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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.

### 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.

### 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

• Drake, M., Francis, J., Beckett, C., Coulston, A., & McIntyre, R. (1995). Learning experiences for level 7 mathematics. Teacher Support Services, Wellington.
• McIntyre, R. (1994). Cooperative mathematics for level seven. Auckland, New Zealand: Longman Paul.
• 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.
• Lovitt, C. (1991). Maths problem solving and modelling: For year 12. Nelson, Australia.
• 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 17, 2018