Following number algorithms
Follow and create algorithms (flowcharts or written step lists) with a sequence of steps, decisions using comparisons (e.g. 'Is the number greater than 20?', 'Is it even?') and repetition until a stop condition, to investigate numbers and describe the patterns that emerge
Lesson
Set out your lesson
“Following 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 Following number algorithms, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Following number algorithms, not mastery.
Share and support
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.
Practice this concept
Start practiceFollowing number algorithms practice
Practice key ideas from Following number algorithms.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Number Line Comparisons
Before you open · source notes
Number Line Comparisons supports following number algorithms. 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 “Number Line Comparisons” 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. “Number Line Comparisons.” 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
- Follow a flowchart: start at 7; if the number is even halve it, otherwise add 1; repeat until you reach 1, and record each number
- Describe what a flowchart with the decision 'Is the number greater than 50?' does to the numbers 34, 51 and 80
- Write a step-by-step algorithm with a decision and a stop condition (e.g. add 7 repeatedly from 0 and stop before 80) and describe the pattern in the numbers it makes
“If your child is given a set of instructions like 'if the number is even, halve it; if it's odd, add 1; keep going until you reach 1', can they follow it step by step and notice any pattern?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 8–10
Standards