Experience Mathematics #6 - A special triangle

Once again Sarthak Parikh (Class VIII, Sardar Patel) gave interesting stories, and made nice pictures in response to our last column. This week’s column is about Pascal’s Triangle and the patterns that can be found in it. Pascal’s triangle has an infinite number of rows, and it begins as follows. 

1  1
1   2   1
1   3   3   1
1   4   6   4   1
1   5   10   10   5   1

Each row has one more entry than the previous row. The row begins and ends with 1. The other entries in the middle are the sum of the two entries above. For example, in the fourth row: $4=1+3; 6= 3+3; 4=3+1$.

Pascal’s triangle is a storehouse of patterns. Make 16 rows of Pascal’s triangle, and find as many patterns as you can. For example, can you find $1, 2, 3, 4,\dots$ in the triangle? What is the sum of entries in each row? If we replace all the even numbers in the triangle by $0$, and all the odd entries by $1$, we get the Fractal known as Sierpinski Triangle. This computer-generated picture shows this pattern. 

Experience Mathematics # 5 -- Mathematical stories

This week’s column is about word problems. Many children find it difficult to solve word problems in mathematics. But can you do the reverse? Can you make word problems based on mathematical statements? Also, make a picture that represents the given statement.

In each of the following questions, you have to write the given mathematical statement in words. Then you have to make a story around it, as in the example below.

Example: $10+2=12$. Ten when added to two is equal to twelve.

Story: I was going along the road when I saw two owls. I was surprised, since owls usually sleep during the day. Then I thought that they must be owls from the Harry Potter books, come to deliver letters. Suddenly I saw 10 more owls. They were carrying a big parcel. In all, it was a strange day, where I saw 12 owls in all.

We leave the picture for you.

Q1.  $8-3=5$.

Q2. $2-6=-4.$

Q3. $6 \times 3=18 $

Q4. $16=4^2$

Q5. $x+20= 37$, where $x$ is some number.