Systematic Listing
Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)
Lesson
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
Extra for the adult
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.
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Systematic listing finds every possible outcome without repeats. An organized table, tree, or fixed order helps prove the list is complete.
List all outcomes for a two-part choice, first informally and then with an organized method.
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
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Jog-A-Thon
Before you open · source notes
Jog-A-Thon supports systematic listing. Not every worksheet pack.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to explain one step of “Jog-A-Thon” in their own words.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Jog-A-Thon.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
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 10–13
Standards