Linear number sequences
Generate and describe constant-step (linear) number sequences whose terms include negative values (counting through and past zero) or whose step is a decimal, using signed-number and decimal addition and subtraction; state the term-to-term rule, continue the sequence and use the rule to find a later term
Lesson
Set out your lesson
Use a constant step to continue a sequence, including decimal and negative steps, and find a specified term.
Before teaching
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Ask the learner to continue a simple repeated addition pattern and explain what repeats. Revisit the indexed Shape patterns source if the rule is unclear. Ask the learner to order −2, 0 and 2 from least to greatest. Expect −2, 0, 2. If negative values are unfamiliar, teach the short signed-number model below before the task; the separate Measuring temperature prerequisite is not available in the source index.
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Use a constant step to continue a sequence, including decimal and negative steps, and find a specified term.
Use a constant step to continue a sequence, including decimal and negative steps, and find a specified term.
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Locating Fractions Less than One on the Number Line
Before you open · source notes
Locating Fractions Less than One on the Number Line supports linear number sequences. Not every worksheet pack.
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Before you openAsk the learner to explain one step of “Locating Fractions Less than One on the Number Line” in their own words.
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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. “Locating Fractions Less than One 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
- Continue the sequence 2.5, 4.0, 5.5, ... and state the rule as 'add 1.5', calculating each decimal term
- Continue the sequence 5, 2, −1, −4, ... past zero into negative values and state its rule as 'subtract 3'
- Use the rule to find a later term of a sequence with negative values or a decimal step, e.g. the 6th term of 4, 1.5, −1, −3.5, ...
“If your child sees a sequence like 5, 2, −1, −4… (going below zero) or 2.5, 4.0, 5.5… (going up in decimals), can they say the rule, keep it going correctly, and work out a later number in the sequence?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 10–13
Standards