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Counter Ideas
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Thinking 3D
How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?
Calendar Activities
Don't get rid of your old calendars! You can get a lot more mathematical mileage out of them before they are thrown away. These activities, using cut up dates from the calendar, provide numbers to practise skills that may be in need of review after a holiday break.
Thinking about Different Ways of Thinking
This article, the first in a series, discusses mathematical-logical intelligence as described by Howard Gardner.
Weigh to Go
This article for teachers recounts the history of measurement, encouraging it to be used as a spring board for cross-curricular study.
Dominant Intelligences
The second in a series, this article looks at the possible opportunities for children who operate from different intelligences to be involved in "typical" maths problems.
Coordinating Classroom Coordinates
This article describes a practical approach to enhance the teaching and learning of coordinates.
Logic, and How it Should Influence Our Teaching
Providing opportunities for children to participate in group narrative in our classrooms is vital. Their contrasting views lead to a high level of revision and improvement, and through this process they become more aware of "thinking". This article looks at the way we handle these narratives.
Generating Number Patterns: an Email Conversation Amongst
This article for teachers describes the exchanges on an email talk list about ideas for an investigation which has the sum of the squares as its solution.
Ratio or Proportion?
An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.
Integrating Rich Tasks - Activity 1.3
This professional development activity encourages you to investigate what is meant by higher-order thinking skills.
Integrating Rich Tasks - Activity 1.5
This professional development activity encourages you to investigate what pupils are doing when they problem solving.
Integrating Rich Tasks - Activity 2.1
This professional development activity looks at what teachers can do to support learners engaging with rich tasks
Integrating Rich Tasks - Activity 3
The aim of this professional development activity is to successfully integrate some rich tasks into your curriculum planning.
A Story about Absolutely Nothing
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
Educating the Gifted Mathematician
What is the classroom culture that you foster to support able learners?
Cultivating Creativity
Creativity in the mathematics classroom is not just about what pupils do but also what we do as teachers. If we are thinking creatively about the mathematical experiences we offer our pupils we can open up opportunities for them to be creative. Jennifer Piggott shares some of her thoughts on creative teaching, and how it can encourage creative learners.
Integrating Rich Tasks - Introduction
This is the introductory page of a set of resources designed to support teachers in using rich tasks in their daily mathematics lesson.
Integrating Rich Tasks - Activity 1.1
This is activity 1.1 in the series of activities designed to support professional development through integrating rich tasks. This activity looks specifically at what makes an activity "rich".
Integrating Rich Tasks - Activity 1.2
These two tasks are designed to support professional development on integrating rich tasks. You are asked to think about what problems that encourage Higher Order Thinking Skills look like.
Pattern Power
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
Closing the Learning and Teaching Gap
This article discusses the findings of the 1995 TIMMS study how to use this information to close the performance gap that exists between nations.
Dice, Routes and Pathways
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to think mathematically, especially geometrically.
Games Related to Nim
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
What Does it Say to You?
Written for teachers, this article discusses mathematical representations and takes, in the second part of the article, examples of reception children's own representations.
Dramatic Mathematics
This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.
Multiplication Series: Number Arrays
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Multiplication Series: Illustrating Number Properties with Arrays
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials, but it can also assist them in forming useful mental pictures to support memory and reasoning.
Problem Solving: Opening up Problems
All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have greater potential.
Using Questioning to Stimulate Mathematical Thinking
Good questioning techniques have long being regarded as a fundamental tool of effective teachers. This article for teachers looks at different categories of questions that can promote mathematical thinking.
Using Questioning to Stimulate Mathematical Thinking: Addendum
In the process of working with some groups of teachers on using questions to promote mathematical thinking, the following table was developed. It provides examples of generic questions that can be used to guide children through a mathematical investigation, and at the same time prompt higher levels of thinking.
Number Sense Series: Developing Early Number Sense
This article for teachers suggests teaching strategies and resources that can help to develop children's number sense.
Number Sense Series: A Sense of 'ten' and Place Value
Once a basic number sense has developed for numbers up to ten, a strong 'sense of ten' needs to be developed as a foundation for both place value and mental calculations.
The Development of Spatial and Geometric Thinking: the Early Years
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the work of Piaget and Inhelder.
The Development of Spatial and Geometric Thinking: Co-ordinating Space in Drawings
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
The Development of Spatial and Geometric Thinking: the Importance of Instruction.
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Learning Mathematics Through Games Series: 4. from Strategy Games
Basic strategy games are particularly suitable as starting points for investigations. Players instinctively try to discover a winning strategy, and usually the best way to do this is to analyse the outcomes of series of 'moves'. With a little encouragement from the teacher, a mathematical investigation is born.
Co-operative Problem Solving: Pieces of the Puzzle Approach
The content of this article is largely drawn from an Australian publication by Peter Gould that has been a source of many successful mathematics lessons for both children and student-teachers. It presents a style of problem-solving activity that has the potential to benefit ALL children in a class, both mathematically and socially, and is readily adaptable to most topics in mathematics curricula.
Working with Dinosaurs
This article for teachers suggests ways in which dinosaurs can be a great context for discussing measurement.
Mechanics in the Primary Years
This article for teachers sets out some ideas for introducing children to some of the concepts at the root of mechanics.
Path of Discovery Series: 1. Uncertain Beginnings
Marion Bond suggests that we try to imagine mathematical knowledge as a broad crazy paving rather than a path of stepping stones. There is no one right place to start and there is no one right route to follow. This article looks at ways of offering children mathematical experiences throughout the day, not just in maths lessons.
Path of Discovery Series: 2. First Steps
This article takes a closer look at some of the toys and games that can enhance a child's mathematical learning.
Path of Discovery Series 3: I Do and I Understand
Marion Bond recommends that children should be allowed to use 'apparatus', so that they can physically handle the numbers involved in their calculations, for longer, or across a wider ability band, than is currently the norm.
Money Problems?
Marion Bond investigates the skills needed in order for children to understand money.
Shaping up with Tesselations
There is so much scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over.
Primary Proof?
Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.
Outside the Box
This article explores the links between maths, art and history, and suggests investigations that are enjoyable as well as challenging.
What’s Inside/outside/under the Box?
This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.
Enriching Data Handling
This article for teachers looks at some suggestions taken from the NRICH website that offer a broad view of data and ask some more probing questions about it.
Natural Born Mathematicians
Helen Joyce interviews the neuropsychologist Brian Butterworth whose research has shown that we are all born with a "built-in" sense of cardinal number.
Difficulties with Division
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Using Games in the Classroom
Gillian Hatch analyses what goes on when mathematical games are used as a pedagogic device.
Pupils' Recording or Pupils Recording
Liz Pumfrey has chosen this article, which is written for teachers. It looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!
Children's Mathematical Writing
Bernard Bagnall discusses the importance of valuing young children's mathematical representations in this article for teachers.
Digital Roots
In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.
Stacks of Maths!
In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.
Exploration Versus Calculation
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
Numbers Numbers Everywhere!
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Meaningful Statistics
This article for teachers describes an activity which encourages meaningful data collection, display and interpretation.
Teaching Fractions with Understanding: Part-whole Concept
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
Maths Trails
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Count the Beat
This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?
I'm Stuck!
Being stuck is usually thought of as being a negative state of affairs. We want our pupils to succeed, not to struggle. Or do we? This article discusses why being stuck can be fruitful.
Interacting with the Geometry of the Circle
Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.
A Brief History of Time Measurement
Noticing the regular movement of the Sun and the stars has led to a desire to measure time. This article for teachers and learners looks at the history of man's need to measure things.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
