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Problem, Clue, Solution, Teachers' note
Lesson idea. Sometimes area and perimeter of rectangles are taught separately, and are often confused. In this problem students consider the relationship between them and are being challenged to engage in some sophisticated mathematical thinking.
Teaching approach. This lesson idea is about working systematically^{(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  Can They Be Equal? 
Topic  Geometry 
Teaching approach  
Learning Objectives  Working systematically 
Subject  
Age of students / grade 

Related ORBIT Wiki Resources 

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  CCBy, with kind permission from NRICH. This resource was adapted from an original NRICH resource. 