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Why and how to teach HCF Highest Common Factor

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How & why to teach HCF MadhurieSingh.com

When do you need to use HCF?

  • When you have to divide something into smaller and equal portions or units
  • When you are planning a party and want to decide how many people should be invited
  • When there are people or things you have arrange in rows  or even in groups

Example 1:

I want to donate pencils and erasers to kids. My sons gave me 72 pencils and 24 erasers that they want me to donate. Since I am a fair person, I need to make packets in such a way the each packet has same number of pencils and erasers. So how many packets will be made with equal number of pencils and erasers? How many pencils and eraser each child will get?

Find the HCF of pencils and erasers. HCF  of 72 and 24 = 24.

That means, I can make 24 packets and give them to 24 kids.

Each packet will contain 72/24 = 3 pencils and 24/24 = 1 eraser.

So here we were grouping pencils and erasers into packets so that each packet has equal number of pencils and eraser.

Example 2: 

As an exam coordinator, I need to arrange 72 boys and 90 girls in a classrooms. I have been told to make all girls rows and all boys rows. Also the number of rows must be equal for boys and girls. What is the highest number of students on one row?

HCF of 72 and 90 = 18

Hence, 18 students can be arranged in one row so that it has only girls or only boys per row.

I can also find out how many rows of girls and boys will be formed.

Girls rows = 90/18 = 5 rows

Boys rows = 72/18 = 4 rows

[tweetthis twitter_handles=”#teaching-in-fun-ways”]Use HCF to arrange people into groups or things into rows[/tweetthis]

 

[tweetthis twitter_handles=”#teaching-in-fun-ways”]If you wish to teach HCF in real life, make your kids plan food for your guests. [/tweetthis]

This was a very simple example. But, it’s good to start with.

If you want more such simple examples of other math principles, you can ask me in the comment section. I will try to post, whenever, I am explaining them to my sons.

If you liked this post, share it on your FaceBook so that other parents too can learn to teach in the fun way.

How & Why to teach LCM Least Common Multiple

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lcm

 

 

 

 

 

 

 

LCM is  an amazing calculation if you know where to use them.

Least Common Multiples aka LCM are used to find the smallest common multiples of any two or more numbers.

Why do we need to calculate LCM?

  • When there is an event that is repeated over and over
  • When we have to find the common time something will happen again for repeated actions

Real life use of LCM should be known to the kids, only then they will understand and appreciate learning LCMs.

Example1: In diwali days, you will decorate your balcony and doors by several color lightings. Blue, Green, Red, White led glowing and twinkling all night. I can watch them for hours.

Each color glows and fades, blue, then green, followed by red and white, and once again they all start to glow in the same sequence. But after a few seconds they will all glow together and then go back to their sequence of glowing one by one.

Have you noticed? Try it.

So after how many seconds do all the color led s glow simultaneously?

Lets say blue glows every 1 sec, red every 2 sec, green every 3 sec and white every 4 secs. When will all four color leds glow together?

This is where LCM is used. After multiplying the least common factors of these 4 numbers.

1 X 2 X 3 X (2 X 2)

1 X 2 X 3 X (2 )

= 12

Therefore at 12th second all these 4 color LED bulbs will glow together.

Try with planets moving in different orbits or train running on intersecting tracks. They will collide at the LCM of their speeds at one point. Planets we can’t really do anything but trains are pretty well managed by our very efficient software programs that use similar computations.

Example 2: 

I want to organize a small informal party for my son’s friends. I know they all love to eat home made burgers. 10 boys in total are going to eat. So I need to make at least 10 burgers.

When I goto buy the burgers and patties I see that buns come in packs of 2 per packet, patties come in a pack of 4. So how many packets of burgers and patties, I must buy to feed the 10 boys so that extra patties or extra buns are not left around? Also each boy will eat 2 burgers.

LCM of 2 bun, 4 patties, 10 boys = 20

So I will have to buy 20/2 bun = 10 bun packs,

20/ 4 patties = 5 pattie packs

so that 20/10 boys =  2 burgers per boy.

[tweetthis twitter_handles=”#teaching-in-fun-ways”]Its quite useful to organise parties with a variety of food items on menu by using LCM.[/tweetthis]

Who makes these software, formulae and applications? The engineers, right?

[tweetthis twitter_handles=”#teaching-in-fun-ways]If the kids want to learn, teach them where these Math principles work in real life.[/tweetthis]

If you want more such simple examples of other math principles, you can ask me in the comment section. I will try to post, whenever, I am explaining them to my sons.

If you liked this post, share it on your FaceBook so that other parents too can learn to teach in the fun way.