Wu Suet Yu's Lesson Plan
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BMED 3021
Micro-teaching Lesson Design
Wu Suet Yu
1155093808
Micro-teaching Lesson Plan
1. Lesson Profile
o Subject: Mathematics
o School type: School with English as the medium of instruction o Grade: Secondary 3
o Class size: 30
o Students ability: Mixed ability, dominated by visual learners o Lesson Length: 30 minutes
o Topic: More about 3D figures – Angles between two planes
- Learning pre-requisite:
o Projection of a point onto a plane
o Projection of a line onto a plane
o Angle between a line and a plane
- Learning objectives: Students will be able to:
o Recall the criteria of an angle between two planes o Indicate the angle between two planes
- Flipped classroom video: Link:
• https://www.youtube.com/watch?v=oY0VFKhScPA&rel=0
• https://www.powtoon.com/online-presentation/c9Ai2JS1i6z/flipped-classroom/?mode=movie#/
- Pre-assessment:
After watching the flipped classroom video at home, students are required completed the worksheet and hand-in the worksheet one day before the lesson.
The worksheet will serve as a pre-assessment of students’ readiness of learning the new knowledge so that the teacher can arrange a little revision of the learning pre-requisite if needed.
6. Grouping:
Heterogeneous grouping will be employed in the classroom.
An abler student will be grouped with a less able student.
7. Learning & teaching activities
For the second activity, students will construct a tool to help produce signs and more concrete meaning of the concept.
For instance, ∠"#$ and
∠"&$ Then, the students will be given a Through step-by-step guidance, students are expected to understand and conclude the two criteria on choosing the angle between two planes:
(1) The angle is enclosed by the two lines meeting at the intersecting line of two planes.
(2) The lines are both perpendicular to the intersecting line and passing through a common point.
The tool is shown below.
8. Lesson Flow:
Time (mins)
Procedures
5 Knowledge review :
- Teachers will explain common mistakes that students committed in the follow-up
worksheet.
- If
no students are able to complete the exercise, the teacher will take the role to
explain the questions.
Teachers may ask:
“How do you know your answer is correct?”
“Do anyone have a different answer as (someone)?”
“What is the key steps in finding a projection of (point/line) on the plane? ”
Remark/ Rationale
- To ensure the students have enough knowledge to learn new concept.
- Guiding question should be used to guide students to find the answer by themselves and explain their answer more clearly.
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Knowledge building: |
- PowerPoint and GeoGebra |
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- First, the teacher will group students talk about first question on worksheet to bring |
will be used |
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out the concept of ‘line of intersection’. |
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- The teacher will ask students to complete question 2 on worksheet, i.e. finding angles between two planes that have different size.
- The teacher will distribute the tablets and protractors to students after the students understand the task.
- The teacher will demonstrate how the program on GeoGebra works before letting the students to work on their own.
- The teacher should walk around to check if students understand the tasks, know how to use the Geogebra program and assist them if needed.
Teachers may ask:
“How many groups of angles can you get?”
- To show that there are angles in different size between two planes
- Teachers may be switch on all tablets, make sure all of them work before the lesson.
- The tablets allow students to check the angles sizes with GeoGebra.
“Which type of angle is it?”
à Induce an important question “Which angle(s) should we choose to represent the angle between two planes?”
- The teacher will guide students to find out the size of the angle between two planes using GeoGebra and protractor.
- The students are required find the group of angles that has same size as the angle between two planes.
Teachers may ask:
“What is special about the angles in a cuboid?”
- The teacher will ask students to find out the relationship between the lines forming the angle and the intersecting lines.
- The screen of the tablet will be projected to the projector screen so that every student can see.
Teachers may ask:
“This group said that …, then does this group agree with them and why?”
- This helps filter the possible candidate of the angle between two planes
- To show that “the lines forming the angles should be perpendicular to the intersecting lines”
- Students are allowed to use GeoGebra in helping them to develop the relationship.
- The teacher should induce discussion within students.
- If students answer correctly but explain unclearly, the teacher may guide them to explain with proper questioning.
- If students answer incorrectly, the teacher should be ready to take the role (which will be shown in GeoGebra).
Debrief:
- The teacher will debrief the activity and ask students to conclude the key points in finding the angle between two planes and write them on the worksheet.
5 Learning tool making:
- The teacher will distribute the material and teach students to make the tools.
- The teacher will demonstrate the usage of the tools.
- To consolidate the knowledge they receive/ discover in the activity
- Use tool to help students to visual the angle and build up a personal meaning of it.
- GeoGebra:
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(Teacher |
version) |
https://www.geogebra.org/3d/t7r8knpc |
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(Student |
version) |
https://www.geogebra.org/3d/pzcbg9re |
- Follow-up Worksheet – Appendix 1
- Lesson PowerPoint – Appendix 2 https://docs.google.com/presentation/d/1zf7EP-jWxCbr0X6vVGLRa-thYSRnabUSydbO0aoY-q4/edit?usp=sharing
- Lesson Worksheet – Appendix 3
- Instruction for Tools Making – Appendix 4
Justification:
Therefore, two-people grouping can also maximize the engagement of each student while it is hoped that abler students could help the weaker students to learn the topic in such grouping.
It is believed that students have a rough idea about the angles between two planes but they do not know the accurate mathematic meaning of
Hence, they can establish a more concrete idea of “angles between two planes”.
The tools made contains signs that help students to internalized the concept and produce a personal meaning of the angle.
It is important to have a student-centered and highly interacted lesson, so that teacher will receive feedback from students to amend the lesson and the students will know how to understand their problems and improve.
