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 7 Fractions

The Num 7 Fractions network begins with two topics in which activities with physical objects develop the concepts of denominator and numerator, leading to viewing fractions as a double operation. Bar notation for fractions is introduced leading to equivalent fractions and decimal fractions (concurrently with supporting decimal fraction activities in NuSp 1, The Number track and the number line network). Fractions also come to be seen as numbers and as quotients. Activities dealing with rounding decimal fractions in place-value notation round out the network.

A listing of the individual activities contained in the Num 7 network follows the Num 7 "concept map."


© Richard R. Skemp, 1993, 1994. SAIL through Mathematics, Volume 1, Volume 2.


Num 7 Fractions


Topic 1 Making equal parts
1/1	Making equal parts
1/2	Same kind, different shapes
1/3	Parts and bits
1/4	Sorting parts
1/5	Match and mix: parts
Topic 2 Take a number of like parts
2/1     Feeding the animals
2/2	Trainee keepers, qualified
2/3	Head keepers
Topic 3 Fractions as a double operation; notation
3/1	Expanding the diagram
3/2	"Please may I have?"
           (Diagrams and notation)
Topic 4 Simple equivalent fractions
4/1	"Will this do instead?"
4/2	Sorting equivalent fractions
4/3	Match and mix: equivalent
Topic 5 Decimal fractions and
5/1	Making jewellery to order
5/2	Equivalent fraction diagrams
5/3	Pair, and explain
5/4	Match and mix: equivalent
           decimal fractions
Topic 6 Decimal fractions in 
           place-value notation
6/1	Reading headed columns in
           two ways
6/2	Same number, or different?
6/3	Claiming and naming
Topic 7 Fractions as numbers.
           Addition of decimal
           fractions in place-value
7/1	Target, 1
7/2	"How do we know that our
           method is still correct?"	
Topic 8 Fractions as quotients
8/1	Fractions for sharing
8/2	Predict, then press
8/3	"Are calculators clever?"
8/4	Number targets by calculator
Topic 9 Rounding decimal fractions in
           place-value notation	
9/1	Rounding decimal fractions
9/2	Fractional number targets