Place value and number-line representation
Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line
Lesson
Set out your lesson
“Place value and number-line representation 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
- Paper strips or a folded circle
- Pencil and labels (1/2, 1/4)
Extra for the adult
Worked example. Fold a strip in half: each piece is 1/2 of the whole.
Optional challenge. For Place value and number-line representation, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Place value and number-line representation, not mastery.
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Teaching approaches
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1 approach
Place value and number-line representation 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: Paper strips or a folded circle; Pencil and labels (1/2, 1/4). 1. Say the goal of Place value and number-line representation in plain words once. 2. Adult folds a strip into halves and labels 1/2. 3. Child makes three fair shares (or fraction operations with strips) and names each result. 4. Fresh check: one fresh equal-part or fraction result. Record and stop. Done: three correctly named fraction results. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
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Practice this concept
Start practicePlace value and number-line representation practice
Practice key ideas from Place value and number-line representation.
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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 Place value and number-line representation. 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
- Identify the value of any digit in numbers of any size including decimals
- Place positive and negative integers, decimals, and fractions on a number line
- Use place value to compare and order numbers across the full number system
“Can your child place a mix of numbers — like 3, −2, 0.5, −1.75, and ¼ — all on the same number line, in the right order?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Number Representation & Place Value
- Age range
- Ages 11–13
Standards