Resources by Something in Common

Misprints Do Hapen

Two proof-readers are checking separate copies of the same manuscript. They each find a different number of errors. The number of errors found by both is given and the task is to calculate how...

Multi-simultaneous

A series of eight simultaneous equations are given and the initial challenge is to discover the single point of intersection of the lines. On each of the examples given the intersection takes as...

Obedient Ray

This investigation looks at two mirrors fixed at a point. A ray of light enters the set-up, bounces around and then exits along the same path. The task is to find the angle between the mirrors....

Parabola in a Parallelogram

A parabola is given with the x-coordinate of the minimum point, and two points on the parallelogram shown. The points are joined and then a parallel line is drawn that is a...

Parallelogram in a Quadrilateral (Construction)

There are a series of quadrilaterals on is presented on plain paper. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each...

Parallelogram in a Quadrilateral (grid version)

There are a series of quadrilaterals presented on a grid. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each case a...

Partial mean

In this resource the mass of a group of objects is given, with the mean matching the number of objects. The mass of a subset of the objects is given, again with the mean mass matching the number of objects. The challenge is to calculate the mean mass of the remaining objects.

Solving the problem requires the...

Pick a Polygon

A square-based dotted grid is given. An initial investigation involved drawing triangles on the grid and determining the area, number of dots on the perimeter, and number of dots enclosed by...

Piscatorial Percentages

The number of fish in a tank is given, together with the percentage of the fish that are small. The challenge is to work out the number of the small fish to remove to achieve a lower given...

Polygon in Annulus

A polygon of side length two is shown with a circle circumscribing its vertices. A second circle is shown with the sides of the polygon tangential to the circle. The challenge is to calculate...