M1Maths

Maths Assignments / Extended Tasks

This is the beginnings of a collection of extended maths tasks on a range of topics at a high school level.

In many cases they are accompanied by model worked solutions.

They might be useful for problem solving practice, reinforcement of ideas or assessment.

Levels 1-6
Years 7-12

Maths trail

Students write questions for a partner relating to the school grounds. They then swap and solve each other's questions. Adaptable to any level.

pdf     docx

Levels 1-3
Years 7-9

Magic squares

Arithmetical calculations and problem solving.

pdf     docx

Levels 1-3
Years 7-9

Four 4s

Arithmetical calculations and order of operations.

pdf     docx

Levels 2-4
Years 8-10

A few random facts about space

Arithmetical calculations and use of formulae in an astronomy context. Could be used as a class activity or the basis of an assignment.

pptx

Levels 2-6
Years 8-12

Ant walks

An informal introduction to paths and loci, and to graphing relations

pdf     docx

Level 3
Year 9

Enlarging shapes

Discovering rules for how lengths, areas and volumes of shapes change when the linear dimensions change.

pdf     docx

Levels 3-4
Years 9-10

Rain

Various tasks on the theme of rainfall, particularly involving measurement and statistics.

pdf     docx

Levels 4-5
Years 10-12

Musical scales

The mathematics behind musical scales: spreadsheets, indices, ratios.

pdf     docx

Levels 4-6
Years 10-12

Helicopters

Data collection, producing tables, graphs and formulae for functions of two independent variables.

pdf     docx

Level 5-6
Years 10-12

Radioactive decay

Simulation or radioactive decay with M&Ms; exponential functions, spreadsheets and regression.

pdf     docx

Level 6
Years 11-12

Roller coaster

Application of algebraic techniques and differential calculus to various types of functions.

pdf     docx

Level 6
Years 11-12

Poker

Calculating probabilities involved in a 6-card variation on poker.

pdf     docx

Level 6
Years 11-12

Maclaurin series

Generating MacLaurin series by repeated differentiation; application to complex numbers.

pdf     docx

Level 6
Years 11-12

Fluttering

Fluttering (shuffling) decks of cards. Combinatorics, number theory.

pdf     docx

Level 6
Years 11-12

Air resistance

Using numerical methods and calculus to calculate projectile trajectories with and without air resistance.

pdf     docx

xlsx

Level 6
Years 11-12

Fractals

Performing iterations of operations on the complex plane as an introduction to fractals.

pdf     docx

Background image: https://pixabay.com/illustrations/beach-background-sea-ocean-3892386/ (cropped) (Creative Commons licence)