←
Teaching Mathematics: Methodology · Chapter 5

Planning: Year Plan, Unit Plan and Lesson Plan

What to remember

  • Planning goes from wide to narrow: the year plan (whole year) leads to the unit plan (a block of related content) and then to the lesson plan (one period). Each is made with the objectives in mind.
  • Herbart's five formal steps are Preparation, Presentation, Comparison and association, Generalisation, Application. Morrison's unit steps are Exploration, Presentation, Assimilation, Organisation, Recitation.
  • A good plan is objective-based, flexible, realistic in time, and ends with evaluation and assignment.

Why planning matters

Teaching without a plan wastes time and leaves topics half covered. Planning helps the teacher to: decide objectives; select content, methods and aids; use time well; connect one lesson to another; keep a balance of teaching, practice and tests; and review what has been taught. A plan is a guide, not a chain: the teacher may change it when the class needs it.

Level of planCoversPreparedMain purpose
Year plan (annual plan)Whole academic yearBefore the year beginsDistribute the course across the working days
Unit planOne unit or group of related topicsBefore the unit startsOrganise a meaningful block
Lesson planOne period (or one topic)Before each periodGuide the daily teaching

Year plan (annual plan)

A year plan is the teacher's overall scheme for the full academic year. It shows what will be taught in which month and how many periods each unit will get.

Points considered:

  • Total number of working days and periods available after holidays, examinations, festivals and school events.
  • The course content, divided into units in a logical order.
  • Weightage: more periods for important or difficult units.
  • Time for revision, tests, remedial teaching and enrichment.
  • Time for activities, mathematics club work and projects.
  • Local conditions and special school events.

Format: a table with columns such as month, unit, number of periods, objectives, methods and aids, evaluation, remarks.

Merits: keeps the pace even; prevents last-minute rush; allows revision; shows the whole picture of the course.

Example of period distribution: a unit with 12 periods may be split as 8 for teaching, 2 for practice, 1 for a unit test and 1 for remedial work.

Unit plan

A unit is a complete, meaningful segment of learning organised around one theme or a group of related ideas, such as "Triangles" or "Linear equations". The unit plan breaks the topic into lessons and links them. The idea of the unit plan was developed by H. C. Morrison, whose pattern also gave a teaching cycle with five stages.

Morrison's five steps:

  • 1. Exploration (finding out what pupils already know).
  • 2. Presentation (the teacher presents the new content).
  • 3. Assimilation (pupils work, practise and absorb).
  • 4. Organisation (pupils arrange and write out what they have learned).
  • 5. Recitation (pupils present or tell it to the class).

Parts of a unit plan:

  • Unit title, class, number of periods
  • General and specific objectives
  • Content analysis (list of concepts, facts, skills and processes)
  • Previous knowledge needed
  • Methods and approaches
  • List of lessons with period allotment
  • Teaching and learning materials
  • Activities and assignments
  • Evaluation (tests and diagnostic checks), and remedial plan

Merits: gives a sense of wholeness and connection between lessons; encourages planning of activities and evaluation for a whole topic; avoids isolated teaching. Limit: needs time and skill to prepare.

Lesson plan

A lesson plan is a teacher's detailed written plan for one period or one topic. It states what the teacher will do and what the pupils will do, within the time available.

Common parts:

PartContent
General informationClass, subject, topic, date, period, duration
ObjectivesSpecific, in behaviour terms
Previous knowledgeWhat pupils already know
Teaching aids (TLM)Charts, models, board, kits
Introduction (motivation)Question, story, activity to arouse interest
Presentation (development)Steps, examples, activities, questions
Practice and applicationExercises, group work
RecapitulationSummary of key points
EvaluationQuestions to check objectives
Assignment (homework)Follow-up work
Blackboard summaryThe neat outline written on the board

Typical time use for a 40-minute period (only an example): introduction 5 minutes, presentation 20, practice and discussion 8, evaluation 5, assignment and closing 2. The teacher fits the time to the content.

