In this unit students investigate variables associated with cars, using a spreadsheet to produce data displays and investigate distributions.
This unit involves students collecting data and analysing them in a variety of ways using technology. The focus of the unit is to explore relationships between numerical variables, but this does not exclude looking at summary and comparison situations.
Criteria for developing good investigative questions
As students develop questions within the investigation cycle, they must be supported to clearly see and understand the difference between investigative questions (questions we ask of the data) and the survey or data collection questions (questions we ask to get the data) that will generate the data to answer the investigation question(s). Broad ideas should be refined in order to generate investigative questions. The purpose of each of these question types should be made explicit within the context of the investigation.Teachers should support the development of such questions through questioning and modelling.
Arnold’s (2013) research identified six criteria for what makes a good investigative question. At curriculum Level 4, students should be introduced to the criteria, potentially through “discovering” them. See for example, the following lesson on CensusAtSchool New Zealand https://new.censusatschool.org.nz/resource/posing-summary-investigative-questions/ .
The six criteria are:
Categorical variables
Categorical variables classify individuals or objects into categories. For example, the method of travel to school, or the colour of students' eyes.
Numerical variables
Numerical variables include variables that are measured e.g. the time taken to travel to school, and variables that are counted e.g. the number of traffic lights between home and school. Measured numerical variables are called continuous numerical variables. Counted numerical variables are called discrete numerical variables.
Scatterplots
A scatterplot is a display for paired numerical variables. At this level we are not concerned with which variable goes on which axes or with defining explanatory and response variables.
The scatterplot below shows how the heights and arm spans of a sample of students might be graphed (from CensusAtSchool).
Analysis of scatterplots at this level includes looking at situations where the variables might be equal e.g. height and arm span. If this is the case the y=x line can be drawn in (as shown below), and a discussion can be led around the areas of the graph – above the line, below the line, on the line – and the closeness of the points to the line is appropriate.
This discussion might include the following points:
Analysis at this level can also involve looking at the relationship between two numerical variables that might not be equal. For example, if we look at wrist circumference and popliteal length. In this case the wrist circumferences range from 10-23 cm and the popliteal lengths range from 30-60cm.
In this situation we can draw in two boundary lines that broadly encompass the data points.
In this case we can describe the general pattern – that those with a greater wrist circumference also tend to have longer popliteal lengths. We can also identify that the data is quite widely spread and for many wrist circumferences there are multiple popliteal lengths.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The context for this unit can be adapted to suit the interests and experiences of your students. For example:
Te reo Māori kupu such as taunga (statistics), taurangi (variable), raraunga (data), taurangi motumotu (discrete variable), taurangi motukore (continuous variable), and tūhura (investigate) could be introduced in this unit and used throughout other mathematical learning.
PROBLEM: Generating ideas for statistical investigation and developing investigative questions
PLAN: Planning to collect data to answer our investigative question
Between this session and the next, import tthe data collected by students into CODAP and share it with the students. Information on importing data into CODAP can be found here.
In this session the students will be using an online tool for data analysis. One suggested free online tool is CODAP. Feel free to use other tools you are familiar with. This session is written with CODAP as the online tool and assumes that students are familiar with CODAP.
If your students are unfamiliar with CODAP see:
The main features that students need to be familiar with is how to draw a graph in CODAP.
ANALYSIS: Graphing and describing our data to explore our investigative questions
In this session students finish their analysis, prepare, and then present to the class.
In this session students explore Figure NZ to find other displays of information about cars. They select at least three that interest them to explore and describe.
For example, Monthly registrations of new and ex-overseas cars in New Zealand June 2015-June 2020 (graph from Figure NZ).
Students will notice the huge drop in April 2020, the actual graph on the website allows them to scan the graph and get exact values for monthly registrations (April was 1329 compared with March which was 13,980 registrations and May which was 14,965 registrations). They can comment on why this was so. (COVID-19 lockdown in New Zealand).
Dear parents and whānau,
In mathematics we have been investigating data about cars. We have collected and collated data, displayed it on graphs, and have discussed the different features of it. Your child will share their presentation with you at home. Can you see any interesting features in the data?
Thank you.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/cars at 8:46pm on the 26th February 2024