Bulletin Board Border
Please help me. I would like to make a geometry bulletin board
that has a border of circles, triangles and squares. I know that
20 shapes will fit across the board and that 12 shapes will fit
down the board. If I start in the top left-hand corner with a
circle, followed by a triangle, then a square, and repeat this
pattern all around the board, how many of each shape will I
need?
Explain your solution using words and pictures.
Bulletin Board Border
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Bulletin Board Border
Suggested Grade Span
3-5
Task
Please help me. I would like to make a geometry bulletin board that has a border of circles,
triangles and squares. I know that 20 shapes will fit across the board and that 12 shapes will fit
down the board. If I start in the top left-hand corner with a circle, followed by a triangle, then a
square, and repeat this pattern all around the board, how many of each shape will I need?
Explain your solution using words and pictures.
Alternate Versions of Task
More Accessible Version:
Please help me. I would like to make a geometry boarder on the wall across my classroom. I
would like to use a pattern of circles, triangles and squares. I know that 21 shapes will fit across
the wall. If I start with a circle, followed by a triangle, then a square and repeat this pattern, how
many of each shape will I need?
Explain your solution using words and pictures.
More Challenging Version:
Please help me. I would like to make a geometry bulletin board that is surrounded by a border
of polygons. I will start in the top left-hand corner with a 4-sided shape, followed by a 5-sided
shape, then a 6-sided and so on all the way up to a 10-sided shape. Once I get to a 10-sided
shape I will start the pattern again with a 4-sided shape. I know that 20 shapes will fit across
the board, and that 12 shapes will fit down the board. How many of each shape will I need to
surround the bulletin board?
Explain your solution using words and pictures.
Context
This problem worked well because it forced students to draw the problem and show all their
work. Students first thought they could add all the numbers given and solve the problem without
a diagram. When they became involved in the problem solving they realized why drawing clear
diagrams is so useful.
Bulletin Board Border
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What This Task Accomplishes
This task allows students to explore a real-life problem using perimeter. It assesses their ability
to take information given and apply it to a diagram.
What the Student Will Do
The task provides information that most students will need to diagram. Some students in my
fourth-grade class had difficulty placing the corner pieces and counted them twice. The more
accurate the diagram, the more accurate the solution.
Time Required for Task
60 minutes
Interdisciplinary Links
None, this is strictly a problem-solving problem.
Teaching Tips
Teachers tell students that a diagram will help them with problem solving, but we often get, "I
did it in my head." This problem allows students to draw a simple diagram to a challenging
problem. Allow students the opportunity to actually make the boarder on a bulletin board.
Suggested Materials
• Paper
• Pencil
• Actual shapes may be used
Possible Solutions
Students may conclude that 64 shapes are needed.
They will add the numbers given in the task and draw a diagram that represents their
interpretation.
Hopefully by drawing a diagram, students will use the corner pieces correctly, and conclude that
60 shapes are needed, 20 of each shape.
More Accessible Version Solution:
21 ÷ 3 shapes = 7 of each shape
Bulletin Board Border
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More Challenging Version Solution:
20 + 20 + 10 + 10= 60 shapes around board ÷ 7 different polygons = 8 polygons with 4 shapes
having an extra one:
Quadrilaterals = 9
Trapezoids = 9
Hexagon = 9
Septagon = 9
Octagon = 9
Nonagon = 9
Decagon = 8
Task Specific Assessment Notes
Novice
The student used inappropriate concepts and procedures to solve the problem (S/he may have
multiplied 20 by 12 to get 240.). There is little evidence in the explanation of a strategy or
reasoning. The diagram does not relate to the problem (there is no evidence of a border).
Apprentice
The student understood part of the problem and showed some mathematical reasoning, (using
a pattern of shapes for the border), but did not use the corner pieces as a continuation of the
pattern. There is some use of a diagram and mathematical notation.
Practitioner
The solution shows a broad understanding of the problem. The strategy was to use an accurate
diagram to organize the solution. A Practitioner may have slight computational errors in their
solution, as long as the explanation and diagram are correct.
Expert
The solution shows a deep understanding of the problem including the ability to identify the
appropriate mathematical concepts. This student makes connection between the border and
the mathematical concept of perimeter. The student verified the solution. ("To check I counted
the perimeter and I got 60.") The diagram is actively used to find the solution and the student
is making an attempt at using a chart, although it ends up just being a way to present the
solution. S/he uses appropriate mathematical notation.
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Novice
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Apprentice
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Practitioner
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Expert
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