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6.2 Add all the numbers from 1 to 20 inclusive. Look for a pattern and a short way. Write down what you did and your answer on the dotted line below. Then check your answer the long way. You may use a calculator to do so.

7. Another interesting pattern can be seen in the answers if you add:

  • 1 to 10 inclusive = _____
  • 11 to 20 inclusive = _____
  • 21 to 30 inclusive = _____
  • 31 to 40 inclusive = _____
  • 41 to 50 inclusive, and so on to 100. Write down the answers, study them and try to explain why this pattern occurs.

8. More patterns with shapes. The following pattern may be made with toothpicks, one for each straight line.

  • Pattern: Each time we add one triangle, we need ______more toothpicks.
  • We could put our information into a table. Please complete it.
Number of triangles 1 2 3 4 5 6 17 25
Number of toothpicks
  • How are the last two answers calculated? There are at least two different ways (without a calculator) and it is important that you should discuss these with your friends.

Hint: Maybe you could look at the toothpicks needed for six triangles and use them to calculate how many toothpicks are needed for 17 triangles, or you could think that you know the general pattern and just apply it to find out how many toothpicks are needed for 17 triangles. Your discussion is important, so the answers are not being given to you.The same applies to the 25 triangles.

8.4 Write down how you calculated the answers for

  1. 17 triangles
  2. 25 triangles

9. Complete the table:

In 1 2 3 4 5 6 10 20 50
Out 8 15 22 29 36

TEST YOUR PROGRESS

1. Do the following show tessellation? Write “yes” or “no” for each one.

  • Using the trapezium and diamond ________
  • Using just the trapezium ________
  • Using circles _______

2. Write down one way in which the sides of a trapezium differ from the sides of a

parallelogram .

3. Why is the triangle used in the building of the framework of the roofs of houses?

4. On a floor there are 10 tiles in a row and there are 17 rows of tiles. How many tiles are there altogether?

5. Dad uses 135 tiles to tile a stoep. He places 9 tiles across the width of the stoep. How many tiles are there in the length of the stoep?

6. Make a diagram to show what a square tiled area would look like if 16 square tiles were used to cover it. Use your ruler to draw in the tiles.

7. Complete the table:

1 2 3 4 5 6 10 12 20
4 7 10 13 16

8. Complete this table:

1 2 3 4 7 8
1 4 9 16 100

9. Thirty squares are made with toothpicks as shown in the diagram (one toothpick for each straight line). How many toothpicks are needed?

  1. Find a pattern and write down the missing numbers: 5; 13; 21; 29; ___;___

Assessment

Learning outcomes(LOs)
LO 2
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment standards(ASs)
We know this when the learner:
2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns:
  • represented in physical or diagrammatic form;
2.1.2 not limited to sequences involving constant difference or ratio.
2.2 describes observed relationships or rules in own words.
LO 4
measurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.
We know this when the learner:
4.8 investigates and approximates (alone and /or as a member of a group or team):
4.8.2 area of polygons (using square grids and tiling) in order to develop an understanding of square units;
  • volume/capacity of three-dimensional objects (by packing or filling them) in order to develop an understanding of cubic units.

Memorandum

ACTIVITY 1area of polygons

1.1 to 1.3 Practical own work and recording of it.

2. 4 whole blocks and 5 and a bit blocks = about 9 blocks

3.1 6

3.2 12

  • about 8 square cm
  • 7 square cm
  • counted the length on the long side and the number of tiles on the short side.
  • 5 x 2 = 10 tiles or 10 square cm
  • Drawing
  • 4m x 3m = 12 square metres
  • Drawing
  • 6 rows
  • Drawing

8.1 Yes

8.2 Drawing

9. 23 x ? =736

32 tiles

10. 75 x 54 = 4 050 tiles!

ACTIVITY 2 Patterns

1.4

4 shapes

2. Multiples of 9 – the digits forming each multiple of 9 add up to 9, so 54 is a multiple of 9; 72 is a multiple of 9. This is useful for checking answers.

  • Missing output numbers: 35; 42; 49; 70; 91
  • Flow diagram: input numbers: 1; 2; 3; 4; 5; 6; 7; 8; 9; 10 Operator: x 7

Output numbers: 7; 14; 21; 28; 35; 42; 49; 56; 63; 70

  • multiplied by 7

4.1

1 2 3 4 7 8 9 10 20 50
7 12 17 22 37 42 47 52 102 252

4.2 Flow diagram:

Input numbers: 1; 2; 3; 4; 7; 8; 9; 10; 20; 50

Operators: x 5 + 2

Output numbers: 7; 12; 17; 22; 37; 42; 47; 52; 102; 252

4.3 multiplied by 5 and 2 was added to the answer.

5.1

1 2 3 4 5 6 9 11 12 20
3 5 7 9 11 13 19 23 25 41

5.2 multiplied by 2 and 1 was added to the answer

5.3

In 1 2 3 4 5 6 7 10 14
Out 3 7 11 15 19 23 27 39 55

5.3 multiplied by 4 and 1 was subtracted from the answer.

  • It can! x 4 – 1
  • Own

6.2 1 + 20; 2 + 19; 3 + 18; 4 + 17; 5 + 16; 6 + 15; 7 + 14; 8 + 13; 9 + 12; 10 + 11

10 x 21 = 210

7. 55; 155; 255; 355; 455 etc.

Own

8.1 2

8.2

Triangles 1 2 3 4 5 6 17 25
Tooth-picks 3 5 7 9 11 13 35 51
  • Discussion

8.4 (a) 17 x 2 + 1

(b) 25 x 2 + 1

9.

In 1 2 3 4 5 6 10 20 50
Out 8 15 22 29 36 43 71 141 351

Test your progress

1.1 Yes

1.2 Yes

1.3 No

2. Only 1 pair of opposite sides are parallel; they are not equal in length.

3. It is a rigid shape.

4. 170 tiles

5. 15 tiles

6. Diagram 4 by 4

7.

1 2 3 4 5 6 10 12 20
4 7 10 13 16 19 31 37 61

8.

1 2 3 4 7 8 10
1 4 9 16 49 64 100

10. 5; 13; 21; 29; 37; 45

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
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 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
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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