Expand brackets and collect like terms

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From users who are members of Transition to university :

Christian Lawson-Perfect	said	Ready to use	7 years, 7 months ago
Bradley Bush	said	Needs to be tested	7 years, 8 months ago
Hannah Aldous	said	Has some problems	7 years, 9 months ago
Chris Graham	said	Has some problems	7 years, 9 months ago

History

○

Christian Lawson-Perfect 5 years, 10 months ago

Saved a checkpoint:

Replaced javascript with pattern restrictions in every part

Restore this checkpoint

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Christian Lawson-Perfect 7 years, 5 months ago

Saved a checkpoint:

I've fixed part h - I was missing a plus-or-minus in the matching pattern.

Restore this checkpoint

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J. Richard Snape commented 7 years, 5 months ago

Thanks for this fantastic question set in "Transition to University". I'm trialling using them in my teaching this year. I have a tiny problem with part h in this question - for some reason when I use it when a student enters a correct answer it marks it wrong, giving feedback that it can be further simplified. I attach a screenshot - not sure what rule is triggering this as even the 419 constant is prime, so I can't see any further gathering of terms possible. I'll try to debug myself, but any help would be appreciated :) It seems to be using "all" for simplification in the marking, but so are other parts in this question that work fine.

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Christian Lawson-Perfect 7 years, 7 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 7 months ago

Saved a checkpoint:

I've set expected variable names for the parts with more than one variable.

Restore this checkpoint

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Aiden McCall 7 years, 8 months ago

Saved a checkpoint:

I can't see anything particularly wrong with this question.

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

○

Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

The string restrictions aren't doing a great job here. I don't think you should require the asterisk.

Talk to Elliott about adding pattern matching.

This should be two questions - a question with each of the items from part a as a separate part, and part b on its own.

Restore this checkpoint

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Has some problems

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Bradley Bush commented 7 years, 8 months ago

Thank you for the feedback and s0rry for the typing errors. Changing the marking order was very difficult but has been done using either string restrictions or marking scripts. Thank you for the advice for the wording of wuestions, I need to get more concise with the way I word things. I am glad you liked it.

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Lauren Richards commented 7 years, 8 months ago

MAIN PARTS

Typo in the statement - "bellow" instead of "below".

Part v) gave me "1ab" as one of the terms. Maybe make sure the 1 cancels.

I think part b) sounds a little complicated when it is your friend. I suggest you make it yourself or a specific person, eg. Jim. "Jim has a fondness of handmade sweets and is trying to work out the amount of money he has spent on them in one week. He eats [blah] lollipops, [blah] toffees and [blah] jelly sweets. Lollipops cost [blah], toffees are £1 more expensive than lollipops and jelly sweets are half the price of toffees."

Make sure all your i), ii)... are in italic in both the main question and the advice.

i) in part b) - "it's" should be "its" and "simplist" should be "simplest". I also think you should specify not to have brackets in your answer.

ii) in part b) - I think you should just say "If the cost of a lollipop was [blah], calculate Jim's total expenditure on sweets for the week." I also think you should put a pound sign before the gap fill as the units are pounds.

Issue with numbas not acccepting answers as terms are in a different order to that which it is expecting. Maybe in the question, specify which order to put the terms to avoid this happening.

ADVICE

In parts vi), vii) and viii), I think I would add a line expanding out the brackets to make it more clear.

I think the advice for b)i) could be more helpful rather than just telling them to read carefully! Explain how (x+1) means toffees are £1 more expensive etc.

Part b)ii), I think you could write "Using the equation we had devised from part b)i), we can substitute the price of lollipops, x=2, to calculate Jim's total expenditure."

Good question, I like it!

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Bradley Bush commented 7 years, 9 months ago

Thank you for the feedback, I agree about the "*" requirement so I've removed that from the answer. I fixed the typos and the latex errors, added some gaps, reworded part b and changed the text layout.

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Hannah Aldous commented 7 years, 9 months ago

all of your part a answers require * using in the answers, however some parts of v don't. Not sure I would require * for the answers.
part b i) typo "tofffee",
make sure x and £ in the question is written in LaTeX,
you need to place gaps in before and after the = for both i and ii,
the question for part i seems a bit clunky and long maybe split it after algerbraic expression and start the next sentence as 'write the answer in...'
in b ii) maybe write '...calculate total cost..'
in the advice part a make sure x^2 and x are in LaTeX
also you've written x^2+x=x^2+2?
in part b i you've centred and aligned part of your text with the equations
for ii use \times instead of *

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Hannah Aldous 7 years, 9 months ago

Gave some feedback: Has some problems

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 9 months ago

typo: "algerbraic". Re-consider part b)

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Chris Graham 7 years, 9 months ago

Gave some feedback: Has some problems

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Bradley Bush commented 7 years, 9 months ago

Thank you for the feedback!

The 'doesn't work' was something Christian set when he came over and the changes we had made to the editor weren't being reflected in the test runs. I have made the statement more direct, added some string restrictions, changed the advice errors and the part b advice.

