Limits of accuracy in measuring weight in a gym scenario

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Christian Lawson-Perfect	said	Ready to use	7 years, 9 months ago
Stanislav Duris	said	Needs to be tested	7 years, 9 months ago

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Stanislav Duris 7 years, 9 months ago

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Christian Lawson-Perfect 7 years, 9 months ago

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Stanislav Duris 7 years, 9 months ago

Merged Stanislav's copy of Limits of accuracy in measuring weight in a gym scenario before needs to be tested

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Stanislav Duris 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Stanislav Duris 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Limits of accuracy in measuring weight in a gym scenario	Ready to use	Stanislav Duris	20/11/2019 14:42
Find bounds for distance and time spent running, given imprecise measurements	Has some problems	Stanislav Duris	02/03/2020 10:31
David's copy of Find bounds for distance and time spent running, given imprecise measurements	draft	David Rickard	07/11/2018 21:06

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Question statement

We use lower and upper bounds to describe intervals. We can use them to identify all the possible values that could round to a given number.

The lower bound is the lowest value that would round up to our rounded number.
The upper bound is the lowest value after the lower bound that would not round down to our rounded number.

For example, for 50 rounded to the nearest ten, the lowest bound is 45 since 45 is the lowest value that rounds to 50. The upper bound is 55 since 55 is the lowest value that rounds to 60 (the following ten).

Give any introductory information the student needs.

			Name	Type	Generated Value

weight1	integer	70
weight2	integer	90
total	integer	160
limit	number	164

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(50..100 #10)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

weight2

Advice
"Part b)" - prompt
"Part b)" → "Gap 0." - Minimum accepted value
"Part b)" → "Gap 0." - Maximum accepted value
"Part b)" → "Gap 1." - Minimum accepted value
"Part b)" → "Gap 1." - Maximum accepted value
"Part c)" → "Gap 0." - Minimum accepted value
"Part c)" → "Gap 0." - Maximum accepted value
"Part c)" → "Gap 1." - Minimum accepted value
"Part c)" → "Gap 1." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Choose one from a list
  Add
2. Gap Gap 1. Choose one from a list
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part d) Gap-fill
1. Gap Choose one from a list
  Add
Part e) Choose one from a list

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Suppose we are given a rounded variable such as weight. Select the inequality signs that denote the interval that contains the true value before rounding:

Lower bound Gap 0.weight Gap 1.upper bound

Advice

a)

When using inequality symbols to show an error interval for $x$ , we use

$\text{lower bound} \leq x \lt \text{upper bound}$

since the lower bound is included within the interval, while the upper bound is not.

b)

To find bounds, we divide the degree of accuracy by 2 and subtract/add to our estimate to get lower and upper bounds respectively.

The degree of accuracy is to the nearest 10 kg.

$10 \text{ kg} \div 2 = 5 \text{ kg}$

$\begin{align} \text{Lower bound} = \var{weight1} - 5 &= \var{weight1 - 5} \text{ kg} \\\text{Upper bound} = \var{weight1} + 5 &= \var{weight1 + 5} \text{ kg}\end{align}$

c)

To calculate the lower bound of Alex and Cathy's total weight, we add the lower bounds of their individual weights:

$\var{weight1 - 5} \text{ kg} + \var{weight2 - 5} \text{ kg} = \var{weight1 + weight2 - 10} \text{ kg.}$

Similarly for the upper bound,

$\var{weight1 + 5} \text{ kg} + \var{weight2 + 5} \text{ kg} = \var{weight1 + weight2 + 10} \text{ kg.}$

The upper bound for their total weight is $\var{weight1 + weight2 + 10}$ kg.

The weight limit is $\var{limit}$ kg.

Hence, the upper bound for their total weight is greater than the weight limit.

We have found that the upper bound is above the weight limit, so we won't consider the first option.

To decide between the second and the third option, we compare the lower bound for Alex's and Cathy's total weight to the weight limit.

Here, the lower bound ( $\var{weight1 + weight2 - 10}$ kg) is in fact less than the weight limit $\var{limit}$ kg.

Therefore, we cannot confirm nor deny whether it is safe for them to use the lift given the information we know.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

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Limits of accuracy in measuring weight in a gym scenario

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Stanislav Duris 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Error

Limits of accuracy in measuring weight in a gym scenario

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Stanislav Duris 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`