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Estimations, equations and variables

Educator section


1. (b) quadrate number



(b) No not quadrate of number

(c) No 1 + 2 + 3 + 4 size 12{ div } {} 4 size 12{ div } {} 5 size 12{<>} {}


(b) 64; 125; 216; 343

(c) 64

(d) 64 000

(e) 274 625

(f) K4: + 64

K5: + 64 + 125 = 225

(g) 1 + 8 + 27 + 64 + 125 + 216 = 441

(h) all square number

Leaner section


Activity: rectangular and triangular numbers [lo 1.3.4, lo 1.7.2, lo 1.7.7, lo 2.3.1, lo 2.3.3]

1. Do you still remember?

In module 1 we learnt about square numbers and triangular numbers.

a) Can you explain to your partner what these patterns are like?

b) What is the synonym for square numbers?

2. Let us have a look at RECTANGULAR NUMBERS.

Did you know?

Each counting number bigger than 0 is a rectangular number. The Greeks used the term rectangular number for the product of two consecutive numbers only,

e.g. 42 = 6 x 7.

When we draw rectangular numbers, they will look like this:

___ ___ ___ ___ ___ ___ ___ ___ ___
6 = 1 × 6 ___ ___ ___
6 = 2 × 3

a) Now draw as many sketches as possible to represent the rectangular number 18.

b) Is 18 a square number? ______________________________ Why/why not?



c) Is 18 a triangular number? ___________________________ Why/why not?



3. Did you know?

a) We also have numbers to the power of three!! These numbers are also known as cubed numbers. Take a good look at the examples:

1 = 1 × 1 × 1

8 = 2 × 2 × 2

27 = 3 × 3 × 3

b) Predict what the following four cubed numbers will be (you may use your pocket calculator).





c) List any of the above numbers that may be a square number:______________

d) What will the 40th cubed number be? _______________________________

e) What is 653 (to the power of 3)? ___________________________________

f) Take a good look at the following. Can you complete the table?

Cubed numbers Sum of the cubed numbers
K1 1
K2 1 + 8 = 9
K3 1 + 8 + 27 = 36
K4 1 + 8 + 27 + ........... = 100
K5 1 + 8 + 27 + ........... + ........... = .........................

g) Can you predict what the sum of the first 6 cubed numbers will be?


h) What do you notice about the numbers in the second column?



Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.3: We know this when the learner recognises, classifies and represents the following numbers in order to describe and compare them:

1.3.4: numbers in exponential form including squares of natural numbers to at least 12 2 , cubes of natural numbers to at least 5 3 , and their square and cube roots.

Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.7.2: multiple operations with integers;

1.7.7: exponents.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:

2.3.1: verbal descriptions;

2.3.3: tables.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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