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NRICH Transformations
This list supports teaching of transformations in secondary mathematics. It provides investigations, problems and games from NRICH as well as classroom activities on the STEM Learning website that compliment them.
Here are a selection of activities selected by the NRICH team.
- Shady Symmetry This problem looks at how many symmetrical patterns can be created by shading in either four squares on a 3 by 3 square grid or two triangles on a 3 by 3 isometric grid. Students are then invited to alter the shading and investigate further the symmetrical patterns formed.
- Attractive Tablecloths This problem considers table cloths made using different colours on a 5 by 5 grid. Students consider different rules concerning line symmetry and rotational symmetry. The investigation is extended to symmetry in an n by n tablecloth.
- Growing Rectangles The problem investigates possible lengths and widths for rectangles of a given area. Students consider what happens as various shapes are enlarged. As extension is made to cuboid.
These are just a few of the activities on transformations that you can find on the NRICH curriculum pages .
The activities below, taken from the STEM Learning website, complement the NRICH activities above.
Working with Photos
Quality Assured Category: Mathematics Publisher: cre8ate maths
This activity from Cre8ate maths the enlargements element of the NRICH activity 'Growing Rectangles'.
The activity consists of four sets of photographs and the task is to identify which have been enlarged from an original. Students must justify their decisions. The final two sets provide lots of room for discussion.
Transforming Shapes SS7
Quality Assured Category: Mathematics Publisher: Department for Education
This DfE Standards Unit covers the majority of topics covered by the NRICH activities on transformations. The activities are an ideal introduction to the NRICH activities.
Topics covered include translation, rotation, reflection and combinations of these transformations. The unit does presume some prior familiarity with transformations and equations of lines of reflection such as y = 3, x = 4, y = x and y = - x
Quality Assured Category: Mathematics Publisher: SMILE
This SMILE resource supports the teaching of the NRICH problems 'Shady Symmetry' and 'Attractive Tablecloths'.
There are two packs of games, investigations and worksheets that cover reflection in one and two lines of symmetry, Rangoli patterns, combined reflections and symmetry of 3-D solids.
Reflection and Translation
Quality Assured Category: Mathematics Publisher: The Virtual Textbook
This 'Virtual Textbook' resource supports the NRICH activities 'Shady Symmetry' and 'Attractive Tablecloths'.
The activities include identifying lines of symmetry in 2D shapes and creating kaleidoscope patterns.
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The Problem-Solving Schools' Charter
The NRICH team has developed this Charter to help you reflect on how you currently promote mathematical problem-solving in your school
Values and ethos
We have a shared belief that:
- Mathematical ability is not fixed: everyone can learn and make progress
- Problem-solving often involves taking wrong turns and making mistakes: every learner has the right to struggle and the right to enjoy success
- Everyone should have the opportunity to develop the skills and attitudes necessary to become confident problem-solvers
- Problem-solving can motivate learners to learn new mathematics, apply previous learning and make mathematical connections
Leadership and professional development
In our setting:
- Our staff promote positive attitudes towards problem-solving
- Time is set aside to discuss problem-solving in our meetings
- Our displays, newsletters, website, and social media content celebrate problem-solving for all
- Our monitoring system ensures that priority is given to problem-solving and mathematical thinking
- We engage with printed, online and face-to-face professional development opportunities offered by subject organisations
Curriculum, pedagogy and assessment
We are committed to:
- Regularly embedding non-standard problem-solving opportunities in our maths curriculum for all
- Ensuring that problems, and classroom support, offer opportunities for all to experience both struggle and success
- Allocating time to developing key problem-solving skills and positive attitudes
- Including non-standard problems in our internal/formative assessments
- Liaising with other subjects so that meaningful cross-curricular links can be made
Classroom culture
- Create a safe environment in which learners explore, take risks, and appreciate the value of learning from their mistakes
- Celebrate multiple approaches to solving problems and discuss the merits of the different strategies offered
- Provide frequent opportunities for individual and collaborative problem-solving, where learners are given both thinking time, and opportunities to share ideas and insights
- Celebrate the mathematical thinking of every learner
Problem-solving beyond the classroom/school
We encourage:
- Learners to engage with school Maths Club(s) and high quality maths books, ideally stocked by the school library
- Learners to take advantage of printed, online and off-site mathematical enrichment opportunities
- Parents and carers to engage with problem-solving through family homeworks and in-school events, while recognising that not every adult has had a positive experience of maths
- Our learners to appreciate, and learn more about, the achievements of a diverse range of mathematicians
Become a Problem-Solving School
Symmetry: Rich Tasks
You cannot beat a good rich task! For me, a rich task is one that both stimulates and challenges students of all ages and abilities. Here is a selection of some of my favourites.
