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## 24 Hours in the life of a smart meter

A three part lesson plan with a student worksheet

1: Introduction to smart meters
2: A series of four challenges covering numbers, ratio, percentages, statistics, information handling and graphs
3: Extension activity • Age groups: 11-14s
• Subjects: Mathematics, Science
• Topics: Energy

## ENGLAND

### KS3 Mathematics

#### Working mathematically

Through the mathematics content, pupils should be taught to:

#### Develop fluency

·       consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots

·       select and use appropriate calculation strategies to solve increasingly complex problems

·       move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]

·       use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

#### Reason mathematically

·       extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

·       extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically

·       interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

#### Solve problems

·       develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

·       develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics

·       begin to model situations mathematically and express the results using a range of formal mathematical representations

·       select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

### Number

Pupils should be taught to:

·       understand and use place value for decimals, measures and integers of any size

·       use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

·       define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

·       interpret fractions and percentages as operators

·       use standard units of mass, length, time, money and other measures, including with decimal quantities

·       round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

·       use approximation through rounding to estimate answers

·       use a calculator and other technologies to calculate results accurately and then interpret them appropriately

#### Ratio, proportion and rates of change

Pupils should be taught to:

·       change freely between related standard units [for example time, length, area, volume/capacity, mass]

·       express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

·       use ratio notation, including reduction to simplest form

·       divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

·       understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

·       relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

·       solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

·       solve problems involving direct and inverse proportion, including graphical and algebraic representations

### Statistics

Pupils should be taught to:

·       describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

·       construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

·       describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

### KS3 Science

#### Working scientifically

Through the content across all three disciplines, pupils should be taught to:

#### Analysis and evaluation

·       apply mathematical concepts and calculate results

·       present observations and data using appropriate methods, including tables and graphs

·       interpret observations and data, including identifying patterns and using observations, measurements and data to draw conclusions

·       present reasoned explanations, including explaining data in relation to predictions and hypotheses

·       evaluate data, showing awareness of potential sources of random and systematic error

·       identify further questions arising from their results.

### Subject content – Physics

#### Energy

Calculation of fuel uses and costs in the domestic context

·       domestic fuel bills, fuel use and costs

·       fuels and energy resources.

## SCOTLAND

### Mathematics

#### Number, money and measure

Estimation and rounding

I can round a number using an appropriate degree of accuracy, having taken into account the context of the problem.

MNU 3-01a

#### Number and number processes

I can use a variety of methods to solve number problems in familiar contexts, clearly communicating my processes and solutions.

MNU 3-03a

I can continue to recall number facts quickly and use them accurately when making calculations.

MNU 3-03b

#### Multiples, factors and primes

I have investigated strategies for identifying common multiples and common factors, explaining my ideas to others, and can apply my understanding to solve related problems.

MTH 3-05a

#### Fractions, decimal fractions and percentages

I can solve problems by carrying out calculations with a wide range of fractions, decimal fractions and percentages, using my answers to make comparisons and informed choices for real-life situations.

MNU 3-07a

By applying my knowledge of equivalent fractions and common multiples, I can add and subtract commonly used fractions.

MTH 3-07b

Having used practical, pictorial and written methods to develop my understanding, I can convert between whole or mixed numbers and fractions.

MTH 3-07c

I can show how quantities that are related can be increased or decreased proportionally and apply this to solve problems in everyday contexts.

MNU 3-08a

#### Data and analysis

I can work collaboratively, making appropriate use of technology, to source information presented in a range of ways, interpret what it conveys and discuss whether I believe the information to be robust, vague or misleading.

MNU 3-20a

When analysing information or collecting data of my own, I can use my understanding of how bias may arise and how sample size can affect precision, to ensure that the data allows for fair conclusions to be drawn.

MTH 3-20b

I can display data in a clear way using a suitable scale, by choosing appropriately from an extended range of tables, charts, diagrams and graphs, making effective use of technology.

MTH 3-21a

### Technologies

#### Technological developments in society and business

Awareness of technological developments (Past, Present and Future), including how they work

I understand how scientific and technological developments have contributed to changes in everyday products.

TCH 3-05a

## WALES

### KS3 Mathematics

#### Developing numerical reasoning

Identify processes and connections

Learners are able to:

·       transfer mathematical skills across the curriculum in a variety of contexts and everyday situations

·       select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks

·       prioritise and organise the relevant steps needed to complete the task or reach a solution

·       choose an appropriate mental or written strategy and know when it is appropriate to use a calculator

·       select appropriate mathematics and techniques to use

·       develop and evaluate mathematical strategies and ideas creatively

·       consider connections between mathematical skills and contextualise these within extended tasks

#### Represent and communicate

Learners are able to:

·       explain results and procedures precisely using appropriate mathematical language

·       select and construct appropriate charts, diagrams and graphs with suitable scales

·       interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading

·       evaluate different forms of recording and presenting information, taking account of the context and audience

#### Review

Learners are able to:

·        select and apply appropriate checking strategies

·        interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible

·        interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data

·        draw conclusions from data and recognise that some conclusions may be misleading or uncertain

