SAIL: Structured Activities in Intelligent Learning

Richard R. Skemp

March 10, 1919 – June 22, 1995

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Selected Concept Maps: Set-based Organisation | Subtraction | Fractions

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


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
2/1     Predicting the result
2/2     What will be left?
2/3     Returning over the stepping
2/4     Crossing back
Topic 3 Notation for subtraction:
           number sentences
3/1	Number sentences for
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 -
Topic 5 Numerical comparison of two
5/1	Capture
5/2	Setting the table
5/3	Diver and wincher
5/4	Number comparison sentences
5/5	Subtraction sentences for 
Topic 6 Giving change
6/1	Change by exchange
6/2	Change by counting on
6/3	Till receipts
Topic 7 Subtraction with all its
7/1	Using set diagrams for taking
7/2	Using set diagrams for
7/3	Using set diagrams for
           finding complements
7/4	Using set diagrams for
           giving change
7/5	Unpacking the parcel
Topic 8  Subtraction up to 20,
            including crossing 10
8/1	 Subtracting from teens:
            choose your method
8/2	 Subtracting from teens:
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
10/3	Airliner
10/4	Candy store: selling and