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This was challenging for me as it’s a new way of looking at student expertise and a new grade level. I took an easier concept. Would love to see other ideas of how to break down other concepts (i.e. decimals, fractions, patterns, geometric concepts…) to use as a model.
So… grade 4 solving problems involving addition and subtraction of 4digit numbers (e.g., 2135 – 1982)
UI: I know I need to stack the numbers (having seen or been taught only the standard algorithm and trying to follow the procedure)
Student might not know what to do when borrowing needed and just subtract the lesser top number from the greater bottom number (e.g., 83 in tens column instead of 13 – 8) and not understanding the difference.
CI: “I know I can use a number line to count up instead of count back, but I can’t remember how to do it.” or “I know I can use base ten blocks to help me subtract, but I don’t know what to do when I don’t have enough tens/hundreds…”
Student also may not know where to start with student generated strategies he/she has seen.
CC: “For me it is easier to add than subtract so I can use a number line to count from on from 1982 by 10s and 1s to get to 2135.” Student may use base ten or number line ideas from CI above and be able to accurately solve problem, although maybe not using the most efficient way.
UC: Student may use a number line still, but be able to make larger jumps, rounding
(1982+18 = 2000 + 135=2135. So 135 + 18 =145 + 5 + 3 = 153)
CM: May be able to see multiple ways to manipulate the numbers (e.g., If I add 18 to 1982, I can round it to 2000, so I’ll have to add 18 to 2135 as well. 2000 from 2153 is 153) and calculate the solution by visualizing the scenario in his/her head.