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Part of the MEI Maths and Climate Change resources

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Climate Change - Extreme Cold Temperatures

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Teach the future proposed new curriculum

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Teach the future proposed new curriculum

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Our current education isn't good enough. Students aren't being prepared to face the effects of climate change, or taught to understand the solutions. But we can change this.

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KS3/4 Study maths for a career in Green Engineering

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KS3/4 Study maths for a career in Green Engineering

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An interview with a green engineer about how maths helps them in their career

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An interview with a digital tech engineer about how maths helps them in their career

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KS3-5 MEI Maths and Climate Change resources produced in collaboration with the Royal Meteorological Society

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KS3-5 MEI Maths and Climate Change resources produced in collaboration with the Royal Meteorological Society

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Registered charity Number 1058911 Copyright © 2023 MEI

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Compare the historical share of global carbon emissions

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Compare the historical share of global carbon emissions

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Simply display the graph and ask 'what do you notice?' 'what do you wonder?' 'what is the story that this graph is telling?'

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Compare the historical share of global carbon emissions - both total emissions and emissions per person - for the world's 23 richest countries to the share from all of the world's other countries.

These graphs show the historical carbon emissions for the world's 23 richest countries and for all other countries. The data visualized in these graphs is the basis for poorer nations asking wealthier ones for a "loss and damage" fund to compensate them for the damage they did not cause and they cannot prevent.

On Wednesday, Dec. 1, we will moderate your responses live online. By Friday morning, Dec. 3, we will provide the "Reveal" - the graphs' free online link, additional background and questions, shout outs for student headlines and Stat Nuggets.

After looking closely at the graphs above (or at this full-size image), answer these four questions:

What do you notice?

What do you wonder?

The questions are intended to build on one another, so try to answer them in order.

2. Next, join the conversation online by clicking on the comment button and posting in the box. (Teachers of students younger than 13 are welcome to post their students' responses.)

3. Below the response box, there is an option to click on "Email me when my comment is published." This sends the link to your response which you can share with your teacher.

4. After you have posted, read what others have said, then respond to someone else by posting a comment. Use the "Reply" button to address that student directly.

On Wednesday, Dec. 1, teachers from our collaborator, the American Statistical Association, will facilitate this discussion from 9 a.m. to 2 p.m. Eastern time.

5. By Friday morning, Dec. 3, we will reveal more information about the graph, including a free link to the article that includes this graph, at the bottom of this post. We encourage you to post additional comments based on the article, possibly using statistical terms defined in the Stat Nuggets.

Updated: Dec. 2, 2021

Carbon dioxide emissions are one of the main contributors to rising temperatures and other climate change. But, which countries are emitting the most carbon? These graphs, which were published on November 12, 2021 in The New York Times article "Figuring Out Who Bears the Most Responsibility for Climate Change," clearly show the emissions of the 23 richest countries, grouped by geographic and political regions, that account for 50 percent of the emissions and the more than 150 countries that are responsible for the other 50 percent.

These graphs are relevant to the following questions that were discussed during the COP 26 United Nations Climate Change Conference held in Glasgow this November: "How should the world's wealthiest nations, which are disproportionately responsible for global warming to date, compensate poorer nations for the damage caused by rising temperatures?" and "How should the need for carbon-generating activities of developing countries be treated when all countries are being pressured into reducing their carbon emissions? How would you answer these questions?

Here are some of the student headlines that capture the stories in these charts: "The Fault of Rich CO2untries" by Block 6 of Middleton High School in Wis., "The Richer the People, the Poorer the Planet" by Conner of Tenn., "Are You a CO2 Bully?" by Mia from Wash., "CO2 Emissions: Rich and Poor" by Khalid of International School Group Dammam inSaudi Arabia, "CO2? More like COYOU" by Sophia from Andover, Mass., "The Wealthy Are Creating the Unhealthy" by Adriana, Gwen and Jeenal in Erie, Pa., and "CO2 is 2 Bad 4 U" and "Rich Nations Are Ruining It for All of Us" both by Statistics at Forest Ridge School of the Sacred Heart in Bellevue, Wash.

You may want to think about these additional questions:

Examine the two other graphs in the article.

1. Notice and wonder from the time series graph, which shows the carbon emissions for the past 170 years by country or group of countries. What are the most noteworthy changes in carbon emissions?

2. Notice and wonder from the bar charts, which show the world's top emitters in 2020 by total emissions and by per capita emissions. What relationship do you see in the amount that a country emits and its population size, economic growth and wealth?

Rather than dividing the world's countries into the "richest" and all others, let's find the largest carbon emitters and all others. To accomplish this, make a list of all countries in descending order of percentage of carbon emissions. Divide this list into two groups - one list with the fewest countries that total about 50 percent of historical emissions and the other list with all of the other countries, including one for "All other countries." How many of the biggest emitters sum to 50 percent of all emissions? What characteristics do these countries have?

