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Space and shape

Educator section


24.2 No, pentagons do not tesselate


(a) 50

(b) 105

(c) 993

(d) 995

(e) 12

(f) 12

(g) 12

(h) 7

(i) 100

(j) 100 000

(k) 5 r. 3

(l) 9 r. 5

(m) 8 r. 6

(n) 9 r. 5

(o) 7 r. 4

Leaner section


Activity: tesselations [lo 1.8]


24.1 Did you know?

When a surface is covered by tiles so that there are no gaps left between the tiles, and no tiles overlap, the pattern that is made is called a tessellation, e.g.

We say the form tessellates.

24.2 Do you think ALL polygons will tessellate? __________ Motivate your answer.






24.3 Use a combination of polygons, e.g. a triangle and a square and design a floor covering for a kitchen or bathroom. It must tessellate! Colour it in neatly.

25. Time for self-assessment

  • Colour in the face that shows your ability:
I was able to group different triangles according to their characteristics.
I can explain the following concepts:
  • acute-angled triangle
  • equilateral triangle
  • obtuse-angled triangle
  • isosceles triangle
  • right-angles triangle
  • scalene triangle
  • symmetry
  • tessellations
I can indicate the axes of symmetry of figures.
I can draw a pattern with shapes that tessellate.

26. Can you improve the mark you got in the previous mental test? Try to complete this one in 2 minutes.

a) 16 + 19 + 15 = ____________

b) 28 + 36 + 41 = ____________

c) 1 009 – 16 = ____________

d) 1 012 – 17 = ____________

e) ____________ x 8 = 96

f) 9 x ____________ = 108

g) 84 ÷ 7 = ____________

h) 63 ÷ ____________= 9

i) 10 5 ÷ 103 = ____________

j) 10³ x 102 = ____________

k) 43 ÷ 8 = ____________

l) 59 ÷ 6 = ____________

m) 78 ÷ 9 = ____________

n) 86 ÷ 9 = ____________

o) 53 ÷ 7 = ____________


  • See if you can get the following correct

27.1 Arrange 20 toothpicks to form seven squares (see sketch). Move three toothpicks so that only five squares of the same size are left.

27.2 Arrange your toothpicks as shown in the example below. Move only two so that you form a parallelogram and three rhombuses.

27.3 Trace the following pieces of a tangram onto a folio sheet and cut them out neatly. (You may use a tangram if you have one in the class.)

Use all the pieces and build a cat in as many different ways as possible!


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 1.8: We know this when the learner performs mental calculations involving squares of natural numbers to at least 10 2 and cubes of natural numbers to at least 5 3 .

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket 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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