# Resources by Something in Common

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### 4 squared fractions presentation

In this resource students are asked to find the value of several calculations that involve addition, subtraction and the squaring of fractions. Students are asked to spot patterns and similarities within the questions in order to generalise. The investigation concludes bu using algebra to prove their conjectures....

### A Circle Journey

The initial task involves using factors of 12 and -12 to set up two points. Compasses are used to draw a circle that has the two points as its diameter. An interesting feature of the resulting...

### A Fractional Sequence

The initial investigation uses an inductive formula and two initial values to derive a sequence that results in a series of fractions before returning to the initial two values of the sequence. A spreadsheet is provided that performs the calculations given in the inductive formula. This is helpful for both checking...

### A Geometric Progression Problem

There is an initial investigation of geometric progressions where the interval between the first and second, and the third and fourth terms are given, with the challenge of discovering two possible values for the first term and associated common ratio. There are ten examples to work on to enable collaboration...

### An interesting pair of simultaneous equations

In this teacher presentation and collection of student worksheets a pair of simultaneous equations is given, one of which is non-linear. A second pair of similar simultaneous equations is given; that has the same solutions. Students are challenged to explain why.

Each student worksheet contains different...

### Angle at Centre, Angle on Arc Investigation

This investigation covers two circles theorems through one demonstration. The theorems are:

• That the angles on the same arc forming a chord are equal

• That the angle at the centre is twice the angle at the arc when drawn from the same chord

The initial...

### Annulus Volume of Revolution

A segment of a circle is created using a chord parallel to the x-axis. The resulting segment of the circle is then revolved 360° about the x-axis. The problem is to calculate the volume of the resulting annulus.

To find a general solution to the problem involves using an elemental disc ring and integrating...

### Area Between Parabolas

Two parabolas are shown, one with a positive quadratic coefficient, the other with a negative quadratic coefficient. Each has the same linear coefficient and between the...

### Awkward Triangle

A triangle is given with the lengths written in of surd form. The challenge is to calculate the area of the triangle, without recourse to a calculator. Two methods are investigated. The first...

### Brackets Out, Brackets In

The problem starts with choosing three distinct, non-zero integers between -5 and 5 that do not sum to zero. These are then used in a six factorisations that make use of...