# Teaching approaches: Reasoning, justifying, convincing and proof

 Algebra Seven Squares Choose a few of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning? This lesson idea is about reasoning, justifying, convincing and proof(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?. Geometry Kite in a Square Can you make sense of the three methods to work out the area of the kite in the square? This lesson idea is about reasoning, justifying, convincing and proof(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?. Handling Data Olympic Records Can you deduce which Olympic athletics events are represented by the graphs? This lesson idea is about reasoning, justifying, convincing and proof(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?. Number What's it Worth? There are lots of different methods to find out what the shapes are worth - how many can you find? This lesson idea is about reasoning, justifying, convincing and proof(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?.