Heating drives a gas out
The bubbles that appear on a beaker wall as water heats are the whole story in one observation.
When water is heated the gases dissolved in it leave. Which is to say that the amount of gas that can stay dissolved in hot water is very small. Temperature is therefore a factor in the solubility of a gas, just as it is for a solid — but it works the other way round.
The two do not agree
Most solutes
Raising the temperature increases the solubility of most solutes in a solvent. This is what the hot repeat of activities 3.1.6 and 3.1.7 showed.
A gas
Raising the temperature decreases the solubility of a gas in a solvent. This is the opposite behaviour, and it has to be learned separately.
A common slip
Having just learned that heating dissolves more, it is easy to carry that across to gases and get it exactly backwards. Boiling water holds almost no dissolved air at all — which is why boiled water tastes flat and why fish suffer in a warm pond.
Something to notice
The bubbles on the beaker wall appear well below 100 °C. They are not the water boiling; they are the dissolved air coming out of solution as the water warms.