Reply To: Lesson 6-1: Question

[Christine Pomatto]

It’s hard sometimes to rethink our tried-and-true lessons, but I’m going to try. I tend to teach integer addition by telling a story (with visuals) about a box suspended in midair. As the story progresses, balloons get tied to the top and weights get tied to the bottom of the box. I tell students that the box goes up if there are more balloons, and the box goes down if there are more weights. The box floats in midair if there are equal numbers of balloons and weights (zero pair).

I’m ready to make over this lesson using the AGES model.

Attention: I can get students’ attention by showing them the opening page of the story, which is a typical brown box floating in midair. I will remove any explanatory text and do a Notice & Wonder. The picture will capture students’ attention because it is a new and unusual situation, and it’s silly. It gets sillier when you think about tying balloons and weights to it, and a balloon’s pull is supposed to be equal to the pull of a weight (students always argue with me about this – but I can use it to start a math fight!)

Generation: Students will be able to generate their own learning if I withhold information from the story. Instead of telling them the box will go up if I tie balloons to it, I can ask them to make predictions. The same with weights. Then I can ask them to draw conclusions about what might happen if there were equal numbers of balloons and weights. Or 5 weights and 3 balloons. I will ask students if they have found any shortcuts – they will literally generate the algorithm and rules for integer addition!

Emotion: This lesson happens very close to the beginning of the school year, and I think it can be a great lesson for building confidence in students (certainty). It can also increase their sense of status when they feel important for making a new mathematical discovery and having the opportunity to teach it to their classmates.

Spacing: Once students are familiar with the scenario, I can revisit it throughout the year to teach more concepts, such as subtracting integers, multiplying integers, and maybe dividing integers. I could even try using it for other rational numbers, like fractions and decimals, although that might be too silly (3/4 of a balloon and 5/6 of a weight). The point is that I can revisit it, especially if students get stuck on a concept.