Straight line equation application: measuring sunflower height

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Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Chris Graham	said	Needs to be tested	7 years, 8 months ago
Bradley Bush	said	Needs to be tested	7 years, 8 months ago
Elliott Fletcher	said	Has some problems	7 years, 8 months ago

History

○

Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Looks OK.

Restore this checkpoint

○

Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect commented 7 years, 8 months ago

Bit of a shame that you didn't set a checkpoint before rewriting Brad's text.

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Chris Graham 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 8 months ago

This was originally "watching grass grow". I have changed the context from 1st to 3rd person and changed grass to a sunflower, which seems a much more likely thing to measure.

Also used the random names extension, and as a result I've changed quite a lot of this, so I'm marking needs to be tested.

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

○

Elliott Fletcher commented 7 years, 8 months ago

Lovely question, definitely one of my favourite questions so far. Just a few grammatical comments

In the statement you probably should put a hyphen between observation and B as you have for "Observation-A"

Main Parts

a) good (the graph looks really nice)

b) I would delete the should in the question here

In the first (top left) bullet point, "take" should be "taken"

In the bottom left bullet point, you could change "millimeters" to just mm if you wanted.

c) you write "3^th day" but this should be "3^rd day"

I don't think you need a colon at the end, i would just put a full stop

e) "The power goes to you head" should be "The power goes to your head".

I would put a "why" after hence and before "this".

Advice

a) I would put the equation to calculate c in the second paragraph on it's own line using display mode.

"point's" should be "points"

I would put the multiplications in brackets here.

c) i don't think you need the colon here

d) Again i don't think you need the colon here.

e) "oustide" should be "outside"

Hopefully this question will inspire many young students to become grass length consultants in the future!

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Has some problems

○

Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Bradley Bush 7 years, 9 months ago

Gave some feedback: Has some problems

○

Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Bradley Bush 7 years, 9 months ago

Created this as a copy of Find the equation of a line through two points - zero gradient.

Name	Status	Author	Last Modified
Find the equation of a line through two points - positive gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Find the equation of a line through two points - negative gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Find the equation of a line through two points - zero gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Straight line equation application: measuring sunflower height	Ready to use	Bradley Bush	03/02/2021 13:59
Louise's copy of Find the equation of a line through two points - positive gradient	draft	Louise Lynch	26/01/2022 19:48
Find the equation of a line through two points - positive gradient	draft	Mark Hodds	03/02/2021 13:59
Ida's copy of Find the equation of a line through two points - positive gradient	draft	Ida Landgärds	03/02/2021 13:59
Spørsmål 1	draft	Ida Landgärds	03/02/2021 13:59
Marte's copy of Find the equation of a line through two points - positive gradient	draft	Marte Bråtalien	03/02/2021 13:59
Thomas's copy of Find the equation of a line through two points - negative gradient	draft	Thomas Strasser	03/02/2021 13:59
Equation de droite	Needs to be tested	Alain Virouleau	30/05/2019 18:52
Linear Equations - Find the equation of a line through two points	draft	Paul Hancock	03/02/2021 13:59
Find the equation of a line through two points - positive gradient [L3]	Needs to be tested	Matthew James Sykes	03/02/2021 13:59
Beer Lambert Law	Doesn't work	Matthew James Sykes	03/02/2021 13:59
Beer Lambert Law Working Back up	Should not be used	Matthew James Sykes	03/02/2021 13:59
Joël's copy of Find the equation of a line through two points - positive gradient	draft	Jo Cohen	03/02/2021 13:59
Beer Lambert Law Working Back up	Should not be used	Matthew James Sykes	03/02/2021 13:59
Ida's copy of Spørsmål 1	draft	Ida Landgärds	09/01/2023 10:54
David's copy of Straight line equation application: measuring sunflower height	draft	David Rickard	03/02/2021 13:59
equation of a line through two points	draft	heike hoffmann	03/02/2021 13:59
Luis's copy of Find the equation of a line through two points - zero gradient	draft	Luis Hernandez	03/02/2021 13:59
Simon's copy of Equation of a line through two points - positive gradient	draft	Simon Thomas	03/02/2021 13:59
Maria's copy of Simon's copy of Equation of a line through two points - positive gradient	draft	Maria Aneiros	03/02/2021 13:59
Maria's copy of Find the equation of a line through two points - negative gradient	draft	Maria Aneiros	03/02/2021 13:59
Heather's copy of Find the equation of a line through two points - positive gradient	draft	Heather Driscoll	03/02/2021 13:59
Equation of a line through two points - positive gradient	draft	Heather Driscoll	03/02/2021 13:59
Equation of a line through two points	draft	Philip Charlton	03/02/2021 13:59
Find the equation of a line through two points - zero gradient	draft	Xiaodan Leng	03/02/2021 13:59
Equation of a line through two points - positive gradient	draft	Xiaodan Leng	03/02/2021 13:59
Straight line equation application: measuring sunflower height	draft	Adelle Colbourn	03/02/2021 13:59
Musa's copy of Find the equation of a line through two points	draft	Musa Mammadov	01/08/2022 08:15
Find the equation of a line through two points - positive gradient	Ready to use	Simon Vaughan	03/02/2021 13:59

