Percentage difference puzzle

What's the difference?

How well do people know the facts about the places they live? Here are some results of a real survey to find out just that. People were asked 'how many people out of 100 in your country are immigrants?' and other questions. In this activity we will compare their perceptions to the reality and explore how we can decide who, if anyone, had the best guess! This is an activity designed to provoke some thought about percentage difference in context. It also involves a good deal of practice of the percentage error calculation and reverse percentage. 



Percentage difference puzzle activity sheet

What to do?

This task is primarily aimed at working with percentages but the context is really interesting too. While you are working with the numbers, try to reflect on their significance.

Part 1 - Consider the first table where you are shown some statistics about employment. A sample of people from each of the countries were asked to guess how many people per 100 in their country were unemployed and looking for work. You are shown both the guess and the actual number. Your task is to work out the percentage error in their guesses. You might watch the video below on calculating percentage difference.

Part 2 - In this survey, the people were asked to say how many people per 100 voted in the last election in their country. For some of the countries you are given the actual number and the percentage error in the guess. You are supposed to use this to work out the guess. For the others you are given the guess and the percentage error. You should use this information to work out the actual number. You might watch the video below on reverse percentages!

Part 3 - This is a puzzle that combines all of the skills you have used in the first part of the exercise. The people were asked about the number of people per hundred in their country that are immigrants. Try to deduce what numbers go in the gaps in the table.

Part 4 - As a class, have a good think about the significance of these results. When is a guess a good guess, when is it not? Which countries did the best? How can we decide? If you were writing an article about these statistics, what would your headline be?

Help Videos 

Watch this video for a quick look at calculating percentage change/error

Watch this video for a quick look at calculating reverse percentages


Teacher Notes

How to run it....

What to expect...


Click on the hidden eye icon to show the answers to the different problems.

How many people out of 100 are out of work?

How many people out of 100 voted in the last election?

How many people out of 100 are immigrants?



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