The purpose of this unit is to engage the student in applying their knowledge and skills of place value and standard form to investigate a problem of global resources. This unit integrates the learning areas of mathematics and social sciences.

Students develop their skills and knowledge on the mathematics learning progressions multiplicative thinking to carry out an investigation using large numbers expressed in standard form, with appropriate rounding.

Students will apply their knowledge and skills of place value and standard form to investigate a problem of global resources.

### Structure

This cross-curricular, context based unit has been built within a framework that has been developed with input from teachers across the curriculum to deliver the mathematics learning area, while meeting the demands of differentiated student-centred learning. The unit has been designed around a six session focus on an aspect of mathematics that is relevant to the integrating curriculum area concerned. For successful delivery of mathematics across the curriculum, the context should be meaningful for the students. With student interest engaged, the mathematical challenges often seem more approachable than when presented in isolation.

The first session is an introductory activity that is aimed to spark the imagination of students, to introduce the need for a particular idea or technique in mathematics that would enable them to explore deeper into that context. It is expected that rich discussion may be had around the context and around the nature of the mathematics involved.

The following five sessions are each based around a model of student-centred differentiated learning.

- There is a starting problem to allow students to settle into the session and to focus on the mathematics within the chosen context. These starting problems might take students around ten minutes to attempt and/or to solve, in groups, pairs or individually.
- It is then expected that the teacher will gather the students together to review the problem and to discuss ideas, issues and mathematical techniques that they noticed during the process. It may be helpful to summarise key outcomes of the discussion at this point.
- The remaining group of activities are designed for differentiating on the basis of individual learning needs. Some students may have managed the focus activity easily and be ready to attempt the
*reinforcing ideas*or even the*extending ideas*activity straight away. These could be attempted individually or in groups or pairs, depending on students’ readiness for the activity concerned. The students remaining with the teacher could begin to work through the*building ideas*activity together, peeling off to complete this activity and/or to attempt the*reinforcing ideas*activity when they feel they have ‘got it’. - It is expected that once all the students have peeled off into independent or group work of the appropriate selection of
*building*,*reinforcing*and*extending*activities, the teacher is freed up to check back with the ‘early peelers’ and to circulate as needed.

### Introductory activity

The average person consumes 12 000 kJ of energy from food per day. The current global population is 7.6 x10^{9}.

- What is the average daily energy consumption in the world?
- Globally, the average diet consists of 45% grains, including rice. What is the total energy from grains consumed in the world daily.

In this activity, the teacher(s) will be able to locate their students on the measurement sense learning progression by observing their management of the quantities under investigation. This activity integrates mathematical skills and knowledge with the social sciences learning area, the economic world. The figures used in this unit are valid for the date of writing, October 2017.

Mathematical discussion that should follow this activity involve:

- Would you expect the 45% of grains to have a similar breakdown of rice, wheat and other grains around the world?
- Is the population of the world evenly distributed?
- Do the more heavily populated countries tend to consume more rice or more wheat?

### Session One

Focusing on investigating a global resource issue using rates measurements in different scales and expressing large numbers in standard form.

**Focus activity**

In 2016, 490 million tonnes of rice was consumed. How much rice is this in g?

Discussion arising from activity:

- What is the best format in which to display your answer?
- How many kg are in one tonne?
- How many g are in 1 kg?

**Building ideas**

The population of the world is around 7.6 x 109. 500 million tonnes of rice are expected to be consumed in 2017;

- What is the current average global daily consumption of rice in tonnes per day?
- What is the current average global daily consumption of rice in g per day?
- What is the current average daily consumption of rice in g per person per day?

**Reinforcing ideas**

The population of the world is around 7.6 x 10^{9}. 500 million tonnes of rice are expected to be consumed in 2017;

- What is the current average daily consumption of rice in g per person per day?
- Estimate the amount of rice, in kg per year, that would be consumed when the population of the world is 8 billion.
- Find the percentage increase in rice production that will be needed to feed the world when the population is at 8 billion.

**Extending ideas**

The population of the world is around 7.6 x 109, with a current rate of growth of 83 million people per year. 500 million tonnes of rice are expected to be consumed in 2017;

- What is the current average daily consumption of rice in g per person per day?
- Using the data given above, estimate the amount of rice, in kg per year, that would be consumed in 2027.

### Session Two

**Focus activity**

Country | Population in 2017 | Average Rice Consumption (g/person/day) |

China | 1.41 x 109 | 251 |

India | 1.34 x 109 | 208 |

Indonesia | 2.65 x 108 | 414 |

Myanmar | 5.34 x 1097 | 578 |

- Which of these four countries has the highest overall consumption of rice?
- Find the annual consumption of rice of that country in kg per year.

- Explain the meaning of the units of the average rice consumption.
- How will you decide which is the country with the highest overall consumption of rice?
- How will you convert a rate in g/person/day to kg/year?

**Building ideas**

At 578 g per person per day, Myanmar (population: 5.34 x 107) has the highest rice consumption per person in the world. Estimate the total mass of rice consumed in Myanmar each year.

**Reinforcing ideas**

The population of the world is around 7.6 x 109. 500 million tonnes of rice were consumed over the past year. China (population: 1.41 x 109) has an average daily consumption of rice of 251 g per person. Find the percentage of the rice consumed around the world that is consumed in China. Give your answer in standard form, using appropriate units.

