Grade 8 Number Patterns Worksheets — Find the Rule PDF
Grade 8 pattern work is about naming the rule precisely enough to keep a sequence going without guessing. Given a few terms, students state what happens at every step — add 120, take away 250, times 3, or a jump that itself grows — and then extend the run. That term-to-term precision is the groundwork the position-to-term rules of linear functions are built on. The six Grade 8 skills each live on their own page: Continue the Sequence and Find the Missing Term for the arithmetic side, Doubling and Halving for a ratio of 2, Multiplying Sequences for ratios of 3, 4 and 5, plus Name the Rule and Two Rules Together.
Set the skill and its level, choose the problem count with the stepper, and the worksheet updates as you adjust it; add the answer key page and print or save a tidy PDF. The link reproduces the exact sheet, so a diagnostic today and the same diagnostic a month on compare fairly.
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Number Patterns · Grade 8
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Grade 8 · 2 pages · A4More Grade 8 number patterns skills
Each one generates a different kind of question, with its own three levels and answer key.
- Continue the SequenceWork out the rule from the terms shown, then write the ones that come next.
- Find the Missing TermThe gap is inside the sequence, so the rule has to be read from both sides of it.
- Name the RuleRead a sequence and write, in words, what its rule does at every step.
- Doubling and HalvingRuns that double at every step, and the same runs read backwards.
- Two Rules TogetherPatterns where two different jumps take turns, one term at a time.
- Multiplying SequencesSequences that grow by a fixed ratio each step, and the same runs in reverse.
What each level generates
Grade 8 continue the sequence — the exact skill behind each difficulty setting, straight from the generator.
- Level 1Count on in equal steps
- Level 2Count back in equal steps
- Level 3Steps that grow
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 →
What Grade 8 number patterns should cover
Most curricula expect Grade 8 students to move from term-to-term rules to position-to-term thinking: describing an arithmetic sequence by a linear rule and recognising a geometric sequence as a first term repeatedly multiplied by a constant ratio. These sheets do the first half of that — they ask what happens at every step and for the terms that follow — because a student who cannot state 'add 40' reliably has nothing to generalise from. Ratios of 2, 3, 4 and 5 keep the geometric terms growing quickly, so the arithmetic stays real work.
Multiplying Sequences is the working page, with Continue the Sequence and Doubling and Halving leading up to it. A fair benchmark is a 12- to 16-problem sheet on which the student states each rule and extends the sequence accurately. To take the next step, ask for a term further along out loud — 'what would the next-but-two term be?' — so the rule gets used rather than the counting; the printed blanks stop at the next two terms, so that jump is yours to ask for.
From term-to-term to a general rule
The move that matters next is linking position to value. For an arithmetic sequence, the step is the multiplier of the position and the rest is a constant adjustment — build it by asking what you would add to the times-table of the common difference to land on the first term. These pages do not print that question, but the rules they do ask for are its raw material: once 'add 40' is written beside the sequence, the times-table of 40 is the obvious next thing to try.
The classic Grade 8 slips are an off-by-one when generalising (using the position where you meant one less) and assuming a sequence is arithmetic when the gaps are actually multiplying. The second is caught on these sheets by testing the proposed rule against a term the student did not use to build it. When a diagnostic sheet is clean, Shuffle a fresh set at the same settings to confirm the rule-finding holds up.
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.