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Mathematics

Grade 4

Numbers, feactions, decimals and number patterns

Module 6

Numeric patterns

Activity 1:

To recognise and represent multiples in order to be able to describe, compare and represent them [LO 1.3]
To investigate numeric patterns [LO 2.1]
To describe numeric patterns in your own words [LO 2.2]
To find output numbers [LO 2.3]

1. When we count in 6’s we are saying the multiples of 6.

1.1 Work with a friend. One of you must count in 6’s from 0 to 102. The other one must use a calculator to check you and stop you if you make a mistake. If that happens the one with the calculator must just say, ”Stop!” and show the calculator. The counting goes on from there. Then swap over.

1.2 Now fill in the missing multiples of 6 in the table below:

1 2 3 4 5 6 7 8 9 10 11 12
× 6 6 12 18 24 30 60 66

1.3 Now count backwards in 6’s from 102 to 0. Let a friend check you. Then swap over. Do you notice anything? Yes, multiples of 6 are all even numbers.

1.4 What patterns do you notice? Yes, the last digits seem to be 6;..2; ..8; ..4; ..0. They are repeated and so form a pattern.

Now that you are aware of this, you can count in 6’s for ever (if you concentrate)!

1.5 Count in 6’s and complete the flow diagram:

1.6 How do we programme the calculator to count in 6’s?

Press clear and

1.7 Write down the multiples of 6 from 102 to 0:

1.8 How do we programme the calculator to count backwards in 6’s from 102?

Press clear and

Now you can really count in 6’s easily, so let’s move on to 7’s.

2. Multiples of 7

2.1 Now use your calculator (if necessary) to count in 7’s and complete the flow diagram:

Can you spot any patterns? Two are written below. Try to spot some more and discuss with a friend.

  • They are both odd and even numbers.
  • They seem to be: odd, even, odd, even.

2.2 Now fill in the missing multiples of 7:

1 2 3 4 5 6 7 8 9 10 11 12
× 7 7 14 21 70 77

There seems to be some sort of repetition after the first 9 multiples. Does it continue?

Are there any other patterns? Write down what you have noticed.

  • Count backwards in 7’s from 105 to 0. Use your calculator to do this if necessary.
  • Write the missing multiples of 6 in the table below and then the multiples of 7 in the next row. Do you notice anything?
1 2 3 4 5 6 7 8 9 10 11 12
× 6 6 12 18 24
× 7 7 14 21 28

2.5 Now compare the two rows (across) of answers. A very interesting pattern appears to be emerging.

Look: 1 × 7 = 1× 6 + 1

5 × 7 = 5 × 6 + ……

9 × 7 = 9 × 6 + ……

2 × 7 = 2 × 6 + …….

6 × 7 = 6 × 6 + ……

10 × 7 = 10 × 6 + …..

  1. × 7 = 3 × 6 + ……
  2. 7 × 7 = 7 × 6 + ……
  3. 11 × 7 = 11 × 6 +……

4 × 7 = 4 × 6 + ……

8 × 7 = 8 × 6 + ……

12 × 7 = 12 × 6 +……

3. Multiples of 8

3.1 The numbers jump in 8 wholes. Use the calculator to count in 8’s and write down the missing multiples of 8.

0, 8, 16, 24, 32,……., ……., …………, ………, ………….,…………,………., …………, ……., …….., …………, ……… .

3.2 Another way of saying: 8 + 8 + 8 + 8 is 4 × 8.

Now complete the flow diagram:

3.3 Spot a pattern. Write down the missing multiples of 8 in the table below and look at the last digit of each one.

1 2 3 4 5 6 7 8 9 10 11 12
× 8 8 16 80 88

Look carefully:

8 ; 1 6 ; 2 4 ; 3 2 ; 4 0 ; 48; 56; 64; 72; 80; 88; 96

Questions & Answers

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
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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
How can I make nanorobot?
Lily
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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