Chocolate
This NRICH maths problem is an excellent problem for helping youngsters to develop their concepts of fractions It's not so much to do with arithmetical manipulation of fractions but more to do with youngsters exploring and developing their ideas of fractions. It involves visualising and calculating mentally. Reasoning skills…
5/5- Publication year: 2000 - 2009
- Open-ended task
Make 37
This NRICH maths investigation offers learners the chance to apply basic number properties and operations, and will challenge the idea of mathematical problems having one right answer. This activity is an opportunity to encourage children to generalise and, even at this level, they can be asked to prove these generalisations. They…
- 5/5
- Publication year: 2000 - 2009
- Open-ended task
Magic Vs
In this maths activity from NRICH children will have to place each of the numbers 1 to 5 in a V shape so that the two arms of the V have the same total. This problem gives opportunities for children to make conjectures, prove these conjectures and make generalisations. They will be practising addition and subtraction, and applying…
- 5/5
- Publication year: 2000 - 2009
- Open-ended task
Which Spinners?
This NRICH maths activity is intended for students who are already familiar with sample space diagrams. The interactive file offers an ideal context in which to consider the messy randomness of experimental results and the certainty of the long run results. Working backwards from the graphs should help students notice more features…
In a Box
This maths problem from NRICH offers opportunities to consider different methods of listing systematically in the context of probability. Students will have to play a game making decisions about its fairness. This problem can be used to introduce or revisit sample space diagrams, and with some students, tree diagrams.
Of All the Areas
This NRICH mathematical problem is about the areas of equilateral triangles. Students will need to measure the area different triangles but in triangles rather than squares. They will need to look for any emerging patterns which might lead to non-linear sequences that need explanation. They will need to use their visualising skills…
Cyclic Quadrilaterals
In this maths problem from NRICH, students will be working with cyclic quadrilaterals. A cyclic quadrilateral is a quadrilateral whose vertices lie on a circle. This maths problem from NRICH is in two parts. The first part consists of four similar challenges which provide building blocks to help you to solve the final challenge.…
Maths Filler
This NRICH maths problem explores the way the water level in a vessel changes when water is added at a constant rate. Students will have to work out volumes of containers, make generalisations about the cross-sectional areas and the volumes, they can then, through analysing the key features of a graph, figure out the shape of the…
Pair Products
This maths investigation from NRICH explores the properties of consecutive numbers under multiplication. For students who are working numerically, this is an excellent context for observing, conjecturing and thinking about proof. It can be a good introduction to the power of algebra. For students who are algebraically fluent,…
- 5/5
- Publication year: 2000 - 2009
- Activity sheet
Tilted Squares
This NRICH maths activity is an investigation on tilted squares. The aim is to be able to predict the area of any tilted square. In the context of calculating areas by 'boxing in' and/or dissection, this problem offers rich opportunities for systematic investigation which should lead to Pythagoras' Theorem.
- 4/5
- Publication year: 2000 - 2009
- Interactive resource
Plus Minus
In this NRICH maths activity a student has been looking at the difference of the squares of pairs of two-digit numbers. She has collected together some answers which she found quite surprising. This problem offers students a chance to discover the identity for the difference of two square numbers. They are expected to work as research…
What's Possible
This NRICH maths activity follows on from Plus Minus by asking students to find which numbers can be expressed as the difference of two square numbers. Many numbers can be expressed as the difference of two perfect squares. How many of the numbers from 1 to 20 can you express as the difference of two perfect squares? Following…
Catalyse That
This NRICH maths exercise is concerned with understanding rates of change, graphs and (possibly) calculus in a way which does not use the usual route of speed-time graphs. The question will need to be read carefully, as it involves the rates of change as used in chemistry. Learners will have to explain what is happening clearly.…