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Achievement objectives

What has changed:

# Achievement objective M8-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• use permutations and combinations.

## Indicators

• Understands the basic terms and notation of permutations and combinations, including:
,
• Selects and uses appropriate methods to find numbers of distinct arrangements or selections from a given number of objects in order to solve problems and calculate probabilities, including:
• the multiplication principle
• factorials
• permutations, including fixed position of items, groups of items, and identical items
• combinations including restrictions on the selections and selecting from more than one group.
• See key mathematical ideas on NZmaths.

## Possible context elaborations

• Straightforward applications such as choosing a sample of 3 girls and 4 boys from a class of 16 girls and 12 boys.
• Calculate probabilities of winning the different Lotto divisions.
• Cases where repetition is permissible such as selecting the three letters for New Zealand vehicle number plates.
• Possible investigations include Pascal’s triangle.
• Opportunities for proof, for example, show nC + nC(n-r) = (n + 1) C.

## Assessment for qualifications

NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.