Josh's shells and pebbles
The purpose of this activity is to engage students in using volume/capacity calculations to solve a problem.
About this resource
This collection of learning activities is designed to provide engaging contexts in which to explore the achievement objectives of The 2007 New Zealand Curriculum. The activities themselves do not represent a complete coverage of learning at this level. Rather, they provide an opportunity to apply the mathematics learned in previous lessons. The activities are intended to reflect the range of approaches that make up a differentiated classroom.
The activity assumes the students have experience in the following areas:
- Metric units of length (include conversions).
- Metric units of area and volume.
- Calculating the area of a rectangle and the volume and/or capacity of a rectangular prism.
- Finding an unknown area or length from a volume or capacity
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.
Josh's shells and pebbles
Required materials
See Materials that come with this resource to download:
- Josh's shells and pebbles activity (.pdf)
Achievement objectives
GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
Activity
Josh has a box with dimensions of 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.
Make sense
Introduce the problem. Allow students time to read it and discuss it in pairs or small groups.
- What do you think the problem is about?
- What information has been given?
- What do you need to find out?
- Can you rephrase the problem in your own words? (How tall would a box with a 25cm x 35cm base need to be to have the same capacity as a 40cm x 3cm x 30cm box?)
Plan approach
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.
- How can you use the information you have to answer the question?
- Do we know the volume of the shells and pebbles or the capacity of the box they are in? How would we calculate this?
- What is the base area of the new box?
- What else do you know about the new box?
- Do we have enough information to calculate the smallest height the new box could have?
- What maths will you need to use to answer the question?
Take action
Allow students time to work through their strategy and find a solution to the problem.
- Have you shown your work in a step-by-step way?
- Do you need any tools to help you with your calculations? (Ākonga may decide to use written methods or a calculator to carry out the multiplication and division.)
- Does your solution make sense?
- Does your solution answer the question?
- How accurate does your answer need to be? (i.e., "To the nearest ...")
- Have you included units?
Convince yourself and others
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.
- How do we know if the answer is correct?
- What could you try differently next time?
- Would this help you solve a similar problem?
- What could I try differently next time?
Examples of work
The student calculates the capacity of a box and uses this value to solve a problem to find an unknown height.
A handwritten set of direction instructions accompanied by a text box depicting the conversation between student and teacher.
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