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Mathematics

Grade 9

Number patterns, graphs, equasions,

Statistics and probability

Module 12

Number patterns

ACTIVITY 1

To use a table to arrange information

[LO 2.1, 2.2]

1. Alice is making necklaces by using triangular motifs that she places on a wire necklet (as shown in Diagram 1 below). Each motif is made from three black beads, six white beads and six coloured beads. It is important that she has the right number of beads of each colour. She wants to make 50 necklaces with black, white and red beads, 40 with black, white and yellow beads, 40 with black, white and blue beads and 30 with black, white and green beads.

Question: Calculate how many beads of each colour she has to buy.

2. She also combines three of these motifs in a bigger necklace (as shown in Diagram 2 above). The two top motifs in each necklace have the same design as before, but the bottom motif is made of 15 coloured beads only. She makes only half as many of these necklaces in each colour as she makes of the smaller necklaces referred to in Question 1.

Question: How many beads of each colour will she need for these necklaces?

3. She finds that the bigger necklaces are very popular, so she decides to use bigger motifs, and to combine more motifs in one necklace. The ne x t two diagrams show her new plans.

Alice wants to use four colours in these motifs. Use the diagram above to make your own four-colour design.

Question: Repeat the calculation exercises above for these necklaces.

4. These triangular motifs can be made larger and larger, of course. Not all of them are suitable for necklaces though!

Exercise: Below you see equilateral triangular Motifs 1 to 4. Draw Motifs 6 and 7 in the same sequence.

The Motif 3 above has 1 black bead, 3 white beads and si x red beads. You will need to refer to it in problem 6 below.

5. Data gathering: The beads in the motifs have a diameter of 1 cm each. Thus, the surrounding triangle in Motif 1 in the sequence has a side length of 2 cm. Complete the table below by referring to the triangles above as well as the ones you have drawn.

Side length of triangle in centimetres 2 3 4 5 6 7 8
Number of beads per triangle 3 6 10
Perimeter of triangle 6 9

6. Investigation: Alice makes her necklaces by combining triangular motifs as in diagrams 2 and 4. She uses the 10-bead motifs (Motif 3). The smallest necklace has one motif (size 1) and the next necklace has three motifs (size 2) with a triangular gap in the middle. Visualise the next sizes (3, 4, etc) of the necklaces (or draw them) and complete the table below. Try to complete the last column as well.

Size of necklace 1 2 3 4 5 X
Number of triangular motifs 6 10
Number of triangular spaces
Number of beads on each side of triangular motif
Total number of beads in necklace
Number of black beads
Total perimeter of pendant with 1 cm-diameter beads 9

7. Investigation: Do the same for the next table, if Alice now uses the 15-bead motif that we saw in the very first diagram.

Size of necklace 1 2 3 4 5 x
Number of triangular motifs 1 3
Number of triangular spaces 0 1
Number of beads on each side of triangular motif 5 10
Total number of beads in necklace 15 45
Number of black beads 3 9
Total perimeter of pendant with 1 cm-diameter beads 12 27

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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