Herbartian approach

Johann Friedrich Herbart, a German educator, gave the idea that teaching should follow steps in the mind. His followers (Ziller and Rein) shaped the five formal steps, often called the Herbartian steps.

StepWhat happensMathematics example (area of a parallelogram)
1. PreparationArouse interest; recall earlier knowledge; state the aimRecall the area of a rectangle
2. PresentationNew content given by activity or examplesCut and shift a triangle from a parallelogram to make a rectangle
3. Comparison and associationCompare examples; note likenesses and differencesCompare base and height with the rectangle
4. GeneralisationThe rule is statedArea = base x height
5. ApplicationThe rule is used in new problemsFind areas of given parallelograms

Some teachers add a sixth step: recapitulation. Herbartian steps use the inductive approach: from examples, through comparison, to a rule. They are teacher-led and tidy, and they are a base for many later lesson formats.

Other lesson formats

  • Evaluation approach (Bloom): the plan begins with objectives, then learning experiences, then the evaluation items that test the objectives. The three go together.
  • Constructivist 5E model: Engage, Explore, Explain, Elaborate, Evaluate. The pupils construct meaning; the teacher is a facilitator. This is common in activity-based classrooms such as those in AP schools.
  • Activity-based plan: starts from an activity (fold, measure, play) and moves to concept and then to practice.

Worked illustration: a short unit on triangles

Suppose the unit "Triangles" has 12 periods. A teacher may allot: 2 for types of triangles (by sides and by angles), 2 for the angle sum property, 2 for congruence conditions, 2 for properties of isosceles and equilateral triangles, 1 for practice, 1 for a unit test, 1 for correction of errors, and 1 for enrichment activities (12 in all). Objectives are written for each lesson, and aids such as straws, paper cut-outs and a geoboard are listed against the lessons where they are needed. The unit test is built from the objectives so that every objective gets at least one item.

Lesson plan in an activity-based classroom

In many AP classrooms the lesson is built around a short pupil activity. The teacher gives a task, pupils work in pairs or groups, the teacher moves among them with questions, groups share their findings, and the teacher closes with a clear statement of the idea. The plan therefore records the task, the questions the teacher will ask, the possible mistakes pupils may make, and the closing statement. A plan for such a class is shorter in teacher talk and longer in pupil work.

Qualities of a good plan

It is based on clear objectives; suited to the age and level of pupils; flexible; realistic in time; uses a variety of methods and aids; has pupil activity in it; includes questions for evaluation; links with earlier and later learning; and is neither too long nor too thin. It should leave room for the teacher's reflection after teaching (what worked, what should change).

Classroom angle

  • Write the plan before the period, and keep a short remarks section after it.
  • Plan questions for each objective, including one or two higher-order questions.
  • Prepare aids in advance and check that they work.
  • Keep a small spare activity for early finishers and a simple help activity for slow learners.
  • After a unit test, use the results to plan remedial work.

Exam traps

  • Year plan vs unit plan vs lesson plan: whole year, one block of content, one period.
  • Herbart vs Morrison: Herbart's steps are for a lesson (five formal steps); Morrison's steps are for a unit.
  • Preparation vs presentation: preparation arouses interest and recalls; presentation gives the new content.
  • Comparison and association vs generalisation: comparing examples comes first; stating the rule comes second.
  • Recapitulation vs evaluation: recapitulation repeats key points; evaluation tests learning.
  • Assignment vs evaluation: assignment is follow-up work after the lesson; evaluation is checking within the lesson.
  • Plan vs rule: a plan is a flexible guide, not a rigid script.
  • Unit vs topic: a unit is a larger, meaningful block that may hold several topics.

