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Problem, Clue, Solution, Teachers' note

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Teaching approach. This lesson idea is about visualising and explaining^(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?.

Resource details
Title	Place Your Orders
Topic
Teaching approach
Learning Objectives	Visualising and explaining
Format / structure
Subject
Age of students / grade
Table of contents
Additional Resources/material needed
Useful information
Related ORBIT Wiki Resources	The following NRICH resources have the teaching approach "[[Teaching Approaches/|]]": Some use of "" in your query was not closed by a matching "". The following NRICH resources have the topic "[[Topics/|]]": Some use of "" in your query was not closed by a matching "".
Other (e.g. time frame)
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.