A flat slope indicates no movement, while a steeper slope indicates faster movement.
  • Direction Changes: A shift from an upward slope to a downward slope, or vice versa, indicates a change in the walker's direction.
By carefully analyzing these elements, students can accurately interpret graph sketches to match walking instructions.
Graph Sketches Analysis
Graph sketches analysis involves examining graph elements and matching them to specific actions described by walking instructions. This requires attention to detail, as well as an understanding of how each graph feature is an indicator of movement or a lack thereof.
  • Flat Lines: These indicate the walker standing still, as there is no mobility over time.
  • V-Shapes: A V-shaped graph depicts a movement towards a point and then away, showing a reversal in direction.
  • Changing Slopes: An initial sharp upward slope that flattens or becomes less steep illustrates the walker's adjustment in speed, either slowing down or stopping before continuing.
By understanding these components, students can effectively match specific graph sketches with the corresponding walking instructions, providing a clear visualization of the walker's journey over time.

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