In this lesson students understand that models are a way to reason quantitatively and abstractly. In the first lesson, allow students to explore freely using Cuisinarie rods before distributing the poem. This allows students to identify the kinds of relationships that they see. Then see if they can apply that abstract reasoning to the problem, if they need a hint, then tell them to start with the dark green.
The next pages: Ask students to solve using any strategy they want then present this type of model illustrated in the answer pages. These problems are applications of algebraic systems. The idea here is that each animal would have a "minimum number" of legs and then build upon that to get left over legs. These are made clearer in the key. Adults are often blown away by this one, because we're so used to the complexities of mathematics not thinking that these complex algebra problems can be solved EFFICIENTLY by a fifth/sixth grader!