The aim here is for students to become comfortable moving up and down a vertical number line (thermometer) to reflect the operation of adding an integer. Adding a positive integer is a rise and adding a negative integer is a drop. For example, if the temperature at Mt Ruapehu was ⁻2 degrees in the morning and rose by 5 degrees it would be recorded as ⁻2 + ⁺5 = ⁺3. If the temperature had dropped by 5 degrees, it would be recorded as ⁻2 + ⁻5 = ⁻7.
Using materials
Problem: Ask students to imagine they are visiting friends in Dunedin during the winter, when temperatures are often below 0. In Dunedin the morning temperature was ⁻3 degrees. If the temperature fell 4 degrees by lunchtime, what is the new temperature?
Using a vertical number line, have students record the starting point on the thermometer and the direction they will need to move (down).
Record this as: ⁻3 + ⁻4 = ⁻7. Now imagine that the temperature at the same time the next day is ⁺4.
How much has the temperature changed in 24 hours?
Using the same number line, ask students record the starting point (⁻7) and the direction they will need to move (up).
Record: ⁻7 + ? = ⁺4.
How have they figured out how many degrees the temperature has risen?
Will this be a positive or a negative integer?
Examples: Pose temperature problems for the thermometers, making sure that students record the rises and falls as additions of integers and use the number lines to track the movements. They can also use red and blue pens to indicate adding positive (red) integers and adding negative (blue) integers.
Using imaging and number properties
Students need to practise these types of problem by imaging the movement up and down a thermometer until they can successfully use part–whole thinking to work back and forth across the 0 point on the number line.
Examples: ⁻30 + ⁻50, ⁻14 + ⁺12, ⁻99 + ⁺107, + 5 + ⁻37, ⁻204 + ⁻102, ⁻204 + ⁺102 …