Generating Sequences
Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither
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Teaching Table
Set out your lesson
Generate terms from two kinds of rule. Use differences and ratios to classify the shown transitions.
First use Linear number sequences and Substituting into Formulae. Ask the learner to distinguish position 3 from the value at position 3 in a sequence. If this is unclear, label a position row before calculating. This lesson supplies and explains ratio notation; it does not assume a complete ratio lesson.
Check readiness directly. Prerequisite availability is not attainment.
Start with the readiness check. Use Show, then Guided, then a fresh Try. These linked lessons may need several short sessions; do not impose a speed target. Read the active sheet on screen and answer on plain paper or by typing. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt. Record any hints, scribing or calculation help. Oral explanations are allowed but do not show independent reading or handwriting. Use as much space and time as needed; pause or split the lesson. Keep this adult guide and all keys private. Share only the active learner sheet. Before Try, put Show, Guided work and notes aside. Keep the fresh Try givens available. Give no answer or target method during the first attempt. If help is needed, give it and mark the attempt supported. Review the key after the attempt. Record the actual response and help; do not invent success or infer mastery from one attempt. These are fictional paper or oral mathematics tasks. No personal information, public sharing, purchase, physical experiment or real measurement is required.
Record the actual response and assistance. These tasks do not establish mastery.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
Teaching limits and safe use
These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.
Finite displayed transitions support a local classification, not a unique law for all later terms. Zero-denominator and constant-sequence cases are deliberately excluded. No application interactive is needed or implemented.
Record the actual response and assistance. These tasks do not establish mastery.
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Teaching approaches
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1 approach
Generate terms from two kinds of rule. Use differences and ratios to classify the shown transitions.
Generate terms from two kinds of rule. Use differences and ratios to classify the shown transitions.
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Learning resources
External links for extra practice. They do not replace Gakuva’s teaching approach.
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Check understanding
- Continue a sequence given a term-to-term rule involving addition, subtraction, or multiplication
- Generate the first five terms from a position-to-term formula such as 3n − 2
- Classify sequences as arithmetic (constant difference), geometric (constant ratio), or other
“Can your child work out the next few terms of a sequence like 5, 8, 11, 14… and explain whether the rule is "add a fixed number each time" or something else?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 11–14
Standards