Designing number algorithms
Design and use algorithms with a sequence of steps, decisions with several alternatives (if / else-if / else) and repetition that apply rules to generate sets of numbers, implementing them in a flowchart, spreadsheet or visual program, and explain the patterns produced
Lesson
Set out your lesson
“Designing number algorithms means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Tally sheet or simple bar sketch
- A short set of category counts
Extra for the adult
Worked example. Cats 4, dogs 2 — cats have more. The tally and comparison are the proof.
Optional challenge. For Designing number algorithms, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Designing number algorithms, not mastery.
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1 approach
Designing number algorithms means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Tally sheet or simple bar sketch; A short set of category counts. Adult tallies one category and sketches a bar. Child tallies three categories and answers one comparison question. Done: three tallies plus one correct comparison. Stop after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceDesigning number algorithms practice
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Hitting The Target Number
Before you open · source notes
Hitting The Target Number supports designing number algorithms. Not every worksheet pack.
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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. “Hitting The Target Number.” 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
- Design a flowchart that classifies each number from 1 to 30 as 'multiple of 3', 'multiple of 5', 'both' or 'neither' and repeats for every number
- Implement 'start at 1; repeat 10 times: multiply by 2 and add 1' in a spreadsheet or block program and list the numbers made
- Explain why every number generated by the 'multiply by 2 and add 1' algorithm is odd
“Could your child design a set of instructions — like a flowchart or a simple spreadsheet — that sorts every number from 1 to 30 into groups such as 'multiple of 3', 'multiple of 5' or 'both', and explain the pattern?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 10–12
Standards