Systematic Listing
Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)
Share and support
Teaching Table · Reviewed guide
Set out your lesson
“Systematic listing finds every possible outcome without repeats. An organized table, tree, or fixed order helps prove the list is complete.”
Bring to the table
- Paper
- Pencil
- Three colored pencils if available
Full guide and materials
- Paper
- Pencil
- Three colored pencils if available
- Step 1. Choose a problem such as 3 shirts and 2 pairs of pants.
- Step 2. Predict the number of combinations.
- Step 3. Hold the first choice fixed while pairing it with every second choice, then repeat.
- Step 4. Check for omissions and duplicates and connect the count to multiplication.
- Quick check. Give a 2-by-4 choice problem. Success means your child lists all eight outcomes exactly once using a visible system.
Worked example. With shirts A, B, C and pants 1, 2, list A1, A2, B1, B2, C1, C2: 3 × 2 = 6 outcomes.
Optional challenge. Extend to three independent choices and compare a tree diagram with multiplication.
What to notice. Save a photo of the complete organized list or tree, or a short note recording how completeness was checked.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
Reviewed external links that reinforce this concept. They do not replace Gakuva’s teaching approach.
No reviewed resources for this concept yet.
The teaching approach above still stands. Curated practice links will appear here as the shelf fills.
Check understanding
- List all possible meal combinations from 3 starters and 4 mains
- Organise combinations into a systematic table to ensure none are missed
- Explain why the total number of combinations equals the product of the options in each category
“If your child can choose any combination of 3 T-shirt colours and 2 trouser colours, can they list every possible outfit without missing any or repeating?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 10–11