Rounding and estimating calculations - painting a room

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Christian Lawson-Perfect

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Christian Lawson-Perfect

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7 years, 9 months ago

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Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 9 months ago

Saved a checkpoint:

I've split this off from a bigger question.

I've used the random names extension, rewritten the advice, and added a testing condition so that the exact amount of paint needed is never a whole number of buckets.

Restore this checkpoint

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Christian Lawson-Perfect 7 years, 9 months ago

Created this as a copy of Rounding and estimating calculations 2.

Name	Status	Author	Last Modified
Rounding and estimating calculations 2	Should not be used	Stanislav Duris	20/11/2019 14:42
Rounding and estimating calculations - adding up prices in a shop	Ready to use	Christian Lawson-Perfect	20/11/2019 14:42
Rounding and estimating calculations - painting a room	Ready to use	Christian Lawson-Perfect	20/11/2019 14:42
Consumer Arithmetic - Rounding and estimating calculations - adding up prices in a shop	draft	Paul Hancock	24/07/2018 03:04
David's copy of Rounding and estimating calculations - painting a room	draft	David Rickard	07/11/2018 21:04

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Question statement

{person['name']} just bought a new house. {capitalise(pronouns['their'])} new bedroom's wall and ceiling are currently painted white, but {pronouns['they']} would like to paint these {colour}.

The dimensions of the floor are $\var{length}\,\mathrm{m} \times \var{width}\,\mathrm{m}$ and the room is $\var{height}\,\mathrm{m}$ high.

{person['name']} want{verbs} to know how much paint to buy so {pronouns['they']} can paint all four walls and the ceiling {colour}.

Give any introductory information the student needs.

			Name	Type	Generated Value

colour	string	blue
height	number	2.35
width	number	2.69
length	number	5.14

			Name	Type	Generated Value

person	dict	Dictionary with 3 entries
pronouns	dict	Dictionary with 5 entries
verbs	string	s

			Name	Type	Generated Value

h	integer	3
w	integer	3
l	integer	6
rwall1	integer	18
rwall2	integer	9
rceiling	integer	18
rall	integer	72
bucket_area	integer	15
buckets	integer	5

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random("green", "red", "orange", "yellow", "blue", "purple", "pink")

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: `string`

blue

This variable doesn't seem to be used anywhere.

Parts

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

Gap-fill

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

Is it better to overestimate or underestimate in this situation?

Unnamed gap

Advice

a)

It is much better to have spare paint than not to have enough of it. So it is better to overestimate the area.

Therefore, we round each measurement up.

b)

We round each of our measurements up to the nearest whole metre:

Length: $\var{length}\,\mathrm{m} \approx \var{l}\,\mathrm{m}$.

Width: $\var{width}\,\mathrm{m} \approx \var{w}\,\mathrm{m}$.

Height: $\var{height}\,\mathrm{m} \approx \var{h}\,\mathrm{m}$.

The total area consists of five areas: two walls of $\var{l}\,\text{m} \times \var{h}\,\text{m}$ (length by height); two walls of $\var{w}\,\text{m} \times \var{h}\,\text{m}$ (width by height); and a ceiling of $\var{l}\,\text{m} \times \var{w}\,\text{m}$ (length by width).

\[ \begin{align}
\var{l}\,\text{m} \times \var{h}\,\text{m} &= \var{l*h}\,\text{m}^2
\\ \var{w}\,\text{m} \times \var{h}\,\text{m} &= \var{w*h}\,\text{m}^2
\\ \var{l}\,\text{m} \times \var{w}\,\text{m} &= \var{l*w}\,\text{m}^2
\end{align}\]

Therefore, the total area {person['name']} needs to paint is

\[ \var{2*l*h} + \var{2*w*h} + \var{l*w} \,\mathrm{m}^2 = \var{rall}\,\mathrm{m}^2 \text{.} \]

c)

The exact number of buckets needed is

\[\var{rall}\,\text{m}^2 \div 15\,\text{m}^2 = \var{rall/15} \text{.}\]

{person['name']} can only buy a whole number of buckets, so {pronouns['they']} need{verbs} to decide between {buckets-1} and {buckets} paint buckets. As it is better to buy more paint than not buy enough, {pronouns['they']} should buy {buckets} buckets of {colour} paint.

Give a worked solution to the whole question.

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Rounding and estimating calculations - painting a room

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

a)

b)

c)

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Rounding and estimating calculations - painting a room

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

a)

b)

c)

Generated value: `string`