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# Computational Thinking · Week 1 — Variables and state CT week 1 builds **representations**: naming quantities, picking datatypes, and tracing state through flowcharts or pseudocode. ## Week map Problem → variables as named state → datatypes → iterators → flowchart symbols → state snapshots → input/output boxes.

Computational Thinking · Week 1 — Variables and state

CT week 1 builds representations: naming quantities, picking datatypes, and tracing state through flowcharts or pseudocode.

Week map

Problem → variables as named state → datatypes → iterators → flowchart symbols → state snapshots → input/output boxes.

Representation notation

Variable → name bound to a value that may change → count, total, name.
State → all current variable values at one instant → snapshot table one row per step.
Iterator → variable stepping through a sequence or count → i from 0 to n-1.
Datatype → kind of value → determines legal operations → number vs string vs list.

Flowchart symbols

Shape	Role	Example action
Oval	start / end	Start, Stop
Rectangle	process	`total ← total + price`
Diamond	decision	`score ≥ 50?`
Parallelogram	input / output	`Read age`, `Print sum`

Arrow direction defines order. At a diamond, follow one branch label (Y/N or T/F).

Choosing a representation

Ask three questions:

Single vs collection? One score → number; list of scores → list.
Fraction allowed? Integer count vs float average.
Text vs number? ID as string even if digits; phone codes not for arithmetic.

Mini-example: Track 5 quiz scores → list scores length 5, not five unrelated names unless table fixed.

State snapshot tracing

Problem: start x=3, y=1. Process: y ← x + y, then x ← y - 2.

step	x	y
init	3	1
after 1st	3	4
after 2nd	2	4

Read as: assignment uses current values when evaluating right-hand side.

Pattern families

Easy — Read flowchart step

Follow arrows; update rectangles; branch at diamond once.
Identify start/end and missing arrow bugs in diagrams.
Match parallelogram to Read/Print in trace.

Medium — Choose datatype and names

From word problem, list variables and types.
Distinguish index (position) vs value at index.
Flowchart with two variables swapping — track both columns.

Hard — Full state table

Multi-step with decision: duplicate row only along taken branch.
Iterator introduced mid-flow: when does i increment?
Detect unreachable rectangle (no arrow in).

Worked mini-examples

Example 1 — Simple trace.

Start a=10, b=2. a ← a - b → a=8. b ← a + b → b=10.

Example 2 — Decision.

n=7. Diamond: n > 5? Yes → msg ← "big". Else branch skipped. msg is "big".

Example 3 — Iterator intro.

i=0, sum=0. Loop body: sum ← sum + i, i ← i + 1, repeat while i < 4.

i	sum after step
0	0
1	0
2	1
3	3
4	6

Loop stops when i becomes 4.

Example 4 — Wrong type choice.

Storing price = "12.50" then total = price + 5 concatenates strings in Python-like semantics — representation error if numeric total intended.

Traps

Skipping decision branch label — both paths mentally.
Same name for two concepts (total for both count and sum).
Using value before rectangle that assigns it.
Iterator confused with stored data value (i vs item[i]).
Flowchart arrow bypassing update rectangle.

Diagnostic (try yourself)

Start p=5, q=3. Execute p ← p + q then q ← p - q. What are final p and q?
A flowchart diamond asks x < 0. If x = 0, which branch (Y/N) is taken for “less than zero”?
You need to store a student’s 8 weekly quiz percentages. One variable or a collection? Which datatype class?
Trace c=1, d=4, then c ← d, d ← c. What are c and d? (Watch order.)
In a state table, why duplicate rows only on the taken branch after a decision?