# Trapezia

Which numbers can be represented by groups of circles in the shape of a trapezium?

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A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.

## Here are some other activities you may be interested in:

#### Jugs

The classic problem of using two unmarked jugs to measure exactly a given quantity. The Transum version is interactive and awards a virtual trophy for each of the levels completed.

#### Remainder Race

A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

Transum.org/go/?to=remainder

#### Fraction Foundations

Recognise simple fractions (halves, quarters and tenths) of whole numbers and shapes. So far this activity has been accessed 261 times and 39 Transum Trophies have been awarded for completing it.

Teacher's notes for this investigation and solutions to Transum puzzles, exercises and activities are available when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.