Using graph paper, you can turn these two lists into two treemap graphs (see Stat Nugget below) similar to those in the article. Make two rectangles with 50 squares each, representing 50 percent of historical emissions. Round the countries' emissions to the nearest whole number percentage. (There are 29 countries with rounded percentages of 1 percent or greater.) Draw polygons in the first rectangle for countries starting with the largest emitter and proceeding in descending order. ("Since the top countries account for 52 percent, add 2 squares to the first rectangle and erase 2 squares from your second rectangle.) After the first rectangle is full, continue in the second rectangle. After all 29 countries are placed in the rectangles, label the remaining polygon "More than 140 other countries."

What do you notice and wonder from your graphs?

Keep noticing and wondering. We continue to welcome your online responses.

Next week's graph on gerrymandering will be released by Friday, Dec. 3 with live-moderation on Wednesday, Dec. 8. You can receive the 2021-2022 "What's Going On In This Graph?" schedule by subscribing here to the Learning Network Friday newsletter. In the meantime, keep noticing and wondering.

________
Below, we define mathematical and statistical terms and how they relate to this graph. To see the archives of all Stat Nuggets with links to their graphs, go to this index.

TREEMAP
A treemap divides a rectangle into groups to illustrate the ranking of groups and their subgroups for a quantitative variable. The rectangle is split up into smaller rectangles representing the different groups. Their areas are proportional to the groups' percentage of the total data. These rectangles can be further divided into subgroups whose rectangle sizes are also proportional to the percentage of the total data.

In the World Carbon treemaps, the groups are continents and political regions. The quantitative variable is the percentage of historical carbon emissions since 1850. Each group is then divided into subgroups of countries. Only the countries with the largest percentage of emissions are identified with the largest of these showing their percentage. It is easy to see that the largest carbon emitters are the United States with 24.6 percent and China with 13.9 percent of total emissions. There are many Asian, African and South American countries which are low emitters of carbon and, therefore, do not have their country names or percentages given.
SEGMENTED BAR GRAPH
A segmented bar graph is a graph that summarizes the values of categorical data or that shows the percentage of a total that can be attributed to subgroups. The categories or subgroups are shown as segments of the bar that are proportional to the percentage of the total. When segmented bar graphs are used to compare groups, the bars of the same length are lined up adjacent to each other with the categories or subgroups in the same order in each bar.

In the Global Carbon segmented bar graphs, the bars represent 100 percent of the total population for all of the countries and the total historical carbon emissions of all of the countries. There are two subcategories - the 23 rich countries and all other countries. By comparing the bars, it is easy to see that the per capita carbon emission of the rich countries far exceeds that of all other countries and that 12 percent of the world's population in rich countries produces 50 percent of the emissions.

________
The graph for "What's Going On in This Graph?" is selected in partnership with Sharon Hessney. Ms. Hessney wrote the "reveal" and Stat Nuggets with Roxy Peck, professor emerita, California Polytechnic State University San Luis Obispo, and moderates online with Leah Lynn, mathematics teacher at Georgia Northwestern Technical College in Rome, Georgia. More?
* See all graphs in this series or collections of 60 of our favorite graphs, 28 graphs that teach about inequality and 24 graphs about climate change.

* View our archives that link to all past releases, organized by topic, graph type and Stat Nugget.

* Learn more about the notice and wonder teaching strategy from this 5-minute video and how and why other teachers are using this strategy from our on-demand webinar.

* Sign up for our free weekly Learning Network newsletter so you never miss a graph. Graphs are always released by the Friday before the Wednesday live-moderation to give teachers time to plan ahead.

* Go to the American Statistical Association K-12 website, which includes teacher statistics resources, Census in the Schools student-generated data, professional development opportunities, and more.

Students 13 and older in the United States and the Britain, and 16 and older elsewhere, are invited to comment. All comments are moderated by the Learning Network staff, but please keep in mind that once your comment is accepted, it will be made public.

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What's Going On in This Graph? | Global Carbon Emissions

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Compare the historical share of global carbon emissions - both total emissions and emissions per person - for the world's 23 richest countries to the share from all of the world's other countries. These graphs show the historical carbon emissions for the world's 23 richest countries and for all other countries.

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KS2-5 Explore the amount of greenhouse-gas emissions produced by different foods, and discuss how to make greener choices

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KS2-5 Explore the amount of greenhouse-gas emissions produced by different foods, and discuss how to make greener choices

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Use this one-hour Headline lesson to help your students:Learn which food produce the most greenhouse gasesExplore how to make greener food choicesDebate whether any food should be banned for the sake of the climateThese teaching resources are supported by KPMG. The Economist Educational Foundation maintained full editorial control.

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In this lesson, students apply the familiar formula y=mx+c to a relevant real-world scenario: buying a car.

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In this lesson, students apply the familiar formula y=mx+c to a relevant real-world scenario: buying a car.

