Resources: KS3
Relevant resources
Algebra  What's Possible?  
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make? 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?.  
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?.  
Algebra  Temperature  
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same? This lesson idea is about applying and consolidating^{(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?  
Algebra  Factorising with Multilink  
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units? 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?.  
Algebra  Diamond Collector  
Collect as many diamonds as you can by drawing three straight lines. This lesson idea is about thinking strategically^{(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?.  
Algebra  Pair Products  
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice? 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?.  
Algebra  Charlie's Delightful Machine  
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light? 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?.  
Algebra  Number Pyramids  
Try entering different sets of numbers in the number pyramids. How does the total at the top change? This lesson idea is about posing questions and making conjectures^{(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?.  
Assessment  Changing KS3 Questions for Engaging Assessment  
A large set of questions grouped by topic, paper, and national curriculum level Test questions are often seen as uninteresting and useful only to assess pupils summatively. This resource however allows questioning^{(ta)} to be used to support pupils’ revision, creativity and higher order^{(ta)} problemsolving in class. The tasks could be conducted via whole class^{(ta)} discussion^{(ta)} or assessment^{(ta)}, perhaps using miniwhiteboards^{(tool)}, or in small group work^{(ta)} situations.
 
Assessment  Using Assessment to Raise Achievement in Maths  
Learning goals; self & peer assessment; effecting questioning; marking and case studies This resource explores approaches to assessment^{(ta)} in maths, including the sharing of learning objectives^{(ta)}, group work^{(ta)}, whole class^{(ta)} assessment, questioning^{(ta)} and more. Four case studies serve as useful discussion prompts to share practice^{(ta)}. This .doc version of the QCA's 'Using assessment^{(ta)} to Raise Achievement in Maths' allows schools to select parts of the document that are most relevant to them.
 
Blogs  Getting a buzz out of blogging  
 
Consecutive Sums  Using Prime and Square Numbers  How Old Am I?  
Last year I was square, but this year I am in my prime. How old am I? This short activity offers opportunity for pupils to engage in mathematical thinking^{(ta)} and higher order^{(ta)} problem solving/reasoning^{(ta)}. They should be able to make links between different areas of mathematics and explore their ideas in whole class^{(ta)} discussion^{(ta)} and questioning^{(ta)}.
 
Digital Media  21st century show and tell  
A DEFT case study with Dinnington Comprehensive, Rotherham This cross curricula^{(i)} case study focusses on Digital Literacy, in particular using Eskills^{(i)} to: support skills in writing/recording for a target audience and to improve communication and research skills through the process of creating OER^{(i)}s. The case study illustrates issues involved in the use of video^{(i)} for educational purposes, with an emphasis on students producing and releasing OERs. The method could also be used for self/peer assessment^{(i)} with pupils.
One of the lesson ideas from the case study is available as a separate resource at Creating Instructional Videos.  
Games  Introduction to games  
 
Geometry  Attractive Tablecloths  
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs? This lesson idea is about applying and consolidating^{(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  Marbles in a Box  
In a threedimensional version of noughts and crosses, how many winning lines can you make? 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?.  
Geometry  Painted Cube  
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces? 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?.  
Geometry  Tilted Squares  
It's easy to work out the areas of most squares that we meet, but what if they were tilted? This lesson idea is about posing questions and making conjectures^{(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  Can They Be Equal?  
Can you find rectangles where the value of the area is the same as the value of the perimeter? 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?.  
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?.  
Geometry  Warmsnug Double Glazing  
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price? This lesson idea is about applying and consolidating^{(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  M, M and M  
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers? 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?.  
Handling Data  Olympic Measures  
These Olympic quantities have been jumbled up! Can you put them back together again? This lesson idea is about applying and consolidating^{(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?.  
Handling Data  Odds and Evens  
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers? This lesson idea is about posing questions and making conjectures^{(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  Which List is Which?  
Six samples were taken from two distributions but they got muddled up. Can you work out which list is which? 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?.  
Handling Data  Which Spinners?  
Can you work out which spinners were used to generate the frequency charts? 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?.  
Handling Data  Nontransitive Dice  
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea? This lesson idea is about thinking strategically^{(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  Place Your Orders  
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings? 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?.  
ICT  Data Logging and Control  
A compendium with numerous ideas for using sensors to teach science. This book provides a set of resources and lesson ideas with ICT^{(i)} as a key focus for use in inquiry^{(ta)} based learning and the scientific method^{(ta)}. It offers opportunities for use of group work^{(ta)} and collaboration^{(ta)} as well as whole class^{(ta)} questioning^{(ta)}.
 
