The purpose of this activity is to engage students in using mathematical strategies to solve a problem involving a sequence.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
Sam the surfer knows that the seventh wave in each set is the biggest. It is also the middle wave in each set.
Sam is surfing with five other surfers. To be safe, they each take a wave in turn. Sam takes the very first wave of the first set.
They are in the water long enough to surf every wave of ten sets. How many 'seventh waves' does Sam get?
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student creates a 10 x 13 array to represent the ten sets of 13 waves. They mark the waves that Sam catches using an x then check how many x’s are in the 7th row.
Click on the image to enlarge it. Click again to close.
The student uses a table representation to match wave numbers to surfers in the first set. They adjust the sequence by one for the next nine sets and recognise when Sam will next get a 7th wave.
Printed from https://nzmaths.co.nz/resource/seventh-wave at 6:16pm on the 18th July 2024