Math Relearning/EngageNY/GPK/Module 5: Addition and Subtraction Stories and Counting to 20
These are my comments on EngageNY's Prekindergarten Module 5.
New propositional concepts from this module:
- Addition situations include (1) adding to an existing set ("add to with result unknown") and (2) composing a whole out of parts ("put together with total unknown").
- Subtraction situations include removing things from an existing set ("take from with result unknown").
- Story problems can be represented visually on a spectrum from concrete (acting out, manipulating objects, representational drawing) to abstract (fingers, cubes, abstract drawings).
- Story problems should be decontextualized to work out the problem (representing the problem abstractly) and then recontextualized when giving the answer (stating the answer in terms of its units and their situation).
- Addition and subtraction situations can be expressed as number sentences, such as "3 plus 1 equals 4."
- One type of structure in math is a pattern.
- Two types of patterns are repeating and growth patterns.
- Growth patterns can be based on different numbers, such as growing a quantity by 1 or by 2.
I'd like to explore the concepts of addition and subtraction further, but I might wait on it, since this module doesn't go into it in much depth. I don't think it even presents subtraction as the opposite of addition.
I've read warnings against having students decode word problems rotely by matching operations to English phrases, which, yes, would be a problem if the students didn't learn to understand what the word problems mean. But I don't think my source gave an alternative method, so I wonder how they'd recommend recognizing and analyzing an addition story and how they'd have students distinguish it from, for example, a multiplication story. In any case, at the pre-K level EngageNY gives the students phrases to recognize.
These kinds of language issues are important, but I don't know if they belong in the propositional concept lists.
Topic B: Contextualizing Addition Stories to Solve
Lesson 6: Act out add to with result unknown story problems to solve
I expected to see some strategy for adding, such as counting on, but the lesson seems to expect the children to just know the answer or else to find their own strategies. The fluency exercises haven't been practicing addition facts, just counting.
Topic F: Duplicating and Extending Patterns
New vocab word: repetend, the repeating part of a pattern. I thought it was a typo at first. I like finding out technical terms like this one.