Expansion of brackets

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From users who are members of Transition to university :

Christian Lawson-Perfect	said	Ready to use	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
Vicky Hall	said	Has some problems	7 years, 9 months ago

History

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Christian Lawson-Perfect 5 years, 10 months ago

Saved a checkpoint:

Replaced string restrictions with pattern restrictions.

Restore this checkpoint

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Looks OK.

You had the expected variables set incorrectly for the last two parts. You should just give the single variable names you expect, not combinations of them. And the whole point was to give a warning when the student types xy, not allow it!

Restore this checkpoint

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Bradley Bush commented 7 years, 8 months ago

It isn't worth fixing the x*( issue so we have left it

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Doesn't work

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Bradley Bush commented 7 years, 8 months ago

Thank you for the advice, I've removed 1 as a variable and I had added expected variable names but I've now added warning messages, although I have run into another problem with x*( being required overriding this message, so I'm going to need to ask how to change that.

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect commented 7 years, 8 months ago

In part a, when a[1]=1, I didn't get any brackets. Either make sure it's greater than 1, or turn off the unitFactor rule.

You need to give feedback messages for the string restrictions. "It doesn't look like you've expanded - make sure you don't use any brackets in your answer" would do.

Did you try adding expected variable names to the parts?

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Bradley Bush commented 7 years, 8 months ago

Thankyou for the advice, I've added string restrictions, moved the answer boxes and i've added brackets to the advice. Although I haven't added fullstops on the end of questions because they're lone 1 line equations with no sentence sturctured around them

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Bradley Bush commented 7 years, 8 months ago

Thank you for the feedback, I have fixed the string restrictions on all the parts, I've added the gap boxes and I've put more brackets into the advice but I haven't added the fullstops because the questions are one line and nowhere near a sentence, I'm not sure it's needed.

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher commented 7 years, 8 months ago

Main Parts

parts a) and b)

Typing in the correct answer works fine, but it also displays the red exclamation mark warning saying "Your answer was interpreted to use the unexpected variable name x". This doesn't appear for any of the other parts, so i would maybe take it out.

For all parts, i would put the answer box on the same line as the question, for example

8x(-3x-3x^2+2) = -24x^2-24x^3+16x.

I think it just looks a bit neater.

Parts i) and j)

I would give a hint for students to use the * when writing a product of two different terms like xy in the answer box, in case some students write this and can't understand why their answer is wrong. I think this can be done in the string restrictions section.

I'm not sure how important this is, but maybe put a full stop at the end of each question (after the answer box), also in the advice section.

Advice

I think there should be brackets around the terms that you are multiplying together (even though i know the point of this question is to expand brackets), for example for part a)

$\begin{align} 10(-4x-9) &= (10 \times -4x)+(-9 \times 10),\\ &= -90-40*x. \end{align}$

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Elliott Fletcher 7 years, 8 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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Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect commented 7 years, 9 months ago

Very nearly there!

Add restrictions to the parts forbidding brackets, to make sure the student has expanded in some way. It'll be too much effort to make sure they've collected like terms in the later parts.

In the parts with more than one variable, make sure you set the "expected variable names" field, so that mistakes like typing ab instead of a*b get caught.

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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 again for the feedback, I see what you mean with the statement, and again I am really sorry about the typos. I had changed the statement before but hadn't considered including the simplest form part in it. I am slightly worried that now without any text to preface the questions, the question is looking a bit boring, I'm not sure if there is anyhting I should be writing inbetween questions that you could suggest?
As for every other question being the same, did you note that the random variable can be both negative and positive. I thought negativity could be a tripping point for someone struggling with expanding brackets, so it would be good to include two versions of each, that way the student wouldn't be put off by a greater variety of the same question? Might it be worth constructing it so that every other example includes negative numbers so they come up less randomly?

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Vicky Hall 7 years, 9 months ago

Gave some feedback: Has some problems

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Vicky Hall commented 7 years, 9 months ago

I agree with Christian that a better statement would be:

Expand the expressions below by multiplying each of the terms inside the brackets by the term outside. Give each answer in its simplest form.

Having the 'simplest form' prompt in the statement will save you having to repeat it in every part of the question.

The questions get progressively more difficult but you essentially have two of each question, which seems unnecessary and makes the page look very long. If a student really wanted to do a particular type of problem multiple times, they could just refresh the page.

