Sets - Progression Points

Dimension

Level

Progression Point

Structure

2.25

• Recognition that one set is or is not a subset of another

2.75

• Construction of lists, venn diagrams and grids to be used for recording combinations of two attributes

3.0 Standard

… Students use lists, venn diagrams and grids to show the possible combinations of two attributes.

They recognise samples as subsets of the population under consideration (for example, pets owned by class members as a subset of pets owned by all children).

3.25

• Conversion between venn diagrams and karnaugh maps as representations of relationships between two sets

3.75

• Construction of diagrams illustrating the possible relationship between two sets and the truth of statements involving the words all, some or none

4.0 Standard

… Students use venn diagrams and karnaugh maps to test the validity of statements using the words none, some or all (for example, test the statement ‘all the multiples of 3, less than 30, are even numbers’).

4.75

• Lists of sets in the power set of a given set and knowledge that the total number of set equals 2n for n elements in the given set

5.0 Standard

… Students identify collections of numbers as subsets of natural numbers, integers, rational numbers and real numbers.

They use venn diagrams and tree diagrams to show the relationships of intersection, union, inclusion (subset) and complement between the sets.

They list the elements of the set of all subsets (power set) of a given finite set and comprehend the partial-order relationship between these subsets with respect to inclusion (for example, given the set {a, b, c} the corresponding power set is {Ø, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}.)

They test the validity of statements formed by the use of the connectives and, or, not, and the quantifiers none, some and all, (for example, ‘some natural numbers can be expressed as the sum of two squares’).

They apply these to the specification of sets defined in terms of one or two attributes, and to searches in data-bases.

5.25

• Relationships between two sets using a venn diagram, tree diagram and karnaugh map

5.5

• Expression of the relationship between sets using membership, ∈, complement, ′ , intersection, ∩, union, ∪, and subset, ⊂, for up to two sets

6.0 Standard

… Students classify and describe the properties of the real number system and the subsets of rational and irrational numbers.

They identify subsets of these as discrete or continuous, finite or infinite and provide examples of their elements and apply these to functions and relations and the solution of related equations.

They express relations between sets using membership, ∈, complement, ′ , intersection, ∩, union, ∪ , and subset, ⊆ , for up to three sets.

They represent a universal set as the disjoint union of intersections of up to three sets and their complements, and illustrate this using a tree diagram, venn diagram or karnaugh map.