Num 4 Subtraction
The Num 4 Subtraction network begins with "taking away" actions on sets of physical objects, leading to the concept of subtraction as a mathematical operation (i.e., as a mental operation using physical aids initially). Once subtraction is familiar verbally and mentally, a notation for subtraction is introduced along with number sentences and stories. Carefully designed activities bring out four different but related meanings of subtraction and these are applied to larger numbers (eventually to numbers up to 999). A listing of the individual activities contained in the Num 4 network follows the Num 4 "concept map."
© Richard R. Skemp, 1993, 1994. SAIL through Mathematics, Volume 1, Volume 2.
Num 4 Subtraction
Topics/Activities
Topic 1 Actions on sets: taking away
1/1 Start, Action, Result
(do and say)
1/2 Taking away on the number
track (do and say)
Topic 2 Subtraction as a mathematical
operation
2/1 Predicting the result
(subtraction)
2/2 What will be left?
2/3 Returning over the stepping
stones
2/4 Crossing back
Topic 3 Notation for subtraction:
number sentences
3/1 Number sentences for
subtraction
3/2 Predicting from number
sentences (subtraction)
Topic 4 Number stories: abstracting
number sentences
4/1 Personalized number stories
4/2 Abstracting number sentences
4/3 Personalized number stories -
predictive
Topic 5 Numerical comparison of two
sets
5/1 Capture
5/2 Setting the table
5/3 Diver and wincher
5/4 Number comparison sentences
5/5 Subtraction sentences for
comparisons
Topic 6 Giving change
6/1 Change by exchange
6/2 Change by counting on
6/3 Till receipts
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Topic 7 Subtraction with all its
meanings
7/1 Using set diagrams for taking
away
7/2 Using set diagrams for
comparison
7/3 Using set diagrams for
finding complements
7/4 Using set diagrams for
giving change
7/5 Unpacking the parcel
(subtraction)
Topic 8 Subtraction up to 20,
including crossing 10
8/1 Subtracting from teens:
choose your method
8/2 Subtracting from teens:
"Check!"
8/3 Till receipts up to 20¢
8/4 Gift shop
Topic 9 Subtraction up to 99
9/1 "Can we subtract?"
9/2 Subtracting two-digit numbers
9/3 Front window, rear window
9/4 Front window, rear window -
make your own
Topic 10 Subtraction up to 999
10/1 Race from 500 to 0
10/2 Subtracting three-digit
numbers
10/3 Airliner
10/4 Candy store: selling and
stocktaking
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