Using resources and classifying resources
This is a level 3 to 4 mathematics in science contexts activity from the Figure It Out series. It is focused on exploring how probability influences the outcomes in a game of chance. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
 Explore how probability infl uences the outcomes in a game of chance.
 Students will discover that:
 probabilities can sometimes be determined theoretically by considering all possible outcomes
 probabilities can be expressed as simple fractions.
Using resources and classifying resources
Achievement objectives
NA42: Understand addition and subtraction of fractions, decimals, and integers.
S33: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.
Required materials
 Figure It Out, Using Resources, Levels 3+–4+, "Using resources and classifying resources", pages 1–3
 classmates
 differentcoloured counters
 a pencil
 a spinner (see Classifying resources CM)
 a paper clip
See Materials that come with this resource to download:
 Using resources activity (.pdf)
 Classifying resources activity (.pdf)
 Classifying resources CM (.pdf)
Activity
Points of entry: Mathematics
The activities and game in "Using resources and classifying resources" challenge students to think about what part of the resources they use is renewable and what the implications are if current patterns of use continue (or accelerate). Students may not realise that every discussion of resources – especially resources that are nonrenewable – inevitably comes back to mathematical understandings, particularly inverses, rates, and ratios: if a nonrenewable resource is consumed at a faster rate, it will run out sooner; if some consume more than their share, others have to make do with less.
Question 2 in "Classifying resources" shifts the focus to the mathematics behind the game: integers and probability. Integers are used to describe the direction of each move (whether forwards or backwards); probability concerns the likelihood of particular outcomes.
The speed at which the students complete the game is largely determined by the probability of landing on a renewable or nonrenewable sector of the spinner. The students explore this in question 2a (see the answers). In terms of probability, the “expected value” for a move is forward 1.5 squares ( 10/16 x 3 + 6/16 x ^{–}1 = 15/8 – 3/8 = 12/8 = 1.5). Question 2b looks at the impact of forwards and backwards movement that results from landing on bonus or penalty squares. The expected value is 3/6 x 2 + 3/6 x ^{–}1 = 1/2 = 0.5.
Not all students will be ready for calculations such as those shown for expected value, but all should
understand that, on any given spin of the spinner, the probability of moving forwards is greater than the probability of moving backwards. They should also be able to see that, on balance, the bonus or penalty spaces are helpful because, although the number of bonus spaces is the same as the number of penalty spaces, the bonus spaces provide for double the movement of the penalty spaces.
Challenge the students to suggest alterations to the spinner and then describe how those alterations would affect the probabilities. For example:
 If the wind segment was replaced with uranium, would that make the game longer or shorter?
 What would make the game harder or easier?
(Including uranium instead of wind would make the game harder and longer because uranium would add another negative move.)
Points of entry: Science
Determine students’ prior understandings of the terms and support the class to explore a variety of sources to add to their understanding. The point of the game is not winning as such but providing the students with opportunities to realise that classifi cations of renewable and nonrenewable can vary.
To get the most out of the activity on page 1, students will need to work cooperatively with a classmate. This gives them an opportunity to develop the key competency participating and contributing. The
"Classifying resources" game and activity require students to interact, share ideas, and work effectively with others, so the key competency relating to others is a suitable focus for development.
As the students play the game, they could record their decisions about resources on a renewable/nonrenewable table.
After the game, discuss the concept that there is not always a clear right answer. Some resources that seem renewable can get used up if we use them faster than they can replace themselves, as was the case with the moa.
Activity (Using resources)
1.
a. Definitions of “resource” will vary, but may include:
 something that people use, especially in the manufacture of goods
 a raw material
 a person, thing, or action needed for living or to improve the quality of life
 anything that is both naturally occurring and of use to humans.
b. Discussion will vary but should arise from the definitions in a. For example, many companies employ a human resources manager, who looks after the needs of the people in the company (the resources), schools have art resources in their classrooms or in a separate art room, and oil is a resource.
2.
Possible points include:
 Renewable resources are resources that can be replaced (replenished), such as trees and plants.
 A renewable resource is a natural resource that can be replaced in a relatively short time, for example, wood, water, wind, and solar energy.
 A nonrenewable resource is a natural resource that is not replaceable after it has been removed from its source, for example, coal or mineral ores. (A natural resource is a material that is found naturally in the environment, for example, coal or timber, and is used for food or energy or to produce other materials.)
 Soil is often classified as a renewable resource (ehow: Why is soil a renewable resource?), but it can also be classified as nonrenewable (University of Illinois: Ensuring equitable access to nature).
Renewable 
Nonrenewable 

Living things that are not endangered 
Fossil fuels: coal, oil, natural gas 
Sustainable forests 
Metals 
Geothermal energy 
Minerals 
Landfill gas 
Nuclear fuel 
Hydroelectricity 

Solar energy 

Tidal energy 

Wind energy 

biofuels 

Soil? 
Soil? 
Game (Classifying Resources)
A game that involves identifying renewable and nonrenewable resources
Activity (Classifying Resources)
1.
a. Ethanol should be classified as a renewable resource because it can be obtained from biological sources, such as dairy products, sugar cane, potatoes, and corn.
b. Answers will vary. Electricity can be either renewable or nonrenewable depending on its source. Hydroelectric, solar, and wind energy are regarded as renewable energy resources. Geothermal energy is usually regarded as a renewable resource, although overuse will result in its depletion. Electricity in New Zealand is also produced from coal and natural gas, both of which are nonrenewable.
2.
a. i.–ii. There are 16 resources on the spinner. 6 of them (coal, natural gas, aluminium, petroleum, plastic, and gold) are nonrenewable, so the probability of moving forwards (3 spaces) by landing on one of the 10 renewable resources is 10:16 and the probability of moving backwards (1 space) is 6:16.
b. There are 3 bonus spaces and 3 penalty spaces, but the reward (forward 2) for landing on a bonus space is greater than the penalty (back 1) for landing on a penalty space, so the overall impact of these spaces is to move the game forward. Note that two of the bonus spaces are recyclable rather than renewable, but the principle of helping our environment still applies.
The quality of the images on this page may vary depending on the device you are using.