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Instructional Plan
All Boxed In
Governor’s Institute for Mathematics Educators
Millersville University 2006
Grade Band 9-12
(Download as Microsoft Word Documents or
Excel Files: Instructional Plan,
Presentation, Rubric for Building a
Structure, Rubric
for Oral Presentation – Excel, Rubric
for Written Part – Excel)
Names of group members: Helen
Hughes-Smith ,Mary McConaughy,
Davina Pike and Lori Sidelinger
Topic/Theme: Spatial
Reasoning and Relationships
Level: Geometry
(8 – 12)
Time
Element: 2 – 42 minute periods
NCTM
Standards Addressed:
Measurement
and Geometry
Reasoning
Representation
Communication
Connections and Problem Solving
PA
Math Standards Addressed:
8th grade
2.3.8.F Use scale measurements to interpret
maps or drawings
2.3.8.G Create
and use scale models
2.9.8.H Use
simple geometric figures (e.g. triangles and squares) to create, through
rotation, transformational figures in three dimension.
11th grade
2.9.11.H Construct a geometric figure and its
image using various transformations.
2.9.11.I Model situations geometrically to
formulate and solve problems.
Math
Assessment Anchors Addressed:
M11.A.2 Understand
the meanings of operations, use operations and understand how they relate to
each other.
M11.C.1 Analyze
characteristics and properties of two- and three-dimensional geometric shapes
and demonstrate understanding of geometric relationships.
M11.C.2 Identify
and/or apply concepts of transformations or symmetry.
Objectives:
·
Students
will be able to draw all 12 pentominoes.
·
Students
will be able to recognize the 8 nets for topless boxes.
·
Students
will use ratios and proportions.
· Students will be able to determine the maximum number of boxes that can be made from each net for a given area.
· Students will be able to determine the net that creates the most boxes with the minimum amount of waste for a given area.
·
Students
will present results and justifications orally and in written form.
·
Students
will construct an open top box.
Instructional
strategies and plan:
1. Teacher will lead a discussion in order to help students determine the definition of a pentomino. (Talk about penta and dominoes and how each piece is connected.)
2.
Students
will then receive graph paper to use as an activity sheet to draw all pentominoes. Allow
the students time to see if they can find all
combinations before telling them that there should be 12.
3.
While
students are working, the teacher will walk around and complete oral and visual
checks of the students’ work. This is
also a good time to use transformation vocabulary with the students as they
look at rotations and reflections of the pieces they are drawing.
4.
The
teacher will now give a brief demonstration of what a net is. Show the class several 3-D figures and open
them up to show the students the 2-D pattern they were folded from.
5.
Students
will then be instructed to circle each of the pentominoes
that could be used as a net for an open top box. As students are working on this, the teacher
will also work on this to model the strategy of cutting out the shapes to
actually see if a topless box can be formed. (They should end up with 8
circled.)
6.
Using
problem solving strategies, the students will now determine the maximum number
of each net that will fit on a given area. (The teacher can have the students
cut extra shapes out or already have extra shapes to give out at this
point.) While everyone is working,
discuss applications of this activity and why a company would want to maximize
the number of nets on a given area, etc.
7.
Using
their activity sheets (graph paper with maximum nets),
students will determine which net can create the most boxes, with the least
amount of waste.
8.
Students
will now collaborate to compare their results.
9.
Students
will now communicate results orally (small group presentation) and in written
form (individual).
Materials/Resources:
Graph paper (1/2 inch)
Scissors
Tape
Presentation
materials (chalkboard, white board, overhead, etc.)
Notebook paper or computer
Extra
cut-outs of pentominoes for student exploration (if
you want to provide the extras instead of having students trace them or cut
out)
Interdisciplinary
Connections:
Reading
Students
can research educational requirements for drafting and/or mechanical
engineering and write a short summary of their findings.
Dimensional or Architectural Drawing
Students
can use graph paper or isometric paper to draw various views of the boxes.
Marketing/Graphics Design
Students can design the outside of the
package for a specific
product.
Assessment
Strategies:
Formative Evaluation
Visual checks while students are
working
Verbal checks during discussions and
while students are working
Teacher questions during activities
Peer review
Summative Evaluation
Presentation of findings
Written summary of findings
Final Product
Student Activity Sheets
Correctives/Remediation:
·
Correctives
can be made as needed by teacher monitoring to determine how the project is
going and by questioning and watching students as they are working.
·
Have
plenty of graph paper on hand for students to use when finding the maximum
number of each net for the given area.
·
If a
student is having trouble visualizing the boxes and has not cut out the shapes,
convince them to cut out the shapes to actually fold them.
·
If
some students are having great difficulty, pair them with other students to
help them.
Enrichment/Extensions:
· Incorporate the cost of making the boxes
·
Numerous
surface area and volume activities
·
Change
dimensions and also make rectangular boxes
·
Make
closed boxes
·
Use
combinations of pentominoes to completely cover the
original area
·
Have a
mechanical engineer come and talk to the students
·
Take
the students on a field trip to see boxes in production or being designed
·
Given
a specific product, determine the most suitable box for packing and shipping
Special
Accomodations:
Description of the special needs student
This students has manual dexterity problems
Accommodations to use with this student
· Partner the student with another student to assist with cutting and folding
·
Use
larger graph paper for the student (1 inch instead of ˝ inch)
·
Give
the student square attribute blocks to make the shapes. They can then trace the shapes once they have
them created.