However, for the part b) question I wanted to test the ability of the student to turn the text they are reading into equations which can then be manipulated as a higher level skill to round off the question, but I would like to hear any further opinion you have on this.

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 9 months ago

I've changed the Doesn't Work status as it seems to run OK. What was the problem?

The statement is currently more of a description of the question, rather than instructions for the student. "For each of the expressions below, collect terms..." would be more direct.

In part b) you can use the string restrictions tab to set the expected variables and warn the student if they use anything other than those.

The prompt in b) starts quite abruptly with "One bag...". Why not say e.g. "Brad has two bags of tokens. The first bag contains..." I think I would move the bag contents to two lists, which is easier for the student to work with.

In the advice you have some small errors e.g. $7z(=$ , and you could make use of the align environment. Similarly with part (b).

In the final part of the advice I would give an expression for each bag first, in terms of $r,b,y$ and then put the two together.

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Chris Graham 7 years, 9 months ago

Gave some feedback: Has some problems

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Bradley Bush commented 7 years, 9 months ago

The error in the marking of the first question seems to have fixed itself.

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Doesn't work

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Doesn't work

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Bradley Bush 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Expand brackets and collect like terms	Ready to use	Bradley Bush	20/11/2019 14:38
Create an algebraic expression from a word problem, simplify, and evaluate	Ready to use	Bradley Bush	19/12/2022 12:26
Hollie's copy of Expand brackets and collect like terms	draft	Hollie Tarr	17/09/2017 15:18
Raphael's copy of Expand brackets and collect like terms	draft	Raphael Stuhlmeier	23/11/2017 13:28
Expand brackets and collect like terms	draft	Owen Jepps	11/01/2018 06:08
samla lika termer	draft	Ida Landgärds	10/04/2018 14:19
Ida's copy of samla lika termer	draft	Ida Landgärds	10/04/2018 14:21
Ida's copy of samla lika termer	draft	Ida Landgärds	10/04/2018 14:24
Marte's copy of Expand brackets and collect like terms	draft	Marte Bråtalien	12/04/2018 11:01
Marte's copy of Expand brackets and collect like terms	draft	Marte Bråtalien	12/04/2018 11:01
Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Samantha Konig	28/06/2018 05:55
Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Samantha Konig	28/06/2018 05:56
Expand brackets and collect like terms	draft	Paul Hancock	24/07/2018 02:40
Expand brackets and collect like terms[L4 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 13:56
Heather's copy of Expand brackets and collect like terms[L4 Randomised]	draft	Heather Driscoll	01/10/2018 15:40
Francis's copy of Expand brackets and collect like terms - two questions	draft	Francis Duah	11/11/2018 15:28
Create an algebraic expression from a word problem, simplify, and evaluate in dollars version	Ready to use	Maria Aneiros	18/05/2019 02:13
Maria's copy of Expand brackets and collect like terms	draft	Maria Aneiros	29/05/2019 05:57
Maria's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Maria Aneiros	29/05/2019 05:09
WordProblem01_NL	Ready to use	Paul Verheyen	28/09/2019 18:14
Musa's copy of Expand brackets	draft	Musa Mammadov	01/08/2022 08:17
Musa's copy of Expand brackets and collect like terms 3	draft	Musa Mammadov	27/06/2023 01:45
Musa's copy of 3 Expand brackets	draft	Musa Mammadov	27/06/2023 01:47

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Question statement

For each expression below, collect like terms and expand brackets.

The * symbol is required between algebraic symbols, e.g. $5ab^2$ should be written 5*a*b^2.

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	6
b1	integer	9
c1	integer	10

			Name	Type	Generated Value

a	list	[ 5, 7, 12, 7, 9 ]
b	list	[ 6, 5, 3, 4, 3 ]
c	list	[ 8, 7, 4, 8, 10 ]
d	list	[ 26, 16, 30, 27, 22, 19 ]
f	list	[ 5, 9, 16, 3, 7, 17, 4 ]
g	list	[ 9, 2, 6, 7, 3, 13, 14 ]
h	list	[ 13, 15, 14, 12, 7, 8, 18 ]
j	list	List of 9 items

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(5..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:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Gap-fill
1. Gap Mathematical expression
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Part e) Gap-fill
1. Gap Mathematical expression
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Part f) Gap-fill
1. Gap Mathematical expression
  Add
Part g) Gap-fill
1. Gap Mathematical expression
  Add
Part h) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$\var{c[0]}x+\var{c[1]}x+\var{c[2]}x=$ Unnamed gap

Advice

When simplifying expressions, only terms of the same type or like terms can be added together.

