Key Understanding in Mathematics Learning: Paper 1 Overview
This review, published by the Nuffield Foundation, presents a synthesis of research on mathematics learning by children from the age of five to the age of sixteen years and identifies the issues that are fundamental to understanding children’s mathematics learning. The report concentrates on three main questions regarding key…
Everyday Mathematics
Planning a Kitchen: SMILE card 1310 is a booklet which requires students to design a kitchen. The first task is to calculate the cost of buying the constituent parts of a kitchen. Students have to measure furniture in their own kitchen and draw a scale diagram. Students are given scale plan drawings of furniture they can use in the…
Imaginings
Imaginings: SMILE card 2112 is a collection of multi-levelled activities to develop mental imagery skills. The activities are grouped together into seven topics; starter, 2D, folds, creases and cuts, cubes, 3D, rotations and bits and pieces. The activities provide an excellent opportunity to use mathematical language. The tasks vary…
The Highway Code
The Highway Code: SMILE card 1314 is a booklet of activities using the signs found in the Highway Code as a context. The booklet begins with a page of road signs. The first task asks students to categorise the signs by placing then into a two way table based upon their shape and their colour. The second activity requires students…
Hexaflexagons
Hexaflexagons: SMILE card 0828 is a booklet giving detailed instructions on how to make a hexaflexagon. The resource includes photographs showing how to flex the hexaflexagon. There are instructions on how to colour the hexaflexagon and how to make a record of all the flexes. The resource concludes by showing a variety of alternative…
Spirals
Archimedes’ Spirals: SMILE card 1998 is a booklet of activities beginning by explaining how to draw Archimedes’ spirals using the ‘cotton reel method’. The second activity uses a ruler, protractor, string and tracing paper to work out which of the spirals given is an Archimedes spiral. Polar graph paper is…
Reckonings
SMILE Card 2324 is a booklet containing six sections; counting activities, place value, addition and subtraction, multiplication and division, number puzzles and types of number. Counting activities gives details of a task explaining how to generate sequences and the game fizz-buzz. Place value has four activities. Number lines:…
Continuing Professional Development for Teacher of Mathematics
Provided by the Advisory Committee on Mathematics Education (ACME), this resource was written in 2002. It includes recommendations on the steps to be taken, at that time, to raise the quality of mathematical provision in schools. Concerns regarding the poor uptake of students continuing to study mathematics at Post 16, the reduced…
Lorenz Cipher Machine
The development of techniques used by code-breakers at Bletchley Park Breaking during World War II is the focus of this resource, from the Centre for Innovations in Mathematics Teaching. New branches of statistical analysis and the development of the electronic computer emerged from this work and here students learn how one of the…
EAN Bar Codes
Bar codes are used extensively and this resource, from the Centre for Innovation in Mathematics Teaching, enables students to explore how they are structured. The activities are designed to prompt class discussion and mathematical thinking as students learn how to check that a code is valid and develop their own examples. European…
Braille
Braille is a system of dots which enables blind people to read and this resource, from the Centre for Innovation in Mathematics Teaching, provides the opportunity for students to explore the patterns used in this code. The activities are designed to prompt class discussion and mathematical thinking, while engaging students in decoding…
Penalty Shoot Out
Simulation of penalty shoot-outs is the focus of this resource, from the Centre for Innovation in Mathematical Teaching. Students use random numbers to decide the probability of a team scoring a goal, as well as investigating the average number of kicks and the most likely result. The tasks are designed to prompt class discussion…
National Lottery
The Centre for Innovation in Mathematics Teaching provide this resource which uses the National Lottery to promote class discussion and mathematical thinking. Students explore how the lottery works and investigate the probability of winning, as well as considering a variety of different investment opportunities. The teachers'…
Physical Fitness
Testing physical fitness is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. Students are provided with sample data, which they apply to the Gallagher and Brouha Test to calculate the fitness index and determine appropriate grades. The resource is designed to prompt class discussion and mathematical…
Reading Age Formula
Formulae is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. Students will be familiar with the term 'reading age' and here they apply different formulae to a selection of text samples, before comparing and considering the accuracy of the results obtained. Substitution into formulae…
Fruit Machines
Probability is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. A fruit machine is used to provide a practical situation which allows students the opportunity to explore the likelihood of obtaining a winning line, while the work is structured to prompt class discussion and mathematical thinking. Frequency…
Easter Date
