Twenty worked life contexts
Original labelled MODEL records/quantities unless a dated primary fact card is named. These are ordinary examples, not held tests or claims about real collections/events.
C01 · Paper repair patch
Source/model: One rectangular fictional patch is divided into two equal-area halves; one is ready.
Question: What is ready and what completes this patch?
Worked reasoning: 1/2 ready + 1/2 needed = 1 whole. A different patch has its own whole; no actual repair is performed.
C02 · Notice layout
Source/model: One same-height panel has four equal-width sections; three have text.
Question: What fraction has text?
Worked reasoning: 3/4; one more 1/4 completes it. Four unequal sections would not justify quarters of area.
C03 · Seed-label groups
Source/model: Twelve fictional paper labels are split into three equal groups of four; two groups are chosen.
Question: What fraction of these labels is chosen?
Worked reasoning: 8 of 12 labels, or 2/3 of this collection. Equal-value/count items and the complete twelve-label whole are stated; not a claim about germination.
C04 · Quiet game kit
Source/model: Eight equally counted tokens in four equal groups of two; three groups in use.
Question: What is in use and what remains?
Worked reasoning: 3/4 of the eight-token whole (six tokens) is in use; 1/4 (two) remains. No actual player preference or motor action is asserted.
C05 · Scene backdrop
Source/model: Five equal-width fictional backdrop panels; two painted.
Question: How much still needs painting?
Worked reasoning: 3/5 of this backdrop. Two-fifths + three-fifths makes the whole; actual painting/material safety is separately reviewed.
C06 · Dollar-value labels
Source/model: Primary F01: $1 = 100 cents. Original model: ten equal 10-cent value labels; seven selected.
Question: What fraction of that dollar value is selected?
Worked reasoning: 7/10 of $1 value = 70 cents; 3/10 = 30 cents completes it. Derived maths, not seven-tenths of coin area or of a mixed coin set.
C07 · Map legend strip
Source/model: One fictional legend line from 0 to 1 is split into three equal gaps; marker at 2/3.
Question: What reaches the endpoint?
Worked reasoning: One further 1/3 gap. Four boundary marks frame three gaps; no geographic distance or journey implied.
C08 · Robot story progress
Source/model: One fictional story line has ten equal intervals; marker at 4/10.
Question: How many one-tenth steps remain?
Worked reasoning: Six steps, or 6/10, to 1. This is a number-line story, not a programmed robot or timed child task.
C09 · Music booklet margin
Source/model: One paper margin has four equal-area parts; one blank and three filled.
Question: How can a no-colour version say the same thing?
Worked reasoning: State "3 of this margin’s 4 equal parts are filled,3/4;1/4 remains". Sound, colour and handwriting are optional, not maths criteria.
C10 · Picture frame guide
Source/model: Whole collection is fifteen equally counted paper squares arranged in five groups of three; four groups selected.
Question: How can a strip show this multiple?
Worked reasoning: Four of five equal strip sections,4/5; one more 1/5. Twelve selected squares alone is not a fraction until the fifteen-square whole is named.
C11 · Tool-label organiser
Source/model: Seven fictional labels: draw,fold,draw,join,fold,draw,join.
Question: Which category needs most labels?
Worked reasoning: draw 3, fold 2, join 2, total 7. It describes these labels, not children’s skills or a real workshop inventory.
C12 · Snack-story cards
Source/model: Six fictional picture titles: fruit,grain,fruit,vegetable,grain,fruit.
Question: How many title cards of each category?
Worked reasoning: fruit 3, grain 2, vegetable 1, total 6. These are story labels, not dietary advice, allergens, food handling or a household survey.
C13 · Animal-book index
Source/model: Eight fictional title-topic cards: bird,bird,fish,insect,fish,bird,insect,bird.
Question: What shelf-label counts fit these cards?
Worked reasoning: bird 4, fish 2, insect 2. Listed reptile has 0 among these eight known cards; this is not wildlife monitoring or a library stock claim.
C14 · Repair tickets with a gap
Source/model: Five known fictional tickets: paper,paper,wood,paper,wood; one ticket type unavailable.
Question: Can we say no metal tickets exist?
Worked reasoning: Known paper 3/wood 2; metal 0 among known records only, unavailable 1. The unknown could be metal, so no all-six absence claim is justified. No physical repair.
C15 · Corner-card folder
Source/model: Five fictional simple-outline cards have 0,3,4,4,5 corners.
Question: How many cards have four corners?
Worked reasoning: 2 cards. The five frequencies sum 5; corner values sum 16. Value 0 is real circle data in this model, not unavailable.
C16 · Packet loading
Source/model: Seven fictional safe paper packets contain 0,1,1,2,2,2,4 pieces.
Question: How many packets need a two-piece label?
Worked reasoning: 3 packets. Table 0→1,1→2,2→3,4→1 totals 7 packets. There are 12 pieces overall, a different total.
C17 · Model weather dashboard
Source/model: Six invented station-card descriptions show counts of recorded checks:0,2,2,3,3,3.
Question: Which count occurs most often?
Worked reasoning: 3 checks occurs on 3 cards. These are fictional counts, not rainfall amounts or current weather observations.
C18 · Model transit sign archive
Source/model: Six invented sign-topic cards: bus,walk,bus,cycle,walk,bus.
Question: What can the table support?
Worked reasoning: bus 3,walk 2,cycle 1 among these six cards. It cannot establish local service frequency, safe routes or preferred transport.
C19 · RRC listed service entries
Source/model: F03’s dated source lists Southside Library, History Centre, Northside Library, Gracemere Library, Mount Morgan Library.
Question: What does a type table count?
Worked reasoning: 4 Library entries and 1 History Centre entry =5 listed services. History Centre and Southside share a listed address; this is not 5 buildings or proof they are all open now.
C20 · Creative project desk
Source/model: A separate fictional five-part sign is 2/5 ready. Six fictional task labels: draw,write,draw,check,write,draw.
Question: What are two different useful checks?
Worked reasoning: 3/5 completes the same sign; table: draw 3/write 2/check 1 totals 6 task labels. The sign’s whole and task-list unit are different; no actual class project or preferences inferred.