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Estimations, equations and variables

Educator section


21. (a)

Days ___ ___ ___ ___ 5 ___ ___ 49
Bo x es ___ ___ 150 200 ___ 600 1 750 ___



Sketch ___ ___ ___ ___ ___ ___
Number of squares 4 7 10 13 25 40

(c) Squares = 1 + (Sketch No. x 3)

(d) (i) 1 + (25 x 3) = 76

  1. 1 + (37 x 3) = 112
  2. 1 + (101 x 3) = 304

(e) (i) 43

  1. 55
  2. 80

23. (a) u = {} i ÷ 4

(b) u = ( i x 2) + 1

24. (a) Input


24. (a) Input money R1 R5 R30 R50 R100
Output : flower bulbs 3 15 90 150 300


InputNights 1 7 10 15 31
Output Cost R280 R1 960 R2 800 R4 200 R8 680


InputKg 1 4 19
OutputAmount R6,20 R17 R27,70 R35,70 R129,78

Leaner section


Activity: estimations, equations and variables (algebraic equations) [lo 2.1, lo 2.3.3, lo 2.2, lo 2.4]

21. Let us see if we can formulate rules to solve equations by looking at patterns.

Every day the Cape Market purchases 50 boxes of grapes

from a farmer.

a) Complete the following table:

Days 1 2 3 4 12 35
Boxes 50 100 250 2 450

b) We can check if you are correct by writing an algebraic equation

for the above:

b (boxes) = d (days) ´ 50

Therefore: c = 3 ´ 50

= 150 (3rd day)

c = d ´ 50

250 = d ´ 50

250 ÷ 50 = d

5 = d

On day 5 the market had already bought 250 boxes of grapes.

c) Work with a partner and check the rest of your work in the same way.

22. Examine the following three sketches:

a) Can you explain to a friend the pattern that is formed here?

b) Complete this table:

Sketch 1 2 3 4 8 13
Number of squares

c) Can you write down the equation by which you can determine your solution?


d) Use your equation to determine the number of squares in

(i) sketch 25: ___________________________________________________

(ii) sketch 37: ___________________________________________________

(iii) sketch 101: ___________________________________________________

e) Which sketches will contain the following number of squares?

(i) 130: _________________________________________________________

(ii) 166: _________________________________________________________

(iii) 241: _________________________________________________________

23. Are you able to write a rule (an algebraic equation) for the relationship between the input and output numbers in the following table?


Input (i) 16 28 48 60
Output (o) 4 7 12 15


Input (i) 105 115 125 135
Output (o) 211 231 251 271

24. Compile tables for the following (You may use your pocket calculator):

a) Flower Pot Nursery sells flower bulbs at 3 for a rand. Indicate in your table how many bulbs would be sold for R1,00 ; R5,00 ; R30,00 ; R50,00 and R100,00.

b) The Good Rest Holiday Resort's tariff is R280,00 per person per night. Indicate in your table the cost for one person for the following number of nights: 1 ; 7 ; 10 ; 15 ; 31.

c) At Sally's Supermarket you can buy grapes at R6,80 a kilogram. Indicate in your table how much you would pay for: 1 kg ; 2 ½ kg ; 4 kg ; 5¼ kg ; 19 kg grapes.

25. Time for Self-Assessment

  • Make a cross on the scale of 1 to 5 for each of the following:
Struggling So-so Capable
1 2 3 4 5
I can determine output numbers from a flow diagram correctly __ __ __ __ __
I can determine input numbers from a flow diagram __ __ __ __ __
I understand the replacing of numbers with letters of the alphabet. __ __ __ __ __
I understand what "variables" are. __ __ __ __ __
I understand the replacing of letters of the alphabet with numbers. __ __ __ __ __
I can write algebraic equations for given number sentences. __ __ __ __ __
I can resolve algebraic equations. __ __ __ __ __
I can write number sentences by making use of inequalities. __ __ __ __ __
I am able to formulate rules for solving equations by looking at patterns and can write down equations for them. __ __ __ __ __
I can compile tables from given information. __ __ __ __ __

Module test

Let us see if we can apply all the previous knowledge.

1. Just write down the answer:

a) 43 = __________ b) 93 = __________ (2)

2. True or false?

a) 125 is a cubed number ________________

b) 125 is a square number ________________

c) v – w = w – v ________________

d) (g + h) x j = (g x j) + (h x j) ________________ (4)

3. If m = 16 ; n = 9 and p = 18, calculate:

a) (m x n) + p ___________________________________

b) p ¸ n x m2 ___________________________________ (2)

4. Write an algebraic equation for the following:

a) If I subtract 347 from a number, the answer is 1706.

______________________________________________ (1)

b) The product of a certain number and 598 is equal to the difference between 80 000 and 6 446

______________________________________________ (2)

5. Write number sentences by using inequalities:

a) One quarter of the red shoes is less than half of the green shoes.

______________________________________________ (1)

b) Everyday more than 100 000 people read the newspaper.

______________________________________________ (1)

6.1 Write an equation for the following table:

Input 5 10 15 20 25 30
Output 28 53 78 103 128 228 328

______________________________________________ (1)

6.2 Use the equation to complete the table. (3)

7. Compile a table for the following:

At the Happy Fruit Stall you can buy 1 kg of apples for R6,99. In your table, indicate the cost of 2 and a half kg ; 8 kg ; 13 kg (3)



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 2.2: : We know this when the learner describes, explains and justifies observed relationships or rules in own words;

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:

2.3.3: tables;

Assessment Standard 2.4: We know this when the learner constructs mathematical models that represent, describe and provide solutions to problem situations, showing responsibility toward the environment and the health of others (including problems within human rights, social, economic, cultural and environmental contexts).

Questions & Answers

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
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Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
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 ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
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
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
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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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