The World's Rice Bowl

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Purpose

The purpose of this unit is to engage students, in an integrated mathematics/social sciences context, in applying their understanding of place value and standard form to investigate a problem of global resources. Students also develop their skills and knowledge on the Multiplicative Thinking learning progression by carrying out an investigation using large numbers expressed in standard form, with appropriate rounding. 

Achievement Objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
NA5-6: Know and apply standard form, significant figures, rounding, and decimal place value.
Specific Learning Outcomes
  • Express large numbers in standard form.
  • Apply rates measurements in different scales to problem solving.
  • Find and use specified rates in a problem solving context.
  • Find and use a fraction or rate from values expressed in standard form. 
  • Display large numbers on a graph with a suitable scale in a given context.
  • Making estimations using large numbers in standard form.
Description of Mathematics

In this unit, students apply their knowledge and skills of place value and standard form to investigate a problem of global resources. This involves the following mathematical ideas, which you should your students' prior knowledge of, prior to introducing the unit:

  • Finding, using, and applying rates in different scales.
  • Finding and applying fractions from given values.
  • Expressing numbers in standard form.
  • Constructing graphs with large numbers.
Opportunities for Adaptation and Differentiation

This cross-curricular, context-based unit aims to deliver mathematics learning, whilst encouraging differentiated, student-centred learning. 

The learning opportunities in this unit can be further differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:

  • roaming and supporting students in a variety of groupings to ensure they understand the task at hand, the skills needed to succeed, and can apply these skills in a suitable process
  • varying the amount of structured scaffolding and guided teaching you provide to students when investigating new tasks
  • providing opportunities for students to create their own problems related to a relevant context
  • providing extended opportunities for students to revise and apply learning from throughout the unit
  • modelling the application of ideas at every stage of the unit
  • strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
  • allowing access to calculators to decrease the cognitive load required in each stage of the unit
  • working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities.

With student interest engaged, mathematical challenges often seem more approachable than when presented in isolation. Therefore, you might find it appropriate to adapt the contexts presented in this unit. For example, you might use more recent statistics, or statistics related to countries that are of increased relevance to your students, to enhance the relevance of this unit to your students.

Structure

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.

Following the introductory session, each subsequent session in the unit is composed of four sections: Introducing Ideas, Building Ideas, Reinforcing Ideas, and Extending Ideas. 

Introducing Ideas: It is recommended that you allow approximately 10 minutes for students to work on these problems, either as a whole class, in groups, pairs, or as individuals. Following this, 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.

Building Ideas, Reinforcing Ideas, and Extending Ideas: Exploration of these stages can be differentiated on the basis of individual learning needs, as demonstrated in the previous stage of each session. 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.

Importantly, students should have multiple opportunities to, throughout and at the conclusion of each session, compare, check, and discuss their ideas with peers and the teacher, and to reflect upon their ideas and developed understandings. These reflections can be demonstrated using a variety of means (e.g. written, digital note, survey, sticky notes, diagrams, marked work, videoed demonstration) and can be used to inform your planning for subsequent sessions.

The relevance of this learning can also be enhanced with the inclusion of key vocabulary from your students' home languages. For example, te reo Māori kupu such as pāpātanga (rate), hautau/hautanga (fraction, proportion, part of a whole), tānga ngahuru (standard form), and kauwhata (graph) could be introduced in this unit and used throughout other mathematical learning.

Required Resource Materials
  • Calculators
  • Graphing software
Activity

Introductory Activity

The aim of this activity, which presents an opportunity to practise mathematical skills and knowledge in a social sciences context, is to motivate students towards the context and to inform teachers of students' understandings. The context of this problem, which uses figures from 2017, relates to the economic world. To engage students in this context, you might ask them to estimate the amount of kilojoules found in different foods consumed on a daily basis in different cultures, and by different groups of people. 

  1. Introduce the following context to students: The average person consumes 12 000 kJ of energy from food per day. The current global population is 7.6 x109

  2. Discuss, drawing attention to the following points:

  • 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.
  • 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?

As students work, observe their management of quantities in an investigation. Use these observations to gauge your students' positions on the Measurement Sense learning progression.

Session One

This session focuses on investigating a global resource issue using rates measurements in different scales, and on expressing large numbers in standard form. 

