Square and cube numbers

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Stanislav Duris

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From users who are members of Transition to university :

Chris Graham	said	Ready to use	7 years, 8 months ago
Stanislav Duris	said	Needs to be tested	7 years, 8 months ago
Christian Lawson-Perfect	said	Has some problems	7 years, 8 months ago

History

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Elliott Fletcher commented 7 years, 8 months ago

Yeah i think there is an always/sometimes/never question already for this.

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Chris Graham 7 years, 8 months ago

Gave some feedback: Ready to use

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Chris Graham commented 7 years, 8 months ago

This is OK. I'm not sure if we wrote an always/sometimes/never question, but if we didn't then it would be an excellent addition.

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Stanislav Duris 7 years, 8 months ago

Published this.

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Stanislav Duris 7 years, 8 months ago

Saved a checkpoint:

If this question isn't ready and someone needs to adjust this question - make sure that the interval in part c) always includes one square number only! The x variable makes sure the numbers increase in ascending order in the question, so don't confuse x1, x2, etc. with x[0], x[1],.. because these may not be the same and x[0], x[1],.. are the ones used in the question.

Restore this checkpoint

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Stanislav Duris 7 years, 8 months ago

Gave some feedback: Needs to be tested

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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 7 years, 8 months ago

Saved a checkpoint:

I don't think you need the $x_i$ notation. This question should test that the student knows what a superscript 2 or 3 means. This question could just be, "Find $5^2$ "; "Find $3^3$ "; "Find the first square number between $124$ and $165$ ".

Restore this checkpoint

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Elliott Fletcher commented 7 years, 8 months ago

Main Parts

a) i would write (x_n)^2 instead of x^2.

b) i would write (x_n)^3 instead of x^3. Also, its up to you but you could maybe include (x_5)^3 as an extra question here.

c) i think there should be a full stop after the inequality here.

Advice

a) i think there should be full stops at the end of each of the calculations, like after the 9 in the calculation for 3^2.

b) again i think there should be full stops at the end of each of the calculations.

c) i would say "Here is a table of square numbers for integers from 1-15"

I would also include an extra sentence before you calculate the square root of y^2. You could say "To calculate y we must calculate the square root of y^2," and then have a full stop at the end of the equation here as well.

Otherwise, this looks good!

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Stanislav Duris 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

I don't think part a is a well-conceived question. First of all, I don't like telling students not to use calculators. You can sometimes hint that a calculator won't be useful, but don't give them the idea that using calculator is ever bad.

When you're told $x$ and $x^3$ but not $x^2$ - why would you ever calculate $(x^3)^{2/3}$ instead of just squaring $x$ ?

Similarly, when you're given $x^3$ and $x^3$ but not $x$ , I don't think anyone would take the cube root instead of the square root. So why show both?

Some ideas for different questions on the same topic:

Calculate $x^2$ for $x$ from 1 to 10.

Calculate $x^3$ for $x$ from 1 to 10.

Find a number such that $x^2 \gt 100$ and $x^2 \lt 120$ .

An "always/sometimes/never" question for some statements. The student has to say if each of the statements is always true, sometimes true, or never true.

$x^3$ is greater than $x^2$ . (sometimes)

If $x$ is negative, $x^2$ is negative (never)

If $x$ is negative, $x^3$ is negative (always)

$x^2 = x$ (sometimes)

$(x+1)^2 \gt x$ (sometimes)

$(x+1)^3 \gt x$ (always)

When $x$ is a whole number, $x^2$ divides $x^3$ (always)

$x^3$ has the opposite sign to $x$ (never)

Part b is good - it could be a separate question, called "calculate powers of ten"

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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, 9 months ago

Created this.

Name	Status	Author	Last Modified
Square and cube numbers	Ready to use	Stanislav Duris	20/11/2019 14:43
Calculate powers of ten	Ready to use	Stanislav Duris	20/11/2019 14:34
Always, sometimes or never: square and cube numbers	Ready to use	Stanislav Duris	20/11/2019 14:32
Positieve en negatieve machten van 10	draft	Johan Maertens	30/12/2022 10:15
Q3.Homework7	draft	Patrick Joyce	07/08/2017 16:32
Q17.(new)	draft	Patrick Joyce	10/08/2017 15:53
Q18.(new)	draft	Patrick Joyce	10/08/2017 15:56
Q17.(new)	Ready to use	Patrick Joyce	05/12/2017 12:47
Q18.(new)	Ready to use	Patrick Joyce	05/12/2017 12:48
Q19.(new)	Ready to use	Patrick Joyce	05/12/2017 12:50
Q20.(new)	Ready to use	Patrick Joyce	30/11/2017 17:16
Grainne's copy of Q19.(new)	draft	Grainne Scanlon	16/01/2018 13:45
Louise's copy of Calculate powers of ten	draft	Louise Lynch	26/01/2022 19:48
Always, sometimes or never: square and cube numbers	draft	Xiaodan Leng	11/07/2019 01:45
Square and cube numbers 1	draft	Leonardo Juliano	19/09/2019 16:05
Immer, manchmal oder nie? (Quadratzahlen und dritte Potenzen)	Ready to use	Ulrich Görtz	30/09/2024 20:07

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Question statement

Try the following questions on square and cube numbers.