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In this lesson, students apply the familiar formula y=mx+b to a relevant real-world scenario: buying a car.

An electric Chevrolet Bolt charging up in Baker, Calif. General Motors announced last month that it would phase out the internal combustion engine by 2035. Credit... Philip Cheung for The New York Times

Students in U.S. high schools can get free digital access to The New York Times until Sept. 1, 2021.
Featured article: "Electric Cars Are Better for the Planet - and Often Your Budget, Too" by Veronica Penney.
Last month, General Motors announced that it will sell only zero-emissions vehicles by 2035. The announcement represents a shift toward not only a more sustainable energy model, but also a more sustainable business model. As electric car technology becomes increasingly efficient and affordable, more Americans are choosing to buy electric vehicles.

This trend raises a question familiar to many drivers: Are we there yet? Specifically, have electric cars become both more environmentally-friendly and more affordable than standard gas cars? In this lesson, you will explore this question algebraically using systems of linear equations. In addition to analyzing broader trends, you'll analyze your own family's (or a friend's) car to see if "going green" with an electric vehicle would mean saving some "wallet green" too.

Tesla Model 3 and Toyota Camry XLE Credit... James Lipman/Tesla Motors, via Associated Press; Toyota

Often the decision to buy a gas or electric vehicle is framed as a trade-off between the cost of the car and its pollution potential. First, we're going to consider this trade-off with respect to two cars: the Tesla Model 3 (electric) and Toyota Camry XLE (gas).

Let's consider economic costs. Respond to the following questions in writing or in class discussion:

Which car do you believe costs more to buy? Why?

Which car do you believe costs more to drive (after initial purchase)? Why?

Which car do you believe costs more over all (to buy and to drive) over its full lifetime? Why?

Next, let's consider environmental impact. One central way to measure environmental impact is by measuring greenhouse gas emissions. Greenhouse gases, such as carbon dioxide (CO2), contribute to climate change.

Greenhouse gases are not just created while driving. For example, most manufacturers have to emit greenhouse gases when creating the materials for, assembling and shipping their newly-sold vehicles. These are considered emissions made "during production." In addition, in many areas, greenhouse gases also power the city's electrical grids that charge electric car batteries.

Which car (Tesla Model 3 or Toyota Camry XLE) do you believe creates more greenhouse gases in its production? Why?

Which car do you believe requires more greenhouse gases to create its power source (fuel/electricity)? Why?

Which car do you believe emits more greenhouse gases over all (during production and while driving) during its full lifetime? Why?

Source: carboncounter.com by the MIT Trancik Lab | Note: The chart shows data for new cars, SUVs and other models that retail for $55,000 or less. The most fuel efficient trim for each car is included and additional trim levels are shown for cars over $35,000 if they have a lower fuel economy rating than other trims shown (they are less efficient) by at least 4 miles per gallon.

Read the article from the beginning ... to this paragraph:

They found electric cars were easily more climate friendly than gas-burning ones. Over a lifetime, they were often cheaper, too.

Answer the following questions:

Now we're going to model the costs of our two chosen cars (the Tesla and the Camry) with data from the carbon counter tool used in the article's analysis. First, let's consider the upfront costs: The Tesla Model 3 retails for $37,990. The Toyota Camry XLE retails for $29,870. We can start modeling the total costs of each car as follows:

Tesla: Total Cost=37990

Camry: Total Cost=29870

The Toyota Camry is about eight thousand dollars cheaper. So, it looks as if we should buy the Camry.

But ... not so fast.

We can use the carbon counter tool (with the reasonable settings used in the "customize" tab here) to estimate the yearly cost of driving these vehicles. For the Tesla, the estimated price for electric charging and maintenance is $1,016 per year. For the Camry, the estimated price for fuel and maintenance is $2,038 per year. How would you include these estimates in the total cost model that we built above?

Answer: Where x represents the number of years you've owned the car:

Tesla: Total Cost= 1016x+37990

Camry: Total Cost= 2038x+29870

Let's briefly break down the mathematical model of total cost ($) for the Tesla:

If youbought the Tesla today, what would the value of x be? What would the total cost be? Hint: No yearshave passed.

If you've had the car for one year (x=1), what is the total cost? How about after two years (x=2)? After three years (x=3)? By how much is the total cost increasing each year?

If you've taken some algebra classes, the above models might remind you of a familiar formula: y = mx+b. In this formula, m represents the slope or rate of change; b represents the y-intercept or starting value. For the Tesla model, what is the rate of change (in $ per year)? What is the starting value (in $)?

Let's imagine that we'll own these cars for their entire lifetimes, which we'll assume to be about 12 years. Which car will have a lower total cost over 12 years of ownership? Exactly how much cheaper will it be? Use the mathematical models to find your answers. Show your work.

