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Mathematics

Estimations, equations and variables

Educator section

Memorandum

1. (b) quadrate number

2.

(a)

(b) No not quadrate of number

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

3.

(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

Content

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?

_____________________________________________________________________

Assessment

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

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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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