A Deconstructed Learning Outcome: Sum of Its Parts

Maybe I’ve seen one too many deconstructed Caesar salad or peanut butter and jam sandwich on TV. Or maybe I’ve heard “This workbook covers the curriculum” one too many times¹.
Whatever my reason, I wanted to take a closer look at a learning outcome from the WNCP Math 8 curriculum document:
It is expected that students will demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically [C, CN, ME, PS]
“It is expected that students will”
It’s about students’ learning. Worked examples on the whiteboard or in a textbook may be evidence of the teacher’s or publisher’s learning.
“demonstrate an understanding of”
Not will be able to. Students need to make sense of mathematics. Justifications and explanations are required for answers and methods.
“multiplying and dividing positive fractions and mixed numbers”
This is a topic. Curriculum is more than a collection of these.
“concretely, pictorially, and symbolically”
No longer just suggested, the use of concrete materials (i.e., manipulatives) is prescribed² as is having students draw to represent their thinking (diagrams not decorations).
[C, CN, ME, PS]
From K to 12, seven processes are to be integrated within the learning of mathematics. The ‘C’, for example, means that students should be provided with opportunities to communicate their learning– to write about and discuss mathematical ideas.
¹ To my US reader(s)– in my province, curriculum is different than recommended learning resource (i.e., the textbook). In theory, the textbook is not the course. In practice…
² For many teachers, this is probably the biggest change to the curriculum. Earlier this year, I created the posters below. My intent was to generate conversations among teachers, not to teach the concept. Plus, I got to be artsy-fartsy. Enjoy.

CPS Poster Algebra Tiles
CPS Poster Counters
CPS Poster Pattern Blocks
CPS Poster Toothpicks