One-liners

  • 1. A year plan distributes the course across the working days of the year.
  • 2. A unit plan organises a block of related topics.
  • 3. A lesson plan is for one period or one topic.
  • 4. Herbart's five formal steps begin with Preparation.
  • 5. The fifth Herbartian step is Application.
  • 6. Herbartian generalisation comes after comparison and association.
  • 7. Morrison's five steps are Exploration, Presentation, Assimilation, Organisation and Recitation.
  • 8. A lesson plan lists objectives, previous knowledge, aids, steps, evaluation and assignment.
  • 9. The 5E model is Engage, Explore, Explain, Elaborate, Evaluate.
  • 10. Objectives are written before content and methods are chosen.
  • 11. A good year plan keeps time for revision and tests.
  • 12. Remedial work follows the results of tests.

Practice questions

  1. A plan for the whole academic year showing units and periods is a

    1. Daily diary
    2. Year plan
    3. Lesson plan
    4. Unit plan
    Answer

    B. Year plan

    The year plan covers the entire academic year.

  2. A plan for one period or one topic is a

    1. Unit plan
    2. Year plan
    3. Syllabus
    4. Lesson plan
    Answer

    D. Lesson plan

    The lesson plan covers one period.

  3. A plan for a block of related topics such as 'Triangles' is a

    1. Unit plan
    2. Lesson plan
    3. Question paper
    4. Year plan
    Answer

    A. Unit plan

    A unit plan organises one meaningful block.

  4. The five formal steps of teaching are associated with

    1. Bruner
    2. Morrison
    3. Polya
    4. Herbart
    Answer

    D. Herbart

    Herbart and his followers gave the five formal steps.

  5. The first Herbartian step is

    1. Generalisation
    2. Preparation
    3. Application
    4. Presentation
    Answer

    B. Preparation

    Preparation starts the lesson.

  6. The correct order of Herbartian steps is

    1. Presentation, preparation, generalisation, comparison, application
    2. Preparation, comparison, presentation, application, generalisation
    3. Preparation, presentation, comparison and association, generalisation, application
    4. Application, preparation, presentation, comparison, generalisation
    Answer

    C. Preparation, presentation, comparison and association, generalisation, application

    The standard order is fixed.

  7. In the Herbartian steps, the rule is stated in the step of

    1. Generalisation
    2. Presentation
    3. Application
    4. Preparation
    Answer

    A. Generalisation

    Generalisation states the rule.

  8. Using the new rule on fresh problems is the Herbartian step of

    1. Preparation
    2. Application
    3. Presentation
    4. Comparison
    Answer

    B. Application

    Application is the last of the five steps.

  9. Morrison's five steps are for

    1. Unit teaching
    2. Daily lesson only
    3. Year planning
    4. Examination only
    Answer

    A. Unit teaching

    Morrison's pattern organises the teaching of a unit.

  10. The correct order of Morrison's steps is

    1. Exploration, assimilation, presentation, recitation, organisation
    2. Recitation, exploration, presentation, organisation, assimilation
    3. Exploration, presentation, assimilation, organisation, recitation
    4. Presentation, exploration, recitation, assimilation, organisation
    Answer

    C. Exploration, presentation, assimilation, organisation, recitation

    This is the order of the five steps.

  11. In Morrison's pattern, finding out what pupils already know is

    1. Organisation
    2. Recitation
    3. Assimilation
    4. Exploration
    Answer

    D. Exploration

    Exploration tests prior knowledge.

  12. The 5E model consists of Engage, Explore, Explain, Elaborate and

    1. Express
    2. Examine
    3. Evaluate
    4. Experiment
    Answer

    C. Evaluate

    The last E is Evaluate.

  13. A plan that begins with objectives, then experiences, then evaluation items follows the

    1. Evaluation approach
    2. Herbartian approach only
    3. Memory approach
    4. Dictation approach
    Answer

    A. Evaluation approach

    Objectives, experiences and evaluation are planned together.

