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# Level 7 learning programme example with a statistics focus

• The following learning programme example is 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 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.

## Term 1 – Surveys

### Ideas for teaching and learning activities

• After-ball parties:
• Develop a questionnaire about after ball parties, but considering who the intended recipient is, for example, the principal, local police, party organiser.
• CensusAtSchools:
• Kiwi Kapers activities see the file of this name on the AO S7-1 page

### 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:
• 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.

## Term 2 – Modelling

### Ideas for teaching and learning activities

• Rice bombing – see the file of this name on the AO S7-4 page
• Armspans – see the file of this name on the AO S7-4 page

### 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 functions and connect the structure of the functions with their graphs.

#### Equations and expressions

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

#### Probability

• S7-4 Investigate situations that involve elements of chance:
• B – calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

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

## Term 3 – Experiments

### Ideas for teaching and learning activities

• Activity: Memory experiment
• Ideas for developing teaching activities.
• Controlling variation by going through the PPDAC cycle more than once to zoom in on the effect, for example, improvement of memory after drinking cola or not. Second stage: ordinary cola versus diet cola (to control for the effect of sugar); also links with sampling to select control group.
• Using the Global Development Quiz. Hans Rosling referred to this in his 2007 TED talk claiming that students score worse in a multiple-choice test on global development than monkeys would.
• Optical illusions, for example, the Muller-Lyer illusion where students try to mark the mid-point of the line. Look at whether one group tends to be better than the other.
• Caffeine or chocolate and memory tests (or tests with other foods and beverages) tests belong together. For example, do students who consume cola improve more in a subsequent memory (or other) activity than those who did not?
• Possible context elaborations for AO S7-3
• Possible context elaborations for AO S7-4

### 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:
• 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.

#### Probability

• S7-4 Investigate situations that involve elements of chance:
• A – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions.

## Book resources

1. Drake, M., Francis, J., Beckett, C., Coulston, A., & McIntyre, R. (1995). Learning experiences for level 7 mathematics. Teacher Support Services, Wellington.

## Possible assessment programme

• AS91257 Mathematics and statistics 2.2 Apply graphical methods in solving problems – 4 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
• AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods – 3 credits; internal
• AS91267 Mathematics and statistics 2.12 Apply probability methods in solving problems – 4 credits; external
• AS91268 Mathematics and statistics 2.13 Investigate a situation involving elements of chance using a simulation – 2 credits; internal

OR

• AS91257 Mathematics and statistics 2.2 Apply graphical methods in solving problems – 4 credits; internal
• AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference – 4 credits; internal
• AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods – 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

• AS91257 Mathematics and statistics 2.2 Apply graphical methods in solving problems – 4 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
• AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods – 3 credits; internal
• AS91266 Mathematics and statistics 2.11 Evaluate a statistically based report – 2 credits; internal
• AS91268 Mathematics and statistics 2.13 Investigate a situation involving elements of chance using a simulation – 2 credits; internal
• AS91269 Mathematics and statistics 2.14 Apply systems of equations in solving problems – 2 credits; internal

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

Last updated May 6, 2021