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Mathematics

Estimations, equations and variables

Educator section

Memorandum

14. (a) 100

(b) 12

(c) 124

(d) 8

15. (a) 10 99 75 5

(c)

______ 8 ______ 21
39 ______ 74 ______

16.2 (a) 5 х + 7 = 22

(b) 8 х - 10 = 46

(c) 5 + 9 х = 59

(d) х - 13 = 6

16.3 (a) 21

(b) 17

(c) 34

18 (a) 72 (j) 30

(b) 12 (k) 5

(c) 7 (l) 57

(d) 141 000 (m) 9

  1. 900 (n) 9 987
  2. 47 (o) 125

(g) 135

(h) 336

(i) 7

20. (a) х >10

(b) y <2 000

(c) ( c +8)>6

(d) y <50

(e) k – ( k ÷ 2)<20

Leaner section

Content

Activity: estimations, equations and variables (algebraic equations) [lo 1.7.2, lo 1.9.1, lo 1.10, lo 2.5]

14. Now replace the letters with the correct numbers in the following flow diagram:

15. Puzzles!

a) Can you solve the following?

I am thinking of a particular number. When I multiply this number by 7, then subtract 6 and divide the answer by 8, the quotient is 8. What is the number that I have in mind?________________________________________________________

I am starting with 9. When I multiply this by 12, than add 2 and subtract 11, the answer is_____________________________________________________________

What answer will I get if I start with 7? ____________________________________

And if I start with 5?____________________________________________________

b) We can compile a table that will help us with problems like these.

Number 9 7 5
Number × 12 + 2 – 11 99 75 51

c) We could replace the word "number" with any letter of the alphabet. Can you fill in the missing numbers in the following table?

k 6 ________ 13 _________
(k × 5) + 9 49 114

d) Tell your partner how you obtained the answers.

16.1 Did you know?

The statement (k x 5) + 9 = 49 is referred to as an algebraic equation. “Algebra” is the “study of number sentences”.

16.2 Write the algebraic equation for the following:

a) A particular number x 5 + 7 = 22

____________________________________________________________________

b) 8 x a number – 10 = 46 ______________________________________

c) 5 + (9 x a number) = 59 _______________________________________

d) When 13 is subtracted from a bigger number the difference is 6.

_____________________________________________________________________

16.3 Solve the following equations: (You may use your pocket calculator).

a) 49 x a – 29 = 1 000

_____________________________________________________________________

b) (b + 15) x 6 = 192

_____________________________________________________________________

c) 16 x c – 15 = 529

_____________________________________________________________________

17. Did you know?

The letters that are used in place of numbers are called variables.

18. Let's first see how you do in your next mental arithmetic test.

a) 9 x 8 = ___________________________

b) ___________________________ x 4 = 48

c) 4 x ___________________________ = 28

d) 6 x 235 x 100 = ______________________

e) 25 x 9 x 4 = _________________________

f) 16 + 17 + 14 = ______________________

g) 104 + 15 + 16 = _____________________

h) Triple: 112: = _________________________

i) 42 ÷ 6 = ___________________________

j) ___________________________ ÷ 6 = 5

k) 35 ÷ ___________________________ = 7

l) (7 x 3) + (4 x 9) =_______________________

m) 4 x 9 + ___________________________ = 45

n) 10 000 – 13 = ___________________________

o) 5 to the power of 3 = _______________________

15

19. Did you know?

When we use>and<-signs in numbers sentences, e.g. when we

want to say that a number divided by 4 is smaller than 5, we write

it like this:

y ÷ 4<5

If we, for example, wished to say that a number multiplied by 5 is greater than 16, we would write it like this:

b x 5>16

Number sentences like these, which do not have the = sign, are called

inequalities.

20. Write the following word sentences as inequalities:

a) The number of sweets that I have is more than 10.

_____________________________________________________________________

b) The number of learners in our school is greater than 2 000.

_____________________________________________________________________

c) A number increased by 8, is greater than 6.

_____________________________________________________________________

d) There are less than 50 learners in our class.

_____________________________________________________________________

e) If I give away half of my marbles, I shall have fewer than 20.

_____________________________________________________________________

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 1.7: 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;

1.10: uses a range of strategies to check solutions and judges the reasonableness of solutions.

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 solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).

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;

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:

2.3.2: flow diagrams;

2.3.3: tables;

Assessment Standard 2.5: We know this when the learner solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).

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
Maciej
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 ?
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
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
what is biological synthesis of nanoparticles
Sanket 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
I'm interested in nanotube
Uday
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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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