  14. Which part of a lesson plan arouses interest at the start?

    1. Blackboard summary
    2. Assignment
    3. Evaluation
    4. Introduction (motivation)
    Answer

    D. Introduction (motivation)

    Motivation opens the lesson.

  15. Follow-up work given after the lesson is the

    1. Presentation
    2. Assignment
    3. Introduction
    4. Recapitulation
    Answer

    B. Assignment

    Homework is assignment.

  16. Which is NOT normally part of a lesson plan?

    1. Evaluation questions
    2. List of all school holidays of the year
    3. Objectives
    4. Teaching aids
    Answer

    B. List of all school holidays of the year

    Holidays belong in year planning.

  17. Which point is most important when making a year plan?

    1. Number of pupils' bags
    2. Colour of the chalk
    3. Total working days after holidays and examinations
    4. The size of the staff room
    Answer

    C. Total working days after holidays and examinations

    Available teaching time determines the distribution.

  18. A good plan should be

    1. Fixed and never changed
    2. Without aids
    3. Without evaluation
    4. Objective-based and flexible
    Answer

    D. Objective-based and flexible

    Plans guide teaching but can be adjusted.

  19. A unit has 12 periods: 8 for teaching, 2 for practice, 1 for a unit test. How many remain for remedial work?

    1. 2
    2. 3
    3. 1
    4. 0
    Answer

    C. 1

    12 - (8 + 2 + 1) = 1.

  20. A year plan has 180 teaching periods, of which 30 are for revision and tests. The share of periods for teaching new content is

    1. 150
    2. 160
    3. 170
    4. 140
    Answer

    A. 150

    180 - 30 = 150.

  21. In a 40-minute period a teacher gives introduction 5, presentation 20, practice 8 and evaluation 5 minutes. The time left for assignment and closing is

    1. 5 minutes
    2. 2 minutes
    3. 7 minutes
    4. 3 minutes
    Answer

    B. 2 minutes

    5 + 20 + 8 + 5 = 38, and 40 - 38 = 2.

  22. A teacher plans 25 periods for algebra, which is one fifth of the periods available for mathematics. The total periods for mathematics are

    1. 100
    2. 75
    3. 150
    4. 125
    Answer

    D. 125

    25 x 5 = 125.

  23. A unit of 15 periods has teaching, practice and testing in the ratio 3 : 1 : 1. The number of teaching periods is

    1. 5
    2. 6
    3. 10
    4. 9
    Answer

    D. 9

    15 x 3/5 = 9.

  24. A class of 40 minutes uses 25 percent for presentation. The time for presentation is

    1. 15 minutes
    2. 8 minutes
    3. 10 minutes
    4. 25 minutes
    Answer

    C. 10 minutes

    25 percent of 40 = 10.

  25. A year plan allots 8 periods to each of 14 units. The total number of periods is

    1. 112
    2. 98
    3. 120
    4. 104
    Answer

    A. 112

    8 x 14 = 112.

  26. Study the statements. 1. A year plan is prepared before the academic year begins. 2. A lesson plan covers the whole year. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    A lesson plan covers one period, so statement 2 is false.

  27. Study the statements. 1. Herbart's steps begin with Preparation. 2. Herbart's steps end with Application. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are true.

  28. Study the statements. 1. A good lesson plan includes evaluation. 2. A good lesson plan must never be altered. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Plans should be flexible, so statement 2 is false.

  29. Study the statements. 1. Morrison's steps belong to the unit plan. 2. Herbart's steps belong to the lesson plan. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both associations are standard.

  30. Study the statements. 1. In the Herbartian plan, generalisation comes before comparison. 2. Application comes after generalisation. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    Comparison and association come before generalisation, so only statement 2 is right.

  31. Study the statements. 1. A unit plan gives wholeness to a block of lessons. 2. A unit plan has no place for evaluation. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Unit plans include evaluation and remedial work.

