Achievement objective NA66
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:
 generalise the properties of operations with rational numbers, including the properties of exponents.
Indicators
 Uses algebra to describe the properties of operations (addition, subtraction, multiplication, and division) as they apply to rational numbers and exponents, for example, expanding, factorising, and simplifying.
 Uses the properties of addition, subtraction, multiplication, division, and exponents in solving problems.
 Uses the operations on rational numbers without technology.
 Makes links with exponents
NA62.
 See
key mathematical ideas on NZmaths.
Progression
NA66 links to M76.
What is new/changed?
 Generalising includes factorising, expanding, and simplifying expressions involving rational numbers and exponents.
Possible context elaborations
 Sue and Jane were asked to factorise 12 + 4u. Sue’s answer was 2(6+2u); Jane’s answer was 4(3+u). Which is the better answer and why?
 Generalising properties of operations (see
Quick Times and
Really Mr. Bond)

Difference of two squares

Napier’s method
 Derive other properties of exponents by applying first principles to specific cases, for example, 3^{2} x 4^{2} = 3 x 3 x 4 x 4 = 12 x 12 = 12^{2} leading to a^{n}b^{n} = (ab)^{n}
Assessment for qualifications
NCEA achievement standards at level 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 following achievement standard(s) could assess learning outcomes from this AO.
 AS91027 Mathematics and statistics 1.2 Apply algebraic procedures in solving problems
Refer to the
mathematics and statistics matrix.
Last updated September 26, 2013
TOP