Number Sets & Infinity
Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers
Lesson
Set out your lesson
“Number Sets & Infinity 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
- Two colours of counters
- Paper for ratio or percent notation
Extra for the adult
Worked example. 2 red and 3 blue is the ratio 2:3.
Optional challenge. For Number Sets & Infinity, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Number Sets & Infinity, 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 practiceNumber Sets & Infinity practice
Practice key ideas from Number Sets & Infinity.
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.
PhET Interactive Simulations · Practice link — not the full lesson
Number Line: Integers
Before you open · source notes
Number Line: Integers supports hands-on exploration for Number Sets & Infinity. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Number Line: Integers.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Explain that rational numbers can be written as a fraction of two integers and have terminating or repeating decimals
- Give examples of irrational numbers and explain why their decimal expansions neither terminate nor repeat
- Appreciate that between any two numbers there are infinitely many other numbers
“Can your child explain that numbers like √2 and π can't be written as exact fractions — and that their decimal expansions go on forever without repeating?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Number Representation & Place Value
- Age range
- Ages 13–14
Standards