A BIT MORE DIFFICULT 

3rd year of secondary education 


1. FINDING THE RIGHT
FORMULA 

In
this window we can see the first five pictures in a sequence containing a
certain number of counters (represented by the blue dots) which are laid out
in a certain way. Change the value of the parameter
"place"
to
see each layout. 


1. Look
carefully at the five layouts and copy them into your exercise book. Write
down the number of counters used in each case. 2. Use
this information to try and work out the number of counters needed for the
arrangement of counters in the following positions in the series: 8,
12 and 15.
Draw each layout. 3. How
many dots are there in the layout of the nth
term in the series? 

2.
CALCULATE AND OBSERVE 

There
are five rows of numbers in this window. All the numbers in any one column are
related to each other. The numbers can be changed by altering the
corresponding parameter in the window. (n1 gives us the first row and so on). 


4. Change
the value of each parameter and copy the numbers that appear into a table in
your exercise book. 5. There is a very straight forward relationship between the first three numbers in each row. Do you know what it is? What's the connection between the first three numbers and the fourth and fifth terms? 6. Look
carefully at the values that are given in the last column. What can you say
about them? Compare them to the last two values given in each row. Show that
the pattern you have found is true for any three consecutive numbers. 

3. SURPRISE SURPRISE! 

In
the following window there are four identical little machines. A certain
number is entered into each one which then undergoes a series of operations,
as illustrated in the window, before giving us a final result when it comes
out of the machine. 
























Josep Mª Navarro Canut 


Spanish Ministry of Education. Year 2001 



Except where otherwise noted, this work is licensed under a Creative Common License