Easter Day varies from year to year and in this resource, from the Centre for Innovation in Mathematics Teaching, students encounter the algorithm used to establish when it will occur. A series of tasks, designed to prompt class discussion and mathematical thinking, lead students to predict when Easter Day will fall. This work…
Global Warming
Global warming is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. Students are provided with data relating to average temperature rises over a 110 year period which are used to prompt class discussion and mathematical thinking. Graphical representation is a key element of this topic, which could…
World Championship for Test Cricket
International cricket is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. Data relating to 2006 is used to demonstrate how the ICC Test Championship Table is constructed and students are guided through a series of activities that have been designed to prompt discussion and develop mathematical thinking. This…
Fair Trade
The relationship between third world countries and the developed world is demonstrated in this resource, from the Centre for Innovation in Teaching Mathematics. Students work in groups to make and sell shapes, which are bought by the class teacher who performs the dual roles of Banker and United Nations. Market forces are applied…
Semaphore
The Centre for Innovation in Teaching Mathematics provide this resource which features the semaphore system of messaging, developed by the Chappe brothers in France in the late 18th century. The activities are designed to prompt discussion and mathematical thinking while students learn to interpret and code messages. A detailed…
Rankings in Sport
How performance is ranked in sport is the focus of this resource from the Centre for Innovation in Mathematics Teaching. Ranking plays a vital role in many sports, providing evidence for sponsors that a particular player, or team, is worth investment. Specific examples from cricket are provided and students learn the difference between…
Earthquakes
The application of logarithms is the focus of this resource from the Centre for Innovation in Mathematics Teaching. The magnitude of an earthquake and its measurement on the Richter Scale is used to develop an understanding of logarithms. Students investigate details of events and learn that an earthquake of 4.7 is actually five…
Darts
The mathematics generated by a dart board is the focus of this resource, from the Centre for Innovation in Mathematics teaching. The apparent randomness of the sector placement on a standard dart board is explained and students explore the possible scores that can be achieved with a selection of darts. Establishing all the possible…
Genetic Fingerprinting
The mathematics behind genetic fingerprinting is explored in this resource, from the Centre for Innovation in Mathematics Teaching. Sketches show, in simplified form, how genetic fingerprinting can be applied to establish paternity and students calculate the probabilities of matching bands from samples. This resource is highly…
Popular Baby Names
Trends in the popularity of names is the focus of this resource, from the Centre for Innovation in Mathematics Teaching, which illustrates the concepts and strategies for interpreting data. Because there is no one explanation for the change of popularity of names this resource raises one of the fundamental issues in applying mathematics,…
Old New Year
Discovering the day of the week upon which a particular date occurred is the focus of this resource, from the Centre for Innovation in Mathematical Teaching. The Julian and Gregorian calendars, amongst others, are discussed and students are provided with an algorithm, which they use to verify the day of their own birth. This is then…
Heptathlon
The scoring system used for the heptathlon event is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. Students are provided with athlete's individual results from the seven events that make up the heptathlon. They then apply relevant formulae to the data and produce tables, or spreadsheets,…
Happy Planet Index
The balance between economic success and the environment is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. It provides an example of how mathematics can help to make people more aware of important issues. Students apply statistical measures to interpret a variety of data which is then summarised…
Carbon Footprint
Mathematical modelling is the focus of this resource, from the Centre for Innovation in Mathematics Teaching. Students explore the mathematics behind carbon emission measurement and the concept of carbon footprints. Basic calculations for the travel component of a carbon footprint are demonstrated here, but many other similar calculations…
Teaching and Learning - Algebra and Geometry
The Royal Society provide these resources which offer an insight into reviews, which took place in the mid 1990s and early 2000s, to investigate the teaching and learning of algebra and geometry. Both reviews took place at a time of considerable discussion over developments in mathematics, both at home and at international level. Teaching…
Researching Effective CPD in Mathematics Education
The Researching Effective CPD in Mathematics Education (RECME) project was set up under the umbrella of the National Centre for Excellence in the Teaching of Mathematics (NCETM) in England, who provide these resources. The project's aim was to provide advice, guidance and recommendations to be used by NCETM to inform future…
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