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
Entire curriculum
1858 concepts · 9 subjects
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
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.
Materials: Two colours of counters; Paper for ratio or percent notation. 1. Say the goal of Number Sets & Infinity in plain words once. 2. Adult shows 2 red : 3 blue and says the ratio (or 40% of 10). 3. Child builds three ratios or percentage amounts and records each notation. 4. Fresh check: one fresh ratio or percent reading. Record and stop. Done: three correct ratio/percent records. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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