g10-01-01 · Core topics
An element or a subset?
Does changing 3 into {3} change the question?
1 MIN · PREDICT ON PAPER
Predict whether a number, its singleton and the empty set belong to A or are subsets of A.
Discuss or write first. No typed answer is required to continue.
The object 2 is an element; subset status is not applicable.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
A contains numbers. A number can be an element; a singleton is a subset exactly when its number belongs to A. Finite displayed cases suggest a conjecture; the justification below states why it holds under the stated conditions.
Conditions: The universe is {1,…,8}; A is the chosen numeric set. A subset question requires a set as its left operand.
Mathematical justification: {n} ⊆ A means every element of {n}, namely n, is in A. The empty set has no element violating inclusion.
1 MIN · EXIT CHECK
For A={2,4}, compare 2∈A, {2}⊆A and {2}∈A.
Check after answering
True, true, false; A contains numbers, not singleton sets.
Teacher guidance and extension
Before: Numbers and braces
Ask: Ask pupils to name the type of the object before choosing a symbol.
Watch for: Membership and inclusion are different relations; the empty set is not the number zero.
Challenge: Construct a set whose elements are themselves sets, then reconsider membership.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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