Give any introductory information the student needs.

			Name	Type	Generated Value

x1	integer	3
x2	integer	4
x3	integer	5
x4	integer	10
x5	integer	11
x	list	[ 3, 4, 5, 10, 11 ]
y2	number	36
y	integer	6
ly	number	26
uy	number	43

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..3)

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:

Parts

Part a) 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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5. Gap Gap 4. Number entry
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Part b) 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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5. Gap Gap 4. 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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Gap-fill

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

Find the following:

$\var{x[0]}^2 =$ Gap 0.

$\var{x[1]}^2 =$ Gap 1.

$\var{x[2]}^2 =$ Gap 2.

$\var{x[3]}^2 =$ Gap 3.

$\var{x[4]}^2 =$ Gap 4.

Advice

a)

Squared integers are called square numbers. It may be useful to remember the first few square numbers to be able to use them without a calculator.

Here:

$\begin{align} \var{x[0]}^2 &= \var{x[0]} \times \var{x[0]} \\&= \var{x[0]^2} \text{.}\end{align}$

$\begin{align} \var{x[1]}^2 &= \var{x[1]} \times \var{x[1]} \\&= \var{x[1]^2} \text{.}\end{align}$

$\begin{align} \var{x[2]}^2 &= \var{x[2]} \times \var{x[2]} \\&= \var{x[2]^2} \text{.}\end{align}$

$\begin{align} \var{x[3]}^2 &= \var{x[3]} \times \var{x[3]} \\&= \var{x[3]^2} \text{.}\end{align}$

$\begin{align} \var{x[4]}^2 &= \var{x[4]} \times \var{x[4]} \\&= \var{x[4]^2} \text{.}\end{align}$

b)

Cubed integers are called cubed numbers. To obtain these, we would typically always use a calculator.

We can either cube the number $x$ :

$\begin{align} \var{x[0]}^3 &= \var{x[0]} \times \var{x[0]} \times \var{x[0]} \\&= \var{x[0]^3} \text{,} \end{align}$

or we can multiply the square number $(x_n)^2$ from part a) by the appropriate $x_n$ :

$\begin{align} \var{x[0]}^3 &= \var{x[0]}^2 \times \var{x[0]} \\&= \var{x[0]^2} \times \var{x[0]}\\&= \var{x[0]^3} \text{.} \end{align}$

$\begin{align} \var{x[1]}^3 &= \var{x[1]} \times \var{x[1]} \times \var{x[1]} \\ &= \var{x[1]^3} \text{.}\end{align}$

$\begin{align} \var{x[2]}^3 &= \var{x[2]} \times \var{x[2]} \times \var{x[2]} \\ &= \var{x[2]^3} \text{.}\end{align}$

$\begin{align} \var{x[3]}^3 &= \var{x[3]} \times \var{x[3]} \times \var{x[3]} \\ &= \var{x[3]^3} \text{.}\end{align}$

$\begin{align} \var{x[3]}^4 &= \var{x[4]} \times \var{x[4]} \times \var{x[4]} \\ &= \var{x[4]^3} \text{.}\end{align}$

c)

Here is a table of square numbers for integers from $1$ to $15$ :

$y$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
$y^2$	$1$	$4$	$9$	$16$	$25$	$36$	$49$	$64$	$81$	$100$	$121$	$144$	$169$	$196$	$225$

The only square number between $\var{ly}$ and $\var{uy}$ is $\var{y2}$ .

To calculate $y$ we must calculate the square root of $y^2$ ,

$\sqrt{\var{y2}} = \var{y} \text{.}$

This is our integer $y$ .

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:

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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History

Comment

Checkpoint description

Elliott Fletcher commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Stanislav Duris 7 years, 8 months ago

Stanislav Duris 7 years, 8 months ago

Stanislav Duris 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Stanislav Duris 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Error

Square and cube numbers

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Stanislav Duris 7 years, 8 months ago

Stanislav Duris 7 years, 8 months ago

Stanislav Duris 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Stanislav Duris 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`