Answer:
Tesla: Total Cost=1016(12)+37990
=12192 + 37990
= $50,182

Camry: Total Cost=2038(12)+29870
=24456 + 29870
= $54,326

The Tesla is less expensive by $54,326 - $50,182 = $4,144

Answer the following in writing:

In two sentences or less, explain to someone what made the Tesla cheaper than the Camry over time.

What does the above example show about the costs of electric cars?

How does the example illuminate why General Motors may have decided to sell only zero-emission vehicles by 2035?

Sometimes we might consider owning cars for a shorter period. This raises the question: How long would I need to own a Tesla for it to "pay off" and become less expensive than the Camry? This question can be answered directly through algebraic solutions (e.g., substitution and elimination). Another method is to explore a table of values and graph:

Provide a written response: At approximately what year does the Camry start to become more expensive to own than the Tesla? Use evidence from both the table and the graph to support your answer.

Answer: At about eight years of ownership, the Camry surpasses the expenses of the Tesla in the table of values. In addition, the lines in the graph representing our models "cross" at Year 8 - at this point, the Camry's higher rate of cost per year finally "catches up" with the Tesla (which had a higher starting cost).

In addition to costs, we can also model the total greenhouse gas emissions associated with each vehicle over time. Although Tesla is better for the climate over time, the Camry puts out less emissions during its production. Answer the next questions to explore the emissions trade-offs for these vehicles:

1. The upfront vehicle and battery production for the Tesla creates emissions in the amount of 11,074 kg CO2-eq (this unit of measurement means "emissions equivalent to the global warming potential of 11,074 kilograms of CO2"). The power sources that create electricity to charge the battery expend about 1,368 kg CO2-eq per year. Create a mathematical model to determine total emissions (in kg CO2-eq) for the Tesla:

Answer: Where x represents the number of years you've owned the car:

Tesla: Total Emissions =1368x+11074

2. The upfront vehicle production for the Camry creates 7,402 kg CO2-eq of emissions. The production of fuel and burning of fuel needed to drive the car produces 4,525 kg CO2-eq per year. Create a mathematical model for the Camry:

Answer: Where x represents the number of years you've owned the car:

Camry: Total Emissions=4525x+7402

3. Approximately how many years will it take for the Camry to produce more total emissions than the Tesla? Show your work using a table of values and a graphical sketch.

Answer: The Tesla becomes more emissions-efficient shortly after the first year of ownership. By Year 2, according to the table, the Tesla has lower overall emissions. In the graph, we see the lines "cross" shortly after Year 1, as the Tesla begins to have lower total emissions because of its lower rate of emissions per year. Hands down, the Tesla is the more environmentally-friendly option, and it grows more environmentally friendly with each passing year.

Analyze your own family's car. Use the carbon counter tool to compare your own family's car with the emissions and costs of electric, hybrid or gas alternatives. Find the car model you'd like to compare by using the search bar. Then, use the "bar chart" feature to directly compare the selected cars. Change different model assumptions (miles driven per year, tax benefits for electric vehicles and so forth) to see how your estimates change. Note: The tool displays data for only new cars.

Broaden your analysis by looking at city-level data. Explore this interactive map of auto emissions in different cities in the United States. Find your local area on the map to analyze auto emissions in your community. Use the line charts to examine the relationship between total emissions and emission rates (per person).

Look for trends among many electric and gas cars. See the recently published " What's Going On in This Graph? " to learn more about comparing the cost and efficiency of many cars. What trends do you notice among the relative cost and fuel efficiency of gas, hybrid and electric cars?

Write a proposal to your family about buying an electric car. Explain the trade-offs between cost and efficiency compared with a gas-burning vehicle. Then, make a case for why buying an electric vehicle would be better or worse in your family's specific situation.

This lesson was written by Dashiell Young-Saver, who is a high school statistics teacher and the founder of About Lesson of the Day Skew The Script. Important contributions were made by Matthew DiSorbo and by Sharon Hessney, who writes the Learning Network's weekly feature "What's Going On in This Graph?"
* Find all our Lessons of the Day in this column.
* Teachers, watch our on-demand webinar to learn how to use this feature in your classroom.

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Gas or Electric? Thinking Algebraically About Car Costs, Emissions and Trade-offs (Published 2021)

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In this lesson, students apply the familiar formula y=mx+b to a relevant real-world scenario: buying a car. Students in U.S. high schools can get free digital access to The New York Times until Sept. 1, 2021. Featured article: " Electric Cars Are Better for the Planet - and Often Your Budget, Too " by Veronica Penney.

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KS3/4 Study maths for a career in climate science

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KS3/4 Study maths for a career in climate science

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An interview with a Climate Scientist about how maths helps them in their career

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An interview with a Climate Scientist about how maths helps them in their career

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KS3-5 Study maths for a career as a renewable technology engineer

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KS3-5 Study maths for a career as a renewable technology engineer

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2 min career video

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Explore careers: renewable technology engineer

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Manipulating climate statistics online activity

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Manipulating climate statistics online activity

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KS4/5 Teach about climate change with NY Times 'What's Going on in this Graph?'

