Having real problems with working out scales for graphs

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Discussion Overview

The discussion revolves around the challenges faced by students in determining appropriate scales for graphs in a practical assessment context. Participants explore the guidelines provided in the marking scheme and share their methods for selecting scales, addressing both theoretical and practical aspects of graphing.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the term "awkward scales" and questions the method of calculating scales based on the range of values divided by the number of squares.
  • Another participant suggests that "awkward scales" refer to those that do not include powers of 10 and proposes using scales that are multiples of 1, 2, or 5, providing specific examples.
  • A similar viewpoint is reiterated by another participant, who emphasizes rounding the calculated scale to the next number in a sequence of 1, 2, 5, 10, etc., and provides a detailed example of how to apply this method.
  • One participant encourages thinking critically about the guidelines for graphing, suggesting that the purpose of the graph should guide the choice of scale rather than strictly adhering to rules.
  • There is a question raised about the relevance of hand-drawn graphs in assessments, with one participant expressing surprise that this practice is still evaluated.
  • Another participant responds to the previous question, asserting that the assessment of hand-drawn graphs remains valid.
  • A participant mentions starting a separate thread on the topic, indicating a desire to keep discussions focused.

Areas of Agreement / Disagreement

Participants express differing interpretations of what constitutes an "awkward scale" and share various methods for determining graph scales. There is no consensus on the best approach, and the discussion remains unresolved regarding the optimal strategies for graphing.

Contextual Notes

Participants' suggestions depend on their interpretations of the assessment guidelines and personal experiences with graphing. The discussion highlights the variability in approaches to scale selection and the subjective nature of what constitutes an effective graph.

ThatOneMidget
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I have no clue what I'm supposed to do with the scales for my graphs. I am an AS level student and in the practical paper we're asked to draw a graph using our readings. The marking scheme has this to say:
Axes Scales must be such that the plotted points occupy at least half the graph grid in both the x and y directions (i.e. 4 x 6 in portrait or 6 x 4 in landscape) Axes must be labelled with the quantity plotted. Ignore units. Do not allow awkward scales or gaps of more than three large squares between the scale markings
I have no idea what they mean by awkward scales and what not, what i usually do to decide the scale is (largest value - smallest value)/(number of squares), is that wrong?
 
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ThatOneMidget said:
have no idea what they mean by awkward scales
To me it means a scale that doesn't include powers of 10. I generally use scales in which the units are multiples of 1, 2 or 5:

1, 2, 3, 4, 5, ...
2, 4, 6, 8, 10, ...
5, 10, 15, 20, 25, ...
10, 20, 30, 40, 50, ...
20, 40, 60, 80, 100, ...

I would not use scales like

3, 6, 9, 12, 15, ...
7, 14, 21, 28, 35, ...
2.3, 4.6, 6.9, 9.1, 11.4, ...

which would never include 10 or 100 or 1000, etc.

I would take the result of your formula and round it upward to the next number in the following sequence: 1, 2, 5, 10, 20, 50, 100, ...

So if you have smallest = 130.2, smallest = 46.3, number of squares = 20, then your formula gives 4.195, which I would round up to 5. This gives a scale of

45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135

which actually requires only 18 squares to accommodate your data, so I might add one square at the beginning and at the end, with the scale running from 40 to 140.
 
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jtbell said:
To me it means a scale that doesn't include powers of 10. I generally use scales in which the units are multiples of 1, 2 or 5:

1, 2, 3, 4, 5, ...
2, 4, 6, 8, 10, ...
5, 10, 15, 20, 25, ...
10, 20, 30, 40, 50, ...
20, 40, 60, 80, 100, ...

I would not use scales like

3, 6, 9, 12, 15, ...
7, 14, 21, 28, 35, ...
2.3, 4.6, 6.9, 9.1, 11.4, ...

which would never include 10 or 100 or 1000, etc.

I would take the result of your formula and round it upward to the next number in the following sequence: 1, 2, 5, 10, 20, 50, 100, ...

So if you have smallest = 130.2, smallest = 46.3, number of squares = 20, then your formula gives 4.195, which I would round up to 5. This gives a scale of

45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135

which actually requires only 18 squares to accommodate your data, so I might add one square at the beginning and at the end, with the scale running from 40 to 140.
Thank you so much!
 
JTBell has given the specifics.
But what I would say is, don't look on these as arbitrary rules. Think about why they suggest these "rules".
Apart from general shape, which might be apparent even without scale markings (so long as the nature of the scale was indicated), one often wants to take readings from the graph. Say you wanted to read a point 4/5th of the way (because that's the sort of rulings on graph paper) between scale markings, see how easy or difficult it is with JTB's good and bad example scales.

As a rider, I always used to get very irritated by students who drew graphs for no good reason, other than they hoped it might earn marks and required little effort or thought on their part, since they had software that did it for them. If you draw a graph for a purpose, then it is usually fairly clear how to do it to best achieve your objective, irrespective of any "rules". Those guidelines seem to be simply an arbitrary low bar, below which one can reasonably say the graph is not serving it's purpose well enough.
 
I didn't realize drawing graphs by hand is still assessable??
 
houlahound said:
I didn't realize drawing graphs by hand is still assessable??
Why would it be any less assessable now than it has ever been?
 
I started a thread on it, don't want to derail this one.
 

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