Numbers on a number line
Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations
Lesson
Set out your lesson
“Numbers on a number line 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
- Balance or equation cards with a box for the unknown
- Pencil
Extra for the adult
Worked example. □ + 3 = 10 → □ = 7 because 7 + 3 = 10.
Optional challenge. For Numbers on a number line, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Numbers on a number line, not mastery.
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Teaching approaches
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1 approach
Numbers on a number line 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: Balance or equation cards with a box for the unknown; Pencil. Adult solves one simple unknown (□ + 3 = 10) and checks by substituting. Child solves three unknowns and checks each by putting the number back in. Done: three checked solutions. Stop after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceNumbers on a number line practice
Practice key ideas from Numbers on a number line.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Find 7/4 starting from 1, Assessment Variation
Before you open · source notes
Find 7/4 starting from 1 supports placing numbers on a number line. Not every coordinate-plane graphing unit.
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 place 7/4 on a number line starting from 1 and explain the jumps.
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. “Find 7/4 starting from 1, Assessment Variation.” 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
- Write an inequality from a worded constraint (e.g., 'must be at least 12' → x ≥ 12)
- Represent the solution set of an inequality on a number line with open or closed circles
- Solve a one-step or two-step inequality such as 3x + 1 < 10
“Can your child solve an inequality like 2x + 1 < 9, show the answer on a number line, and explain what all the solutions have in common?”
Curriculum record
- Type
- Representational
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 9–14
Standards