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KS4/5 Teach about climate change with NY Times 'What's Going on in this Graph?'

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Teach About Climate Change With These 24 New York Times Graphs (Published 2019)

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We've gathered graphs previously published in The Times that illustrate different aspects of climate change. Plus, we suggest strategies for helping students analyze what they see.

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KS2-4 Climate Detectives tasks teams of young people to work with real climate data.

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KS2-4 Climate Detectives tasks teams of young people to work with real climate data.

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Climate Detectives is a European Space Agency initiative that tasks teams of young people to work with real climate data.

For the first time, ESERO-UK is excited to announce that there are two ways young people can take part.

Climate Detectives UK – open for registration!

Climate Detectives UK is a spin-off of the ESA Climate Detectives challenge, running for the first time this year. The competition is open to 11-14 years old.

This shorter, more focused programme challenges participating teams with answering questions in one of several proposed research areas, using a range of tools and data carefully curated by ESERO-UK with the help of climate experts at the Met Office.

Registration for this challenge closes on 28th October.

Find out more and register

ESA Climate Detectives

ESERO-UK invites teachers and teams of students, between the ages of 8 and 15, to team up and join the ESA Climate Detectives school project.

Teams of students, supported by their teacher, are called to make a difference by identifying a climate problem, investigating it by using available Earth Observation data or taking measurements on the ground, and then proposing a way to help reduce the problem.

Registration for this challenge closes on 25th November.

Find out more and register

Supporting Resources

Teachers and teams taking part in either challenge can make use of a specially curated collection of resources to inspire ideas, reinforce learning, or take things a step further.

View the resources here

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Teams of students between the ages of 8 and 15 are being asked to team up and join the Climate Detectives school project, in which you identify a climate problem, investigate it by using available Earth Observation data or taking measurements on the ground, and then propose a way to help reduce the problem.

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Stefan Gates explores how shapes are used to sort and re-use rubbish at a recycling plant. He helps children sort their recycling and then shows them what can be made out of it.

Stefan Gates finds out that machines can sort rubbish into different 2D and 3D shapes when he visits a vast recycling plant. He speaks to Richard Kirkman who explains how they use different machines to sort the rubbish by weight and shape. Stefan throws some items from his own recycling into a machine like a giant sieve - a cylinder (plastic bottle), a flat rectangle (piece of paper), and a cube (cardboard box). We see that the machine lets some shapes through but others travel across onto a conveyor belt. The different machines and conveyor belts continue to separate the different materials. At the end a machine squashes them into cuboid bales of the same size and shape, but made from different materials - cardboard, aluminium or plastic. Stefan shows us the new items that can be made from the recycled material - cardboard boxes, drinks cans, plastic bottles and a recycled plastic chair. Stefan then visits pupils from John Donne School in South London who show him how they reuse plastic bottles by first sorting them into different sizes and shapes, just like the machines. Then they can make new things out of them, from bird feeders to planters to a whole greenhouse with walls made from 1500 plastic bottles.

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BBC Two - Ecomaths, Primary, Using maths to recycle rubbish

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Stefan Gates explores how shapes are used to sort and re-use rubbish at a recycling plant. He helps children sort their recycling and then shows them what can be made out of it. Stefan Gates finds out that machines can sort rubbish into different 2D and 3D shapes when he visits a vast recycling plant.

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R4 More or Less podcast - Is it easy being green

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R4 More or Less podcast - Is it easy being green

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Is our electricity extra expensive and our insulation inadequate?

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Is our electricity extra expensive and our insulation inadequate? And a tale of tumbling trees.

Is our electricity extra expensive and our insulation inadequate? And a tale of tumbling trees.

Internet infographics suggest we're paying way more for our energy than countries in the EU. Are they being interpreted correctly? And what part, if any, has Brexit had to play?

Insulation Britain activists have been gluing themselves to motorway slip-roads to raise awareness about poor home insulation. Their website says we have the least energy efficient homes in Europe. What's the evidence?

Plus, what do the numbers tell us about migrants trying to cross the Channel in small boats? Are stereotypes about different generations backed up by the data? And is it or is it not true that the UK has lots of trees?

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BBC Radio 4 - More or Less, Is it easy being green?

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Is our electricity extra expensive and our insulation inadequate? And a tale of tumbling trees. Is our electricity extra expensive and our insulation inadequate? And a tale of tumbling trees. Internet infographics suggest we're paying way more for our energy than countries in the EU. Are they being interpreted correctly?

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EY/KS1 Dr Sammie Buzzard, climate scientist, reads Planet Rescue for Maths Week England

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EY/KS1 Dr Sammie Buzzard, climate scientist, reads Planet Rescue for Maths Week England

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Dr Sammie Buzzard reads PLANET RESCUE by Patrick George

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by Mark Dawes

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This is interesting because it contains an error, a lack of clarity and something misleading.  Perfect for a Quibans!

