Use this Scratch program to list the first ten even numbers starting at 1.

Remix or create your own program for each recursive pattern rule:

a) list the even numbers starting at 12

b) list the odd numbers starting at 1

c) list numbers that start at 36 and add 5 each time

d) list five numbers that start at 1 and add the odd numbers starting at 3

e) list the first five numbers of Fibonacci's sequence that starts with 1,1 then adds the two previous terms

f) design your own number pattern and see if a peer can provide the recursive pattern rule.

Students may use an algebraic expression (explicit pattern rule) to list the numbers.

After students have created a program to display the Fibonacci's sequence that begins with 1, 1, have students use the program to study different patterns within the sequence.

Sample Investigation: What is a Fibonacci Triplet?

Three consecutive numbers in the Fibonacci sequence are called a Fibonacci Triplet.

a) Choose any three consecutive numbers in the Fibonacci sequence.

b) Square the middle number.

c) Multiply the first and last number in the triplet. What do you notice?

d) Choose another Fibonacci Triplet and repeat steps b and c. What do you notice?

Does this apply to other Fibonacci Sequences?

Use the program to list another Fibonacci Sequence by starting with a different number. What do you notice when you repeat the above procedure? Continue this process until you see a pattern.

Create linear patterns with blue and red cubes and have students graph the patterns with bingo dabbers (red represents the constant and the blue represents the variable). Connect the recursive pattern rule to the explicit pattern rule. Discuss steepness of the slope of the line.

Students create a program that calculates the term value for different geometric patterns or explicit pattern rules (algebraic expressions). Students practise evaluating an expression to make sure their program is working.