Median Rich Tasks and Purposeful Practise keyboard_arrow_up Back to Top
There are no words to express how much I love Don Steward and his amazing resources on his Median Blog . They allow for purposeful practise, to enable students to gain fluency in key skills. But they also have more than a sprinkling of richness, that leads students merrily along the path towards hypotheses and generalisations. Amazing.
NRICH keyboard_arrow_up Back to Top
NRICH is simply one of the best websites for rich maths problems in the whole wide world.
Other Rich Tasks keyboard_arrow_up Back to Top
A selection of some of my favourite rich tasks, including – I must confess – some of my own. For my complete collection, including my thoughts on what makes a good rich task, please visit the Rich Tasks page .
IMAGES
VIDEO
COMMENTS
Shady Symmetry downloadable slides - images. Printable isometric grid template. Charlie created a symmetrical pattern by shading in four squares on a 3 by 3 square grid: Alison created a symmetrical pattern by shading in two triangles on a 3 by 3 isometric grid: Choose whether you would like to work on square grids or isometric grids.
Symmetry Challenge printable sheet. In this activity, we are going to shade the squares of this grid with one colour to make different designs. There are a few rules that our designs need to follow: Whole squares have to be shaded, rather than parts of squares. Each design must have at least one line of symmetry.
Developing excellence in problem solving with young learners Becoming confident and competent as a problem solver is a complex process that requires a range of skills and experience. In this article, Jennie suggests that we can support this process in three principal ways.
Shading 1 little triangle: No matter which you shade there is exactly one line of reflective symmetry. That gives 9 patterns, or only 3 according to Damien, because any other can be rotated to look like one of these: 9 or 3 ways with 1 triangle shaded. Shading 2 little triangles: To get a line of symmetry you need to choose carefully.
Symmetry Challenge printable sheet In this activity, we are going to shade the squares of this grid with one colour to make different designs. There are a few rules that our designs need to follow: Whole squares have to be shaded, rather than parts of squares. Each design must have at least one line of symmetry.
The problem requires learners to recognise and visualise the transformation of a 2D shape, and invites them to work systematically in a spatial environment. It is a problem that is accessible to most pupils even if they need support in organising and presenting their ideas and ensuring the completeness of their solution.
We have found 35 NRICH Mathematical resources connected to Symmetry, you may find related items under Transformations and constructions Resources tagged with: Symmetry ... Problem Primary curriculum Secondary curriculum. Attractive Rotations.
Caesium Chloride assumes a 'body centred cubic structure' in which each caesium ion is surrounded by 8 chlorine ions located at the vertices of a cube, and vice-versa. Mathematically, we can choose cartesian coordinates such that the ions lie on the integer lattice comprising the points ( l, m, n) with l, m, n integers.
A selection of rich tasks ideal for developing subject content knowledge, mathematical thinking, and problem-solving skills. The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.
We have found 35 NRICH Mathematical resources connected to Symmetry, you may find related items under Transformations and constructions
Quality Assured Category: Mathematics Publisher: SMILE. This SMILE resource supports the teaching of the NRICH problems 'Shady Symmetry' and 'Attractive Tablecloths'. There are two packs of games, investigations and worksheets that cover reflection in one and two lines of symmetry, Rangoli patterns, combined reflections and symmetry of 3-D solids.
The Problem-solving ClassroomThis article forms part of our Problem-solving Classroom Feature, exploring how to create a space in which mathematical. problem solving can flourish. At NRICH, we believe that there are. ing a productive dispositionDe. loping independent learners.This article will address each of these in turn, drawing attention to ...
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?
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.
Our NRICH programme has launched a new initiative to help schools prioritise problem-solving in maths. The NRICH Problem-Solving Schools programme will offer free resources, advice and teacher professional development training.
Mathias is given a grid of twelve small squares. He is asked to shade exactly 4 of the squares so that the grid has 2 lines of reflection symmetry. How many different grids could he produce? This problem is taken from the UKMT Mathematical Challenges. The NRICH Project aims to enrich the mathematical experiences of all learners.
NRICH keyboard_arrow_up NRICH is simply one of the best websites for rich maths problems in the whole wide world.
Advanced Problem Solving Module 1. Working through this module will help you to consolidate your existing knowledge before extending your thinking. For more details about the Advanced Problem Solving programme, READ THIS. This module is intended to improve your problem-solving skills. What does a good mathematical problem solver do when ...
Symmetry, Substitutions and Surprises. In this feature you will be challenged to exploit the symmetries of a range of equations to derive elegant and efficient solutions to problems which, at first sight, might seem very difficult.
Problem-solving Schools Learn about our exciting new intiative to embed non-routine problem-solving opportunities in your maths curriculum
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.