Numbers on a number line
Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagram
Lesson
Set out your lesson
“On a scaled number line, consecutive whole-number marks are equally spaced. The position of 38 is 38 units from zero. Addition moves right or forward by the length being added; subtraction moves left or backward by the length being subtracted. On a paper open number line, jump arcs are not drawn to scale—the labeled endpoints and + or − values show each jump. We can split a long jump into tens and ones while keeping the same total.”
Bring to the table
- A flexible cloth or plastic measuring tape marked from 0 to 100, handled by the parent
- Paper
- Pencil
Extra for the adult
Worked example. For 48 + 35, begin at 48, move +30 to 78, then +5 to 83. The jumps total 35, so 48 + 35 = 83. Reverse the same length: 83 − 35 uses −30 to 53 and −5 to 48.
Optional challenge. Show the inverse pair 60 + 35 = 95 and 95 − 35 = 60 on the same number line. Explain that both equations use the same 35-unit jump, forward in the addition and backward in the subtraction.
What to notice. Save a photo of the paper showing one placed number, one correct addition diagram, and one correct subtraction diagram, or a short parent note recording all three results and the child’s explanation of forward and backward jumps.
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Teaching approaches
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1 approach
On a scaled number line, consecutive whole-number marks are equally spaced. The position of 38 is 38 units from zero. Addition moves right or forward by the length being added; subtraction moves left or backward by the length being subtracted. On a paper open number line, jump arcs are not drawn to scale—the labeled endpoints and + or − values show each jump. We can split a long jump into tens and ones while keeping the same total.
Spend 15 minutes using the 0–100 scale as a number line. Place whole numbers, then sketch efficient tens-and-ones jumps on paper to represent one addition and one subtraction within 100.
Family records and proof options
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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
Frog and Toad on the number line
Before you open · source notes
Frog and Toad jumps are shown on a number line to model addition and subtraction. Use it for whole-number jumps, not every measurement skill.
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 show one jump forward or back on the line and name the landing number.
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 2026-11-11 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. “Frog and Toad on the number line.” 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
- Place whole numbers on a number line with equally spaced points
- Show an addition as a jump forward on the number line (e.g. 38 + 27 shown as jumps)
- Show a subtraction as a jump backward on the number line
“Can your child mark numbers on a number line and show what happens when they add or subtract — for example, jumping forward 35 places from 48?”
Curriculum record
- Type
- Representational
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 7–8
Standards