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# Level 7 mathematics and statistics learning programme example

• The following learning programme examples are divided into three terms of work. Each term has an overarching mathematical and statistical 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 term 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 selecting 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.

## Term 1 – Patterns focus

### 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.
• M7-2 Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs.
• M7-3 Use arithmetic and geometric sequences and series.

#### Equations and expressions

• *M7-6 Manipulate rational, exponential, and logarithmic algebraic expressions.
• *M7-7 Form and use linear [and] quadratic … equations

* 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.

## Term 2 – Variation focus

### 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 inquiry cycle:
• A – conducting surveys that require random sampling techniques …
• B – evaluating … 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:
• 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 …

#### 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.

## Term 3 – Functions focus

### Suggested achievement objectives

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

#### Patterns and relationships

• M7-2 Display the graphs of linear and non-linear [quadratic, exponential and logarithmic] functions and connect the structure of the functions with their graphs.

#### Calculus

• M7-9 Sketch the graphs of functions and their gradient functions and describe the relationship between these graphs.
• M7-10 Apply differentiation and anti-differentiation techniques to polynomials.

## 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. 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.
3. Ackerley, G. (2004). Counting fish: Real life mathematics for secondary school students. Fish and Game, New Zealand.
4. Barnes, M. (1991). The investigating change series. Curriculum Corporation, Australia.

## Possible assessment programme

• AS91256 Mathematics and statistics 2.1 Apply co-ordinate geometry methods in solving problems – 2 credits; internal
• AS91257 Mathematics and statistics 2.2 Apply graphical methods in solving problems – 4 credits; internal
• AS91258 Mathematics and statistics 2.3 Apply sequences and series in solving problems – 2 credits; internal
• AS91262 Mathematics and statistics 2.7 Apply calculus methods in solving problems – 5 credits; external
• 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

NOTE: The teaching and learning programme encompasses the achievement objective M7-6 Manipulate rational, exponential, and logarithmic algebraic expressions, but AS91261 Apply algebraic methods in solving problems (2.6) is not assessed as an outcome for this course.

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

Last updated March 29, 2021