**Extending ideas**

The population of the world is around 7.6 x 109. 500 million tonnes of rice were consumed over the past year. Use the data below to find:

- The percentage of the world’s population who live in one of the three countries, China, India and Indonesia.
- The percentage of the worlds annual rice consumption that is the rice consumed in China, India and Indonesia.

Country | Population in 2017 | Average Rice Consumption (g/person/day) |

China | 1.41 x 109 | 251 |

India | 1.34 x 109 | 208 |

Indonesia | 2.65 x 108 | 414 |

Myanmar | 5.34 x 107 | 578 |

### Session Three

Focusing finding and using a fraction or rate from values expressed in standard form.

**Focus activity**

The 4.79 x 106 people who live in New Zealand consume 44 000 tonnes of processed rice each year.

What fraction of the world’s population (7.6 x 109) is the population of New Zealand?

What fraction of the world’s annual rice consumption (5 x 108 tonne) is the consumed in New Zealand?

Discussion arising from activity, how Discussion arising from activity:

- Comment on the differences between these two fractions.
- Do you expect either of these fractions to remain relatively constant over the next ten years? Why/why not?

**Building ideas**

New Zealanders consume 4.4 x 107 kg of processed rice each year. Australian’s consume 4.58 x 108 kg of processed rice each year.

- Find the average amount of rice consumed daily in New Zealand. Give your answer in standard form with appropriate units.
- Find the average amount of rice consumed daily in Australia. Give your answer in standard form with appropriate units.
- Compare these two values, giving suggestions for the similarities and/or differences.

**Reinforcing ideas**

The 4.79 x 10^{6} people who live in New Zealand consume 4.4 x 10^{7} kg of processed rice each year. The 2.47 x 107 people who live in Australia consume 4.58 x 10^{8} kg of processed rice each year.

- Find the average amount of rice consumed per person per year in New Zealand. Give your answer with appropriate units.
- Find the average amount of rice consumed per person per year in Australia. Give your answer with appropriate units.
- Compare these two values, giving suggestions for the similarities and/or differences.

**Extending ideas**

The 4.79 x 106 people who live in New Zealand consume 4.4 x 107 kg of processed rice each year. The 2.47 x 107 people who live in Australia consume 4.58 x 108 kg of processed rice each year.

- Compare the daily rice consumption per person in New Zealand with that of Australia. Give your answer in an appropriate format with units. The global population of 7.6 x 109 consumes a total of 500 million tonnes of rice annually.
- Compare the daily rice consumption per person in New Zealand the world’s consumption rate. Give your answer in an appropriate format with units.
- Suggest reasons for the similarity and/or differences between these daily rice consumption rates.

### Session Four

Focusing on displaying large numbers on a graph with a suitable scale in the context of global population.

**Focus activity**

The population of the world reached 1 billion in 1804, 2 billion in 1927, 3 billion in 1960, 4 billion in 1974, 5 billion in 1987 and 6 billion in 1999. Today the population is over 7.6 billion.

- Show this information on a graph.
- Use your graph to estimate when the population reached 7 billion.

Discussion arising from activity:

- If we write 1 billion as a 1 followed by 0s, how many 0s will there be?
- What is a suitable scale to use on each of your axes?
- The axes of your graph should be linear (go up in even amounts).Can the population data be graphed on these axes?

**Building ideas**

One billion can be written in standard form as 1 x 109.

- What is the global population today in standard form?
- How much has the global population increased by since 1999? Give your answer in standard form.
- What is the current rate of population growth per year? Give your answer to the nearest 108.

**Reinforcing ideas**

Using the global population data you have graphed:

- Find the average rate of population growth per year twenty years ago, ten years ago and today. Give your answers to the nearest 108.
- Describe the trend in global population growth over the past twenty years.
- Predict the global population ten years from now. Give your answer in standard form.

**Extending ideas**

Using the global population data you have graphed, and expressing numbers larger than 10 000 in standard form:

- Find the rate of population growth per decade, for each of the past 10 decades.
- Graph the rate of population growth per decade for the past 100 years.
- Describe the trend shown by your graph.

### Session Five

Focusing on working with large numbers in standard form to estimate a global resource issue.

**Focus activity**

There are currently around 170 million tonnes of rice stores, rice that has been produced in previous years and not consumed. The population of the world is around 7.6 x 109. How many grams of rice stores are there per person?

Discussion arising from activity:

The United Nations Food and Agriculture Organisation have suggested that we are heading for a global shortage in rice.

- What factors affect global rice production?
- What factors affect global rice consumption?
- What will this mean in terms of the rice held in store?

**Building ideas**

The current global production of rice is around 490 million tonnes per year. If 500 million tonnes of rice were consumed over the past year:

- What is the current annual global production of rice in standard form?
- What is the current annual global consumption of rice in standard form?
- What is the global shortfall in rice production each year? Give your answer in standard form.

**Reinforcing ideas**

The population of the world is around 7.6 x 109. The current global production of rice is around 490 million tonnes per year. If 500 million tonnes of rice were consumed over the past year;

- What is the percentage shortfall in rice production?
- Estimate the amount of rice, in kg per year, that would be consumed when the population of the world is 8 billion.
- If the same amount of rice is produced when the global population is 8 billion, what would the percentage shortfall in rice be?

**Extending ideas**

The population of the world is around 7.6 x 109. The current global production of rice is around 490 million tonnes per year and there are 170 million tonnes of rice stores. 500 million tonnes of rice were consumed over the past year. If the world’s population, rice production and rice consumption were to remain the same, how long would the current rice stores last?