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Mathematics

Number concept

Educator section

Memorandum

1.1 5

1.2 3

1.3 8

1.4 6

2.1 (39 x 27) + 496 1 549

2.2 (23 x 18) + 852 – 256 1 010

2.3 (67 + 48); 7 705 ÷ answer 67

2.4 3 600 ÷ 30; 82 x 10; answer + answer 940

2.5 2 934 – 816 + 905 – 205 2 818

2. different solutions are possible. you are aloud to use a number more than once.

Test 1

  • 13 800; 13 750
  • 24 360; 24 375

2. 300 000 + 60 000 + 8 000 + 400 + 20 + 9

  • <
  • =
  • 20 500
  • 358 490

5. six million eight hundred twenty three thousand four hundred and seventeen

6.1 1296

6.2 6

  • 40 000
  • 6 million
  • 37 000
  • 149 000
  • 48; 56; 64; 72
  • 1; 2; 3; 4; 5; 6; 8; 12; 24
  • 11; 13; 17; 19

10.1 true

  • false
  • false
  • 114
  • 34
  • 70

11.4 6

Leaner section

Content

Activity:to calculate by selecting appropriate operations for solving problems [lo 1.8.10]

It is very important to really understand and remember the following; otherwise you will not be able to perform easy (or difficult) operations, so that you will get wrong answers!

SEQUENCE OF CALCULATIONS TAKE NOTE AND LEARN THE

FOLLOWING!

The order in which calculations are done is:

1. Brackets

2. Of

3. Division

4. Multiplication

5. Addition

6. Subtraction

The following rules are also applicable:

1. When the operation is + only or x only, e.g. 6 + 3 + 9 + 5:

work from LEFT TO RIGHT.

2. When there is only + and − , e.g. 6 − 3 + 2 − 4 + 9:

work from LEFT TO RIGHT

Thus: 6 − 3 à 3 + 2 à 5 − 4 à 1 + 9 = 10

3. When you only have x and ¸ is, e.g. 2 x 24 ¸ 4 x 10 ¸ 5:

Work from LEFT TO RIGHT

Thus: 2 x 24 à 48 ¸ 4 à 12 x 10 à 120 ¸ 5 = 24

1. Let’s see if you are able to apply the preceding knowledge correctly. Work with a partner and calculate the following:

1.1 f = 9 + 6 ¸ 2 − 7 _____________________________________________

1.2 c = 7 − (18 + 2) ¸ 5___________________________________________

1.3 k = 23 − 16 + 4 − 3___________________________________________

1.4 e = 36 ¸ 12 x 4 ¸ 2_____________________________________________

You may use your pocket calculator now, but it might not help if you do not know the correct sequence of operations. If you are uncertain, read the previous page again. Try to complete the following table correctly:

Calculate Key to sequence Answer
E.g. 15 + 6 × 2 (6 × 2) + 15 27
2.1 496 + 39 × 27
2.2 852 + (23 × 18) − 256
2.3 7 705  (67 + 48)
2.4 3 600  30 + 82 × 10
2.5 2 934 − 816 + 905 − 205

Time for peer-assessment

How well do you know the last part of the work that we have been doing? Explain the following to a partner. Your partner can then assess you by circling the relevant code:

Altogether unsure Not very sure Fairly sure Very sure
I can explain what multiples are. (LO 1.3) 1 2 3 4
I can explain what factors are. (LO 1.3) 1 2 3 4
I can explain what prime numbers are. (LO 1.3) 1 2 3 4
I can use the constant function on my pocket calculator to determine multiples. (LO 1.8) 1 2 3 4
I can explain what a palindrome is. (LO 1.3) 1 2 3 4
I can explain the properties of 1 and 0 to my friend. (LO 1.3) 1 2 3 4
I know the sequence of calculations and can apply it correctly. (LO 1.8) 1 2 3 4

Puzzles!

1. Place the numbers 1 to 9 in the diagram in such a way that all the number sentences are true.

2. Place numbers between 1 and 12 in the diagram in such a way that the

sum totals of the different sides are the same.

Test 1

1. Complete the following number patterns:

1.1 13 850 ; ________________ ; ________________ ; 13 700 ; 13 650

1.2 24 330 ; 24 345 ; ________________ ; ________________

(4)

2. Write in expanded notation:

2.1 368 429 = ____________ + ____________ + ___________ + ___________ +

____________ + ____________

(2)

3. Fill in:<;>or = :

3.1 489 653 * 498 653____________

3.2 10 x 10 x 10 x 10 * 100 000 x 10____________

(2)

4. Which number is:

4.1 350 more than 20 150? ________________________

4.2 10 000 less than 368 490? ______________________

(2)

5. Write in words:

6 832 419

(2)

6. Complete:

6.1 64 = ____________________________________

6.2 one million = 1 x 10¨______________________

(2)

7. What is the value of the digit printed in bold?

7.1 1 4 7 689________________________________________

7.2 6 823 417_______________________________________

(2)

8. Round off to the nearest 1 000:

8.1 36 842________________________________________

8.2 149 099________________________________________

(2)

9. Write down:

9.1 the multiple of 8 between 40 and 80

_____________________________________________________________________

9.2 the factors of 24

_____________________________________________________________________

9.3 the prime numbers between 10 and 20

___________________________________________________________________ (6)

10. True or False?

10.1 42 624 is a palindrome_____________________________

10.2 1 is a prime number________________________________

10.3 36 ¸ 0 = 0________________________________________

(3)

11. Calculate:

11.1 90 + 6 x 12 ¸ 3__________________________________

11.2 36 − (5 x 4) ¸ 10_________________________________

11.3 80 − 6 + 4 − 13 + 5_____________________________

11.4 8 x 5 ¸ 8 x 6 ¸ 5_________________________________

(8)

I got _______________________________ out of 35 right.

Colour in: I feel

VERY SATISFIED
HAPPY
CONCERNED
I AM ABLE TO DO BETTER

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

1.8.10: multiple operations on whole numbers with or without brackets.

Questions & Answers

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 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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
Difference between extinct and extici spicies
Amanpreet Reply
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly Reply
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Source:  OpenStax, Mathematics grade 6. OpenStax CNX. Sep 10, 2009 Download for free at http://cnx.org/content/col11030/1.1
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