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 inclass formative or summative assessment. Not all achievement objectives need to be assessed.
Term 1 – Surveys
Ideas for teaching and learning activities
 Afterball 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 S71 page
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Statistical investigation
 S71 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.
 S72 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
 S73 Evaluate statistically based reports:
 A – interpreting risk and relative risk
 B – identifying sampling and possible nonsampling errors in surveys, including polls.
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Term 2 – Modelling
Ideas for teaching and learning activities

Rice bombing – see the file of this name on the AO S74 page

Armspans – see the file of this name on the AO S74 page
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Patterns and relationships
 M72 Display the graphs of linear and nonlinear functions and connect the structure of the functions with their graphs.
Equations and expressions
 *M76 Manipulate rational, exponential, and logarithmic algebraic expressions.
 M78 Form and use pairs of simultaneous equations, one of which may be nonlinear.
Probability
 S74 Investigate situations that involve elements of chance:
 B – calculating probabilities, using such tools as twoway 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.
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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 multiplechoice test on global development than monkeys would.
 Optical illusions, for example, the
MullerLyer illusion where students try to mark the midpoint 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 S73

Possible context elaborations for AO S74
Suggested achievement objectives
Select from below depending on the teaching and learning activities chosen.
Statistical investigation
 S71 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.
 S72 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
 S73 Evaluate statistically based reports.
Probability
 S74 Investigate situations that involve elements of chance:
 A – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions.
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Book resources

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