Algebra
Students begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or two operations. They use brackets and apply algebra to real word problems.
See also the "Number Patterns", "Negative Numbers" and "Simultaneous Equations" Starters.
Angles
Students should understand that angles represent an amount of turning and be able to estimate the size of angle. When constructing models and drawing students should be able to measure and draw angles to the nearest degree and use language associated with angles. They should know the angle sum of a polygons and that of angles at a point and on a straight line.
Approximation
The objective of rounding is often to get a number that is easier to use, at the cost of making it less precise. This approximation is very important in dealing with answers to mathematical problems and making them relevant to the real world. Rounding to a given number of decimal places or significant figures is required of students.
See also the "Rounding" and "Estimating" Starters.
Area
See also the topic called Mensuration. Students should not only be able to apply area formulae but they should also have a good understanding of what area means. This can be achieved by beginning the study of area with plenty of practical examples. The Pin Board provides an open-ended interactive experimental activity to secure a good fundamental understanding of area.
Arithmetic
The ability to perform mathematical calculations is still very important and supports the understanding of Mathematics. Mathematicians still consider mastery of the manual algorithms to be a necessary foundation for the study of algebra and computer science.
See also the "Mental Methods" Starters.
The English National Curriculum states that at Level 5 "Pupils use their understanding of place value to multiply and divide whole numbers and decimals. They order, add and subtract negative numbers in context. They use all four operations
with decimals to two places. They solve simple problems involving ratio and direct proportion. They calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate."
Averages
Students should understand and use the mean of discrete data. They should be able to compare two simple distributions using the range and one of the mode, median or mean.
See also the topics called Data Handling and Statistics.
Bearings
A bearing is a description of a direction. It is the number of degrees measured in a clockwise direction from north as seen from above. This study of spacial concepts is an important aspect of geometry.
Calculator
The English National Curriculul states that pupils should calculate accurately, selecting mental methods or calculating devices as appropriate. It then goes on to say that it is appropriate to use a calculator when performing a calculation without a calculator will take an inappropriate amount of time.
Transum has provided activities wich help pupils practise calculator skills and also use a calculator to investigate number patterns, properties and other aspects of Mathematics.
Circles
This is all to do with pi and why it is such an important number. From finding the circumference and area of circles to problem solving and investigation.
Combinations
"A combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange." - Wikipedia
Coordinates
It is important that students become proficient at understanding coordinates at a basic level before using them in their study of graphs.
Creativity
We often hear the term creativity used in terms of art, music or drama. This higher order thinking skill has a big part to play in Mathematics. We endeavour to develop creative problem solving strategies and investigative techniques in our students by providing them with motivating open ended situations to think about.
Cube Root
Just how do find the cube root of a number? By trial and improvement, iterative calculations or by learning to use a calculator efficiently
Data Handling
See also the topics called Statistics and Averages.
The English National Curriculum states that at level 6 "Pupils collect and record continuous data, choosing appropriate equal class intervals over a sensible range to create frequency tables. They construct and interpret frequency diagrams. They construct pie charts. They draw conclusions from scatter diagrams, and have a basic understanding of correlation. When dealing with a combination of two experiments, they identify all the outcomes.
When solving problems, they use their knowledge that the total probability of all the mutually exclusive outcomes of an experiment is 1."
Decimals
The English National Curriculum states that at level 5 "Pupils use their understanding of place value to multiply and divide whole numbers and decimals. They order, add and subtract negative numbers in context. They use all four operations with decimals to two places."
Enlargements
When areas and volumes are enlarged the results are far from intuitive. Doubling the dimensions of a cuboid produces a similar shape with eight times the volume!
Estimating
The ability to estimate values is an often overlooked part of Mathematics. Estimating lengths, weights, time, angles and solutions to problems should be practised regularly. Studends should make sensible estimates of a range of measures in relation to everyday situations.
Factors
A factor is a whole number that divides exactly into another whole number. We say the first number is a factor of the second number. Prime numbers only have two factors, one and themselves.
