Home - Solving Problems With Data Map
In this Big Idea students explore what data is and how it can be used to help us investigate and understand our world. Students will explore the data relevant to things they find interesting, in ways in which it can be communicated, reasoned with and used to solve problems. Students will enjoy exploring a range of infographics as used in the book "Animals by the Numbers" by Steve Jenkins.
Students will understand:
In Stage 2, students should consider the use of graphs in real-world contexts. Graphs are frequently used to persuade and/or influence the reader, and are often biased.
Data
Length
Mass
Notes:
'Hefting' is testing the weight of an object by lifting and balancing it; estimating its mass by feel. Where possible, students can compare the weights of two objects by holding one object in each hand.
At Stage Two, use of the terms weigh and weight are acceptable and can be used interchangeably with mass as is consistent with common use. In technical/scientific terms "Weight is a force that changes with gravity, while mass remains constant."
The kilogram is the only SI base unit whose name and symbol include a prefix. In length, the metre is the base unit, in volume, the litre is the base unit. For the kilogram multiples and submultiples of this unit are formed by attaching the appropriate prefix name to the unit name gram, and the appropriate prefix symbol to the unit symbol g. For example, one millionth of a kilogram is one milligram (1 mg)
Students investigate a graph of the lengths of different animals' tongues to develop ways of interpreting data displays, with a focus on reading a scaled axis. Then students choose a set of animal measurement data (length, mass/weight, other) and create their own data displays to compare and discuss. - See page 25
Allow time for students to explore a range of infographics as used in the book "Animals by the Numbers" by Steve Jenkins.
Questions for reflection:
When discussing student graphs:
Students play with finding errors in data by looking for what doesn't make sense. Partners construct their own set of data and then try to detect errors in the data displays created by the rest of the class. - See page 36
Questions for reflection:
What is the most common car colour where you live? Students develop and try-out a data collection plan to answer the question, and then look across the data collected by the whole class to see what can be learned, the similarities and differences. - See page 41
Questions for reflection:
How much do all of our school bags weigh? There is a growing concern about the weight of school bags and the answer to the problem can be found by analysing the data. In this investigation students will need to measure the weight of the items in their school bag and use data to analyse and share the results of their investigation. Students will need to agree on the best method for weighing each item and for calculating or measuring combined weights. Students will also need to consider what questions they might be able to answer with the data that they have and what conclusions and recommendations they can make to their parents and teachers.
Questions for reflection:
Further investigation options are listed in Mindset Mathematics on Page 45. Look Fors indicated for Investigate One apply to the data component of Investigate Two, see page 46.
Look fors:
How are students weighing items? - When weighing items students need to consider accuracy. This is particularly important when students are weighing light items. Using a digital scale can improve accuracy or students could weigh multiple identical items and then divide to determine a weight for a single sample. With large items students may need to use a set of bathroom scales. Students will need to problem solve how they can place these items on the scale and may not think of weighing themselves holding the item and then subtracting their weight. Students need to be thinking about what data they need to develop their argument. Knowing the total weight of the bag is unlikely to provide them with information that they can act on. If they plan to remove or replace items they will need to know the weight of individual items.
How do students record their data? - Students will be using a mix of units for their measurements but will need to total and compare amounts. Students will need to think about what units they record and then when it comes to combining weights or comparing weights should use one unit e.g. kilograms (with decimals) or grams but not both. Using a single unit, rather than recording weights as kilograms and grams will make it easier to total weights, particularly if students use a spreadsheet.
Are students fluent with conversions? - This investigation will also allow students opportunities to convert from one unit to another which builds an understanding of units as a relationship and also multiplication and division by powers of ten. When having students multiply and divide by ten (or powers of ten, 100, 1000) it is common to have students add a 0 for multiplication or remove a 0 for division. This may be practical but it stands in the way of an understanding of what is actually happening. If we teach students to 'add a zero' we should not be surprised if they think that (1.3 x 10) equals 1.30 rather than 13. Students need to have a sound understanding of place value and this should allow them to see that multiplication and division by powers of ten shifts the whole number to the left for multiplication and to the right for division.
Students will need to know the relationship between the units and understanding the naming convention should make this easier and transferable.
In the case of mass/weight the Kilogram is the base unit but for practical matters of conversion, the relationship between units is consistent with other measures if the gram is seen the unit from which others are derived.
Interesting Fact - The Kilogram has recently changed. It was the only unit which was still defined by the properties of a physical object; a cylinder of polished platinum-iridium alloy that had been used since 1889. - Read More