ICT  Creating Instructional Videos  
Children create instructional videos to upload to YouTube This activity is a crosscurricular^{(subject)} activity with a literacy focus, involving a collaborative^{(tool)} approach, giving children to opportunity to work together to produce a set of instructional resources. Children were encouraged to engage in group talk^{(ta)} and discussion^{(ta)} in the classroom to reflect on what they should include in their videos. The activity furthers eskills^{(topic)} through the use of whole class^{(ta)} participation. It develops esafety^{(topic)} skills through discussion of the issues relating to posting digital content online. Children were allowed to choose their own subject for the video, although this could be set by a teacher with a specific outcome in mind, or could be tailored to cover a particular topic or subject. It could, for instance, be used to explain their mathematical thinking^{(ta)}.
 
Investigation  Consecutive Sums  
Can all numbers be made in this way? For example 9=2+3+4, 11=5+6, 12=3+4+5, 20=2+3+4+5+6 By definition, a problem is something that you do not immediately know how to solve, so learning how to solve something unfamiliar is not straightforward. Tackling an extended problem is difficult.
This lesson gives pupils an opportunity to engage in mathematical thinking^{(ta)} and develop their higher order^{(ta)} thinking skills on a problem that is accessible but which has interest. For example, the problem is presented in diagrammatic and numerical ways. The plan suggests several visualisation^{(ta)} methods to present the same underlying task. It should be useful for teachers to compare these different presentations and either to select the one that they feel will be most useful for their pupils or explore ways for the pupils to see the links between the different methods. The assessment^{(ta)} ideas, using other pupils' solutions from the NRICH website are widely applicable to other problems too.  
Modelling  Models in Science  
Teachers use models to help pupils make sense of their observations An opportunity for teachers to discuss the use of modelling^{(ta)} and visualisation^{(ta)} in Key stage 3 science
 
Models  Different types of model in science  
"When you use a model, you should make it clear to pupils that it is a model that you are using." This resource provides some examples of the types of models^{(tool)} used in science teaching, their roles, and importance for teaching.
 
Multimedia  Working with multimedia  
 
Number  Factors and Multiples Game  
A game in which players take it in turns to choose a number. Can you block your opponent? This lesson idea is about thinking strategically^{(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?.  
Number  What Numbers Can We Make?  
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make? 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?.  
Number  Mixing Lemonade  
Can you work out which drink has the stronger flavour? This lesson idea is about applying and consolidating^{(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  GOT IT  
Can you develop a strategy for winning this game with any target? 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?.  
Number  Summing Consecutive Numbers  
Many numbers can be expressed as the sum of two or more consecutive integers. Can you say which numbers can be expressed in this way? 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?.  
Probability  Playing with Probability  Efron's Dice  
I have some dice that are coloured green, yellow, red and purple... Efron's dice provide a discussion^{(ta)} topic for joint reasoning^{(ta)}  whole class^{(ta)} or in group work^{(ta)}. Pupils can explore aspects of mathematical thinking^{(ta)} particularly with relation to probability.
 