Fractions
A fraction is a part of a number. Fractions are either vulgar or decimal. Vulgar fractions can be proper, improper or mixed. Equivalent fractions have the same value.
Fun
If you are looking for fun and games for the end of term the best place to start is the Fun Maths page where you'll find lots of enjoyable activities all with a mathematical theme.We also have Maths Games and a number of Strategy Games which, while not being explicitly mathematical, involve similar thought processes to solving mathematical problems. They are ideal for two people sharing one computer.
Game
Make drill and practice fun by turning it into a game! Playing against a friend adds an extra incentive to do well. The memory game (Kim's game) can be used for general revision as it involves a number of different mathematical topics.
See also Fun Maths
We also have a number of Strategy Games which, while not being explicitly mathematical, involve similar thought processes to solving mathematical problems. They are ideal for two people sharing one computer.
Geometry
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early 6th Century BC.
See also the topics of Angles, Area, Bearings, Circles, Enlargements, Mensuration, Pythagoras, Shape, Shape (3D), Symmetry, Transformations and Trigonometry.
Graphs
This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts.
Indices
Where do lots if fish live? Indices (in the seas! ) This topic involves the use of the index, power or exponent. The concept is easily misunderstood and a surprisingly large number of students will evaluate 62 as 12 and not 36.
Investigations
An investigation, as defined by a dictionary, is a searching enquiry for ascertaining facts. In mathematics this enquiry is a journey into the unknown without a map. Students should enjoy choosing the direction they will take in exploring a situation which has been described in an open-ended way. They will also develop pride in describing their findings to their classmates and may even stumble across findings that will suprise their teacher.
Take a look at our main page of investigation starting points which can be the seed of creative and exciting course work.
LCM
LCM stands for lowest common multiple. It is the technique used to find the denominator when adding two fractions together. It also describes the points when two periodic repetitions coincide.
Live Data
One of the big differences between Maths from a textbook and Maths from the web is the possibility of using live data. This possibility gives problem solving real context and allows investigating statistical connections to be far more meaningful.
Logic
Wouldn't it be nice to live in a world where everything obeyed the rules and operated as predicted. This area of Mathematics explores the fundamentals of logical thinking and its application in problem solving.
Memory
The origins of Kim's Game are embedded in a time when memory was a fundamental life skill. Try these activities which are aimed in encouraging students to exercise their memory muscles and to develop strategies to improve their skills.
Mensuration
Mensuration is the branch of Mathematics dealing with measurement of angles, length, area, and volume. It is linked closely to the topic of Estimation and related to the topics of Angles, Shape and Shave (3D).
It is essential for students to have an understanding of the units used to measure which include both the more common metric units and the Imperial units still in common usage. We have found a good teaching strategy is to ask each of the students to "Bring to the next Maths lesson some visual aid which will help the rest of the class remember the size of a unit of measurement". Here are some Printable Instructions. This activity provides an association with a unit, a visual aid and another person which is a great memory enhancer.
Mental Methods
Though using pencil and paper are as useful as having up-to-date technology skills. There is no substitute for strategic mental methods for working out calculations and solving problems. The activities in this topic are designed to improve students' abilities to use their brains.
Mixed
A healthy mashup of activities and ideas to use and apply mathematical knowledge in a variety of situations.
Money
For many students the ability they have to understand financial transactions is a skill they thank their mathematics teacher for. This is a real, practical application of mathematics to the real world.
Multiple Intelligences
See also Thinking Skills.
The theory of multiple intelligences was proposed by Howard Gardner in 1983 as a model of intelligence that differentiates intelligence into various specific modalities rather than seeing it as dominated by a single general ability.
Gardner argues that there is a wide range of cognitive abilities, and that there are only very weak correlations among them. For example, the theory predicts that a child who learns to multiply easily is not necessarily generally more intelligent than a child who has more difficulty on this task. The child who takes more time to master simple multiplication:
1) may best learn to multiply through a different approach,
2) may excel in a field outside of mathematics, or
3) may even be looking at and understanding the multiplication process at a fundamentally deeper level, or perhaps as an entirely different process.