Article from the Daily Telegraph:

Ferrero Rocher shamed as Christmas chocolates with the least recyclable packaging

12 DECEMBER 2018

F errero Rocher has been named and shamed as the Christmas chocolate box with the least recyclable packaging.

The vast majority (89 per cent) of the packaging in a 359g Ferrero Rocher Collection box may be destined for landfill as it is made from non-recyclable plastic and foil, a study by consumer group Which? found.

By contrast the most recyclable chocolate boxes were Waitrose Christmas Chocolate Favourites 240g which is 96.3 per cent recyclable) Cadbury's Milk Tray, which is 92.5 per cent easily recyclable. The second least recyclable packaging was for Marks & Spencer's The Big One Selection 600g, which is 71.4 per cent recyclable.

In addition Which? analysed chocolate boxes for their packaging to chocolate weight ratio, and found boxes of Ferrero Rocher Collections had by far the highest.

Nearly half of the weight of a 359g Ferrero Rocher Collection box is made up of packaging (42.4 per cent), with the rest constituting (67.6 per cent) the chocolates themselves, it found.

The boxes with the highest proportion of chocolate weight were Marks & Spencer's The Big One Selection 600g (just 8.5 per cent packaging), and Lindt Lindor Assorted Mix 384g (just 11.5 per cent packaging), the study showed.

Questions:

2)

The lack of clarity is that ‘359g’ is the weight of the chocolate (and nuts, etc) in the box.  The packaging weighs more on top of that.  42.4% of the total is the packaging, so what is the weight of packaging?

3)

The misleading part is that an implication of the two mentions of M&S is not followed up.  What is going on there?

(Answers are below.)

Further info:

Here are screenshots of the tables from the Which? report:

Here it is as a single table (to be pasted into Excel?)

Chocolate

Official weight (g)

Weight in packaging (g)

Packaging weight (g)

Percentage packaging

Percentage easily recyclable

Cadbury's Heroes

660

808

144

17.80%

88.90%

Cadbury's Milk Tray

360

470

106

22.60%

92.50%

Cadbury's Roses

660

810

144

17.80%

90.30%

Chocolate Treats By Sainsburys

650

806

154

19.10%

88.30%

Ferrero Rocher Collection

359

642

272

42.40%

11%

Lindt Lindor Assorted Mix

337

384

44

11.50%

90.90%

Marks & Spencer The Big One Selection

600

662

56

8.50%

71.40%

Mars Celebrations

650

812

150

18.50%

90.70%

Mars Malteaser Teasers

275

364

70

19.20%

88.60%

Morrisons Mega Mix

1050

1216

162

13.30%

81.50%

Nestle Quality Street

720

846

130

15.40%

83.10%

Thorntons Continental Selection

284

408

120

29.40%

86.70%

Waitrose Christmas Chocolate Favourites

240

356

108

30.30%

96.30%

Additional questions:

4) What should happen when you add up the Official Weight and the Packaging Weight columns?
5) Do any of them mis-state the amount of chocolate they contain?
6) Work out the percentage of the Total Weight for each product that cannot be recycled. How does M&S compare?

Answers:

1)

The error is that 42.4% plus 67.6% doesn’t equal 100% (and it should).  The former figure is correct (as seen in the Which? tables).

2)

The chocolate in the Rochers are 57.6%, so when we divide 359g by 0.576 we get the total weight (623g) and this leads to a packaging weight of 264g.  This doesn’t agree with the figures from Which? because there is slightly over 359g of choc.

3)

M&S may have the second-least recyclable packaging, but there is much less of it, so maybe they have cut down on the packaging overall (which seems like a good thing: just because something is ‘recyclable’ doesn’t mean everyone will recycle it!).

4)

You should get the ‘Weight in packaging’ column.

5)

Most of them give us slightly more chocolate than advertised, with only Nestle falling under (but that is presumably only on the single box that Which? tested).

6)

I used Excel to work this out.  38% of the weight of the in-package Ferrero Rocher is non-recyclable, but only 2% of the M&S.  The median was 2%.

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This is interesting because it contains an error, a lack of clarity and something misleading. Perfect for a Quibans! Article from th...

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This selection has been especially created to celebrate Maths Week England 2021 and each image is linked to climate change in order to mark COP26.

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New for Maths Week England 2021!

We'd love to see them on Twitter: #MathsWeekEngland #MWE21 .