Reference
Vygotsky, L. S. (1978) Mind in Society: The Development of Higher Psychological Processes Cole, V. John-Steiner, S. Scribner, & E. Souberman, transl.) Cambridge, MA: Harvard University Press
Ch.6 More about 3-D Figures
Pre-lesson Worksheet
Name:_____________________________ Class:___________ Class no. :__________
Instruction:
Ø Watch the flipped classroom video link:
https://www.youtube.com/watch?v=oY0VFKhScPA&rel=0 https://www.powtoon.com/online-presentation/c9Ai2JS1i6z/flipped-classroom/?mode=movie#/
Ø Complete the following questions
Ø For challenging questions, you will receive bonus points if you can answer correctly.
- In the figure, ABDEGF is triangular prism with a right-angled triangle base.
(a) Find the projection of point B on the plane DEGF.
(b) Find the projection of point F on the plane BDE.
(c) [Challenging question]
Find the projection of point D on the plane ABEG.
- In the figure, ABCDEFGH is a cuboid.
(a) Find the projection of point C on the plane EFGH.
(b) Find the projection of line CE on the plane EFGH.
(c) Find the projection of line CF on the plane EFGH.
(d) Find the projection of line DG on the plane CDEH.
- VE is the height of the pyramid.
(a) Find the projection of line VB on plane ABCD.
(b) Name the angle between line VB and plane ABCD
(c) Name the angle between VF and plane ABCD.
- E, F, G, H and I are the mid-points of AD, CD, AB, BC and AC respectively.
(a) Find the projection of line EI on plane ABC.
(b) Name the angle between EI and plane ABC.
(c) Name the angle between FG and plane ABC.
(d) [Challenging]
Name the angle between AF and plane BCD.
Ch.6 More about 3-D Figures
Pre-lesson Worksheet
Name:_____________________________ Class:___________ Class no. :__________
Instruction:
Ø Watch the flipped classroom video link:
https://www.youtube.com/watch?v=oY0VFKhScPA&rel=0 https://www.powtoon.com/online-presentation/c9Ai2JS1i6z/flipped-classroom/?mode=movie#/
Ø Complete the following questions
Ø For challenging questions, you will receive bonus points if you can answer correctly.
- In the figure, ABDEGF is triangular prism with a right-angled triangle base.
(a) Find the projection of point B on the plane DEGF.
(b) Find the projection of point F on the plane BDE.
(c) [Challenging question]
Find the projection of point D on the plane ABEG.
(a) Point D
(b) Point D
(c) Let M be a point on BE such that DM ⊥ Then, point M is the projection of point D on the plane ABEG.
- In the figure, ABCDEFGH is a cuboid.
(a) Find the projection of point C on the plane EFGH.
(b) Find the projection of line CE on the plane EFGH.
(c) Find the projection of line CF on the plane EFGH.
(d) Find the projection of line DG on the plane CDEH.
(a) Point H
(b) Line CH
(c) Line FH
(d) Line DH
- VE is the height of the pyramid.
(a) Find the projection of line VB on plane ABCD.
(b) Name the angle between line VB and plane ABCD
(c) Name the angle between VF and plane ABCD.
(a) Line BE
(b) ∠ VBE
(c) ∠VFE
- E, F, G, H and I are the mid-points of AD, CD, AB, BC and AC respectively.
(a) Find the projection of line EI on plane ABC.
(b) Name the angle between EI and plane ABC.
(c) Name the angle between FG and plane ABC.
(d) [Challenging]
Name the angle between AF and plane BCD.
(a) Line GI
(b) ∠EIG
(c) ∠FGH
(d) Then, ∠ AFB is the required angle.
Angles between two planes
(You can choose more than one)
(a) ∠ ADE
(b) ∠ ACB
(c) ∠ ACF
(d) ∠ GHI
https://www.geogebra.org/3d/pzcbg9re
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Line of intersection |
Which one is an angle |
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between these two plane? |
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(You can choose more than |
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one) |
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(a) ∠ A D E |
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(b) ∠ A C B |
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(c) ∠ A C F |
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(d) ∠ G H I |
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Form angles between two planes with different size!
Which one should I choose?
of angles!
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∠ A D E , ∠ A D F , ∠ |
∠ G C I |
∠ G C E |
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A D I , ∠ A C F , ∠ G D E , |
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∠ G C F , ∠ B C F , ∠ |
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B D E , ∠ B H I , |
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∠ A H E |
∠ G H F |
∠ B D I |
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∠ A H I |
∠ G H I |
∠ B H E |
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∠ A H F |
∠ G D F |
∠ B H I |
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∠ A C E , ∠ B D F |
∠ G H E |
∠ B H F |
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∠ A C I |
∠ G D I |
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Hints:
● Find out the relationship between
○ the lines forming the angle
○ The intersecting lines
Angles between two planes
What are the key steps in find angles between two planes?
Ch.6 More about 3-D Figures
Worksheet I
Angles Between Two Planes
Name:_____________________________ Class:___________ Class no. :__________
- (You can choose more than one)
(a) ADE
(b) ACB
(c) ACF
(d) GHI
- Write as many as possible!
- Measure the angle using the protractor.
(a) Size of the angle between two planes = _____________
(b) Which groups of angle in the question 2 has the same size as the measured angle?
(i) List out the angles in the group.
(ii) Why?
4. What are the keys steps in finding angles between two planes?
Ch.6 More about 3-D Figures
Angles Between Two Planes
Tools Making Instruction
Materials:
o Transparent plastic card x 10 (for class size: 30) o Scissors
o Blue marker pen, black marker pen
Instructions:
- Cut the card into size of “20cm x 10 cm”
- Fold the card in half
- Draw a line on the line of folding using blue marker pen
- Draw two perpendicular line using black marker pen
Examples:
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