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Question statement

{person['name']} is given a sunflower seedling for {person['pronouns']['their']} 30th birthday (day $0$ ) and observes its height. {capitalise(person['pronouns']['they'])} make{s} the following observations later that week:

Observation	A	B
Day	$\var{xa}$	$\var{xb}$
height (cm)	$\var{ya}$	$\var{yb}$

{person['name']} plots the 2 points:

{plotPoints()}

Give any introductory information the student needs.

			Name	Type	Generated Value

xa	integer	5
xb	integer	6
ya	integer	19
yb	integer	22

			Name	Type	Generated Value

			person	dict	Dictionary with 3 entries
			s	string	s

			Name	Type	Generated Value

m	integer	3
c	integer	4
d	integer	20

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..5)

JME function reference

Description

x coordinate of point a

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:

Statement
Advice

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Choose one from a list
Part e) Gap-fill
1. Gap Number entry
  Add
Part f) Gap-fill
1. Gap Number entry
  Add
Part g) Choose several from a list

Gap-fill

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

What is the gradient, $m$, of the straight line between the two points?

$m =$ Unnamed gap

Advice

a)

The gradient is the ratio of vertical change ($y_2-y_1$) to horizontal change ($x_2-x_1$).

\[ m = \frac{y_2-y_1}{x_2-x_1}=\frac{\simplify[!collectNumbers]{{yb}-{ya}}}{\simplify[!collectNumbers]{{xb}-{xa}}}=\frac{\simplify{{yb}-{ya}}}{\simplify{{xb}-{xa}}}=\simplify[simplifyFractions,unitDenominator]{({yb-ya})/({xb-xa})}\text{.}\]

b)

Rearranging the equation $y=mx+c$ for $c$ and using point A:

\[ c = y_1-mx_1 = \var{ya}-\var{m}\times\var{xa}=\simplify{{ya-m*xa}}\text{.}\]

We then check this against point $B$:

\[ y_2 = mx_2 + c = \simplify[fractionNumbers]{{m}{xb}+{c}}=\simplify{{m}*{xb}+{c}}\text{.}\]

b)

We now substitute the values for $m$ and $c$ into the equation of a straight line, $y=mx+c$,

\[y=\simplify[!noLeadingMinus,unitFactor]{{m} x+ {c}}\text{.}\]

{advicePoints()}

c)

The gradient represents the vertical change (height in cm) per unit of the horizontal axis (days): the change in height of the sunflower per day.

d)

Substituting $x=\var{d}$ into the straight line equation, the height $y$ after $\var{d}$ days is

\begin{align}
y&=\simplify{{m}}x+\var{c}\\
&=\simplify[]{{m}{d}}+\var{c}\\
&=\var{m*d+c}\text{cm.}
\end{align}

e)

Substituting $x=\var{1826}$ into the straight line equation, the height $y$ after $1826$ days is

\begin{align}
y&=\simplify{{m}}x+\var{c}\\
&=\simplify[]{{m}1826} + \var{c}\\
&=\var{m*1826+c}\text{cm.}
\end{align}

Note that this is $\var{(m*1826+c)/100}$ metres. In 2014, a sunflower of $9.17$ metres was entered into the Guinness World Records as tallest sunflower.

f)

Possible reasons that the prediction will not be accurate are:

from everyday observations and basic biology that a sunflower cannot keep growing forever, but our straight line equation would predict otherwise.
the set of observations are limited in their time frame. In particular another relationship could easily fit the 2 data points.

Invalid reasons that the prediction will not be accurate are:

There can only be one straight line between two points; only one equation describes this.
Based on common sense, we know that sunflowers do grow over time.

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
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Number entry
Number entry		Hasn't run yet
Gap-fill
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Number entry
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Gap-fill
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Mathematical expression
Mathematical expression		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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
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Choose several from a list
Choose several from a list		Hasn't run yet

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Straight line equation application: measuring sunflower height

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

b)

c)

d)

e)

f)

Loading...

Error

Straight line equation application: measuring sunflower height

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

b)

c)

d)

e)

f)

Generated value: `integer`