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Mathematics

Estimations, equations and variables

Educator section

Memorandum

21. (a)

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

22.

(b)

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

money

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

(b)

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

(c)

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

Leaner section

Content

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?

a)

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

b)

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)

20

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 2.2: : 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

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
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 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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