Most of the students learn about Distributive Property in Grade 4 or Grade 5 and this is how they usually get introduced to this topic.
a * (b + c) = a * b + a * c
I feel that we can introduce this beautiful & useful mathematical property in a more interesting manner.
I want my students to be amazed by the beauty of Math. I want them to be curious about this subject. My job is not just to ‘teach’, my job is to create the desire for learning .
We teach our children tricks to calculate 42 x 15 mentally. If they can “see” 42 x 15, they won’t need to remember any trick. They can develop their own tricks 😉
Me – You already know that addition is like walking on a line (1 – dimensional activity) How does multiplication look like? Say 2 x 5 ?
Student – Umm….?
Me – Multiplication ( 2 x 5) is like walking on a 2 – dimensional plane.
If I give you 2 building blocks every day, how many total blocks would you get in 5 days?
Student – Easy! 2 x 5 = 10 blocks
Me – Won’t it look like this ?
Does it look a 2- dimensional activity now?
Student – Yeah, multiplication looks like area of a rectangle ( 2 x 5 ) now.
Me – Great. That’s exactly the point I wanted to make here. I wanted you to see that multiplication (a x b) is nothing but the area of a rectangle with sides a units and b units.
Let’s think one step ahead. How will 3 x 4 x 5 look like ? Can you visualise a 3-dimensional cuboid?
It’s better to have a few interesting questions hanging around in our mind 😉
Let’s get back to 42 x 15.
Me – Now that you know how multiplication looks like, let’s have a look at distribution.
How will ‘distributive property’ look like if we apply it in addition?
Student – Distributive property in addition?
Me – Do you remember the story of Target 10 in Addition ? How will you calculate 8 + 7 ?
Student – Yes! I can do 8 + 2 + 5.
Me – Great! That’s exactly how distributive property should be working in addition. So the idea behind distribution is to break the problem into smaller & simpler ones. Now, let’s implement it to simplify multiplication.
Area of big rectangle = Sum of Areas of small rectangles
42 x 15 = 40 x 15 + 2 x 15
Area of big rectangle = Sum of Areas of small rectangles.
42 x 15 = 20 x 15 + 20 x 15 + 2 x 15
Yes, it was that simple :). Enjoy the simplicity !
A simple example from real life
We use distributive property while counting money.
If I have to count 13 notes of $20, what is the simplest way to do so?
I believe that it will be simplest to break this counting into 10 &3.
10 notes of $20 = $200
3 notes of $20 = $60
13 notes of $20 = $200 + $60 = $260
And , this is nothing but distributive property.
Distributive property is about breaking down a big problem into smaller & simpler problems.
Breaking down a big problem into smaller ones helps in Maths and in life as well.
Making Maths Simple & Visual @ Maths2Art with Priya Asthana !