24/05/2021

Appreciations

Free Program for SEAMEO School Networkfrom the University of Tsukuba, Affiliate Member of SEAMEO
Teaching Mathematics to Develop Mathematical Thinking as Higher Order Thinking:How do you teach? Why?

Lesson 19: How to extend division with remainderThose
terminology
distinguishtasks andexplain task
sequence
for thepreparationof futurelearning.

Reflection

Isoda, Masami. Prof., Faculty of Human Sciences
Director of CRICED, The University of Tsukuba, Japan
With collaborations ofWe are reading the JP textbook by using terminology to explain to distinguish every
content of learning and sequence of content for knowing the way to develop children
who learn and think by and for themselves through the preparation of future learning.

Revitalizing
Teacher Education

Adopting a 21stCentury Curriculum

Acquisition

Nguyen Chi Thanh and Teh Kim Hong

HOTS isMath. T.

2
ReviewCurriculum Standards: SEABES-CCRLS( by SEAMEO-RECSAM (Mangao, Ahmad, Isoda; 2017)

ReviewUsing what you already knew on the past 18 lessons!
 Participants ofthis program areable to imagine
the ways oflearning from thepast process oflearning.
 Participants needto consider what’snew.

What is division with remainder?
Q1. Which situation do you use to teach remainder?:Partitive Division situation
12 candies distribute 4 children equally. How many candies each child will
receive.
12÷4＝3, Ans. 3 candies for each child: 4 x 3 =12 in English(3 x 4 =12 in Japan)

Quotative Division situation
There is 12 candies and each child receive 4 candies equally. How manychildren will receive it.
12÷4＝3, Ans. 3 children: 3 x 4 =12 in English(4 x 3 =12 in Japan)

Q2. Please answer (- 5)÷3Have you ever discuss the remainder?

Before Division with Reminder: Why we teach it?

(- 5)÷3 ? … Remainder is -2 or +1?
□ 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Answer for □÷3 3 2 2 2 1 1 1 0 0 0 00

Partitive vs Quotative situations
Integrate as one division operation

Permanence of Form

Proceduralization byCompare division expressions in order-1 -1 -1 -2

Remainder for □÷3 0 2 1 0 2 1 0 2 1 0 -1 -2 0-1 -20Less□ 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Answer for □÷3 3 2 2 2 1 1 1 0 0 0 ?

?

?

?

?

?

Remainder for □÷3 0 2 1 0 2 1 0 2 1 0 ?

?

?

?

?

?

Permanenceof Form

A=B x Q +r (r≧0)

Q2. Do you teach Less?
Remainder□ 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Answer for □÷3 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 -2 -2 -2
Remainder for □÷3 0 2 1 0 2 1 0 2 1 0 21021

Given an integer n > 1, called a modulus, two integers are said to be congruent modulo n, if n isa divisor of their difference (i.e., if there is an integer k such that a − b = kn).
Congruence modulo n is denoted: a ≡ b (mod n)
For example: 1 ≡ -5 (mod 3), i. e. 1 – (-5) = 2 x 3

Relationshipbetweendivision andmultiplication0
See division as multiplication
These arenecessary
to find thequotient.

Equivalentclass ofdivision1

24/05/2021

Introduction of Division with Remainder
Introduced by quotative
division situation

Beautifulness of pattern
by using remainder

Extend it to partitive
division situations

Think about how to calculate:
Preparation for long division.
Which idea is a base for the long division?

RemainderShort

Gakko Tosho: Study with your friends:
Mathematics for Elementary School Series

References

Primary School Textbook
2001 Curriculum2005 Japanese Edition
2005 English Edition↓
2010
Thai Ed.

2005 Edition

10 Editions

2010 Edition

Junior High S. Textbook
2012 Curriculum2016 Japanese-Edition
2019 English-Edition2020 Indonesian-Edition
202X Thai Ed.

4 Editions

9Isoda, M., Tall, D. (2019). Junior High School
Mathematics Textbook, Gakko Tosho

4 Editions

NEWEST EDITION

2012 Mexico Ed.
2019 Chile Pro. Ed.
2011 Curriculum2011 Japanese Edition
2011 English Edition↓
2019 Papua N.G. Edit.
2020 Indonesian Edi.
2020 Chile Ed.
2015 Japanese-Edition
2015 English-Edition2020 Curriculum2020 Japanese Edition2020 English Edition
10References
Masami Isoda, Raimundo Olfos edited (2020). Teaching Multiplication with Lesson Study: Japanese and Ibero-American Theories forInternational Mathematics Education. Cham, Switzerland: Springer. (Open Access)
Masami Isoda, Aki Murata (2020). Study with your friends: Mathematics for Elementary School (12 vols.). Tokyo, Japan: Gakko Tosho.
Masami Isoda, Aki Murata, Aida Yap (2015). Study with your friends: Mathematics for Elementary School (12 vols.). Tokyo, Japan:Gakko Tosho.
Masami Isoda, David Tall (2019). Mathematics for Junior High School (3 vols.). Tokyo, Japan: Gakko Tosho.

Dominador Dizon Mangao, Nur Jahan Ahmad, Masami Isoda edited (2017).SEAMEO basic education standards (SEA-BES): Common
core regional learning standards (CCRLS) in mathematics and science . Penang, Malaysia: SEAMEO-RECSAM,
http://www.recsam.edu.my/sub_sea-bes/images/docs/SEAMEO-ASEAN-Curriculum-SEABES-CCRLS-Standards.pdf
Maitree Inprasitha, Masami Isoda, Patsy Wang Iverson, Ban Har Yap (2015). Lesson Study: Challenges in Mathematics Education . NewJersey, USA: World Scientific
Masami Isoda, Shigeo Katagiri (2012). Mathematical Thinking: How to develop it in the classroom. New Jersey, USA: World Scientific
TEH Kim Hong, ISODA Masami, GAN Teck Hock (in printing). Mathematics Challenges for Classroom Practices at the Lower Primary
Level. Penang, Malaysia: SEAMEO-RECSAMISODA Masami, TEH Kim Hong, GAN Teck Hock (in printing). Mathematics Challenges for Classroom Practices at the Upper Primary
Level. Penang, Malaysia: SEAMEO-RECSAMGAN Teck Hock, ISODA Masami, TEH Kim Hong (2021). Mathematics Challenges for Classroom Practices at the Lower Secondary
Level. Penang, Malaysia: SEAMEO-RECSAMHosomizu, Y. translated by Gould, P. Isoda, M., Foo, C. (2010). Red dragonfly mathematics challenge. Department of Education, NewSouth Wealth. https://schoolsequella.det.nsw.edu.au/file/20a29ac1-c6f3-4ca3-84b1-2d8488a4cbcd/1/reddragonfly.zip/index.html
Hosomizu, Y. translated by Gould, P. Isoda, M., Foo, C. (2011). Companion: Mathematics Challenges. Department of Education, NewSouth Wealth. https://www.mansw.nsw.edu.au/shop/pre-k-8-books/dragonfly-companion

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