3 5 Sample Spanish Math Task. Borde Para el Tablón de Anuncios

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

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 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?

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.

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

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.

Novice

Novice

The student reaches an incorrect solution.

It is unclear what the student is doing here.

The student shows no evidence of understanding

Apprentice

Apprentice

An error in the pattern is made here.

Some work is shown.

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Practitioner

Practitioner

The student obtains a correct answer. The student explains his/her solution. The student’s diagram is accurate and appropriate.

The student has an approach that

Expert

Expert

The student creates accurate and appropriate

math representation.

The student uses accurate and appropriate

math language to communicate. The student verifies

his/her solution. The student clearly states