  32. Study the statements. 1. The 5E model suits constructivist teaching. 2. In 5E, the teacher is a facilitator. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

  33. Study the statements. 1. Recapitulation is the same as assignment. 2. Evaluation checks whether objectives were met. Which is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    Recapitulation repeats key points; assignment is follow-up work.

  34. Match: (a) Year plan (b) Unit plan (c) Lesson plan with (p) One period (q) Whole academic year (r) Block of related topics.

    1. a-q, b-p, c-r
    2. a-r, b-q, c-p
    3. a-p, b-r, c-q
    4. a-q, b-r, c-p
    Answer

    D. a-q, b-r, c-p

    Year is whole-year; unit is a block; lesson is one period.

  35. Match: (a) Preparation (b) Presentation (c) Generalisation (d) Application with (p) New content given (q) Use of rule in new problems (r) Interest and recall (s) Rule stated.

    1. a-p, b-r, c-s, d-q
    2. a-r, b-p, c-q, d-s
    3. a-s, b-r, c-p, d-q
    4. a-r, b-p, c-s, d-q
    Answer

    D. a-r, b-p, c-s, d-q

    Preparation: interest and recall; presentation: new content; generalisation: rule; application: use.

  36. Match: (a) Exploration (b) Assimilation (c) Organisation (d) Recitation with (p) Pupils tell or present (q) Pupils arrange what they learned (r) Pupils practise and absorb (s) Find out what pupils know.

    1. a-s, b-q, c-r, d-p
    2. a-s, b-r, c-q, d-p
    3. a-p, b-r, c-q, d-s
    4. a-r, b-s, c-q, d-p
    Answer

    B. a-s, b-r, c-q, d-p

    These are the Morrison steps in order.

  37. A teacher begins a lesson on the area of a parallelogram by asking the area of a rectangle. This is the step of

    1. Recitation
    2. Generalisation
    3. Application
    4. Preparation
    Answer

    D. Preparation

    Recalling earlier knowledge is preparation.

  38. Pupils cut a triangle from a parallelogram and shift it to form a rectangle. The step is

    1. Assignment
    2. Presentation
    3. Preparation
    4. Application
    Answer

    B. Presentation

    New content is given through an activity.

  39. After solving examples the class states 'Area = base x height'. The step is

    1. Generalisation
    2. Preparation
    3. Comparison
    4. Application
    Answer

    A. Generalisation

    Stating the rule is generalisation.

  40. Giving ten fresh problems on the rule just learned is the step of

    1. Presentation
    2. Exploration
    3. Preparation
    4. Application
    Answer

    D. Application

    Applying the rule to new cases is application.

  41. Which is the best reason for writing objectives first in a lesson plan?

    1. The principal asks for it
    2. Pupils must read them
    3. Methods, aids and tests are chosen to match them
    4. The plan looks longer
    Answer

    C. Methods, aids and tests are chosen to match them

    Objectives guide everything else.

  42. After a unit test shows many pupils weak in fractions, the teacher should

    1. Reduce practice
    2. Plan remedial teaching
    3. Move to the next unit without change
    4. Cancel tests
    Answer

    B. Plan remedial teaching

    Test results guide remedial work.

  43. A teacher notes after each lesson what worked and what failed. This serves

    1. Reflection and later planning
    2. Fixing the timetable
    3. Punishing pupils
    4. Printing the textbook
    Answer

    A. Reflection and later planning

    Remarks help improve later plans.

  44. Which is a weakness of a unit plan?

    1. It isolates lessons
    2. It needs time and skill to prepare
    3. It has no objectives
    4. It has no evaluation
    Answer

    B. It needs time and skill to prepare

    Careful unit planning demands effort.

  45. A year plan that gives equal periods to every unit, easy or hard, ignores the idea of

    1. Timetable
    2. Revision
    3. Weightage
    4. Objectives
    Answer

    C. Weightage

    Important and difficult units need more time.

Page 1 of 1
‹
›