#### Year 7

Learners are able to:

read and write numbers of any size and use the four operations and the connections between them, e.g. apply division as the inverse of multiplication
recognise and apply key mental facts and strategies
use appropriate strategies for multiplication and division, including application of known facts

#### Year 8

Learners are able to:

recognise and apply key mental facts and strategies
use known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6

#### Year 9

Learners are able to:

·       use known facts to derive others, e.g. use 7 x 6 to derive 42 ÷ 0.0006

#### Year 7

Learners are able to:

·        use equivalence of fractions, decimals, percentages and ratio to compare proportions

·        calculate percentages of quantities using non-calculator methods where appropriate

·        express two or more quantities as a ratio using the correct notation

·        simplify ratio

#### Year 8

Learners are able to:

·        use equivalence of fractions, decimals, percentages and ratio to select the most appropriate for a calculation

·        simplify a calculation by using fractions in their simplest terms

·        calculate a percentage, fraction, decimal of any quantity with a calculator where appropriate

·        calculate the outcome of a given percentage increase or decrease

·        express one quantity as a percentage of another

·        simplify ratios including those given in different units

·        use ratio and proportion to calculate quantities, including cases where the ‘total’ is not given

#### Year 9

Learners are able to:

·        use equivalence of fractions, decimals, percentages and ratio to select the most appropriate for a calculation

·        calculate a percentage increase or decrease

·        express one quantity as a percentage of another, including those given in different units

·        use ratio and proportion to calculate quantities, including cases where the ‘total’ is not given

#### Year 7

Learners are able to:

·        use efficient written methods to add and subtract numbers with up to 2 decimal places

·        use the order of operations

#### Year 8

Learners are able to:

·        use efficient written methods to add and subtract numbers with up to 2 decimal places

·        use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.06

#### Year 9

Learners are able to:

·        use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places

·        multiply and divide whole numbers and decimals

#### Year 7

Learners are able to:

·        use rounding to estimate answers

·        present answers to a given number of decimal places

#### Year 8

Learners are able to:

·       use rounding to estimate answers to a given number of significant figures

·       present answers to a given number of significant figures

#### Using data skills

Collect and record data / Present and analyse data / Interpret results

#### Year 7

Learners are able to:

·        collect own data for a survey

·        construct frequency tables for sets of data, grouped where appropriate, in equal class intervals (groups given to learners)

·        construct a wide range of graphs and diagrams to represent the data and reflect the importance of scale

·        interpret diagrams and graphs (including pie charts)

·        use mean, median, mode and range to compare two distributions (discrete data)

#### Year 8

Learners are able to:

·        construct a wide range of graphs and diagrams to represent discrete and continuous data

·        construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate

·        construct graphs to represent data including scatter diagrams to investigate correlation

·        interpret diagrams and graphs to compare sets of data

·        find the mean, median, mode and range from ungrouped frequency tables

·        use mean, median, mode and range to compare two distributions (continuous data)

#### Year 9

Learners are able to:

·        construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, with the learner choosing an appropriate scale

·        select and justify statistics most appropriate to the problem considering extreme values (outliers)

·        examine results critically, select and justify choice of statistics recognising the limitations of any assumptions and their effect on the conclusions drawn

### KS3 Science

#### Communication

Pupils should be given opportunities to:

·       search systematically for, process and analyse information for a specific purpose, including ICT as appropriate

communicate logically by speech, writing, drawings, diagrams, charts, tables, bar charts, line graphs, videos and ICT packages using a wide range of scientific vocabulary, terms, symbols and conventions

#### Interdependence of organisms

Pupils use and develop their skills, knowledge and understanding by investigating how humans are independent yet rely on other organisms for survival, applying this to life in countries with different levels of economic development.

·       applications of science, medicine and technology that are used to improve health and the quality of life, including those in countries with different levels of economic development.

#### How things work

Pupils should use and develop their skills, knowledge and understanding by investigating the science involved in a range of contemporary devices/machines and evaluate different energy resources and possibilities.

·       technologies under development, which may lead to more efficient use of energy resources or using them in new ways

## NORTHERN IRELAND

### Mathematics with Financial Capability

#### Developing pupils’ knowledge, understanding and skills

Pupils should have opportunities, through the contexts below, to develop:

·       knowledge and understanding of

·    Number

·    Handling Data;

·       knowledge and understanding of personal finance issues;

·       and skills to enable competent and responsible financial decision making;

·       the application of mathematical skills to real life and work situations;

#### Developing pupils as Individuals

Young people should have opportunities to:

·       Work collaboratively in problem solving, taking account of others’ viewpoints to reach consensus.

·       Demonstrate an ability and willingness to develop logical arguments

#### Developing pupils as Contributors to Society

Young people should have opportunities to:

·       Analyse and interpret information patterns relating to local and global trends

·       Critically examine the use and misuse of mathematics to justify/support particular attitudes/opinions in different media, and the interpretation of data

#### Developing pupils as Contributors to the Economy and the Environment

Young people should have opportunities to:

·       Apply mathematical skills in everyday financial planning and decision making

·       Explore issues related to Education for Sustainable Development

### Science

#### Developing pupils’ Knowledge, Understanding and Skills

Pupils should have opportunities, through the contexts below, to develop:

·       research scientific information from a range of sources;