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Grade 8 Name the Rule Worksheets

Read a sequence and write, in words, what its rule does at every step.

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Number Patterns · Grade 8

Grade
Topic
SkillEach skill is a different kind of question, with its own levels.
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12

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Grade 8 · 2 pages · A4

Number Patterns Practice

Grade 8 • Name the Rule • Rules that count back
Name:Date:

Look at each sequence, then write its rule in words.

  1. 1) 1553, 1473, 1393, 1313, 1233 Rule: ___
  1. 2) 868, 718, 568, 418, 268 Rule: ___
  1. 3) 692, 572, 452, 332, 212 Rule: ___
  1. 4) 1845, 1695, 1545, 1395, 1245 Rule: ___
  1. 5) 1590, 1510, 1430, 1350, 1270 Rule: ___
  1. 6) 868, 788, 708, 628, 548 Rule: ___
  1. 7) 1688, 1568, 1448, 1328, 1208 Rule: ___
  1. 8) 713, 633, 553, 473, 393 Rule: ___
  1. 9) 2053, 1903, 1753, 1603, 1453 Rule: ___
  1. 10) 1244, 994, 744, 494, 244 Rule: ___
  1. 11) 1711, 1631, 1551, 1471, 1391 Rule: ___
  1. 12) 1604, 1484, 1364, 1244, 1124 Rule: ___
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Page 1 of 2

Answer Key

  1. 1. Take away 80 each time
  2. 2. Take away 150 each time
  1. 3. Take away 120 each time
  2. 4. Take away 150 each time
  1. 5. Take away 80 each time
  2. 6. Take away 80 each time
  1. 7. Take away 120 each time
  2. 8. Take away 80 each time
  1. 9. Take away 150 each time
  2. 10. Take away 250 each time
  1. 11. Take away 80 each time
  2. 12. Take away 120 each time
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Page 2 of 2

What each level generates

Grade 8 name the rule — the exact skill behind each difficulty setting, straight from the generator.

  1. Level 1Rules that count on
  2. Level 2Rules that count back
  3. Level 3Rules where the jump grows

Grade levels follow the progression common to most English-language curricula — not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence →

More Grade 8 number patterns skills

Each one generates a different kind of question, with its own three levels and answer key.

Frequently asked questions

▸What does 'find the rule' mean in Grade 8?

On these sheets it means describing what happens at every step, precisely enough to continue the run: 'add 120 each time', 'take away 250 each time', 'times 3', or — where the jump itself grows — 'each jump grows by 14'. That is a term-to-term rule. The position-to-term (nth term) rule that names any term directly is the step after, and it is built out of exactly these.

▸What sequences are expected in Grade 8?

Arithmetic sequences with any constant difference and geometric sequences with ratios of 2, 3, 4 and 5, continued with the rule stated in words. Doubling and Halving covers the ratio of 2; Multiplying Sequences runs Triple it each time, Cut it into thirds each time, then Bigger ratios, with a gap.

▸How does this help with algebra?

Reading a list of terms and naming its rule is the reasoning behind linear functions and expressions. These sheets build the term-to-term half of it; a student who can state a rule reliably turns it into a position-to-term rule far more easily, and reads tables and graphs of functions far more fluently.

▸Should students see arithmetic and geometric sequences together?

Yes, but across sheets rather than inside one. Each page here is a single skill so it can be taught cleanly; print a Continue the Sequence sheet and a Multiplying Sequences sheet and hand them over together, and the diagnose-then-rule habit still has to do its work.

▸Does the download match the screen exactly?

Yes — the preview is the worksheet, on your chosen A4 or US Letter size, and the PDF reproduces it precisely, answer key included. The shareable link brings back the identical sheet whenever you need it.