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Mathematics

Space and shape

Educator section

Memorandum

1. General discussion about geometry.

2. (1) EARTH (geo)

(2) MEASUREMENT (metry)

4. (a) a point

(b) angle

(c) figures

6. (a) construction line

(b) drawing line

(c) a broken line

7.1 (a) horizontal

vertical

diagonal

(b) parallel

⁄ ⁄

(c) perpendicular

right

8 (a) 6

AB; AD; BC; CD; AC; BD

BD: 40 mm

(b) HJ; JH; IJ; IH

(c)

(d)

(e)

(f)

(g)

Leaner section

Content

Activity: geometry [lo 1.8, lo 3.4]

1. Let us begin with a class discussion. What, do you think, is GEOMETRY all about?

2. Did you know?

Geometry is derived from two Greek words? Decipher the code and find out what the two words are.

1.

a) 72 ÷ 8

b) 7 x 6

c) 9 x 4

d) 9 x 6

e) 144 ÷ 12

________________

(geo)

2.

a) 12 x 8

b) 36 ÷ 4

c) 29 + 13

d) 56 − 18

e) 11 x 4

f) 12 x 3

_________________

(metry)

3. Did you know?

More than 5 000 years ago, the Ancient Egyptians in the Nile Valley applies geometrical rules to build their pyramids. The Babylonians also used geometry to build their temples and to develop their irrigation systems. The famous Greek geometrician, Euclid, lived 300 B.C. According to him, the foundations of geometry are points, lines and planes.

4. BRAIN TEASER!

a) What is the shortest possible line?___________________________________

b) What do we get when we join two lines together so that they bisect each other? ______________________________________________________________

c) What do we get when we add more lines to b?_________________________

5. IMPORTANT FACTS to KNOW

POINT: A point only has a position and no size.

We indicate it with a small dot ( Ÿ ).

LINE: When we have two points, we can draw a line through them.

A line only has length and neither breadth nor height

A straight line has no beginning or end.

LINE SEGMENT: A line segment is part of a line. It has a starting point and an end point.

RAY: A ray has a beginning point. It continues indefinitely in the same direction and doesn’t have an end point. (Think of the rays of the sun.)

PLANE: A plane has length and breadth (two-dimensional), but not height. You can perceive it as a “flat” space, e.g. a rectangle.

6. BRAIN-TEASER!

a) What do we call this line? . . . . . . . . . . . . . . . . .

It is used when we are constructing a figure.

_____________________________________________________________________

b) What do we call this line? _____________________

It is usually dark and is used for the final lines of a drawing.

_____________________________________________________________________

c) This line is used for hidden or invisible lines. _ _ _ _ _ _ _

(it is not a dotted line)

_____________________________________________________________________

7.1 Do you still remember?

§ Can you fill in the missing answers?

a) Kinds of lines: Lines can be:

i)

ii)

:

iii)

b) Lines that are equidistant from each other and never meet are called

_________________________________________________________ lines.

We use the symbol _________________to show the lines “are parallel to each other.”

c) Two lines are ______________________________ to each other when they bisect each other, forming a 90° angle.

We call this angle a _______________________________________________ angle.

We use the symbol ___________________ to indicate “is perpendicular to”.

7.2 Design a wall hanging by making use of horizontal and vertical lines only. Colour it in neatly.

7.3 Can you explain to a friend how one draws a perpendicular line?

7.4 Can you explain how we draw parallel lines?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

8. LET US TEST YOUR KNOWLEDGE!

a)

How many line segments are in the sketch?__________________________________

Please name them: _____________________________________________________

_____________________________________________________________________

Measure the length of each line segment: ___________________________________

_____________________________________________________________________

b)

Name the four rays in the sketch.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

c) Draw line EF.

d) Draw line segment GH 32 mm long.

e) Draw ray MN.

f) Draw KL // OP.

g) Draw VW XY.

Assessment

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 .

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 3.4: We know this when the learner designs and uses nets to make models of geometric solids studied up to and including this grade.

Questions & Answers

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 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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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 ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket 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
I'm interested in nanotube
Uday
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
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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