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Mathematics in the world around us

Educator section


Critical and developmental outcomes:

The learners must be able to:

1. identify and solve problems and make decisions using critical and creative thinking;

2. work effectively with others as members of a team, group, organisation and community;

3. organise and manage themselves and their activities responsibly and effectively;

4. collect, analyse, organise and critically evaluate information;

5. communicate effectively using visual, symbolic and/or language skills in various modes;

6. use science and technology effectively and critically, showing responsibility towards the environment and the health of others;

6. demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation;

7. reflect on and explore a variety of strategies to learn more effectively;

8. participate as responsible citizens in the life of local, national, and global communities;

9. be culturally and aesthetically sensitive across a range of social contexts;

10. explore education and career opportunities; and

develop entrepreneurial opportunities.

  • Integration of Themes:
  • Social justice: The story of the secret signs shows how history can be important. What are the advantages of knowing things about the past?

Learners can divide into groups, visit the library and do more research on the origin of our number system, the Roman numerals, etc.

Learners can do projects on Mathematics found in nature, in the classroom and in the home. They learn to work together in a team, listen to one another and to share ideas.

Discuss whether so called “bargains” are always bargains. What is your attitude towards “sales” in shops? Is it always necessary to give / receive birthday presents? Why do you give presents? When would not giving presents be acceptable?

  • With the inclusion of the story of the secret sign at this stage, learners are able to understand the significance of the “0” as “place holder” (indegrated with Literacy).
  • The patterns with addition and subtraction of 6, 7, 8 and 9 are emphasised.
  • Telling the time in minutes become easy as learners count the minutes in 5’s.
  • Codes are used to find the answer to a puzzle.
  • As preparation for the Christmas celebrations, the month of December is used for activities involving the calendar.
  • Module 8 concludes with a game where crackers with number sentences are matched to lights on the Christmas tree.

Leaner section


Activity: place value [lo 1.5, lo 1.9, lo 3.1]

  • Read the story of the secret sign.

(“History of numbers”, MacDonald’s First Library, “Number”)

Abelard was a monk who lived in the twelfth century A.D. He lived in England.

Abelard loved to solve number puzzles.

He used Roman figures such as these with which to count:


One day some Arab merchants told Abelard about a secret sign and nine numbers used by the Arabs for counting. They said any total could be written using nine numbers and the secret sign.

One night Abelard climbed over the wall of the monastery in England and set off to Cordova in Spain. It took him many months to get there and to learn the language. After many exciting and dangerous adventures, he returned to England bringing with him the Arabs’ secret. He used the Arabic numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 AND the “0” - the secret sign - as a placeholder. Making use of the secret sign “0” he could write any number.

The Arabs learnt much from the Hindus. So Abelard returned to England with the new numbers and the secret sign.

  • Our number system, which we use today, is really a combination of the work of the Arabs and the Hindus.
  • When we draw 20 like this,
  • Draw the picture numbers for:

68 90

Values and places

  • Look at:

The value of 23, when renamed, is 20 + 3

The place value of the 2 in 23 is 2 tens and the place value of the 3 in 23 is 3 units.

LO 1.5

Mathematics in shape

  • Work in groups of 4.
  • Here is the key to the sums.
LO 1.9 LO 3.1
  • Work with a partner.
  • Use this key to make up your own sums in shapes. Use “+”, “-“ and “x”.
  • Ask someone in the class to write in the answers. Mark the sums.








How many were correct? _____________________________________

Name: ______________________________________________


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 1.5: We know this when the learner recognises the place value of digits in whole numbers to at least 2-digit numbers;

Assessment Standard 1.9: We know this when the learner performs mental calculations;

Learning Outcome 3: The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

Assessment Standard 3.1: We know this when the learner recognises, identifies and names two-dimensional shapes and three-dimensional objects in the school environment and in pictures.


Questions & Answers

what is the VA Ha D R X int Y int of f(x) =x²+4x+4/x+2 f(x) =x³-1/x-1
Shadow Reply
can I get help with this?
Are they two separate problems or are the two functions a system?
Also, is the first x squared in "x+4x+4"
thank you
Please see ***imgur.com/a/lpTpDZk for solutions
f(x)=x square-root 2 +2x+1 how to solve this value
Marjun Reply
factor or use quadratic formula
what is algebra
Ige Reply
The product of two is 32. Find a function that represents the sum of their squares.
if theta =30degree so COS2 theta = 1- 10 square theta upon 1 + tan squared theta
Martin Reply
how to compute this 1. g(1-x) 2. f(x-2) 3. g (-x-/5) 4. f (x)- g (x)
Yanah Reply
what sup friend
not much For functions, there are two conditions for a function to be the inverse function:   1--- g(f(x)) = x for all x in the domain of f     2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the  element that you started with, namely, x.
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
acha se dhek ke bata sin theta ke value
sin theta ke ja gha sin square theta hoga
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
which part of trig?
differentiation doubhts
Prove that 4sin50-3tan 50=1
Sudip Reply
False statement so you cannot prove it
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
thanks bro
maybe when i start calculus in a few months i won't be that lost 😎
what's the derivative of 4x^6
Axmed Reply
comment écrire les symboles de math par un clavier normal
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
what is the k.e before it land
what is the function of carbon nanotubes?
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
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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 2. OpenStax CNX. Oct 15, 2009 Download for free at http://cnx.org/content/col11131/1.1
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