Monday, August 30, 2010

Week 33 (16 Aug – 20 Aug 2010)

Week 33 (16 Aug – 20 Aug 2010)

16/8/10(Monday)

Class :

4S3, 4S4, 4K2

Date :

16/8/10

Time :

0705-0805, 0805-0905, 1120-1150

Subject :

Mathematics

Learning Area :

Chapter 8: Circles III

Learning Objectives :

8.1 Understand and use the concept of Tangents of a circle

Learning Outcomes :

At the end of the lesson, students will be able to

  1. identify tangents to a circle
  2. make inference that the tangent to a circle is a straight line perpendicular to the radius that passes through the contact point

iii construct the tangent to a circle passing through a point:

  1. on the circumference of the circle
  2. outside the circle

iv. determine the properties related to two tangents to a circle from a given point outside the circle

v. solve problems involving tangents to a circle

Learning activities :

  1. Teacher introduce the new chapter by asking some of the questions in daily life.
  2. Discuss a few examples.
  3. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students could followed the lesson because they had learn this concept before.


 

17/8/10 (Tuesday)

Class :

4S2

Date :

17/8/10

Time :

0805-0905

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.4 Evaluating electrolysis in industry

Learning Outcomes :

At the end of the lesson, students will be able to

  • Write chemical equations to represent electrolysis process in industries,
  • Justify uses of electrolysis in industries,
  • Describe the problem of pollution from electrolysis in industry.

Learning activities :

  1. Teacher explain the way how to write chemical equations to represent electrolysis process in industries.
  2. Students are required to do exercise from workbook.

Teaching Aids :

Teaching courseware and workbook

Noble values :

Think objectively

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

18/8/10 (Wednesday)

Class :

4K2, 4S4

Date :

18/8/10

Time :

0705-0805, 1120-1150

Subject :

Mathematics

Learning Area :

Chapter 8: Circles III

Learning Objectives :

8.2 Understand and use the properties of Angle between tangent and chord

Learning Outcomes :

At the end of the lesson, students will be able to

  1. identify the angle in the alternate segment which is subtended by the chord through the contact point of the tangent
  2. verify the relationship between the angle formed by the tangent and the chord with the angle in the alternate segment which is subtended by the chord
  3. perform calculations involving the angle in alternate segment
  4. solve problems involving tangent to a circle and angle in alternate segment

Learning activities :

  1. Discuss and do correction for previous exercise.
  2. Teacher show the way how to find the angle between tangent and chord by discussing a few examples.
  3. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interesting and could followed the new concept very well.


 

19/8/10 (Thursday)

Class :

4S4

Date :

19/8/10

Time :

0705-0805

Subject :

Mathematics

Learning Area :

Chapter 8: Circles III

Learning Objectives :

8.3 Understand and use the properties of common tangents to solve problem

Learning Outcomes :

At the end of the lesson, students will be able to

  1. determine the number of common tangents which can be drawn to two circles which:
    1. intersect at two points
    2. intersect only at one point
    3. do not intersect
  2. determine the properties related to the common tangent to two circles which:
    1. intersect at two points
    2. intersect only at one point
    3. do not intersect

Learning activities :

  1. Discuss and do correction for the previous exercise.
  2. Discuss a few examples for the new concept.
  3. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient, tidy

Reflections :

Learning outcomes had been achieved. Students could followed the concept very well. There had 3 students who did not concentrated during the lesson, teacher had gave them a warning.


 

Class :

4S3

Date :

19/8/10

Time :

0805-0905

Subject :

Mathematics

Learning Area :

Chapter 8: Circles III

Learning Objectives :

8.2 Understand and use the properties of Angle between tangent and chord

Learning Outcomes :

At the end of the lesson, students will be able to

  1. identify the angle in the alternate segment which is subtended by the chord through the contact point of the tangent
  2. verify the relationship between the angle formed by the tangent and the chord with the angle in the alternate segment which is subtended by the chord
  3. perform calculations involving the angle in alternate segment
  4. solve problems involving tangent to a circle and angle in alternate segment

Learning activities :

  1. Discuss and do correction for previous exercise.
  2. Teacher show the way how to find the angle between tangent and chord by discussing a few examples.
  3. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interesting and could followed the new concept very well.