QR codes  QR codes with Magna Science Adventure Centre in Rotherham  
A DEFT case study with Winterhill High School, Rotherham This cross curricula^{(i)} case study focusses on Digital Literacy, in particular using Eskills^{(topic)} to: support English skills as pupils are writing for a specific audience (exhibition visitors), improve research skills through the process of creating OERs and to gain a better understanding of the use of QR codes for marketing and educational purposes.
One of the lesson ideas from the case study is available as a separate resource at Using QR Codes to Link to Pupil Created Information  
QR codes  Using QR Codes to Link to Pupil Created Information  
Children creating digital resources for use at Magna This series of lessons provided opportunity for active learning^{(ta)} though the visit to the Science Centre. It enabled the development of Eskills^{(topic)} through the creation of the media and the use of QR codes. It encouraged collaboration^{(ta)} between students, teachers from different subjects, and between the school and the wider community. It also provided a
crosscurricular^{(subject)} opportunity for the development of language^{(ta)}. Esafety^{(topic)} was developed through discussion with the students about ensuring that their work was appropriate for a wider audience. It also provided opportunities for whole class^{(ta)} and whole school collaboration^{(ta)} on a project where they were able to share practice^{(ta)} and examples of their work with others.  
Reading skills  Reading and discussing popular science articles  
Read. Get the world's view and see how science works for real The resource relates to the importance of:
It can be delivered through a combination of homework^{(ta)} (perhaps to find an interesting article), group work^{(ta)} to explore various articles (perhaps in a carousel), and/or use of ICT^{(i)} including PowerPoint files to encourage students to present an area they are interested in.  
Simultaneous Equations  Love Food, Hate Waste  Simultaneous Equations  
Using real world data to explore simultaneous equations Using a source that was not intended by its creators as a mathematical resource, pupils are introduced to informal ways of solving simultaneous equations.
The lesson starts with an intriguing ‘hook’, pupils are able to use reasoning^{(ta)} skills to find an answer to the problem and can then, later, formalise this in an algebraic context, using their informal work to support the transition to mathematical thinking^{(ta)}. whole class^{(ta)} work supports this inquiry^{(ta)} into the data provided. Using a resource not targeted at mathematics specifically encourages pupils to think about maths outside of the classroom.  
Standard Index Form  An Introduction to the Standard Index Form  
Working out the rules according to which a calculator displays large numbers The Standard Index Form is a key idea for mathematicians and scientists. The notion that we choose to write numbers in this way requires some explanation. So in this activity, pupils take part in an investigation^{(ta)} on how standard index form works. This is a higher order^{(ta)} problem solving context where students are encouraged to engage in mathematical thinking^{(ta)}. They may be involved in whole class^{(ta)} or small group work^{(ta)} discussion^{(ta)}, so they have a good opportunity to practice using mathematical language^{(ta)} and questioning^{(ta)}.
This means that students do not need to be able to explain their ideas in full: they can use the calculator's feedback to discover whether their ideas are correct or not. This is also an exciting way for pupils to realise an initial idea that fits the data may need to be extended when new data arises. This resource therefore aims to develop investigative skills, as well as introduce pupils to standard index form in a memorable way. The pupils can later use their knowledge of indices in discussion^{(ta)} and group talk^{(ta)} as they explain what is happening.  
Statistics  Cubic Equations and Their Roots  
To interactiviley explore and understand complex mathematics with GeoGebra This lesson features a ‘real life’ example for students to explore using visualisation^{(ta)} via GeoGebra. The focus on ‘real life’ increases student motivation.
The activity engages pupils in group talk^{(ta)}, mathematical thinking^{(ta)} and vocabulary^{(ta)}. This open ended^{(ta)} task encourages higher order^{(ta)} thinking, and encourages whole class^{(ta)} discussion^{(ta)}/questioning^{(ta)} and inquiry^{(ta)} projects.  
VLE  Using a VLE in the Classroom  
Using a VLE to support the teaching of French This activity uses a VLE to help pupils develop their language^{(ta)} and vocabulary^{(ta)} skills using games^{(tool)} and a range of teacherproduced digital media. These resources were also available to the pupils out of school to support them with their homework^{(ta)}, thus equipping pupils with more independent study skills^{(topic)}. The teacher also used the VLE to support their own classroom management^{(ta)}, using data from the VLE to record which tasks the pupils has worked on.
 
Video  Making Movies in the Classroom  
Using Movies to develop communication and literacy skills This activity is a crosscurricular^{(subject)} activity, involving a collaborative^{(ta)} approach, giving children to opportunity to engage in group work^{(ta)} whilst making digital media in the form of films. The activity furthers eskills^{(topic)} and esafety^{(topic)}. The topic of esafety^{(topic)} provided a great stimulus for the video^{(tool)}. Equally, however, this approach could be applied to any topic or subject in school. The use of video also encourage active learning^{(ta)} as the portability of video recording equipment allows it to be used outside the classroom in a range of contexts.
