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Mathematics

Number patterns

Educator section

Memorandum

2.

a) 12 321

1 234 321

123 454 321

b) 12 345 654 321

3. a)

i) 9 109

ii) 18 218

iii) 27 327

iv) 36 436

b)

i) 633 763

ii) 81 981

4. a)

i) 111

ii) 222

iii) 333

b) Increases with111

c)

i) 12

ii) 15

d) 888

5. a)

i) 37 037

ii) 37 037

iii) 37 037

b)

i) 444 444 ÷ 12

ii) 555 555 ÷ 15

6. a)

i) 111 111

ii) 222 222

iii) 333 333

b)

i) 555 555

ii) 777 777

7.

i) 1 089

ii) 2 178

iii) 3 267

iv) 4 356

b) First 2 numbers increases with one at a time.

Last 2 numbers decreases with one at a time

c)

i) 99 x 55 = 5 445

ii) 99 x 66 = 6 534

Leaner section

Content

Activity: number patterns (patterns) [lo 1.9.2]

2. Use your pocket calculator and investigate the following patterns:

a) 1 × 1 = 1

11 × 11 = 121

111 × 111 = ________________________

1 111 × 1 111 = _____________________

11 111 × 11 111 = ___________________

b) Now predict: 111 111 × 111 111 = _________________

c) Validate your answer with your pocket calculator.

3 . Complete the following patterns:

a) i) 9 109 × 1 = __________________

ii) 9 109 × 2 = __________________

iii) 9 109 × 3 = __________________

iv) 9 109 × 4 = __________________

b) What will be the answer to:

i) 9 109 × 7? __________________

ii) 9 109 × 9? __________________

c) Now explain the pattern to a friend.

4 . a) Here is another interesting pattern to investigate.

i) 37 × 3 = __________________

ii) 37 × 6 = __________________

iii) 37 × 9 = __________________

b) What have you noticed? _________________________________________

_____________________________________________________________

c) Fill in the missing answers:

i) 37 × ________________ = 444

ii) 37 × ________________ = 555

d) What will the product of 37 and 24 be? ______________________

e) Check your answer with the help of your pocket calculator.

5 . a) Calculate the following:

i) 111 111 ÷ 3 = ________________

ii) 222 222 ÷ 6 = ________________

iii) 333 333 ÷ 9 = . ________________

b) Write down 2 similar sums which will give the same answer.

i) __________________________________________________________

ii) __________________________________________________________

6 . a) Also investigate the following pattern:

i) 1 × 15 873 × 7 = ______________________________

ii) 2 × 15 873 × 7 = ______________________________

iii) 3 × 15 873 × 7 = ______________________________

b) Without using your pocket calculator, predict:

i) 5 × 15 873 × 7 = ______________________________

ii) 7 × 15 873 × 7 = ______________________________

7 . a) With the help of your pocket calculator write down the following answers:

i) 99 × 11 = ______________________________

ii) 99 × 22 = ______________________________

iii) 99 × 33 = ______________________________

iv) 99 × 44 = ______________________________

b) Examine the pattern carefully. Explain it to a friend.

c) Write down the following two sums in the series, with their answers:

i) _______________ × _______________ = _______________

ii) _______________ × _______________ = _______________

Self-assessment

Complete the following by colouring the appropriate blocks: yes no
I can complete number patterns with the help of my pocket calculator
I can predict patterns without the help of my pocket calculator
I still need help to really understand this particular learning unit

Assessment

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 2.1: We know this when the learner investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns.

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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