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.
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:
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:
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.
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.
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.
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.
Discuss, drawing attention to the following points:
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.
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
Introduce the following problem to students: In 2016, 490 million tonnes of rice was consumed. How much rice is this in g?
Discuss, drawing attention to the following points:
Building Ideas
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.
Provide time for students to work through the following questions:
Reinforcing Ideas
Extending Ideas
Introduce the table below to students. This gives the average daily consumption of rice for several countries which have a rice based diet.
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 |
Discuss, drawing attention to the following points:
Building ideas
Reinforcing ideas
Extending ideas
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 |
This session focuses on finding and using a fraction or rate from values expressed in standard form.
Introducing Ideas
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.
Discuss, drawing attention to the following points:
Building Ideas
Reinforcing Ideas
Extending Ideas
This session focuses on displaying large numbers on a graph with a suitable scale in the context of global population.
Introducing Ideas
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.
Support students to show this information on a graph and estimate when the population reached 7 billion.
Discuss, drawing attention to the following points:
Building Ideas
Reinforcing Ideas
Extending Ideas
This session focuses on working with large numbers in standard form to estimate a global resource issue.
Introducing Ideas
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.
Together, calculate how many grams of rice stores there are per person.
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:
Building Ideas
Reinforcing Ideas
Extending Ideas
Dear parents and whānau,
Recently, we have been applying our understanding of place value and standard form to investigate a problem of global resources. Ask your child to share their learning with you.
Printed from https://nzmaths.co.nz/resource/world-s-rice-bowl at 9:25pm on the 26th April 2024