Rectangular and triangular numbers

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Memorandum

1. (b) quadrate number

2.

(a)

(b) No not quadrate of number

(c) No 1 + 2 + 3 + 4  4  5 

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

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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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