Maths Week England 2020 resources

Using these resources

The idea behind this piece of work is to provide a structure for students which demonstrates that maths can be found all around them. It will help them see what that maths is and, by using photographs and pictures, encourage creativity. Using pictures to stimulate discussion and debate shows students that they can talk about maths and that maths is not always about right and wrong answers and written methods.
How to use the slides
The slides are designed for you to use as many or as few as you like and for as long or as short a time as you like. You might like to use them with your tutor group, in a maths lesson, another subject or even an assembly. The slides have been designed to be as flexible as possible. We suggest that resource A is suitable for years 5-8, resource B are suitable for years 7-10 and resource C is suitable for years 9-12, depending on the strengths and interests of your students.
Simply:

1. Choose a photograph and display it

2. Ask "Where is the Maths in that?"

3. Let the ideas flow!

Aim to show:

maths is all around us

maths is creative

maths is not always about being right or wrong

In order to promote discussion

Emphasise - Nobody can be wrong

It's just about explaining your thoughts

Note: There is a hidden slide after every photograph with suggestions of the maths in the picture but they are in no-way exhaustive! They also range in complexity and so you may consider some to be beyond what you would like to use with your students. Use as many or as few as you wish. Some of the slides also contain links for developing some of the ideas into longer activities or lessons.

Ideas: Consider what maths is used to model the situation in the photo. What maths might the people in the pictures need? Discuss what questions the photographs raise in the students' minds.

Going further: You might like to use your own photographs or encourage the students to provide their own photographs - especially ones where they think there is no maths involved and then the class can persuade them otherwise! You could print out some of the photos and use as a carousel activity. The students move around in groups with a few minutes at each picture to come up with ideas and then feedback as a class after each group has seen all the pictures.

Why not share that you have had a go at this resource? We'd love to hear how you got on - tweet from your school account and tag @Advanced_Maths and @Maths_Week . We hope you enjoy them.

These resources were designed as part of the AMSP's support for Maths Week England .

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We'd love to see them on Twitter: #MathsWeekEngland #MWE21 . The idea behind this piece of work is to provide a structure for students which demonstrates that maths can be found all around them. It will help them see what that maths is and, by using photographs and pictures, encourage creativity.

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KS3/4 Desmos online activity on food's carbon footprint

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KS3/4 Desmos online activity on food's carbon footprint

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KS3/4 Climate maths resources from Leeds dec

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KS3/4 Climate maths resources from Leeds dec

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frameworks and Maths lessons to help teachers unpack contemporary global issues. Using the Sustainable Development Goals as a starting point the resources address global challenges such as Climate Change, Gender Equality, Migration, International Inequalities and Intercultural Understanding and many more.

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Global Learning Lessons | Maths - Leeds DEC

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frameworks and Maths lessons to help teachers unpack contemporary global issues. Using the Sustainable Development Goals as a starting point the resources address global challenges such as Climate Change, Gender Equality, Migration, International Inequalities and Intercultural Understanding and many more.

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GOV.UK

Climate Change

Climate change statistics

A prototype portal for data and insights on climate change.

Emissions

Greenhouse gas emissions, UK, 1990 to 2020 and provisional 2021 (Mt CO2e)

All Emissions data

Drivers

Fossil fuel energy use (Mtoe) for the four highest sectors in the UK

All Drivers data

Mitigation

Renewable energy share (%) in total energy consumption, UK, 2020

All Mitigation data

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New planting of UK woodlands, thousand hectares, 1976 to 2021

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KS5 Skew the Script - Stats tests - is climate change real?

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KS5 Skew the Script - Stats tests - is climate change real?

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US based

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Lesson 8.5 - Inference for Matched Pairs

Relevant Topics Covered

Climate Change

Evaluating Expert Claims

Statistical Concepts Covered

Matched Pairs t-Interval

Matched Pairs t-Test

“Cherry Picking” Data

All lesson materials are included below. Before using them: Make a free account for unlimited access. Read our helpful guides for using our materials in online, flipped, or traditional classrooms. Read our tips for teaching socially relevant math.

8.5 Video

Incorporate the guided notes video into your online, flipped, or traditional classroom - see our helpful guide.

8.5 Student Items

Handout: pdf, docx

Video Reflection Q’s: form*

Desmos: link*

*these resources are mainly used in online or flipped classrooms. See guide.

Note: This lesson also has an Experience-First-Formalize-Later (EFFL) version, created in collaboration with Stats Medic. Find it here.

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AP Statistics lesson 8.5. Students investigate the validity of climate change arguments using inference for matched pairs.

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KS4/5 Questions Inspired by a News Story - bottles of water

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KS4/5 Questions Inspired by a News Story - bottles of water

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by Mark Dawes

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I started by giving out just this paragraph from the Guardian article that follows:

Imagine laying out half-litre bottles on the pitch at Wembley Stadium. You could fit ### bottles on the grass, packed into a tight grid. Now imagine building up layers of bottles, covering the same area, to build a tower. To contain all the bottled water we buy each year [in the UK], you would end up with a ###-metre skyscraper.

There are some nice Fermi estimations required here.

What are the dimensions of a football pitch? What are the dimensions of a water bottle? How many bottles are used in this country in a year?

Then we need to convert some units and carry out the calculations, not forgetting to round off sensibly.

