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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

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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