This problem solving activity has an algebra focus.
Paul is talking to Pesi on the phone.
He is trying to describe a pattern to Pesi but he can’t find the words.
If Paul’s pattern is: 3, 7, 11, 15, …how can he describe to Pesi how to get any member of the number pattern?
How can Paul tell Pesi how to get the 50th number in as simple a way as possible?
In this problem students must describe a sequence in words, and state a rule for any term in the sequence, using an expression for the nth term of a sequence. Note that the focus is on students using their own language to describe a rule. They are not expected to create a rule using variables (e.g. letters). This could be an extra focus for students ready for further extension. Students exploring the rule in further detail could be encouraged to use a table, or create a graph, to show the continuation of the pattern.
Other related Level 3 Algebra problems include: Toothpick Squares and Race To 100.
Paul is talking to Pesi on the phone. He is trying to describe a pattern to Pesi but he can’t find the words.
If Paul’s pattern is:
3, 7, 11, 15, …how can he describe to Pesi how to get any member of the number pattern?
How can Paul tell Pesi how to get the 50th number in as simple a way as possible?
Pesi has a pattern. It is 3, 6, 12, 24, …
How can Pesi describe to Paul how to get any member of the number pattern? How can Pesi tell Paul how to get the 50th number in as simple a way as possible?
Paul’s sequence is 3, 7, 11, 15, …
The first term is 3. From there, Paul keeps adding 4. Paul can say "Pesi, you start at 3 and keep adding 4. That way you’ll get all members of my pattern."
The 50th term can be found by ‘adding 4’ until Pesi gets to the 50th term.
The more efficient way is to tell Pesi, "You just take 3 and add 49 4s." To which Pesi replies "Great, so the 50th term is 3 + (49 x 4) = 199."
Using variables, this rule could be expressed as 3 + 4(T - 1) where T represents the term number in the pattern.
Pesi's sequence is 3, 6, 12, 24, …
He starts with 3 and doubles each time to get the next number in the sequence. He says, "Paul, take 3 and keep doubling."
Since doubling is done one less time than the number of the term in the sequence, he tells Paul, "Take 3 and double it, then double it again and keep doing this for 49 doublings. So the 50th term is 3 x 2 x 2 x … x 2, where there are 49 2s." A calculator may be needed to work that one out. The number 3 x 249 is very big! It’s roughly 3 with 15 zeros after it!
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/paul-s-patterns at 8:57pm on the 26th February 2024