Resources tagged with: Maths Supporting SET

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Broad Topics > Cross-curricular Contexts > Maths Supporting SET

Matrix Meaning

Age 16 to 18 Challenge Level:

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Air Routes

Age 16 to 18 Challenge Level:

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Polygon Walk

Age 16 to 18 Challenge Level:

Go on a vector walk and determine which points on the walk are closest to the origin.

Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Fix Me or Crush Me

Age 16 to 18 Challenge Level:

Can you make matrices which will fix one lucky vector and crush another to zero?

Vector Walk

Age 14 to 18 Challenge Level:

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Cross with the Scalar Product

Age 16 to 18 Challenge Level:

Explore the meaning of the scalar and vector cross products and see how the two are related.

Transformations for 10

Age 16 to 18 Challenge Level:

Explore the properties of matrix transformations with these 10 stimulating questions.

Square Pair

Age 16 to 18 Challenge Level:

Explore the shape of a square after it is transformed by the action of a matrix.

Operating Machines

Age 16 to 18 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Debt Race

Age 16 to 18 Challenge Level:

Who will be the first investor to pay off their debt?

How Do You React?

Age 14 to 16 Challenge Level:

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

Crystal Symmetry

Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

Maths Filler 2

Age 14 to 16 Challenge Level:

Can you draw the height-time chart as this complicated vessel fills with water?

Air Nets

Age 7 to 18 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Curve Fitter 2

Age 16 to 18 Challenge Level:

Can you construct a cubic equation with a certain distance between its turning points?

Brimful 2

Age 16 to 18 Challenge Level:

Which of these infinitely deep vessels will eventually full up?

Truth Tables and Electronic Circuits

Age 11 to 18

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Aim High

Age 16 to 18 Challenge Level:

How do you choose your planting levels to minimise the total loss at harvest time?

Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

Stadium Sightline

Age 14 to 18 Challenge Level:

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Production Equation

Age 16 to 18 Challenge Level:

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Spherical Triangles on Very Big Spheres

Age 16 to 18 Challenge Level:

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

Stirling Work

Age 16 to 18 Challenge Level:

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Ball Bearings

Age 16 to 18 Challenge Level:

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Scientific Curves

Age 16 to 18 Challenge Level:

Can you sketch these difficult curves, which have uses in mathematical modelling?

Constantly Changing

Age 14 to 16 Challenge Level:

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Perfect Eclipse

Age 14 to 16 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Speed-time Problems at the Olympics

Age 14 to 16 Challenge Level:

Have you ever wondered what it would be like to race against Usain Bolt?

Construct the Solar System

Age 14 to 18 Challenge Level:

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Robot Camera

Age 14 to 16 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

Investigating Epidemics

Age 11 to 16 Challenge Level:

Simple models which help us to investigate how epidemics grow and die out.

Track Design

Age 14 to 16 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

Perspective Drawing

Age 11 to 16 Challenge Level:

Explore the properties of perspective drawing.

Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

What Do Functions Do for Tiny X?

Age 16 to 18 Challenge Level:

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Elastic Maths

Age 14 to 18

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

3D Drawing

Age 11 to 16

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

Witch's Hat

Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Guessing the Graph

Age 14 to 16 Challenge Level:

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Pdf Stories

Age 16 to 18 Challenge Level:

Invent scenarios which would give rise to these probability density functions.

Fill Me up Too

Age 14 to 16 Challenge Level:

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Designing Table Mats

Age 11 to 16 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

What's That Graph?

Age 14 to 16 Challenge Level:

Can you work out which processes are represented by the graphs?

Alternative Record Book

Age 14 to 18 Challenge Level:

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Mystery Procedure

Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing?

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

Genetics

Age 14 to 16 Challenge Level:

A problem about genetics and the transmission of disease.

Population Dynamics Collection

Age 16 to 18 Challenge Level:

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.