Algebraic symbols or letters can be added together provided that they are raised to the same power. For example, we can add $x^2+x^2=2x^2$, but we cannot collect both $x^2$ and $x$ into one term.

a)

\[
\begin{align}
\var{c[0]}x+\var{c[1]}x+\var{c[2]}x&=(\var{c[0]}+\var{c[1]}+\var{c[2]})x\\
&=\simplify{({c[0]}+{c[1]}+{c[2]})}x
\end{align}
\]

b)

\[
\begin{align}
\var{a[1]}x^2+\var{a[2]}x^2+\var{a[3]}x+\var{a[4]}x +\var{a[0]}&=(\var{a[1]}+\var{a[2]})x^2+(\var{a[3]}+\var{a[4]})x +\var{a[0]}\\
&=\simplify{({a[1]}+{a[2]})}x^2+\simplify{({a[3]}+{a[4]})}x+\var{a[0]}
\end{align}
\]

c)

\[
\begin{align}
\var{b[0]}y^5+\var{b[1]}y^5+\var{b[2]}y^5+\var{b[4]}y^5+\var{b[3]}y^5&=(\var{b[0]}+\var{b[1]}+\var{b[2]}+\var{b[4]}+\var{b[3]})y^5\\
&=\simplify{({b[1]}+{b[2]}+{b[3]}+{b[4]}+{b[0]})}y^5
\end{align}
\]

d)

\[
\begin{align}
\var{d[0]}ab+\var{d[1]}abc+\var{d[2]}a+\var{d[3]}b+\var{d[4]}c+\var{d[5]}abc
&=(\var{d[1]}+\var{d[5]})abc+\var{d[0]}ab+\var{d[2]}a+\var{d[3]}b+\var{d[4]}c\\
&=\simplify{{d[1]}+{d[5]}}abc+\var{d[0]}ab+\var{d[2]}a+\var{d[3]}b+\var{d[4]}c
\end{align}
\]

e)

\[
\begin{align}
\var{f[0]}a^2b+\var{f[1]}ab^2+\var{f[2]}ab+\var{f[3]}a^2b+\var{f[4]}ab^2
&=(\var{f[0]}+\var{f[3]})a^2b+(\var{f[1]}+\var{f[4]})ab^2+\var{f[2]}ab\\
&=\simplify{{f[0]}+{f[3]}}a^2b+\simplify{{f[1]}+{f[4]}}ab^2+\var{f[2]}ab
\end{align}
\]

f)

\[
\begin{align}
\var{g[0]}(\var{g[1]}x+\var{g[2]}y)+\var{g[4]}x+\var{g[5]}y
&=(\var{g[0]}\times \var{g[1]}+\var{g[4]})x+(\var{g[0]} \times\var{g[2]}+\var{g[5]})y\\
&=(\simplify{{g[0]}*{g[1]}}+\var{g[4]})x+(\simplify{{g[0]}*{g[2]}}+\var{g[5]})y\\
&=\simplify{{g[0]}*{g[1]}+{g[4]}}x+\simplify{{g[0]}*{g[2]}+{g[5]}}y
\end{align}
\]

g)

\[
\begin{align}
\var{h[0]}x(\var{h[1]}x+\var{h[2]}z)+\var{h[3]}x+\var{h[6]}z+\var{h[4]}x^2+\var{h[5]}z^2
&=(\simplify[]{{h[0]}{h[1]}}+\var{h[4]})x^2+(\simplify[]{{h[0]}{h[2]}})zx+\var{h[3]}x+\var{h[5]}z^2+\var{h[6]}z\\
&=(\simplify{{h[0]}{h[1]}}+\var{h[4]})x^2+(\simplify[]{{h[0]}{h[2]}})zx+\var{h[3]}x+\var{h[5]}z^2+\var{h[6]}z\\
&=\simplify{{h[0]}*{h[1]}+{h[4]}}x^2+\simplify{{h[0]}*{h[2]}}zx+\simplify{{h[3]}x+{h[5]}}z^2+\var{h[6]}z
\end{align}
\]

h)

\[
\begin{align}
\var{j[0]}(\var{j[1]}x-\var{j[2]}y)+\var{j[3]}(\var{j[4]}x-\var{j[5]}y)+\var{j[6]}(\var{j[7]}x-\var{j[8]}y)
&= (\simplify[]{{j[0]}{j[1]}}+\simplify[]{{j[3]}{j[4]}}+\simplify[]{{j[6]}{j[7]}})x-(\simplify[]{{j[0]}{j[2]}}+\simplify[]{{j[3]}{j[5]}}+\simplify[]{{j[6]}{j[8]}})y\\
&= (\simplify{{j[0]}{j[1]}}+\simplify{{j[3]}{j[4]}}+\simplify{{j[6]}{j[7]}})x-(\simplify{{j[0]}{j[2]}}+\simplify{{j[3]}{j[5]}}+\simplify{{j[6]}{j[8]}})y\\
&= \simplify{({j[0]}*{j[1]}+{j[4]*j[3]}+{j[6]}*{j[7]})x}-\simplify{({j[0]}*{j[2]}+{j[5]}{j[3]}+{j[6]}*{j[8]})y}
\end{align}
\]

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Checkpoint description

Christian Lawson-Perfect 5 years, 10 months ago

Christian Lawson-Perfect 7 years, 5 months ago

J. Richard Snape commented 7 years, 5 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Bradley Bush commented 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush commented 7 years, 9 months ago

Hannah Aldous commented 7 years, 9 months ago

Hannah Aldous 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Bradley Bush commented 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Bradley Bush commented 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)

c)

d)

e)

f)

g)

h)

Generated value: `integer`