EDSE mathematics Wi 2010 Modeling Mathematics Lesson Plan 1 Grade: 8 Stream: General Strand or Topic: Shape and Space The Curriculum AIM: General Outcome: Use direct and indirect measurement to solve problems. Specific Outcome(s) + Mathematical Processes: SO #2. Draw and construct nets for 3-D objects. [C,CN,PS,V] SO #3. Determine the surface area of: - right rectangular prisms - right triangular prisms to solve problems[C,CN,PS,R,V] Intended Learning Outcomes (ref Achievement Indicators): - Match a given net to the 3-D object it represents. - Construct a 3-D object from a given net. - Draw nets for a given right rectangular prism and right triangular prism, and verify by constructing the 3-D objects from the nets. - Predict 3-D objects that can be created from a given net, and verify the prediction. - Explain, using examples, the relationship between the area of 2-D shapes and the surface area of a given 3-D object. - Identify all the faces of a given prism, including right rectangular and right triangular prisms. - Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism. - Solve a given problem involving surface area. PRIOR SKILLS/KNOWLEDGE required Grade 6, Strand: Number, SO #2. - Solve problems involving whole numbers and decimal numbers. [ME, PS, T] [ICT: C6–2.4] Grade 6, Strand: Shape and Space, SO #3. - Develop and apply a formula for determining the: - Area of rectangles.[C, CN, PS, R, V] Grade 7, Strand: Shape and Space, SO #2. - Develop and apply a formula for determining the area of: - Triangles. [CN, PS, R, V] Grade 8, Strand: Shape and Space, SO #1. - Develop and apply the Pythagorean Theorem to solve problems. [CN, PS, R, T, V] [ICT: P2–3.4]
Transcript
EDSE mathematics Wi 2010
Modeling Mathematics Lesson Plan
1
Grade: 8 Stream: General Strand or Topic: Shape and Space
The Curriculum
AIM: General Outcome: Use direct and indirect measurement to solve problems.
Specific Outcome(s) +
Mathematical Processes:
SO #2. Draw and construct nets for 3-D objects. [C,CN,PS,V]
SO #3. Determine the surface area of:
- right rectangular prisms
- right triangular prisms
to solve problems[C,CN,PS,R,V]
Intended Learning
Outcomes (ref
Achievement
Indicators):
- Match a given net to the 3-D object it represents.
- Construct a 3-D object from a given net.
- Draw nets for a given right rectangular prism and right triangular
prism, and verify by constructing the 3-D objects from the nets.
- Predict 3-D objects that can be created from a given net, and verify
the prediction.
- Explain, using examples, the relationship between the area of 2-D
shapes and the surface area of a given 3-D object.
- Identify all the faces of a given prism, including right rectangular
and right triangular prisms.
- Describe and apply strategies for determining the surface area of a
given right rectangular or right triangular prism.
- Solve a given problem involving surface area.
PRIOR
SKILLS/KNOWLEDGE
required
Grade 6, Strand: Number, SO #2.
- Solve problems involving whole numbers and decimal numbers.
[ME, PS, T] [ICT: C6–2.4]
Grade 6, Strand: Shape and Space, SO #3.
- Develop and apply a formula for determining the:
- Area of rectangles.[C, CN, PS, R, V]
Grade 7, Strand: Shape and Space, SO #2.
- Develop and apply a formula for determining the area of:
- Triangles. [CN, PS, R, V]
Grade 8, Strand: Shape and Space, SO #1.
- Develop and apply the Pythagorean Theorem to solve problems.
[CN, PS, R, T, V] [ICT: P2–3.4]
EDSE mathematics Wi 2010
Modeling Mathematics Lesson Plan
2
OPENING or START-
UP activity
- Students will be separated into
groups (of 4 or 5 individuals).
- Each group will be given a “gift-
box” of a different shape or size (i.e.
rectangular prism or triangular
prism), which needs to be gift-
wrapped.
- Each group is faced with the
following problem: “Which pile of
wrapper paper is the right amount needed to wrap our
gift-box?”
- Student groups will predict (i.e. by estimation) which
pile of wrapping paper actually contains the right
amount to wrap their gift-box.
MOTIVATION for
activity
- The start-up activity will “hook” students by showing them the
application of surface area problems in daily life.
- Students will then construct 3-D objects using nets and use the
product to explore their understanding of 3-D objects and connect it
to the calculation of surface area.
BODY
Exploration,
Investigation &
Discovery
Student & Teacher Actions
Teacher Action Student Action
- Hand out the worksheets
- Explain how to create and identify
3-D objects using nets and how to
calculate surface area for given
prisms (use the cube as an
example; its corresponding
sections are already filled out on
the worksheet)
- Students will observe how to
fill out the worksheet and
how to create 3-D objects
from nets.
- Hand out nets of either a right
rectangular prism or a right
triangular prism to the students.