All Boxed In
By: Helen, Davina, Mary and Lori
This is a layered project in which students first learn what pentominoes are and then try drawing as many as possible. (There are only 12.) After this, students learn that a net is a 2-D shape that can be folded to make a 3-D shape. Then they try to determine which of their 12 pentominoes are a net for an open top box. After that they work to try and determine which of the pentominoes could make the most boxes on a given area with the least amount of waste. They will then collaborate to compare and present their findings to the class, as well as write a summary of their findings.
Objectives:
· Students
will be able to draw all 12 pentominoes.
· Students
will be able to recognize the 8 nets for topless boxes.
· Students
will use ratios and proportions.
· Students
will be able to determine the maximum number of boxes that can be made from
each net for a given area.
· Students
will be able to determine the net that creates the most boxes with the minimum
amount of waste for a given area.
· Students
will present results and justifications orally and in written form.
· Students will construct an open top box.
Enrichment/Extensions:
· Incorporate the cost of
making the boxes
· Numerous
surface area and volume activities
· Change
dimensions and also make rectangular boxes
· Make
closed boxes
· Use
combinations of pentominoes to completely cover the
original area
· Have
a mechanical engineer come and talk to the students
· Take
the students on a field trip to see boxes in production or being designed
· Given a specific product, determine the most suitable box for packing and shipping
Building a Structure : All Boxed in
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CATEGORY |
10 |
9 |
8 |
7 |
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Construction – Care
Taken |
Great care taken in construction process so that the structure is neat, attractive and follows plans accurately. |
Construction was careful and accurate for the most part, but 1-2 details could have been refined for a more attractive product. |
Construction accurately followed the plans, but 3-4 details could have been refined for a more attractive product. |
Construction appears careless or haphazard. Many details need refinement for a strong or attractive product. |
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Oral Presentation: All Boxed In |
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Student
Name:
________________________________________ |
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5 |
4 |
3 |
2 |
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Speaks
Clearly |
Speaks
clearly and distinctly all (100%-95%) of the time and mispronounces no words. |
Speaks
clearly and distinctly all (100%-95%) of the time, but mispronounces one
word. |
Speaks
clearly and distinctly most(94%-85%) of the time.
Mispronounces no more than one word. |
Often
mumbles or cannot be underderstood OR mispronounces
more than one word. |
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Visuals |
Uses
several visuals that show considerable work/creativity and which make the
presentation better. |
Uses one
visual that shows considerable work/creativity and which makes the
presentation better. |
Uses one
visual which makes the presentation better. |
Student
uses no visuals OR the visuals chosen detract from the presentation. |
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Posture and
Eye Contact |
Stands up
straight, looks relaxed and confident. Establishes eye contact with everyone
in the room during presentation. |
Stands up
straight and establishes eye contact with everyone in the room during the
presentation. |
Sometimes
stands up straight and establishes eye contact. |
Slouches
and/or does not look at people during the presentation. |
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Content |
Shows a
full understanding of the topic. |
Shows a
good understanding of the topic. |
Shows a
good understanding of the parts of the topic. |
Does not
seem to understand the concept very well. |
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Written Summary: All Boxed In |
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Student
Name:
________________________________________ |
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CATEGORY |
5 |
4 |
3 |
2 |
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Writing:
Organization |
The
summary paragraph has a clear beginning (introductory sentence), middle (3 suppportive statements), and end (summary/conclu- sive sentence). |
The
summary paragraph has a clear beginning (introductory sentence), middle (2 suppportive statements), and end (summary/conclu- sive sentence). |
The
summary paragraph has a somewhat clear beginning (introductory sentence),
middle (2 suppportive statements), and end
(summary/conclu- sive
sentence). |
The
summary paragraph has a somewhat clear beginning, middle, and end. |
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Writing:
Grammar |
The
summary paragraph contains no grammatical errors. |
The
summary paragraph contains no grammatical errors after feedback being
provided by an adult. |
The
summary paragraph contains 1 to 2 grammatical errors even after feedback
being provided by an adult. |
The
summary paragraph contains several grammatical errors even after feedback
being provided by an adult. |
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Spelling
& Proofreading |
No
spelling errors remain after one person other than the writer reads and
corrects the summary paragraph. |
No more
than 1 spelling error remains after one person other than the writer reads
and corrects the summary paragraph. |
No more
than 3 spelling errors remain after one person other than the writer reads
and corrects the summary paragraph. |
There are
several spelling errors in the summary paragraph. |
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Writing:
Vocabulary |
The
writer correctly uses several new words and defines words unfamiliar to the
reader. |
The
writer correctly uses a few new words and defines words unfamiliar to the
reader. |
The
writer tries to use some new vocabulary , but may
use 1 to 2 words correctly. |
The
writer does not incorporate new vocabulary. |
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