 

Class :

4S2

Date :

19/8/10

Time :

1050-1150

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.5 Analysing voltaic cell

6.6 Synthesising electrochemical series

6.7 Develop awareness and responsible practices when handing chemicals used in electrochemical industries

Learning Outcomes :

At the end of the lesson, students will be able to

  • Describe the structure of a simple voltaic cell and Daniell cell,
  • Explain the production of electricity from a simple voltaic cell,
  • Explain the reactions in a simple voltaic cell and Daniell cell,
  • Compare and contrast the advantages of various voltaic cells,
  • Describe the differences between electrolytic and voltaic cells.
  • Describe the principles used in constructing the electrochemical series,
  • Construct the electrochemical series,
  • Explain the importance of electrochemical series,
  • Predict the ability of a metal to displace another metal from its salt solution,
  • Write the chemical equations for metal displacement reactions
  • Justify the fact that electrochemical industries can improve the quality of life,
  • Describe the problem of pollution caused by the industrial processes involving electrolysis,
  • Justify the need to dispose of waste from electrochemical industries in a safe and orderly manner,
  • Practice safe and systematic disposal of used batteries

Learning activities :

  1. Discuss a few examples.
  2. Students are required to do exercise from workbook.

Teaching Aids :

Teaching courseware and workbook

Noble values :

Think objectively and cooperative

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

20/8/10 (Friday)

Class :

4K2, 4S3

Date :

20/8/10

Time :

0940-1040, 1040-1140

Subject :

Mathematics

Learning Area :

Chapter 8: Circles III

Learning Objectives :

8.3 Understand and use the properties of common tangents to solve problem

Learning Outcomes :

At the end of the lesson, students will be able to

  1. determine the number of common tangents which can be drawn to two circles which:
    1. intersect at two points
    2. intersect only at one point
    3. do not intersect
  2. determine the properties related to the common tangent to two circles which:
    1. intersect at two points
    2. intersect only at one point
    3. do not intersect

Learning activities :

  1. Discuss and do correction for the previous exercise.
  2. Discuss a few examples for the new concept.
  3. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient, tidy

Reflections :

Learning outcomes had been achieved. Students could followed the concept very well.

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Friday, August 13, 2010

Week 32 (9 – 13 August 2010)

Week 32 (9 – 13 August 2010)

9/8/10(Monday)

Class :

4S3, 4S4, 4K2

Date :

9/8/10

Time :

0705-0815, 0815-0925, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 6 & 7

Learning activities :

Monthly Test 2 (Section A)

Noble values :

Patient

Reflections :

Learning outcomes had been achieved.


 

10/8/10 (Tuesday)

Class :

4S2

Date :

10/8/10

Time :

0815-0925

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.3 Analysing the electrolysis of aqueous solutions

Learning Outcomes :

At the end of the lesson, students will be able to

  • Explain using examples factors affecting electrolysis of an aqueous solution
  • Write half equations for the discharge of ions at the anode and the cathode
  • Predict the products of electrolysis of aqueous solutions

Learning activities :

  1. Teacher explain the factors affecting electrolysis of an aqueous solution.
  2. Teacher show the way how to write half equations for the discharge of ions at the anode and the cathode.
  3. Discuss a few multiple choices questions to ensure that students could follow and understand the concept.
  4. Teacher do summary.
  5. Teacher asks students to complete the exercise from their workbook.

Teaching Aids :

ICT, hand out (note), workbook

Noble values :

Think rationally

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

11/8/10 (Wednesday)

Class :

4K2, 4S4

Date :

11/8/10

Time :

0705-0805, 1120-1150

Subject :

Mathematics

Learning Area :

Chapter 6 & 7

Learning activities :

Monthly Test 2 (Section B)

Noble values :

Patient

Reflections :

Learning outcomes had been achieved.


 

12/8/10 (Thursday)

Class :

4S4

Date :

12/8/10

Time :

0705-0805

Subject :

Mathematics

Learning Area :

Chapter 6 & 7

Learning activities :

Do correction for the Monthly Test 2.

Noble values :

Patient

Reflections :

Learning outcomes had been achieved.


 

Class :

4S3

Date :

12/8/10

Time :

0805-0905

Subject :

Mathematics

Learning Area :

Chapter 6 & 7

Learning activities :

Monthly Test 2 (Section B)

Noble values :

Patient

Reflections :

Learning outcomes had been achieved.


