NRICH Activities at Stage 5
This sample of problems produced by NRICH include topics on rates of change, vectors and statistics, but they also offer opportunities to develop powers of reasoning, logical thought and mathematical communication.
Some of the problems are short whilst others encourage the use of visual and practical skills. They can all be used to enhance the post sixteen curriculum.
HEALTH and SAFETY
Any use of a resource that includes a practical activity must include a risk assessment. Please note that collections may contain ARCHIVE resources, which were developed at a much earlier date. Since that time there have been significant changes in the rules and guidance affecting laboratory practical work. Further information is provided in our Health and Safety guidance.
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.…
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
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.…
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.…
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
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…
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…
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. HEALTH and SAFETY Any use of a resource that includes a practical activity must include a risk assessment. Please note that collections may contain ARCHIVE resources, which were developed at a…
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…
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…
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Resource by: NRICH
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