# Fermi Problems

- Numbers

- ISCED 2 = Upper Secondary Education

- English

## Introduction

Fermi problems are problematic mathematical problems that do not have an exact answer. They are executive for encouraging pupils to think mathematically and require them to make reasonable assumptions and estimates in order to arrive at an approximate solution. The more assumptions they make, the more accurate the estimate.

## Learning Outcomes

The learner will learn to:

- Use a numerical expression in a set of natural numbers with zero and model a problem situation.
- Apply estimation skills to solve Fermi problems.
- Use critical thinking and problem-solving strategies to analyze and break down complex problems.
- Make connections between mathematics and real-world situations.
- Communicate and justify their reasoning and estimations.
- Foster a growth mindset by embracing uncertainty and ambiguity.

## How Does It Work

**Activity 1**

Divide pupils into teams. Divide the tasks to be solved on the worksheet.

Tasks that pupils solve:

- How many pupils together have a mass like an elephant?
- How many packets of candy do we need to put together a 100m long candy bar?
- Imagine you have a pile of 2 kuna coins like Mt Everest, how much would it be worth?
- How long should it take to count to a million?
- How many pizzas does our class eat in one year?

For each task, write the solution and the procedures for solving it, and the way you thought and solved the task. After solving within the team, you will present solutions to the whole class.

**Activity 2**

Pupils present their solutions and procedures and present the assumptions they used in solving. Teams compare results and comment on the obtained solutions.

**Activity 3**

Ask pupils for homework to come up with a few questions for themselves to ask their friends as a new homework assignment.

**Activity 4**

Pupils complete a performance evaluation. They respond to how they have collaborated within it and whether they want us to work more often this way by solving tasks of this type.

## Why Is It A Good Practice?

Pupils need to think mathematically and make good assumptions. An important element of problem solving is the ability to break problems down into parts and determine the order in which they are solved. At the end they have to explain how they arrived at their solutions.

## Assessment

Assess students based on their ability to collect data, make estimations, and draw conclusions from their investigations. Evaluate their understanding of the scope of the problem and the accuracy of their estimations.

Evaluate their ability to collaborate, divide tasks, and reach consensus on estimations.

Assess their final solutions, the accuracy of their estimations, and their ability to communicate and justify their reasoning as a group.

## Inclusion

Tips for teachers when implementing this good practice in an inclusive classroom:

Instruct the pupil in detail about each step and element of the mathematical activity and familiarise them with the structure of the tasks. Explain the individual operations and the sequence.

Attract attention with different didactic tools and encourage active participation.

Minimise distractions (do not sit by the window or in the middle of restless pupils, but in a quiet place in the classroom, e.g. with quiet pupils or pupils with whom they work well, so that they are disturbed as little as possible by what is happening in class, the work area should only contain what is necessary for the work). The instructions given to him should be brief. Reward the perseverance of attention (the completion of a task is accompanied by praise, which is recorded in a notebook).

Pay no attention to spelling mistakes or misspellings. Read the instructions for the written exam, check that the pupil has understood the instructions/tasks well and take account of subsequent corrections in the exams. Use cream-coloured paper if possible and avoid red and green print. Increase the font size in comprehensible reading texts. Use sans serif letters for the text to be read by a pupil with dyslexia; the font size should be at least 14 pt. Use bold or highlighted letters. Avoid underlining titles or strings of words, which can cause words to blend visually. Increase the spacing between letters and lines and separate lines by double spacing. Break the text into smaller units and divide it into individual lines, not a continuous sequence.