# Whats Possible

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Teaching approach. This lesson idea is about exploring and noticing structure(ta).

The collection of NRICH activities are designed to develop students capacity to work as a mathematician. Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, justifying, proving are all at the heart of mathematical thinking.

This particular resource has been adapted from an original NRICH resource. NRICH promotes the learning of mathematics through problem solving. NRICH provides engaging problems, linked to the curriculum, with support for teachers in the classroom. Working on these problems will introduce students to key mathematical process skills. They offer students an opportunity to learn by exploring, noticing structure and discussing their insights, which in turn can lead to conjecturing, explaining, generalising, convincing and proof.

The Teachers’ Notes provided focus on the pedagogical implications of teaching a curriculum that aims to provoke mathematical thinking. They assume that teachers will aim to do for students only what they cannot yet do for themselves. As a teacher, consider how this particular lesson idea can provoke mathematical thinking. How can you support students' exploration? How can you support conjecturing, explaining, generalising, convincing and proof?. (edit)

 Resource details Title What's Possible? Topic Algebra Teaching approach Learning Objectives Exploring and noticing structure Subject Age of students / grade Related ORBIT Wiki Resources The following NRICH resources have the teaching approach "Exploring and noticing structure": Painted Cube, Summing Consecutive Numbers, Whats Possible, Which List is Which, Which Spinners The following NRICH resources have the topic "Algebra": Charlies Delightful Machine, Diamond Collector, Factorising with Multilink, Number Pyramids, Pair Products, Seven Squares, Temperature, Visualisations, Whats Possible Files and resources to view and download The following parts are available: Problem, Clue, Solution, Teachers' note. The original problem is available on the NRICH website here. Acknowledgement The NRICH website http://nrich.maths.org publishes free mathematics resources designed to challenge, engage and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support for teachers by publishing Teachers’ Resources for use in the classroom. License CC-By, with kind permission from NRICH. This resource was adapted from an original NRICH resource.