How much colder?

Achievement objectives

NA4-6: Know the relative size and place value structure of positive and negative integers and decimals to three places.

Required materials

See Materials that come with this resource to download:

• How much colder activity (.pdf)
• How much colder Antartica climate data and graphs (.pdf)

Activity 

If you were to visit a base station in Antarctica, would the temperature be very different depending on where and when you went?

Use the tables of average daily maximum and minimum temperatures by month for each of the three stations to find the difference between the warmest and the coldest of all these temperatures.

 (How much colder Antartica climate data and graphs (.pdf) accessed from Cool Antarctica.)

The following prompts illustrate how this activity can be structured around the phases of the mathematics investigation cycle.

Make sense

Introduce the problem. Allow students time to read it and discuss in pairs or small groups.

• Do I understand the situation and the words? (Students may need support to understand the meaning of average, maximum and minimum. They may also not be familiar with a difference and how to calculate it by subtraction.)
• What are the important numbers and what do they mean (The maximums and minimums will need to be accessed from the data set. The averages are already calculated but students should recognise averages as measures of centre, in this case.)
• Where else in my life/the world can I see this happen? (Students should be familiar with maximum and minimum temperatures from weather reports.)
• What will my solution look like? (The solution will be the difference between maximum and minimum average temperatures with supporting calculations.)

Plan approach

Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.

• What are the maths ideas involves in this problem?
• Have I accessed all the information I need? Is anything important missing?
• What do I expect the solution might be? What is a sensible estimate?
• What could the solution not be? How do you know?
• How could I show this problem using numbers, diagrams, graphs, tables, or materials? (A number line is a form of diagrammatic representation.)
• What strategies can I use to get started?
• What tools (digital or physical) could help my investigation? (Calculators could be useful to students to find and check answers.)

Take action

Allow students time to work through their strategy and find a solution to the problem.

• Is my recording organised so I can check calculations and verify my answers?
• Hat strategies am I using? Are those strategies working to help solve the problem? If not, what else could I try?
• Have I tried all the important cases and not missed any from the data set?
• Do I need to review how to calculate differences with integers?
• How do my results look different to others? Why could this be?
• Does my solution make sense? Does it match my expected difference?
• Is there another possible answer or way to solve it?

Convince yourself and others

Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.

• What is the solution?
• Is my working clear and systematic for someone else to follow?
• How would I convince someone else I am correct?
• Could I have solved the problem in a more efficient way?
• Would my answer work in a different situation? Could I find differences between other amounts in the same way?
• Which ideas or tools worked well in my investigation?
• What could I try differently next time?
• What could I find out next?