Introducing Ideas

  1. Introduce the following problem to students: In 2016, 490 million tonnes of rice was consumed. How much rice is this in g? 

  2. Discuss, drawing attention to the following points:

  • 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

  1. Introduce the following context to students: The population of the world is around 7.6 x 109.  500 million tonnes of rice are expected to be consumed in 2017.

  2. Provide time for students to work through the following questions:

  • 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

  1. Refer to the tonnes of rice are expected to be consumed in 2017. Support students to calculate the following: 
  • The current average daily consumption of rice in g per person per day.
  • An estimate of the amount of rice, in kg per year, that would be consumed when the population of the world is 8 billion.
  • The percentage increase in rice production that will be needed to feed the world when the population is at 8 billion. 

Extending Ideas

  1. Revise the following context to students: 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. Support students to calculate the following: 
  • The current average daily consumption of rice in g per person per day
  • An estimate of the amount of rice, in kg per year, that would be consumed in 2027. 

Session Two 

This session uses values in standard form to find and use specified rates in the context of rice consumption. 
 
Introducing Ideas
  1. Introduce the table below to students. This gives the average daily consumption of rice for several countries which have a rice based diet.

CountryPopulation in 2017 Average Rice Consumption (g/person/day) 
China1.41 x 109251
India1.34 x 109208
Indonesia 2.65 x 108414
Myanmar5.34 x 1097578
  1. Discuss, drawing attention to the following points:

  • Which of these four countries has the highest overall consumption of rice?
  • What is the annual consumption of rice of that country in kg per year?
  • What is 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

  1. Explain: At 578 g per person per day, Myanmar (population: 5.34 x 107) has the highest rice consumption per person in the world. 
  2. Support students to estimate the total mass of rice consumed in Myanmar each year.

Reinforcing ideas

  1. Explain: 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. 
  2. Support students to find the percentage of the rice consumed around the world that is consumed in China. Ensure your students give their answers in standard form, using appropriate units.

Extending ideas

  1. Explain: The population of the world is around 7.6 x 109. 500 million tonnes of rice were consumed over the past year. 
  2. Support students to use the data, given in the table 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. 
CountryPopulation in 2017 Average Rice Consumption (g/person/day) 
China1.41 x 109251
India1.34 x 109208
Indonesia 2.65 x 108414
Myanmar5.34 x 107578

Session Three

This session focuses on finding and using a fraction or rate from values expressed in standard form. 

Introducing Ideas

  1. Introduce the following context to students: The 4.79 x 106 people who live in New Zealand consume 44 000 tonnes of processed rice each year. 

  2. Discuss, drawing attention to the following points:

  • 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?
  • 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

  1. Explain: 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. 
  2. Support students to work through the following tasks:
  • 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

  1. Explain: 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. 
  2. Support students to work through the following tasks:
  • 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

  1. Explain: The 4.79 x 106 people who live in New Zealand consume 4.4 x 10kg of processed rice each year. The 2.47 x 10people who live in Australia consume 4.58 x 108 kg of processed rice each year. 
  2. Support students to work through the following tasks:
  • 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

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

Introducing Ideas

  1. Introduce the following context to students: 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. 

  2. Support students to show this information on a graph and estimate when the population reached 7 billion.

  3. Discuss, drawing attention to the following points:

  • 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

  1. Explain: One billion can be written in standard form as 1 x 109.
  2. Support students to work through the following tasks:
  • 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

  1. Support students to use the global population data they have graphed and do the following: 
  • Find the average rate of population growth per year twenty years ago, ten years ago and today. Give 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 answers in standard form. 

Extending Ideas

  1. Support students to use the global population data they have graphed and express numbers larger than 10 000 in standard form by doing the following:
  • 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 in the graph. 

Session Five

This session focuses on working with large numbers in standard form to estimate a global resource issue. 

Introducing Ideas

  1. Introduce the following context to students: 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.  

  2. Together, calculate how many grams of rice stores there are per person.

  3. Explain: The United Nations Food and Agriculture Organisation have suggested that we are heading for a global shortage in rice. Discuss, emphasising the following points:

  • 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

  1. Explain: 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

  1. Explain: 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

  1. Explain: 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? 
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Level Five