Enrichment

=Enrichment for gifted students=

Enrichment can be informally described as moving sideways rather than up in terms of the curriculum. It refers to students covering standard school-work in more depth than their peers. Some of examples of achieving this for some the mathematics strands in the New Zealand curriculum follow, these vary from short activities, to longer term research projects that a student may turn to when the regular classroom work is something they have already mastered. Lengths are indicated in brackets.

Some of these activities may be suitable for non-gifted students (indeed it is argued that enrichment benefits all students), but provide material to engage gifted students when they have already mastered the regular classroom material, rather than being forced to repeat it.

**Number**

 * [Medium] Comparing the decimal system to other base systems.
 * [Long] Investigation into costings of various items/activities. Use knowledge of rates to find the best available option.
 * [Short/medium] Investigate types of numbers such as prime numbers, perfect numbers, or untouchable numbers.
 * [Short] Investigation into fractions which make recurring decimals.

**Algebra**

 * [Short] Finding as many expressions as possible that simplify to the same expression.
 * [Short] Exploring the Fibonacci sequence, and its many special properties.

Geometry

 * [Medium/Long] Euclid's elements introduces a variety of proofs in addition to those typically studied at school.
 * [Short/Medium] Exploring tessellating patterns.
 * [Short] Formulas for areas of shapes which are not usually studied - regular pentagons and hexagons, ellipses etc.
 * [Short] Exploring three dimensional co-ordinate systems.

Measurement

 * [Short] Studying imperial units and conversion factors.
 * [Short/medium] Studying forms of measurement in other cultures.
 * [Medium] Maximising volumes/areas without calculus (combines measurement and graphing skills).
 * [Medium] Use measurement techniques to approximate complex areas or volumes such as the surface area of skin, the area of a natural feature (pond, swamp etc) in the area.

Statistics

 * [Long] Individual research projects on a topic of the students choice.
 * [Medium] Gather examples of statistics in the media - discuss the validity of their claims.
 * [Short] Using statistics to guess possible values for data. For example: Five number have a mean of 5 and a range of 7, what could they be? Use larger sets of numbers, and more clues, to add challenge to the problem.

Probability

 * [Medium/long] Using probabilistic skills to model real-life problems.
 * [Medium/long] Designing probability based board games.
 * [Medium] Consider the probabilities involved in real life gambling - for example Lotto, or card games.

(Ministry of Education, 1996) (Ministry of Education, 2007)

Mixed enrichment
http://www.nzamt.org.nz/sites/cms/index.php?option=com_content&task=view&id=140&Itemid=142
 * The NZAMT website provides a series of enrichment papers suitable for junior high school students. These could be used when regular classroom work is completed. Please be aware these are in a mixed order, and therefore would not run alongside normal maths programs, but cover material which ties in with the regular curriculum. Some students may require additional help with new concepts such as working in different base systems.