Here are some mathematical activities that call upon a student's multiple intelligences.
Negative Numbers
A negative number is a real number that is less than zero. Such numbers are often used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are also used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature.
here are some activities designed to strengthen a student's understanding of negative numbers.
Number Patterns
When investigating prime numbers take time to listen to the prologue of a 'This American Life' podcast. Host Ira Glass talks with science writer Paul Hoffman about a mathematician named Frank Nelson Cole, who demonstrated a groundbreaking idea at a conference in 1903.
Percentages
A useful and common way to express a fraction of a quantity. The word is derived from the Latin per centum meaning “by the hundred”. Although percentages are usually used to express numbers between zero and one, any ratio can be expressed as a percentage. For instance, 125% is 1.25 and −0.95% is −0.0095.
Place Value
Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations (such as Roman numerals) for its use of the same symbol for the different orders of magnitude (for example, the "ones place", "tens place", "hundreds place"). This greatly simplified arithmetic and led to the quick spread of the notation across the world.
Probability
We believe that even adults can in many cases have a poor intuition regarding the effects of probability. These activities are designed to help students calculate but also get a 'feeling' for the principles of probability.
Problem Solving
What good is being a master of calculation if you cannot apply your skills to problem solving? This topic provides lots of examples, activities and situations in which students can practise their problem solving skills.
Puzzles
Engaging and addictive, puzzles have been an irresistible lure for inquisitive minds throughout history. This topic introduces students to some interesting puzzles.
Pythagoras
Pythagoras was a Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He is most famous for his theorem connecting the lengths of the sides of right angled triangles.
Ratio
A ratio is a relationship between two numbers of the same kind. In layman's terms a ratio represents, simply, for every amount of one thing, how much there is of another thing.
This topic presents a number if different ways students can represent ratios and apply their meaning to problem solving situations.
Riddles
An old and respected way of describing mathematical situations, connections and puzzles.
Rounding
The objective of rounding is often to get a number that is easier to use, at the cost of making it less precise. This approximation is very important in dealing with answers to mathematical problems and making them relevant to the real world. Rounding to a given number of decimal places or significant figures is required of students.
See also the "Approximating" Starters.
Once the principles of rounding have been understood, a fun way to practise the skills is to play "Rounding Snap".
Sequences
A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces students to many of them.
Shape
This topic is aimed at the learners of basic geometry, which is the study of size, shape and position. More than other areas of Maths this topic helps students to learn about the definitions and properties of basic shapes.
Shape (3D)
A particular skill is required to be able to excel in this area of Mathematics. Spatial awareness is important for solving multi-step problems that arise in areas such as architecture, engineering, science, art, games, and everyday life. Children have varying abilities visualizing three dimensional relationships but these abilities can be developed through practical activities and working through mathematical problems. Breaking down three dimensional situations into smaller two dimensional parts in an important strategy for problem solving.
See also the "Shape" Starters.
Simultaneous Equations
This topic covers simultaneous equations with two different variables. The starters pose real world problems which can be solved using the techniques taught at school or my other intuitive means.
Statistics
See also the topics called Data Handling and Averages.
Symmetry
This topic covers line symmetry and rotational symmetry. The innate appeal of symmetry can be found in our reactions to finding symmetry in natural objects, such as precisely formed crystals or seashells.
Tables
Here's a plan for learning a new times table in only five days!
Time
This topic provides opportunities for pupils to practise the calculations that are required in time based problems. After mastering the decimal system manipulating units of time can prove to be very difficult for many.
Transformations
This topic includes reflection, translation, rotations and enlargements.
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Here's a Trigonometry Wordsearch
Vocabulary
Mathematics is a language but we also need to understand the language that describes mathematical concepts and techniques.
Xmas
Christmas activities make those December Maths lessons interesting, exciting and relevant. If students have access to computers there are some online activities to keep them engaged such as Christmas Ornaments and Christmas Light Up.
As a whole class why not finish of the term with a fun game of Two Dice Bingo?