Have a check that your advice headers are in heading 4. There are also some typos in the advice.

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Bradley Bush commented 7 years, 9 months ago

Thank you for the feedback, I have now acted on the comments you gave by chaning all the questions into the mathematical expressions format, adjusting the variable sizes to make the mental maths easier and trying to make both the question statement and the advice more straight forward.

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Bradley Bush 7 years, 9 months ago

Saved a checkpoint:

before removing the gap fill

Restore this checkpoint

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Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect commented 7 years, 9 months ago

The question statement is a bit of a run-on sentence. Try something like:

Expand each of the expressions below.

Multiply each of the terms inside the brackets by the term outside the brackets.

One of the GCSE textbooks might have a good formulation of this prompt that you can use for inspiration.

Why have you made your own part headers instead of splitting each expression into its own part?

Think about the difficulty curve for these problems: you should start with a very simple example, and slowly add more complicated elements, one at a time. So you might start with $2(x+1)$ , then follow that with $x(x+1)$ , which requires multiplying $x \times x = x^2$ . Think about how games do this: you begin with very simple challenges while you get used to the controls, then more elements are added in as you become more secure in those.

While randomised numbers are good, this question is about algebra so maybe restrict coefficients to single digits. I don't know my 17 times table! Don't let students fail for the wrong reason: a mental arithmetic error is a distraction here.

The advice is written in the passive voice: "Brackets are expanded by..." Give a concise explanation of what "expanding brackets" means - you multiply terms so that no brackets are left - and then give a few generic examples, such as $a(x+2) = ax + 2a$ .

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Bradley Bush 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Expansion of brackets	Ready to use	Bradley Bush	23/03/2020 14:02
haken met distributieve eig uitwerken	draft	Johan Maertens	08/07/2020 16:05
spørsmål 1	draft	Ida Landgärds	02/12/2020 15:42
spørsmål 1	draft	Ida Landgärds	02/12/2020 15:42
Ida's copy of spørsmål 1	draft	Ida Landgärds	02/12/2020 15:42
Maria's copy of Expansion of brackets	draft	Maria Aneiros	29/05/2019 05:59
ahmad's copy of Expansion of brackets	draft	ahmad yahya	30/05/2019 11:27
Øystein's copy of Expansion of brackets	draft	Øystein Hildre	02/12/2020 15:42
AB5 Expand single brackets	Ready to use	Megan Oliver	09/04/2024 15:05

There are 42 other versions that do you not have access to.

Question statement

Expand the expressions below by multiplying each of the terms inside the brackets by the term outside. Give each answer in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

list

List of 50 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(-10..10 except [-1,0,1] ),50)

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: `list`

[ -2, 10, 2, 3, 4, 8, 6, -9, -10, 8, 2, -4, -6, -10, 2, 2, -2, -10, -3, -6, 4, -10, 2, -4, 3, -10, 10, -6, 7, 2, 6, 10, -8, -5, -10, -4, 9, 10, 9, 6, -3, -5, -2, -9, 8, 9, 6, -2, -5, -3 ]

This variable doesn't seem to be used anywhere.

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Gap-fill

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

$\simplify{{a[1]}({a[2]}x+{a[3]})}=$ Unnamed gap

Advice

Expand brackets using the general formula $\displaystyle a(x+c)=ax+ac$ . This means we multiply each term inside the brackets by the term outside the brackets.

It is easy to forget that the sign outside the brackets also needs to be involved in the multiplication so remember that when two of the same sign are multiplied, the resultant term is positive and when opposite signs are multiplied, the result is negative.

a)

$\begin{align} \simplify[terms]{{a[1]}({a[2]}x+{a[3]})}&= \simplify[!collectNumbers]{({a[1]}{a[2]})x+({a[1]}{a[3]})}\\& =\simplify{{a[1]}*{a[2]}x+{a[1]}{a[3]}}\text{.} \end{align}$

b)

$\begin{align} \simplify[terms]{{a[4]}({a[5]}x+{a[6]})}&= \simplify[!collectNumbers]{{a[4]}{a[5]}x+{a[4]}{a[6]}}\\&= \simplify{{a[4]}*{a[5]}x+{a[4]}{a[6]}}\text{.} \end{align}$

c)