- Have students predict which net
they have, draw the net on their
worksheet in the correct row,
construct the 3-D object and then
fill out the worksheet.
- Students will predict which
net they have been given,
write it on their worksheet,
construct their prism and
proceed in filling out the
worksheet. From the 3D-
prism, they will sketch the
prism from the angle view;
and record the number of
EDSE mathematics Wi 2010
Modeling Mathematics Lesson Plan
3
Right Rectangular Prism
Template (Pg. 8):
Right Triangular Prism
Template (Pg. 9):
faces, the description of the
faces (i.e. what shape and
how many of that shape), and
the area of each face as well
as surface area for the prism.
Worksheet Template (Pg. 10):
- See Appendix for full-size
templates that can be
photocopied and pre-cut for
students (Pg. 8-10).
- *Note: the markings (i.e.
arrows, axis labels, etc) were
added by Pascal El Cid and
Jessica Quinlan to the
original blank templates, as
obtained from our source
(see resources list for the
websites).
- Provide coloring utensils to help
the students identify how many
faces there are and which shapes
they represent.
- Use the coloring utensils to
color code similar faces (i.e.
similar in area and shape).
- If time permits, there are two - Students will repeat the steps
EDSE mathematics Wi 2010
Modeling Mathematics Lesson Plan
4
options for students:
(1) Have students construct the
second prism and fill out the
rest of the worksheet (i.e. if
they finish the right rectangular
prism, have them construct the
right triangular prism).
(2) Allow students to explore
the concepts of 2D-nets and
3D- prisms using an online
interactive program available
through LearnAlberta.ca [See
Appendix (Pg. 11) for website
link, and sample screenshots of
the interactive program].
above for the other prism and
complete the worksheet,
either in class or as
homework.
- If no time is left, complete the
worksheet as a homework
assignment.
- Students may explore the
concepts learned using online
interactive programs to
further their learning (the
website link will be provided
by the teacher).
DIFFERENTIATION
PATHS
- All students will work individually on the worksheet.
- Students of known average ability will receive the standard
worksheet, as shown in the “BODY” section of this lesson plan.
- Scaffolding for students with various abilities, including:
Students can explore the concepts of 2D-nets and 3D- prisms
using an online interactive program available through
LearnAlberta.ca [See Appendix for website link, and sample
screenshots of the interactive program].
Students who need extra help will receive worksheets with
additional guides and clues [See Appendix (Pg. 12) for
template].
EDSE mathematics Wi 2010
Modeling Mathematics Lesson Plan
5
Clincher
CONCLUSION or
WRAP-UP
- After filling in the worksheet and practicing calculations of surface
areas, students will return to their groups and
calculate the surface area of their given gift-box as
a group.
- Students will select the correct pile of wrapping
paper that corresponds to their gift-box, and wrap
their gift to check if their calculations are correct.
- On a blank piece of paper, students will provide feedback about the
class activities by answering the following inquiries:
o Something new I‟ve learned today is:
o A concept that I need to practice more is:
o Today‟s lesson is applicable to the “real-world” because:
INDEPENDENT SEAT
WORK or
HOMEWORK
- After analyzing two labeled prisms, students will be asked to:
o Draw a 2D-net that corresponds to their prism.
o Calculate the surface area of their prism based on their drawing
of the 2D-net.
- [See Appendix for templates (Pg. 13-14) and sample responses (Pg.
15-16)].
EXTENSION (brain
teaser, puzzle, problem
of the week, etc.)
- Students will be given a question to
solve as a “problem of the week”
[See Appendix for template (Pg.
17) and solutions key (Pg. 18)].
EDSE mathematics Wi 2010
Modeling Mathematics Lesson Plan
6
Assessment, Rationale
Assessment:
Formative (for)
- One formative piece is the worksheet; students complete the
worksheet assignment as a measure of their understanding of the
topic, and to inform the teacher whether further exploration of the
topic is necessary. Worksheets will be retained as a display of
student class work during parent-teacher interviews.
- Another formative piece is the start-up/clincher activity: if students
grasped the concepts of 3D-prisms then they will be able to
correctly solve the proposed problem.
Summative (of)
- The first summative component is the independent seat work:
assignments will be marked for grades to assess student ability
- The extension question (i.e. “problem of the week”) is the second
component of the summative portion of assessment; it is a one-
problem scenario that will be graded for marks.
Self (as)
- The start-up/clincher activity may also be used by the individual to
assess their own learning: students will compare their “estimate” of
surface area prior to the lesson with their understanding of surface
area calculations following the lesson (i.e. students refer to their
prior work to compare their own understanding).
- The wrap-up activity involves student reflection of understandings,
confusions, and real-world applications of the lesson.
References: - Alberta Mathematics Program of Studies with Illustrative Examples
K-9 (1996)
- Altes, G. K. Paper Model of a Triangular Prism. Retrieved from