 

Class :

4S2

Date :

12/8/10

Time :

1050-1150

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.4 Evaluating electrolysis in industry

Learning Outcomes :

At the end of the lesson, students will be able to

  • State uses of electrolysis in industries
  • Explain the extraction, purification and electroplating of metals involving electrolysis in industries

Learning activities :

  1. Teacher explains the uses of electrolysis in industries.
  2. Explain the process of extraction, purification and electroplating of metals involving electrolysis in industries.
  3. Discuss a few examples in daily life.
  4. Students are required to do exercise from workbook.

Teaching Aids :

Teaching courseware and workbook

Noble values :

Daring to try

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

13/8/10 (Friday)

Class :

4K2, 4S3

Date :

13/8/10

Time :

0940-1040, 1040-1140

Subject :

Mathematics

Learning Area :

Chapter 6 & 7

Learning activities :

Do correction for the Monthly Test 2.

Noble values :

Patient

Reflections :

Learning outcomes had been achieved.

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Tuesday, August 10, 2010

Week 31 (2-6 August 2010)

Week 31 (2 – 6 August 2010)

2/8/10(Monday)

Class :

4S3, 4S4, 4K2

Date :

2/8/10

Time :

0705-0815, 0815-0925, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.2 Understand the concept of Events

Learning Outcomes :

At the end of the lesson, students will be able to

  1. identify the elements of a sample space which satisfy given conditions
  2. list all the elements of a sample which satisfy certain conditions using set notations

iii determine whether an event is possible for a sample space

Learning activities :

  1. Teacher explain the meaning of events.
  2. Discuss a few examples in format SPM.
  3. Students are required to do the exercise from workbook.

Teaching Aids :

Workbook

Noble values :

Careful

Reflections :

Learning outcomes had been achieved. All the students could follow the lesson very well.


 

3/8/10 (Tuesday)

Class :

4S2

Date :

3/8/10

Time :

0815-0925

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.2 Analysing electrolysis of molten compounds

Learning Outcomes :

At the end of the lesson, students will be able to

  • Describe electrolysis
  • Describe electrolytic cell
  • Identify cations and anions in a molten compound
  • Describe evidens for the existence of ions held in a lattice in solid state but move freely in molten state,
  • Describe electrolysis of a molten compound,
  • Write half-equations for the discharge of ions at anode and cathode
  • Predict products of the electrolysis of molten compounds.

Learning activities :

  1. Teacher explain the concept of free moving ions through the example.
  2. Teacher show the way how to write half-equations for the discharge of ions at anode and cathode.
  3. Discuss a few multiple choices questions to ensure that students could follow and understand the concept.
  4. Teacher do summary.
  5. Teacher asks students to complete the exercise from their workbook.

Teaching Aids :

ICT, hand out (note), workbook

Noble values :

Think rationally

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

4/8/10 (Wednesday)

Class :

4K2, 4S4

Date :

4/8/10

Time :

0705-0815, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.3 Understand and use the concept of Probability of an event

Learning Outcomes :

At the end of the lesson, students will be able to

  1. find the ratio of the number of times an event occurs to the number of trials
  2. find the probability of an event from a big enough of trials

    iii calculate the expected number of times an event will occur, given the probability of the use event and number of trials

Learning activities :

  1. Discuss a few examples in format SPM.
  2. Students are required to do teh exercise from workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in this lesson.


 

5/8/10 (Thursday)

Class :

4S4

Date :

5/8/10

Time :

0705-0815

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.3 Understand and use the concept of Probability of an event

Learning Outcomes :

At the end of the lesson, students will be able to

  1. solve problems involving probability
  2. predict the occurrence of an outcome and make a decision based on known information

Learning activities :

  1. Discuss a few examples.
  2. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in this lesson. However, still had 15% of the students confused of this concept.


 

Class :

4S3

Date :

5/8/10

Time :

0815-0925

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.3 Understand and use the concept of Probability of an event

Learning Outcomes :

At the end of the lesson, students will be able to

  1. find the ratio of the number of times an event occurs to the number of trials
    1. find the probability of an event from a big enough of trials

    iii calculate the expected number of times an event will occur, given the probability of the use event and number of trials

Learning activities :

  1. Discuss a few examples in format SPM.
  2. Students are required to do teh exercise from workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in this lesson.


