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## Senior Secondary navigation

Achievement objectives

What has changed:

# Achievement objective S7-1

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• 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.

## Indicators

• Uses the statistical enquiry cycle to conduct surveys and experiments and to analyse existing data sets.
• Conducts surveys to find solutions to problems (or uses existing data sets):
• Poses survey questions, considering sources of variation, for example, what are the variables to be collected, how each variable will be measured.
• Designs, trials, and improves questionnaires using a range of appropriate questions types, checking the survey questions using, for example, desk review, conducting pilot surveys.
• Selects and uses appropriate sampling methods, for example, simple random, systematic, stratified, cluster, and quota.
• Evaluates sampling method used, for example, is a sample sufficiently large, randomly chosen, and representative of the population.
• Collects and manages data.
• Uses exploratory data analysis to explore features of the data:
• Uses appropriate statistical graphs and tables to explore the data and communicates relevant detail and overall distributions.
• Uses appropriate measures to communicate features of the data.
• Uses relevant contextual knowledge when communicating findings.
• Makes statistical inferences.
• Communicates findings in a report which includes:
• relevant summary statistics, graphs and tables to support the findings of the survey
• quantitative and qualitative statements
• statistical inferences
• justified conclusions.
• Conducts experiments to find solutions to problems:
• Poses investigative questions about an experimental situation.
• Plans experiments:
• Considers sources of variation, for example, what are the variables to be collected, how each variable will be measured.
• Evaluates the choice of variables and measures used in the experiment.
• Selects and uses appropriate data collection and recording methods.
• Conducts the experiment and collects data.
• Communicates findings in a report which includes:
• relevant summary statistics, graphs and tables to support the findings of the survey
• quantitative and qualitative statements
• statistical inferences
• justified conclusions.
• See key mathematical ideas on NZmaths.

## Progression

S7-1 links from S6-1 and to S7-2, S7-3, S8-1.

## What is new/changed?

• Conducting experiments.
• Use of exploratory data analysis.
• Using relevant contextual knowledge (given).

## Possible context elaborations

• CensusAtSchool is a valuable website for classroom activities and information for teachers on all things statistics.
• Using Statistics New Zealand SURFS – New Zealand Income Survey; Household Savings Survey; 2006 New Zealand Census to explore investigative questions posed about the data sets.
• You have been asked by the Ministry of Health to design a questionnaire that would enable them to find out more about the effects of high sugar intake on teenagers.
• Statistics New Zealand: A Guide to Good Survey Design
• Investigate a given claim from the media, where the raw data is available.
• Conduct an experiment to see if drinking a caffeinated drink improves reflexes, or memory, or athletic performance.
• Kiwi Kapers – uses a simulated data set of Kiwis to explore some of the big ideas.
• Sampling variation and making inferences:
• Teaching notes
• Data cards
• Information about the variables
• Population graphs and statistics
• Blank dot plot sheet for collecting weights
• Kiwi data in Excel
• Kiwi data in Fathom
• Deciding on the sample size:
• Teaching notes
• Student worksheet
• Fathom taking samples
• Example of output (different sample sizes)
• Fathom collecting sample medians
• Example of output (sample medians)
• Median
• Example of output (collation of class medians)
• Introduction to stratified sampling:
• Teacher notes
• Dot plot blank sheet for collecting heights
• Data cards
• Kiwi population (excel)
• Fathom taking samples
• Example of output (samples)
• Fathom taking counts of species
• PPDAC cycle – using stratified sampling:
• Teacher notes
• Student worksheet
• School population (fathom)
• School population (excel)
• Fathom file for taking sample
• Fathom file used for teacher notes
• Two further examples that can be used for the entire statistical enquiry cycle. Set up for sampling:
• the kiwi population is the same as used in Kiwi Kapers and introduction to stratified sampling:
• Fathom file for taking sample
• Kiwi population (excel)
• Information about variables
• SURF Income survey from Statistics New Zealand:

## Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO:

• AS91263 Mathematics and statistics 2.8 Design a questionnaire
• AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference
• AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods

Refer to the mathematics and statistics matrix.

Last updated September 26, 2013