$\begin{align} \simplify[terms]{{a[7]}({a[8]}x^2+{a[9]}y)}&= \simplify[!collectNumbers]{{a[7]}{a[8]}x^2+{a[7]}{a[9]}y}\\&= \simplify{{a[7]}*{a[8]}x^2+{a[7]}*{a[9]}y}\text{.} \end{align}$

d)

$\begin{align} \simplify[terms]{{a[10]}({a[11]}x^2+{a[12]}y)}&= \simplify[!collectNumbers]{{a[10]}{a[11]}x^2+{a[10]}{a[12]}y}\\&= \simplify{{a[10]}*{a[11]}x^2+{a[10]}*{a[12]}y}\text{.} \end{align}$

e)

$\begin{align} \simplify[terms]{{a[13]}x({a[14]}x^2+{a[15]}x+{a[16]})}&= \simplify[!collectNumbers]{{a[13]}x{a[14]}x^2+{a[13]}x{a[15]}x+{a[13]}x{a[16]}}\\&= \simplify{{a[13]}{a[14]}x^3+{a[13]}{a[15]}x^2+{a[13]}{a[16]}x}\text{.} \end{align}$

f)

$\begin{align} \simplify[terms]{{a[17]}x({a[18]}x^2+{a[19]}x+{a[20]})}&= \simplify[!collectNumbers]{{a[17]}x{a[18]}x^2+{a[17]}x{a[19]}x+{a[17]}x{a[20]}}\\&= \simplify{{a[17]}{a[18]}x^3+{a[17]}{a[19]}x^2+{a[17]}{a[20]}x}\text{.} \end{align}$

g)

$\begin{align} \simplify[terms]{{a[21]}x({a[22]}x^2+{a[23]}x)+{a[24]}x^2+{a[25]}x^3}&= \simplify[!collectNumbers]{x^2({a[21]}{a[23]})+x^2{a[24]}+x^3({a[21]}{a[22]})+x^3{a[25]}}\\&= \simplify[!collectNumbers]{x^2({a[21]}{a[23]}+{a[24]})+x^3({a[21]}{a[22]}+{a[25]})}\\&= \simplify{x^2({a[21]}{a[23]}+{a[24]})+x^3({a[21]}{a[22]}+{a[25]})}\text{.} \end{align}$

h)

$\begin{align} \simplify[terms]{({a[26]}x^2+{a[27]}x^3)+{a[28]}x({a[29]}x^2+{a[30]}x)}&= \simplify[!collectNumbers]{x^2({a[26]})+x^2({a[28]}{a[30]})+x^3({a[28]}{a[29]})+x^3({a[27]})}\\&= \simplify[!collectNumbers]{x^2({a[26]}+{a[28]}{a[30]})+x^3({a[28]}{a[29]}+{a[27]})}\\&= \simplify{x^2({a[26]}+{a[28]}{a[30]})+x^3({a[28]}{a[29]}+{a[27]})}\text{.} \end{align}$

i)

$\begin{align} \simplify[terms]{{a[31]}({a[32]}x+{a[33]}y)+{a[34]}x({a[42]}+{a[35]}y)}&= \simplify[!collectNumbers]{({a[31]}{a[32]})x+({a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\&= \simplify[!collectNumbers]{({a[31]}{a[32]}+{a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\&= \simplify{({a[31]}{a[32]}+{a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\text{.} \end{align}$

j)

$\begin{align} \simplify[terms]{{a[36]}a^2({a[37]}+{a[38]}b)+{a[39]}b^2({a[40]}a+{a[41]}b)}&= \simplify[!collectNumbers]{{a[37]}{a[36]}a^2+{a[38]}{a[36]}a^2b+{a[40]}{a[39]}a*b^2+{a[39]}{a[41]}b^3}\\&= \simplify{{a[37]}{a[36]}a^2+{a[38]}{a[36]}a^2b+{a[40]}{a[39]}a*b^2+{a[39]}{a[41]}b^3}\text{.} \end{align}$

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Checkpoint description

Christian Lawson-Perfect 5 years, 10 months ago

Elliott Fletcher 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

Bradley Bush 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Bradley Bush commented 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect commented 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Bradley Bush commented 7 years, 8 months ago

Bradley Bush commented 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

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush commented 7 years, 9 months ago

Vicky Hall 7 years, 9 months ago

Vicky Hall commented 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

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 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: list

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

Generated value: `list`