This mathematics investigation was designed for use by children of Year 6 - under the guidance and encouragement of a suitable mentor. It was not intended to be a 'fire and forget' worksheet, but rather a framework for discussion and exploration. The theme is using mathematics to guide (almost) real life decision-making. The focus is on using ratio and fractions to establish probability. Although the material is designed to be challenging but accessible to children working within the government's expectation for children at the end of Key Stage 2, it is possible that teachers of children in KS3 may find the resources useful.

This mathematics investigation (in the field of static mechanics) was designed for use by (very) able GCSE maths students or those just beginning an A level in maths or physics. I anticipate its use in helping to introduce the topic, or as formative assessment/revision. The investigation is a light-hearted look at using trigonometry and other basic mathematics to establish and solve equations describing the balanced forces on a body in equilibrium - in this case an ice core propped up carefully against an ice cliff. The intention is that enough explanation of the underlying physics is provided so that only a knowledge of the relevant mathematics is assumed. (The investigation will be continued and extended with more material when I have time to write it.)

This mathematics investigation was designed primarily for use by children of Year 6 - for exploring and understanding integer sequences. The material could alternatively be used for consolidation or assessment purposes. Most of the sequences are arithmetic (i.e. linear) but there are also more challenging ones such as squares, cubes, geometric progressions and good old Fibonacci’s sequence. There are sixteen sequences, and four levels of solution: Simply fill in the missing values in the sequence (least challenging). Find and express a rule which describes the sequence (more challenging). Find an algebraic expression to define a sequence value from the previous one. Find an algebraic expression to define a value from its position n in the sequence. Steps 3 and 4 provides the greatest challenge. Sometimes it is easier to determine one kind of expression than the other and so the challenge is increased considerably when both expressions are required for each sequence (i.e. steps 3 and 4). Although the material is designed to be challenging but accessible (with guidance) to children working within the government’s expectation for children at the end of Key Stage 2, it is possible that teachers of children in KS3 and potentially KS4 may find the resources useful. In addition, children of earlier KS2 years may be able to access and complete many of the sequences, even if a grasp of the more complex rules might currently elude them.

This mathematics investigation was designed for use by children of Year 6 - under the guidance and encouragement of a suitable mentor. It was not intended to be a ‘fire and forget’ worksheet, but rather a framework for discussion and exploration. The theme is using mathematics to guide real-life (well, almost) problem solving. The focus is on using the length and volume of an (arbitrarily shaped) prism to calculate its cross-sectional area - thus developing and consolidating an understanding of each and the relationship between them. The investigation also reinforces the need to maintain a consistent set of units when performing calculations: to this end, conversion between different metric units (e.g. litres to cubic centimetres and cubic metres) is required. Although the material is designed to be challenging but accessible (with guidance) to children working within the government’s expectation for children at the end of Key Stage 2, it is possible that teachers of children in KS3 may find the resources useful.

This mathematics investigation was designed for use by children of Year 6 - under the guidance and encouragement of a suitable mentor. It was not intended to be a ‘fire and forget’ worksheet, but rather a framework for discussion and exploration. The students are presented with a problem in which there are two mystery numbers to be found. Two clues are provided, namely the Sum of the two numbers and the Difference between them. Initially, the numbers given are sufficiently small so that a ‘straightforward’ and accessible strategy can be used to determine the solution. In the second part of the question, the sizes of the numbers are increased, which greatly increases the difficulty of the problem and suggests the need to discover alternative strategies. Some of these are provided in the teacher’s commentary. Although the material is designed to be challenging but accessible to children working within the government’s expectation for children at the end of Key Stage 2, it is possible that teachers of children in KS3 may find the resources useful.