 

Class :

4S2

Date :

5/8/10

Time :

1130-1240

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.3 Analysing the electrolysis of aqueous solutions

Learning Outcomes :

At the end of the lesson, students will be able to

  • Identify cations and anions in an aqueous solution
  • Describe the electrolysis of an aqueous solution

Learning activities :

  1. Teacher explain the way how to identify cations and anions in an aqueous solution.
  2. Teacher explain the process of electrolysis of an aqueous solution.
  3. Teacher do summary.
  4. Teacher asks students to complete the exercise from their workbook.

Teaching Aids :

ICT, hand out (note), workbook

Noble values :

Think rationally

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

6/8/10 (Friday)

Class :

4K2, 4S3

Date :

6/8/10

Time :

0940-1040, 1040-1140

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.3 Understand and use the concept of Probability of an event

Learning Outcomes :

At the end of the lesson, students will be able to

  1. solve problems involving probability
  2. predict the occurrence of an outcome and make a decision based on known information

Learning activities :

  1. Discuss a few examples.
  2. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in this lesson. However, still had 15% of the students confused of this concept.
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Monday, August 2, 2010

Week 30 (26 – 30 July 2010)

Week 30 (26 July - 30 July 2010)

26/7/10(Monday)

Class :

4S3, 4S4, 4K2

Date :

26/7/10

Time :

0705-0815, 0815-0925, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 6: Statistics

Learning Objectives :

6.6 Understand and use the concept of Measures of dispersion

Learning Outcomes :

At the end of the lesson, students will be able to

  • determine the range of a set data
  • determine:
  1. the median
  2. the first quartile
  • the third quartile
  • the interquartile range

from the ogive

  1. interpret information from an ogive
    1. solve problems involving data representations and measures of dispersion

Learning activities :

  1. Teacher explain the way how to determine the range of set data.
  2. Teacher shows the way how to determine the median, first quartile, third quartile and interquartile range from the ogive.
  3. Discuss a few examples.
  4. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Some of the students still weak in this concept.


 

27/7/10 (Tuesday)

Class :

4S2

Date :

27/7/10

Time :

0815-0925

Subject :

Chemistry

Learning Area :

Chapter 6: Electrochemistry

Learning Objectives :

6.1 Understanding properties of electrolytes and non-electrolytes

Learning Outcomes :

At the end of the lesson, students will be able to

  • State the meaning of electrolyte,
  • Classify substances into electrolytes and non-electrolytes
  • Relate the presence of freely moving ions to electrical conductivity

Learning activities :

  1. Teacher introduces the new topic by using computer simulation (Will the bulb light up?)
  2. Teacher explain the meaning of electrolytes, non-electrolytes and conductor.
  3. Teacher explain the concept of free moving ions through the example.
  4. Discuss a few multiple choices questions to ensure that students could follow and understand the concept.
  5. Teacher do summary.
  6. Teacher asks students to complete the exercise from their workbook.

Teaching Aids :

ICT, hand out (note), workbook

Noble values :

Think rationally

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

28/7/10 (Wednesday)

Class :

4K2, 4S4

Date :

28/7/10

Time :

0705-0815, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.1 Understand the concept of Sample space

Learning Outcomes :

At the end of the lesson, students will be able to

  • determine whether an outcome is a possible outcome of an experiment
  • list all the possible outcomes of an experiment:
  1. from activities
  2. by reasoning

iii determine the sample space of an experiment

iv write the sample space by using set notations

Learning activities :

  1. Teacher explain the meaning of probability.
  2. Discuss a few examples in daily life.
  3. Discuss a few examples in format SPM.
  4. Students are required to do teh exercise from workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in this new topic.


 

29/7/10 (Thursday)

Apply MC


 

30/7/10 (Friday)

Class :

4K2, 4S3

Date :

30/7/10

Time :

0940-1040, 1040-1140

Subject :

Mathematics

Learning Area :

Chapter 7: Probability I

Learning Objectives :

7.1 Understand the concept of Sample space

Learning Outcomes :

At the end of the lesson, students will be able to

  1. determine whether an outcome is a possible outcome of an experiment
  2. list all the possible outcomes of an experiment:
    1. from activities
    1. by reasoning

iii determine the sample space of an experiment

iv write the sample space by using set notations

Learning activities :

  1. Teacher explain the meaning of probability.
  2. Discuss a few examples in daily life.
  3. Discuss a few examples in format SPM.
  4. Students are required to do teh exercise from workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in this new topic.
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Week 29 (19- 23 July 2010)

Week 29 (19 July - 23 July 2010)

19/7/10(Monday)

Class :

4S3, 4S4, 4K2

Date :

19/7/10

Time :

0705-0815, 0815-0925, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 6: Statistics

Learning Objectives :

6.5 Understand the concept of Cumulative frequency

Learning Outcomes :

At the end of the lesson, students will be able to

  1. construct the cumulative frequency table for:
    1. ungrouped data
    2. grouped data
  2. draw the ogive for:
  • ungrouped data
    • grouped data

Learning activities :

  1. Teacher explain the way how to draw a ogive and how the marking scheme for ogive.
  2. Discuss a few examples.
  3. Students are required to do the exercise at workbook.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in drawing graph.