The students worked in groups. A typical estimate for the size of a football pitch was 110m by 60m. Some measured their water bottles (!) and found a diameter of about 6cm and a height of 20cm.

If working out the area covered by the pitch and by a bottle we need to be careful when converting units (10,000 cm ² = 1m ²). We also need to decide what "packed into a tight grid means" (we took it to mean a rectangular grid). The easiest way is to work out how many bottles fit along each side of the pitch and then to multiply these. These figures gave us 1.8 million (pleasingly close to the 1.7 million in the article). Other estimates in the room varied between 1.6 million and 2.8 million.

Working out the height is more difficult. If everyone in the country has one bottle per week then that would give us about 1.7 billion bottles per year. That would need to be stacked 1000 rows high, which means a height of about 200m. In fact the article says it's 2.2 billion _litres_ per year (each bottle holds 500ml), so we have underestimated the answer.

I then gave out a fuller version of the article (below) and asked what things they could work out.

If we care about plastic waste, why won't we stop drinking bottled water?

Sun 28 Apr 2019

For all the innovation and choice that define the food and drink industries, if you want to make money, you could do a lot worse than bung some water in a bottle and flog it. A litre of tap water, the stuff we have ingeniously piped into our homes, costs less than half a penny. A litre of bottled water can cost well over a pound, especially for something fancy that has been sucked through a mountain.

Yet the bottled water market is more buoyant than ever, defying the plastics backlash inspired by stricken albatrosses on the BBC's Blue Planet, and a broader, growing sense that something has to change.

Sales in the UK were worth a record £558.4m in the year to last November, an increase of 7%, according to the latest figures from the market analyst Kantar. Separate data from the analysts Nielsen show that last year we guzzled more than 2.2bn litres of bottled water, including "take-home" and "on-the-go" products. That's an annual rise in volume of 8.5%.

Imagine laying out half-litre bottles on the pitch at Wembley Stadium. You could fit 1.7m bottles on the grass, packed into a tight grid. Now imagine building up layers of bottles, covering the same area, to build a tower. To contain all the bottled water we buy each year, you would end up with a 514-metre skyscraper - 200 metres taller than the Shard.
Hope is not entirely out of reach. That plastic skyscraper conceals attempts in the bottled water industry to change. If nothing else, the rate of growth has begun to ease (sales were up 7% in the year to November 2018, compared with 8% the previous year).

But even if large numbers of us are quitting bottled water because of care for the environment, others are taking it up. The introduction of the "sugar tax" on juices and fizzy drinks has pushed more people to bottled water, while health awareness has boosted its desirability. Kantar says tap water consumption is growing at roughly the same pace (we still drink almost three times as much tap water as bottled water).

So the plastic tide only creeps higher. The industry is quick to point out that all its bottles are recyclable. "But collection rates are, at the most generous estimates, 56%, so the actual recycling rate will be lower than that," Chetan-Walsh says. And while bottles may be recyclable, very few are made of recycled plastic. Highland Spring launched recycled half-litre "eco" bottles alongside its standard bottles in January; Evian has vowed to use only recycled plastic across its range by 2025.

Kinvara Carey, general manager of the Natural Hydration Council, an association of the biggest bottled water manufacturers, cites a survey in which people were asked what they would do if bottled water were not available. "Forty-four per cent would buy another drink, which is not great, 14% would go without and 4.5% said they would find a fountain," she says. "The choice is important."

We can work out things like:

1) The cost of a litre of bottled water
2) How the price has changed in the past year
3) What the amounts were last year
4) How many bottles are recycled
5) The volume of landfill taken up by bottles
6) Why the percentages in the final paragraph don't add up to 100%
7) How much water each person drinks each day

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I started by giving out just this paragraph from the Guardian article that follows: Imagine laying out half-litre bottles on the pitch at ...

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@geography_paul collection of resource and support

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@geography_paul collection of resource and support

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Climate Breakdown scheme of work - section 4 useful for maths classroom

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Take inspiration from the world's first Climate Breakdown scheme of work which has now been downloaded more than 7000 times around the world. 14 lessons exploring the science of climate change, discussing broad societal questions and culminating in a debate.

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KS2-5 Resources to demonstrate climate impact of fast fashion

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KS2-5 Resources to demonstrate climate impact of fast fashion

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Based on Christmas Jumpers but could change to other items of clothing.

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Increasing participation in Core Maths, AS/A level Mathematics and Further Mathematics

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Geographical teaching and learning resources

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Information is Beautiful - nature and climate graphs

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Information is Beautiful - nature and climate graphs

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Ask your students 'what do you notice?' 'what do you wonder?' 'what is the story this graph is telling?'

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Our mission

Distilling the world's data, information and knowledge into beautiful infographics and visualizations.

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Nature & Climate - Information is Beautiful

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Distilling the world's data, information and knowledge into beautiful infographics and visualizations.