Lesson 1

• Statements of how the ideas in the lesson sequence are progressing and what this lesson will be about and how it relates to last lesson;
• recap names, definitions, facts, and other observations.
• Introduces new aspect -asks what it might mean.
• Offers example, gets them to explain
• identifies properties
• gives another example
• More examples with multiple features; students to identify properties of them.
• Asks them to produce examples of objects with several features,
• Three concurrent tasks:
• properties in simple cases;
• properties in complex cases;
• creating own objects.
• individual and small group work
• vary variables deliberately
• classification task.
• identify some spatial relationships.
• teacher circulates asking questions about concepts and properties. 

Lesson 2

• announces lesson topic
• guessing mystery object
• adapt procedures,
• students suggest ways to find object
• teacher leads deduction of effects
• to and fro between LGEs and teacher showing them on board,
• interplay between LGEs expressed in own words and formal language,
• emphasise mathematical language,
• explication,
• justification
• inductive prediction and deduction 
• teacher tells what to think about and application to context,
• classifies,
• compares,
• find answers using procedure 
• compares answers,
• use of techniques,
• redescribe in formal mathematical language
• discusses implications and justification,
• adapts procedures,
• summarise lesson focusing on formal description of newly met maths

Lesson 3

Groups of students are teaching a topic each; they have researched it and created teaching tasks in their own words; associating ideas, using prior knowledge and adapting ideas, transforming them for teaching, and redescribing them. This includes them giving answers and following  and evaluating procedures shown to them by other students.

Lesson 4

• asks questions about a solid object, name and properties,
• asks for new properties
• use of procedures to find answers,
• justification of answers
• students work individually and write answers in board
• compare answers
• classify them
• now continue and predict answers
• students use their answers as empirical data to
• classify
• seek pattern
• compare
• informally induce
• identify relationships;
• they write conclusion comparing two similar concepts

Lesson 5

• Students are asked to imagine
• visualise spatial movement;
• own visualisation,
• creating object with two features;
• name object;
• teacher draws objects with imagined features;
• teacher says what the lesson is about and how this fits in sequence.
• Information giving,
• show multiple objects with same feature
• students describe procedure, in own words,  
• teacher asks for clarification;
• students think about how procedure will give them the desired outcome;
• students practise following procedures:
• teacher demonstrates object with multiple features. 
• info for doing task.
• students make shapes using with given procedure,
• choice of procedure by varying variables.
• Teacher indicates application to more complex maths next
• shows one s.a.s object
• sts predict
• how to complete shape
• identify missing features
• deduce further facts.

Probes & Prompts

Taking Action

Case Studies

Research Sources

See Also