 

20/7/10 (Tuesday)

Class :

4S2

Date :

20/7/10

Time :

0815-0925

Subject :

Chemistry

Learning Area :

Chapter 5: Chemical Bonds

Learning Objectives :

5.4 Analysing properties of ionic and covalent compounds

Learning Outcomes :

At the end of the lesson, students will be able to

  • list properties of ionic compounds,
  • list properties of covalent compounds
  • explain differences in the electrical conductivity of ionic and covalent compounds

Learning activities :

  1. Discuss the properties of ionic compounds and covalent compounds.
  2. Discuss the differences in the electrical conductivity of ionic and covalent compounds.
  3. Students are required to do exercise from workbook.

Teaching Aids :

Teaching courseware and workbook

Noble values :

Think rationally

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

21/7/10 (Wednesday)

Class :

4K2, 4S4

Date :

21/7/10

Time :

0705-0815, 1205-1240

Subject :

Mathematics

Learning Area :

Chapter 6: Statistics

Learning Objectives :

6.5 Understand the concept of Cumulative frequency

Learning Outcomes :

At the end of the lesson, students will be able to

  1. construct the cumulative frequency table for:
  1. ungrouped data
    1. grouped data
  2. draw the ogive for:
  • ungrouped data
  • grouped data

Learning activities :

  1. Students continue doing their exercises.

Teaching Aids :

Workbook

Noble values :

Patient

Reflections :

Learning outcomes had been achieved. Students were very interested in drawing graph.


 

22/7/10 (Thursday)

Class :

4S4, 4S3

Date :

22/7/10

Time :

0705-0815, 0815-0925

Subject :

Mathematics

Learning Area :

Chapter 6: Statistics

Learning Objectives :

6.5 Understand the concept of Cumulative frequency

Learning Outcomes :

At the end of the lesson, students will be able to

  1. construct the cumulative frequency table for:
  1. ungrouped data
    1. grouped data
  2. draw the ogive for:
  • ungrouped data
  • grouped data

Learning activities :

  1. Students continue doing their exercises.

Teaching Aids :

Workbook

Noble values :

Patient, tidy

Reflections :

Learning outcomes had been achieved. Students were very interested in drawing graph.


 

Class :

4S2

Date :

22/7/10

Time :

1130-1240

Subject :

Chemistry

Learning Area :

Chapter 5: Chemical Bonds

Learning Objectives :

5.4 Analysing properties of ionic and covalent compounds

Learning Outcomes :

At the end of the lesson, students will be able to

  • describe differences in melting and boiling points of ionic and covalent compounds,
  • compare and contrast the solubility of ionic and covalent compounds
  • state uses of covalent compounds as solvents

Learning activities :

  1. Discuss the differences in melting and boiling points of ionic and covalent compounds.
  2. Students are asked to state the uses of covalent compounds as solvents.
  3. Students are required to do exercise from workbook.

Teaching Aids :

Teaching courseware and workbook

Noble values :

Appreciate the contribution of science and technology

Reflections :

Learning outcomes had been achieved. Students could followed the lesson very well.


 

23/7/10 (Friday)

Class :

4K2, 4S3

Date :

23/7/10

Time :

0940-1040, 1040-1140

Subject :

Mathematics

Learning Area :

Chapter 6: Statistics

Learning Objectives :

6.5 Understand the concept of Cumulative frequency

Learning Outcomes :

At the end of the lesson, students will be able to

  1. construct the cumulative frequency table for:
    1. ungrouped data
  2. grouped data
  1. draw the ogive for:
  • ungrouped data
  • grouped data

Learning activities :

  1. Students continue doing their exercises.

Teaching Aids :

Workbook

Noble values :

Patient, tidy

Reflections :

Learning outcomes had been achieved. Students were very interested in drawing graph.
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