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Level 7 applied mathematics and statistics learning programme example

  • The following learning programme example is divided into two semesters of work. Each semester has an overarching mathematics and/or statistics focus to support the learning.
  • Possible teaching and learning activities are given, from which teachers could select activities that best meet the needs of the students in their class/school. In addition teachers could select teaching and learning activities that they currently use, or source others that would meet student needs and address the focus.
  • Each semester has a list of possible achievement objectives to select from, the choice of which will depend on the selected teaching and learning activities.
  • The intent is to be more holistic in the selection of achievement objects to allow for natural connections between and within strands.
  • Some achievement objectives could be summatively assessed directly through achievement standards; others could be assessed through in-class formative or summative assessment. Not all achievement objectives need to be assessed.

Semester 1 – Applied mathematics and algebra focus

Applied mathematics and algebra focuses on the development of mathematical thinking and reasoning in patterns, relationships, equations, and expressions.

Ideas for teaching and learning activities

Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Patterns and relationships

  • M7-1 Apply co-ordinate geometry techniques to points and lines.
  • M7-3 Use arithmetic and geometric sequences and series.
  • M7-4 Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.
  • M7-5 Choose appropriate networks to find optimal solutions.

Equations and expressions

  • *M7-6 Manipulate rational, exponential, and logarithmic algebraic expressions.
  • *M7-7 Form and use linear, quadratic, and simple trigonometric equations.
  • M7-8 Form and use pairs of simultaneous equations, one of which may be non-linear.

*Some aspects of these two AOs are integral to the other AOs, but not all aspects would be expected to included in the teaching and learning programme.

Semester 2 – Statistics

Statistics and probability focuses on the development of statistical thinking, reasoning and literacy.

Ideas for teaching and learning activities

Suggested achievement objectives

Select from below depending on the teaching and learning activities chosen.

Statistical investigation

  • S7-1 Carry out investigations of phenomena, using the statistical enquiry cycle:
    • A – conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets
    • B – evaluating the choice of measures for variables and the sampling and data collection methods used
    • C – using relevant contextual knowledge, exploratory data analysis, and statistical inference.
  • S7-2 Make inferences from surveys and experiments:
    • A – making informal predictions, interpolations, and extrapolations
    • B – using sample statistics to make point estimates of population parameters
    • C – recognising the effect of sample size on the variability of an estimate.

Statistical literacy

  • S7-3 Evaluate statistically based reports:
    • A – interpreting risk and relative risk
    • B – identifying sampling and possible non-sampling errors in surveys, including polls.

Probability

  • S7-4 Investigate situations that involve elements of chance:
    • A – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
    • B – calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

Book resources

  1. Drake, M., Francis, J., Beckett, C., Coulston, A., & McIntyre, R. (1995). Learning experiences for level 7 mathematics. Teacher Support Services, Wellington.
  2. McIntyre, R. (1994). Cooperative mathematics for level seven. Longman Paul, Auckland. This book is out of print but pdf versions are available on Wikispaces: Auck SNP 2011 with the author’s permission for distribution and use.
  3. Fergusson, S., Jessup, E., Snow, P., Stewart, A., & Valente, F. (1990). Mathematics projects and investigations for years 11 & 12 (NZ Years 12 & 13). Nelson, Australia.
  4. Lovitt, C. (1991). Maths problem solving and modelling: For year 12. Nelson, Australia.
  5. Britt, M., Gargiulo, S. V., Hughes, P. (1988). Investigations in mathematics. New House, Auckland.

Possible assessment programme

It is envisaged that this course could lead to assessment for a wide range of achievement standards enabling teachers to select appropriate assessment programme to suit individual students within the class/school. It is important that these are selected with a view to future courses.

  • AS91256 Mathematics and statistics 2.1 Apply co-ordinate geometry methods in solving problems – 2 credits; internal
  • AS91259 Mathematics and statistics 2.4 Apply trigonometric relationships in solving problems – 3 credits; internal
  • AS91260 Mathematics and statistics 2.5 Apply network methods in solving problems – 2 credits; internal
  • AS91263 Mathematics and statistics 2.8 Design a questionnaire – 3 credits; internal
  • AS91266 Mathematics and statistics 2.11 Evaluate a statistically based report – 2 credits; internal
  • AS91267 Mathematics and statistics 2.12 Apply probability methods in solving problems – 4 credits; external
  • AS91269 Mathematics and statistics 2.14 Apply systems of equations in solving problems – 2 credits; internal

OR

  • AS91256 Mathematics and statistics 2.1 Apply co-ordinate geometry methods in solving problems – 2 credits; internal
  • AS91258 Mathematics and statistics 2.3 Apply sequences and series in solving problems – 2 credits; Internal
  • AS91259 Mathematics and statistics 2.4 Apply trigonometric relationships in solving problems – 3 credits; internal
  • AS91260 Mathematics and statistics 2.5 Apply network methods in solving problems – 2 credits; internal
  • AS91263 Mathematics and statistics 2.8 Design a questionnaire – 3 credits; internal
  • AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference – 4 credits; internal
  • AS91267 Mathematics and statistics 2.12 Apply probability methods in solving problems – 4 credits; external

OR other combinations that fit with the achievement objectives selected for teaching and learning.

Last updated September 26, 2012



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