Rounding and estimating calculations

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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

Published this.

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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:

Lovely question!

Restore this checkpoint

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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, 10 months ago

Gave some feedback: Has some problems

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Bradley Bush commented 7 years, 10 months ago

I really like this question, especially the gap fills! I would just suggest a few small improvements.

In each part you have the question then the gap fills and then you say "Therefore, x*y=z", I think this would be better if it said "Therefore, your estimate for: x*y=z." because that way you are making clear to the student that this is an estimate, not the real answer.

In the first part of the advice, you write "we look at the first non-zero digit, increasing this digit by one if the following digit is 5 or more", I think it might be better to write what happens if the following digit is bellow 5 as well as this. I know it seems obvious, but there might be a student decreasing the figure by one if it's bellow 5.

Finally, it also might be nice to restate the original equation in the advice so the student doesn't have to scroll back to the question.

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Lauren Richards commented 7 years, 10 months ago

Hi Stanislav,

I think for part c) and d) you could rearrange the format for inputting answers into an actual fraction with gap fills included. Then it will match the form of the question when it is asked and might make it easier to understand. I have included this in some of my questions so if you are not sure how to do this, I can show you.

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Stanislav Duris 7 years, 10 months ago

Gave some feedback: Needs to be tested

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Stanislav Duris 7 years, 10 months ago

Created this.

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There are 4 other versions that do you not have access to.

Question statement

It is often appropriate to estimate calculations. The sign ≈ denotes "approximately equal to".

In this question, approximate calculations by rounding the numbers in the question to 1 significant figure before calculating answers.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	17.2
int	list	[ 75, 68, 99, 35, 49, 61 ]
integers	range	1..100
sint	integer	4
b	number	35.295
c	number	22.228
ran	integer	4
tens	range	10..100#10

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..40 #0.1 except integers)

JME function reference

Description

A decimal number.

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

Can an exam override the value of this variable?

Generated value: `number`

17.2

← Depends on:

integers

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Part c) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Part d) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Gap-fill

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

Estimate $\var{int[0]} \times \var{int[1]}$ .

Gap 0. $\times$ Gap 1. $=$ Gap 2.

Therefore, $\var{int[0]} \times \var{int[1]} ≈$ Gap 2..

Advice

To round to 1 significant figure, we look at the first non-zero digit, increasing this digit by one if the following digit is 5 or more and keeping the digit the same if the following digit is below 5. We replace the rest of the digits by 0.

a)

$\var{int[0]} \times \var{int[1]} ≈ \text{ ?}$

Rounding to 1 significant figure gives:

$\begin{align} \var{siground(int[0], 1)} \times \var{siground(int[1], 1)} = \var{siground(int[0], 1)*siground(int[1], 1)} \text{.} \end{align}$

b)

$\var{sint} \times \var{int[2]} ≈ \text{ ?}$

Rounding to 1 significant figure:

$\begin{align} \var{siground(sint, 1)} \times \var{siground(int[2], 1)} = \var{siground(sint, 1)*siground(int[2], 1)} \text{.} \end{align}$

A common mistake may be rounding $\var{sint}$ to the nearest 10 instead of 1 significant figure (in this case the number itself already consists of 1 s.f. only).

c)

$\displaystyle \frac{\var{int[3]} - \var{int[4]}}{\var{b}} ≈ \text{ ?}$

Rounding to 1 significant figure:

$\begin{align} \displaystyle \frac{\var{siground(int[3], 1)} - \var{siground(int[4], 1)}}{\var{siground(b, 1)}} &=\frac{\var{siground(int[3], 1) - siground(int[4], 1)}}{\var{siground(b, 1)}} \\&= \var{(siground(int[3], 1) - siground(int[4], 1)) / siground(b,1)} \text{.} \end{align}$

d)

$\displaystyle \frac{\var{int[5]*10 + ran}}{\var{c}} - \var{a} ≈ \text{ ?}$

Rounding to 1 significant figure:

$\begin{align} \displaystyle \frac{\var{siground(int[5]*10, 1)}}{\var{siground(c, 1)}} - \var{siground(a, 1)} &= \frac{\var{siground(int[5]*10, 1)/10}}{\var{siground(c, 1)/10}} - \var{siground(a, 1)} \\&= \var{(siground(int[5]*10, 1))/siground(c, 1)} - \var{siground(a, 1)} \\&= \var{siground(int[5]*10, 1)/siground(c, 1) - siground(a, 1)} \text{.} \end{align}$

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:

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This question is used in the following exams:

trial run by Lesley Davis in Lesley's workspace.
maths practice-revision by David Martin in David's workspace.
QTS by Lyn Gardner in Lyn's workspace.
Significant Figures by Jim Kelly in Jim's workspace.
Level 1 Biol by Mary McVey in Mary's workspace.
Nick's copy of Rounding and estimating by Nick Walker in Nick's workspace.
Possible applicable questions from previous year by Tom Bold in Transition to university maths.
Arithmetic Quiz by Chetna Patel in Chetna's workspace.
resit mock2 by Heike Wanke in Heike's workspace.
Module 3 by Niharika Singh in Niharika's workspace.
Rounding and estimating by Anna Cartlidge in Glasgow Numbas Question Pool.
Transition Rounding by Chris Templet in Chris's workspace.
claire's copy of Rounding and estimating by claire lines in claire's workspace.
ME0006 Wk 1 Test 1 by claire lines in claire's workspace.
Test for Nic Terry and Venusha - with Password - GO by claire lines in claire's workspace.
Rounding and estimating by Christian Lawson-Perfect in Transition to university.
Заокружувања и приближни пресметувања by Snezana Zlatkovska in Snezana's workspace.

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Metadata

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, 10 months ago

Bradley Bush commented 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Stanislav Duris 7 years, 10 months ago

Stanislav Duris 7 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

a)

b)

c)

d)

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Rounding and estimating calculations

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, 10 months ago

Bradley Bush commented 7 years, 10 months ago

Lauren Richards commented 7 years, 10 months ago

Stanislav Duris 7 years, 10 months ago

Stanislav Duris 7 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `number`