Root Hunter
In this NRICH short problem, students try to find the location of the roots of some unusual functions by finding where they change sign.
M, M and M
This maths problem from NRICH offers the students an opportunity to consolidate what they are expected to know about mean, mode and median whilst also challenging them to work systematically, and justify their reasoning. This problem asks which set of five positive whole numbers have the following properties: Mean = 4 Median…
Temperature
This maths problem from NRICH allows the student to explore the relationships within the temperature scales. As well as developing a better understanding of temperature, this problem presents a number of ways in which it can be solved (trial and improvement, graphically, algebraically) so can offer a useful opportunity for discussing…
Peaches Today, Peaches Tomorrow
This NRICH maths problem could replace repetitive textbook work on calculating fractions of integers. It offers plenty of practice of these calculations while requiring students to come up with problem-solving strategies. It offers a good context for thinking about factors of numbers.
Notty Logic
The overall goal of this NRICH maths activity is for students to leave with an enhanced understanding of clear mathematical communication which they can apply in all other areas of mathematics. It encourages this clarity of mathematical communication by means of trying to negate statements. This provides a good way for students…
Cross with the Scalar Product
This NRICH maths problem helps to reinforce students' understanding of the vector and scalar product by encouraging them to think about how they are related geometrically. This problem can begin with a recap of the scalar and vector product to make sure students are clear about what each product is and how it is calculated.…
Polygon Walk
In this maths problem from NRICH, students are encouraged to think geometrically about vectors in order to deduce which vectors could generate particular sets of points. When students have a feel for how two vectors can be used to reach a variety of points on the plane, they can be asked to sketch possible arrangements of points…
Integration Matcher
This NRICH maths activity will give students insights into differentiation, integration and the relationships between the two without needing to get involved with technical manipulations. It would be well suited to use as an introduction or summary to differentiation or integration. It is very good for giving intuitive meaning to…
5/5- Publication year: 2000 - 2009
- Activity sheet
Contrary Logic
This NRICH maths activity takes students' logical thinking one step beyond the logical thinking required to follow direct proofs. It will sharpen their understanding of proof and mathematical thinking to a level beyond that normally required in school mathematics, albeit in a simple context. This problem is in two parts.…
- 4/5
- Publication year: 2000 - 2009
- Activity sheet
Stats Statements
The NRICH maths problem will get students into statistics without them necessarily needing to engage in detailed calculation. Students are asked if a set of statistical statements sometimes, always or never true? If they are only sometimes true, can they give examples or conditions under which they are true and under which they…
Impossible Triangles
This NRICH maths problem will make students experiment, conjecture and prove. They will need to understand the interplay between rational and irrational numbers. This activity lends itself to hands-on experimentation with cut-outs of triangles before algebraic proof is attempted. Without cut-out shapes it is a good exercise in visualisation.…
Spotting the Loophole
This NRICH maths problem shows students the power of using visual representations to solve vector problems. This can help them spot a solution which can then be verified using algebra . This could form a short introduction to work on vectors. In 2D, vectors may be thought of as arrows with a fixed length and direction. The place…
Noah
A maths activity from NRICH which introduces humour to counting and recording to add to the enjoyment. The children will find this number activity funny. It is a good opportunity for them to practise counting and to record findings in different ways. And there's the added bonus that everyone could have a different answer and…
Skeleton Shapes
This NRICH maths activity focuses on the properties of solids especially edges and vertices by comparing the solid shape and the number of balls of modelling clay and straws required to make a skeleton of it. This activity helps children begin to understand the various properties of common geometric solid shapes, concentrating on…
Building with Solid Shapes
This practical NRICH maths activity focuses on the properties of common geometric shapes. Shapes Using sketches of structures made with solid shapes including cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons children are asked to decide which are stable and which are not. This helps children begin to understand…
Chairs and Tables
This practical maths activity from NRICH asks children to make various objects using interlocking cubes starting with a chair before making a table to go with the chair. Children will find the matter of building the table to match the chair quite a challenge. Using the Three Bears as inspiration children are asked to make a…
Lots of Lollies
This NRICH maths activity requires children to apply their knowledge of factors and multiples, and is a good way of making the link between sharing, division and multiples/factors. It may also be used to introduce learners to the fact that a problem can have more than one solution and that the solutions can be generalised. It can…
Biscuit Decorations
This NRICH maths problem gives children practice not just in counting in ones but also counting in other multiples. It can be solved by physically modelling the biscuits and decorations with whatever objects are convenient. It is a good opportunity for children to choose the way they represent the problem in order to solve…
Fair Feast
In this NRICH maths problem, the familiar context of sharing provides an opportunity in which to explore fractions in a variety of ways. The task involves finding fractional quantities of whole numbers as well as dividing a unit into equal pieces. It is set in the context of a picnic.
- 4/5
- Publication year: 2000 - 2009
- Activity sheet
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Two Clocks
This practical NRICH maths activity can help children understand that the analogue clock is really two scales superimposed on each other. This is what makes it so difficult for children to read. Focusing on the hands separately will help children understand what each one indicates. The novel context of this problem could provide…
- 5/5
- Publication year: 2000 - 2009
- Activity sheet
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.
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
Fair Shares
This NRICH maths activity starts with a simple situation which can be analysed quickly using mental methods, but which provides a starting point for tackling a more challenging problem. The challenge of finding a connection between the number of children, the amount of money they each receive, and the fraction used to share the…
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.…