Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1? Class 6

Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1? Class 6

Question 1.

Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1? Class 6

Do you believe the conjecture of Collatz that all such sequences will eventually reach 1? Why or why not?

Solution:

Note: Do as directed. Yes. Because it is still an unsolved conjecture.

Question 2.

We shall do some simple estimates. It is a fun exercise, and you may find it amusing to know the various numbers around us. Remember, we are not interested in the exact numbers for the following questions. Share your methods of estimation with the class. Class 6

1. Steps you would take to walk :

(a) From the place you are sitting to the classroom door

(b) Across the school ground from start to end

(c) From your classroom door to the school gate

(d) From your school to your home

Solution:

Note: Do as directed. Some examples are given.

(a) 10 steps

(c) 200 steps

(b) 1500 steps

(d) 6000 steps