Math Relearning/EngageNY/GPK/Module 4: Comparison of Length, Weight, Capacity, and Numbers to 5

These are my comments on EngageNY's Prekindergarten Module 4.

Overview
New propositional concepts from this module:


 * Objects have attributes that are measurable, such as length, weight, and capacity.
 * Objects can be compared to each other on the basis of a measurable attribute using certain terms related to that attribute.
 * When comparing lengths, one endpoint of each object must be aligned with the other.
 * A balance scale can be used to compare weights.
 * With respect to an attribute, one object can be more than, less than, or about the same as another object.
 * Events such as counting happen in a sequence in time, which gives them an order.
 * The first event, which starts the sequence, and the last event, which ends the sequence, can be especially important, such as when keeping track of which objects in a group have been counted.
 * The order of objects can also refer to their spatial arrangement, such as when they're in a line and facing a particular direction.
 * The same object can occupy different positions in different counting sequences.
 * The quantity of objects in a group remains the same even if the order in which they're counted changes.
 * Objects in two groups can be matched to determine if one group contains more objects than the other, which can be specified with the phrases "fewer than," "more than," and "the same as."
 * Numbers can be compared even when they don't refer to quantities of objects, and in this case the terms are "less than" and "greater than."
 * In certain cases, a group has enough objects if it has at least as many (exactly enough or enough with extras) as another group whose objects need to be matched with those of the first group.
 * If a group doesn't have enough objects, it can have enough if more objects are brought into it.

I'm going to skip the connections with earlier concepts for now.

Lesson 3: Compare length using longer than, shorter than, and about the same as with a stick of linking cubes
I don't know if I should keep track of techniques like the "Say Ten Way," where the teen numbers are stated by saying "ten" and the number added to ten (ten 1, ten 2, etc.).