3–5 Sample Spanish Math Task
Borde Para el Tablón de Anuncios
Ayúdame, por favor. Quiero hacer un tablón de anuncios
geométrico que tenga un borde de círculos, triángulos y
cuadrados. Se que 20 formas cabrán a lo ancho del tablón
y que 12 formas cabrán a lo largo del tablón. Si empiezo
con la esquina de la izquierda de arriba con un círculo,
seguido de un triángulo, después un cuadrado y repito
este patrón, alrededor del tablón, ¿cuántas de cada forma
voy a necesitar? Explica tu solución usando palabras y
dibujos.
© 2013
exemplars.com
1
3–5 Sample Spanish 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 lefthand 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
2
Bulletin Board Border
Suggested Grade Span
Grades 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.
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.
3
exemplars.com
800-450-4050
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 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
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
• Numbers and Operations
• Geometry and Measurement
Concepts To Be Assessed and Skills To Be Developed
•
•
•
•
•
Problem solving
Reasoning
Communication
Patterns
Perimeter
Suggested Materials
• Paper
• Pencil
• Actual shapes may be used
4
exemplars.com
800-450-4050
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 Novice will use inappropriate concepts and procedures to solve the problem (s/
he may have multiplied 20 by 12 to get 240). There will use little evidence 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 Apprentice 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 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.
5
exemplars.com
800-450-4050
Novice
Novice
The student shows no
evidence of understanding
the concept of perimeter.
The student reaches an
incorrect solution.
It is unclear what the
student is doing here.
6
Bulletin Board Border
exemplars.com
Copyright 2014, Exemplars, Inc. All rights reserved.
4 of 7
800-450-4050
Apprentice
Apprentice
The student
shows his/her
incorrect solution.
An error in the
pattern is made here.
Some work
is shown.
An error in the
pattern is made here.
Bulletin Board Border
7
Copyright 2014, Exemplars, Inc. All rights reserved.
exemplars.com
5 of 7
800-450-4050
Practitioner
Practitioner
The student’s
diagram is accurate
and appropriate.
The student has
an approach that
works.
The student
explains his/her
solution.
8
exemplars.com
Bulletin Board Border
The student obtains
a correct answer.
800-450-4050
Expert
Expert
The student creates
accurate and appropriate
math representation.
The student verifies
his/her solution. The
student clearly states
his/her solution.
9
Bulletin Board Border
exemplars.com
Copyright 2014, Exemplars, Inc. All rights reserved.
The student uses
accurate and appropriate
math language to
communicate.
7 of 7
800-450-4050