Finding All Solutions

These problems invite students to find all possible solutions. One of the best answers to "How do you know you have found them all" is to be able to say "I worked systematically!"

Shady Symmetry

Age 11 to 14
Challenge Level

This problem is a good activity for the visualisation of symmetry, and for encouraging students to work systematically.

Isosceles Triangles

Age 11 to 14
Challenge Level

This problem encourages students to use coordinates, area and isosceles triangles to solve a non-standard problem. To find all possible solutions they will need to work systematically.

M, M and M

Age 11 to 14
Challenge Level

This problem offers the students an opportunity to consolidate what they are expected to know about mean, mode and median whilst also challenging them to work systematically, and justify their reasoning

Peaches Today, Peaches Tomorrow...

Age 11 to 14
Challenge Level

This problem could replace repetitive textbook work on calculating fractions of integers. It offers plenty of practice of these calculations while requiring students to come up with problem-solving strategies.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Copyright © 1997 - 2023. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.