The purpose of this activity is to engage students in using volume/capacity calculations to solve a problem.
To solve this problem, the students will need to calculate the capacity of a box from the dimensions given and to use this to solve a problem. The dimensions have been given in cm, so it is expected that the capacity will be found in cm³. The activity assumes the students have experience in the following areas:
The activity should be 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.
Josh has a box with dimensions 40 cm x 30 cm x 30 cm full of shells and pebbles he has collected.
He wants to put them in the back of a cupboard where there is a space with a base area of 25 cm x 35 cm.
If he is to make a new box to fit all the shells and pebbles in, to fit in this space, what is the minimum height this box should be?
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 calculates the capacity of a box and uses this value to solve a problem to find an unknown height.
Click on the image to enlarge it. Click again to close.
The student finds a method of solution that will allow him/her to find an unknown dimension of a container, within the context and specifications given.
Printed from https://nzmaths.co.nz/resource/josh-s-shells-and-pebbles at 10:53am on the 15th May 2024