MCI - Worchester State University Singapore Math Institute Classroom Session A3

CLASSROOM SESSION A3  
Whole Numbers Multiplication & Division
Slides are available at
www.banhar.blogspot.com
and
Marshall Cavendish Institute’s Facebook
Princess Elizabeth Primary School, Singapore

This session took on a Forum format participants decide what they want to learn through the questions they asked.
Three key activities were used to seed the discussion.
One was to count rows of (many) dots.
Another was to share a number of paper clips quickly. Some groups had a small number, others had a large number of paper clips.
A third was a conversation between two students in Grade 5.
The discussion led to
Knowing that the focus of teaching is different in small number and large number multiplication and division
A deeper understanding of Spiral Approach and CPA Approach
How teacher can help students learn multiplication and division

Activity

Desde los primeros años, los estudiantes aprenden a hacer conjuntos o grupos iguales utilizando materiales concretos.
From the early grades, students learn to make equal groups using concrete materials.

CPA Approach

Luego, representan estas situaciones concretas utilizando, en primer lugar, los dibujos y, …
After that they represent these concrete situations using, first, drawings ..

… más tarde, diagramas (modelos de barras). Después de eso, escriben multiplicaciones. Por supuesto, los profesores volverán a las representaciones concretas y pictóricas una y otra vez en aprendizajes posteriores.

… and, later, diagrams. After that they write multiplication sentences.

CPA Approach
Transition is Important

An example of how students use paper clips to make the transition from equal groups to bar model,
EscuelaNo.1577 TenienteDagobertoGodoy, Santiago, Chile
Singapore Math in Chile

Spiral Approach

Multiplication involving whole numbers is taught over five years, starting in Primary 1. The focus is on one of the meanings of multiplication – equal sets or equal groups.
La multiplicación con números enteros se imparte en cinco años, a partir de 1º básico. La atención se centra en uno de los significados de la multiplicación; conjuntos iguales o grupos iguales. Los estudiantes aprenden a representar 3 platos de frutas como de 3 x 6, cuando hay 6 frutas en cada plato. No se espera que recuerden las tablas de multiplicar.

conjuntos iguales o grupos iguales

There is a progression from equal groups to skip-counting.
Hay una progresión de los grupos de iguales para saltar de conteo.

In Primary 2, students learn multiplication facts of 2, 5, 10, and 3 and 4. In Primary 3, they learn the multiplication facts of 6, 7, 8 and 9.
En 2º básico, los alumnos aprenden las tablas de multiplicación del 2, 3, 4, 5 y 10. En 3º básico, aprenden las tablas de multiplicación, de 6, 7, 8 y 9.

Later, the array meaning of multiplication is introduced.
Más tarde, se introduce el significado del producto vectorial.

Catholic High School (Primary), Singapore

Da Qiao Primary School, Singapore

Students apply their understanding of multiplication to solve word problems including those that include multiplicative comparison, and at the same time, deepen their understanding of multiplication.
Los estudiantes aplican sus conocimientos de la multiplicación para resolver problemas que incluyen la comparación multiplicativa, y al mismo tiempo, profundizan su comprensión de la multiplicación.

Multiplication is also applied to find the area of rectangles and square when Primary 3 students learn the concept of area.
La multiplicación se aplica también para encontrar el área de rectángulos y cuadrados cuando los estudiantes de 3º básico aprenden el concepto de área, contando unidades cuadradas al final de 3º básico.

In Grade 3 they learn multiplication of 2-digit with 1-digit numbers as well as multiplication of 3-digit and 1-digit numbers.
Después de completar las tablas de multiplicar, los estudiantes aprenden multiplicaciones que van más allá de la tabla de multiplicar. Ellos aprenden a multiplicar números de dos dígitos con números de 1 dígito, así como la multiplicación de números de tres dígitos y números de un dígito.

42
4

In Primary 4, the learn multiplication of 4-digit and 1-digit numbers as well as multiplication of 3-digit and 2-digit numbers. The focus is on partial products.
34
En 4º básico, aprenden a multiplicarnúmeros de cuatrodígitos y un dígito, asícomomultiplicarnúmeros de tresdígitos y dos dígitos. La atención se centra en productosparciales.

National Institute of Education, Singapore

Finally in Primary 5, students learn to use calculator to multiply larger numbers.
Porúltimo, en 5º básico los estudiantesaprenden a utilizar la calculadoraparamultiplicargrandescantidades.

The combination situation is not usually used to learn multiplication in elementary school. In this case the teacher has decided to extend the learning of a high-achieving class.

4 x 6 = 24
8 x 6 = ….
Aquí se muestra la estrategia de duplicidad.

A continuación se muestran las estrategias de adición.

A continuación se muestran las estrategias de sustracción.

The sharing and grouping meaning of division are introduced in Grade 1 and are used in the learning of division of other number types.
El significado de compartir y reagrupar de la división se introduce en 1º básico y se utilizan en el aprendizaje de la división de otras clases de números.

BinaBangsa School, Bandung, Indonesia
Singapore Math in Indonesia

Overheard in a Primary 5 class (Singlish)
Ah Beng: Eh! Why last time in P3, teacher said 14 ÷ 4 is 3 remainder 2?
Now this teacher say 14 ÷ 4 is 3.5?
Ah Seng: Because we bigger what!
Small that time division is different. Now different.
Overheard in a Primary 5 class (translated, for your benefit, into Standard English)
Ah Beng: Hey! Why was it that when we were in P3, the teacher told us 14 ÷ 4 is 3 remainder 2?
Now, this teacher says 14 ÷ 4 is 3.5?
Ah Seng: That is because we are older. Silly!
Division was different when we were little. It is different now.
Explain to your colleague why 14 ÷ 4 = 3 remainder 2, and, at some point, 14 ÷ 4 = 3.5 .

choice of
materials

Pedagogical Principles of Singapore Method
Spiral Approach
10 : 5 = 2
12 : 5 = 2 remainder 2

En 1º básico no se utiliza el símbolo÷ o : para la división. El símbolo se introduce en 2º básico. La idea de resto se introduce en 3º básico.

.
In Grade 1, the symbol ÷ or : is not used. The symbol is introduced in Grade 2. The idea of remainder is introduced in Grade 3.

“Un plan de estudios de la manera que se desarrolla debe revisar estas ideas básicas en varias ocasiones, construyéndose sobre ellos hasta que el estudiante ha comprendido todo el aparato formal que conllevan”. (Bruner 1960 en El Proceso de la Educación).

.
“A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.” (Bruner 1960 in The Process of Education).

En los cursos de 1º a 4º básico, se utilizancantidadesdiscretas, porejemplopiedrecillas y los niños. En 5º básico se utilizancantidadescontinuascomolasmedidasestándar de 13 kg y 13 cm.

In Grades 1 to 4, quantities used are discrete ones e.g. pebbles and children. In Grade 5, continuous quantities like standard measures 13 kg and 13 cm are used.

Activity
Find a quick way to share the given number of paper clips among the members of your group.

Keys Grade School, Manila, The Philippines
The idea of regrouping before dividing is introduced later in Grade 3 and is taught in Grade 4 as well.

La idea de reagrupar antes de dividirse se introduce al finalizar 3º básico y también se enseña en 4 º básico.

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MCI - Worchester State University Singapore Math Institute Classroom Session A3

by Jimmy Keng on Jul 07, 2011

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MCI - Worchester State University Singapore Math Institute Classroom Session A3 — Presentation Transcript