Spanish 3–5 Sample Math Task
Marco para un tablón de anuncios
Necesito tu ayuda. Quiero hacer un tablón de anuncios
geométrico que tenga un marco de círculos, triángulos
y cuadrados. Sé que 20 formas cabrán en el ancho del
tablón y que 12 formas cabrán en el largo del tablón. Si
empiezo en el extremo superior a mano izquierda con
un círculo seguido de un triángulo y luego un cuadrado,
y si repito esta secuencia por todo el borde del tablón,
¿cuántas de cada forma usaré?
Explica tu solución usando palabras y dibujos.
© 2013
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Spanish 3–5 Sample Math Task
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.
© 2013
exemplars.com
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Bulletin Board Border
Suggested Grade Span
Grades 3–5
Common Core Task Alignments
Mathematical Practices: 1, 3, 4,
Grade 4 Content Standards:
4.OA.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.
Alternative Versions of the Task
More Accessible Spanish Version:
Ayúdame, por favor. Quiero hacer un borde geométrico en la pared alrededor de la sala
de clase. Me gustaría usar un patrón de círculos, triángulos y cuadrados. Se que 21 formas
cabrán en la pared alrededor de la clase. Si empiezo con un círculo, después pongo un
triángulo y después un cuadrado y repito este patrón, ¿cuántas de cada forma voy a
necesitar? Explica tu solución usando palabras y dibujos.
More Accessible English 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 Spanish Version:
Ayúdame, por favor. Quiero hacer un tablón de anuncios geométrico rodeado de un borde
de polígonos. Voy a empezar en la esquina de la izquierda, arriba, con una forma de 4 lados,
seguido de una forma de 5 lados, después una forma con 6 lados y seguir así hasta llegar
a una forma de 10 lados. Una vez llegue a la forma de 10 lados voy a empezar el patrón de
nuevo con una forma de 4 lados. Se que las 20 formas cabrán a lo ancho del tablón y que 12
formas cabrán a lo largo del tablón. ¿Cuántas de cada forma voy a necesitar para rodear el
tablón de anuncios? Explica tu solución usando palabras y dibujos.
More Challenging English 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.
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Context
This problem worked well because it allows students to diagram 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.
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 Students 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
Approximately 60 minutes
Interdisciplinary Links
None, this is strictly a problem-solving task.
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. It allows students the opportunity to actually make the border on a bulletin board.
NCTM Standards
• Number and Operations
• Geometry and Measurement
Concepts to be Assessed and Skills to be Developed
• Problem solving
• Reasoning
• Communication
• Patterns
• Perimeter
Suggested Materials
• Paper and pencil
• Actual shapes may be used
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Possible Solutions
Original Version:
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:
21 ÷ 3 shapes = 7 of each shape
More Challenging Version:
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 will use inappropriate concepts and procedures to solve the problem (s/
he may have multiplied 20 by 12 to get 240). Little evidence will be used in the explanation of
a strategy or reasoning. The diagram will not relate to the problem (there will be no evidence
of a border).
Apprentice: The student will understand part of the problem and will show some
mathematical reasoning, (using a pattern of shapes for the border) but will not use the
corner pieces as a continuation of the pattern. There will be some use of a diagram and
mathematical notation.
Practitioner: The Practitioner will have an understanding of the problem and a strategy will
be used that successfully solves all parts of the task. The student will use an accurate pattern
of the geometric shapes in the corners and a connection, observation or verification of the
solution will be made.
Expert: The Expert will have a clear understanding of the problem and all of the parameters.
The pattern of geometric shapes will continue around the corners. Accurate mathematical
representation will be shown, and mathematical reasoning will reflect refined reasoning skills.
A connection, observation or verification of the solution will be made.
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Novice
The student shows no
evidence of understanding
the concept of perimeter.
It is unclear what the
student is doing here.
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The student reaches
an incorrect solution.
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Apprentice
Some work is shown.
An error in the
pattern is made here.
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Practitioner
The student has
an approach that
works.
The student explains
his/her solution and makes
a relevant mathematical
observation.
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The student uses
appropriate and accurate
math language and notation.
The student obtains
a correct answer.
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Expert
The student uses
accurate and appropriate
math language and
notation to communicate.
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The student creates
accurate and appropriate
math representation.
The student verifies
his/her solution. The
student clearly states his/
her solution.
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