Teaching objectives
Recognising several parameters at once is a challenge for primary-school students — and often for secondary students too! This lab uses cards with 3–4 different attributes, similar to those in the game Set. It combines simple combinatorics exercises with attention practice. No prior knowledge is needed: the lab builds everything from scratch. It is a great warm-up before playing our Trios game, and it is highly recommended for developing patience and focus.
What you'll learn
Students practise attention to detail, logical reasoning by attributes, and elementary combinatorics: counting in an organised way without missing or repeating any case.
- They discover the trio rule: for each attribute (number, colour, shape, fill), the three values must be all the same or all different; if two match and one does not, the trio is invalid.
- Using interactive explorers (sliders), students build collections of 2D and 3D cards and discover that the total number of cards is always a product of the possible values of each attribute.
- They practise identifying which attributes are all the same or all different in a given trio (param_same and param_diff rooms).
- Students count how many distinct cards exist with 4 attributes of 3 values each and arrive at the formula 3⁴ = 81.
- They move on to identifying whether three cards form a trio (yes/no), then to completing a trio by choosing the third card from 6 options, and finally to finding the hidden trio within a group of 6, 7, or 8 cards.
- In the final rooms the challenge is reversed: select the maximum number of cards possible without any group of three forming a trio, which requires thinking carefully about how trios overlap.
Key mathematical ideas
- A trio is valid if and only if, for each attribute, the three values are all the same or all different (never "two the same and one different").
- The total number of cards in a deck with several independent attributes is the product of the number of values per attribute: with 4 attributes of 3 values, 3 × 3 × 3 × 3 = 3⁴ = 81.
- Finding the largest trio-free set is a combinatorics problem: at least one card must be removed from every possible trio, which introduces the idea of independent sets.
Room-by-room contents
Room 1 · Welcome to the Trios Lab
The trio rule is introduced: 3 cards form a valid trio if, in each of their 4 attributes (number, colour, shape, fill), the 3 values are all the same or all different. A valid example and an invalid one are shown with an attribute-by-attribute explanation.
Student tasks
- Read the trio rule and the two annotated examples.
Room 2 · Exploring combinations
An interactive explorer shows all possible cards with only 2 properties (number and shape). The student moves sliders to change how many values each property has and observes how many cards are generated.
Student tasks
- Move the sliders and observe how the total number of cards changes.
Room 3 · How many cards? (2 properties)
A calculation question: if there are 5 numbers and 3 shapes, how many distinct cards exist? The answer is 15 (5 × 3).
Student tasks
- Calculate the number of cards with 5 numbers and 3 shapes and write the answer.
Room 4 · Three properties
The explorer now has three properties (number, shape and colour). The student experiments with the sliders and observes the increase in cards when a further dimension is added.
Student tasks
- Move the sliders with 3 properties and observe the new total number of cards.
Room 5 · How many cards now? (3 properties)
A calculation question with three properties: 4 numbers, 5 shapes and 2 colours. The answer is 40 (4 × 5 × 2).
Student tasks
- Calculate the number of cards with 4 numbers, 5 shapes and 2 colours and write the answer.
Room 6 · Equal attributes (1)
3 cards that form a trio are shown. The student must identify which attribute(s) are exactly the same across all three cards. In this case the number is 1 in all three, and colour, shape and fill are all different.
Student tasks
- Select the attributes that are the same in the 3 cards (answer: number).
Room 7 · Equal attributes (2)
The 3 cards share number (2), colour (orange) and fill (solid); only shape varies. The student must tick the three equal attributes.
Student tasks
- Select the equal attributes in the 3 cards (answer: number, colour, fill).
Room 8 · Equal attributes (3)
The 3 cards have number 3 and triangle shape in common; colour and fill are all different. The student identifies the two equal attributes.
Student tasks
- Select the equal attributes in the 3 cards (answer: number, shape).
Room 9 · Different attributes (1)
The 3 cards are identical in number, colour and shape; only fill varies (empty, half, solid). The student marks the single attribute where all three values are all different.
Student tasks
- Select the all-different attributes in the 3 cards (answer: fill).
Room 10 · Different attributes (2)
The 3 cards share the same fill (half) but number, colour and shape are all different. The student marks the three attributes that have full variety.
Student tasks
- Select the all-different attributes in the 3 cards (answer: number, colour, shape).
Room 11 · Different attributes (3)
The 3 cards have number 2 and star shape fixed; colour and fill are all different. The student identifies the two attributes with full variety.
Student tasks
- Select the all-different attributes in the 3 cards (answer: colour, fill).
Room 12 · How many cards are there?
A combinatorics question: with 4 attributes and 3 values each, how many distinct cards exist? There is a visual clue with the 2-attribute grid (3² = 9 cards) and the formula 3⁴ = 81.
Student tasks
- Calculate the total number of cards in the real game (4 attributes × 3 values) and write 81.
Room 13 · Is it a trio? (1)
3 cards are shown where number, colour, shape and fill are all different. The student must answer yes or no as to whether they form a valid trio.
Student tasks
- Decide whether the 3 cards form a valid trio (answer: yes).
Room 14 · Is it a trio? (2)
3 cards are shown with numbers 3, 3 and 1: two are the same and one is different, which invalidates the trio. The student practises spotting the attribute that breaks the rule.
Student tasks
- Decide whether the 3 cards form a valid trio (answer: no) and identify the incorrect attribute.
Room 15 · Complete the trio (1)
2 cards and 6 options for the third are shown. The incorrect options differ from the correct one in 2 attributes. The correct answer forms a trio where all attributes are all different.
Student tasks
- Choose from the 6 options the card that completes the trio.
Room 16 · Complete the trio (2)
The two given cards share number (3) and fill (half). The correct third card keeps those values and introduces the missing colour and shape. The incorrect options differ in only 1 attribute.
Student tasks
- Choose from the 6 options the card that completes the trio.
Room 17 · Complete the trio (3)
The two given cards share orange colour and solid fill; number and shape are all different. The student must find the third card that fits, choosing from 6 options.
Student tasks
- Choose from the 6 options the card that completes the trio.
Room 18 · Find the trio (1)
There are 6 mixed cards and exactly one hidden trio among them (all attributes different). The student must select the 3 correct cards.
Student tasks
- Examine the 6 cards and select the 3 that form the only valid trio.
Room 19 · Find the trio (2)
With 7 available cards, the student looks for the only valid trio (all attributes different). There is one more distractor card than in the previous room.
Student tasks
- Examine the 7 cards and select the 3 that form the only valid trio.
Room 20 · Find the trio (3)
The largest search board: 8 cards arranged in a 4-column grid. The student locates the only valid trio among more distractors.
Student tasks
- Examine the 8 cards on the grid and select the 3 that form the only valid trio.
Room 21 · Maximum without a trio (1)
There are 12 cards with 4 interlocking trios. The challenge is to mark as many cards as possible without any group of 3 selected cards forming a trio. The answer is 8 cards.
Student tasks
- Identify which cards to avoid so that no trio is formed.
- Mark the maximum number of cards (8) and press Submit.
Room 22 · Maximum without a trio (2)
Advanced version with 15 cards and 5 interlocking trios. The student must find the maximum trio-free selection, which in this case is 10 cards.
Student tasks
- Analyse the 5 trios present and decide which cards to exclude.
- Mark the maximum number of cards (10) without forming any trio and press Submit.
Rooms to project
The most striking ones to show and discuss in class.