Japan Activity
Unit Overview
Grade: 5, Elementary School (2 months into the
school year)
Unit: Multiplying and dividing decimal numbers
(decimal x whole; decimal
whole)
Goals of the
Unit:
¯
Students
will understand the meaning of and procedures for multiplying decimal numbers
by whole numbers.
¯ Students will understand the meaning of
and procedures for dividing decimal numbers by whole numbers or dividing whole
numbers by whole numbers with decimal quotients.
¯ Students will further develop their
ability to use these computations.
[Interest,
Desire, Attitude]
¯ Students will try to relate what they
learned previously about multiplying and dividing whole numbers to multiplying
and dividing decimal numbers by whole numbers.
[Mathematical
Thinking]
¯ Students will think about how to multiply
and divide decimal numbers based on their understanding of multiplication and
division of whole numbers.
¯ Students will be able to identify the
correct operation needed by using tools such as double number lines to
understand the relationship between two quantities.
[Representations,
Procedures]
¯
Students
will be able to calculate a decimal number x a whole number and a decimal
number a whole number.
¯
Students will
be able to represent the relationship between two quantities using such tools
as double number lines.
[Knowledge,
Understanding]
¯
Students
will understand the meaning of and procedures for multiplying decimal numbers
by whole numbers.
Unit Plan:
1. Multiplying
decimal numbers 4
lessons
2. Dividing
decimal numbers 6
lessons
3. Using
multiplication and division 2
lessons*
4. ÒTimes as
muchÓ and decimal numbers 1
lesson
5. Summary 1
lesson
Multiplication
and Division Across the Grades:
Grade 1: Foundations—make groups of same
size; determine number of groups
Grade 2: Intro to multiplication—develop
meanings of multiplication, i.e. Òtimes as many/muchÓ; construct basic multiplication
table (1x1 to 9x9); develop reverse thinking of multiplication.
Grade 3: Intro to division—Students will
understand the two situations of division (Measurement: If we give 3 pieces to
each person, how many people can get pieces? Fair sharing: If we share equally
among 3 people, how many will each get?); determine quotients using basic
multiplication facts.
Grade 4: Division algorithm—Students will
develop division algorithm using distributive property, meanings of division,
and the relationship between multiplication and division; introduction of
fractions and decimal numbers
Grade 5: Multiplying and dividing decimal
numbers—develop methods, including looking at decimal numbers using 0.1
as the base unit; extend the meaning of multiplication and division by using
decimal numbers
Grade 6: Multiplication and division of
fractions—develop methods and understand procedures
TodayÕs Lesson
Goals:
¯
Students
will be able to graph the relationship between two quantities by using tools
such as double number lines, and write correct mathematical expressions.
[Mathematical Thinking]
¯
Students
will be able to express the reason for writing a particular mathematical
expression. [Mathematical Thinking][Representations, Procedures]
Flow of Lesson:
¯ Pose / understand the problem
¯ Develop a plan—group or individual
¯ Individual / group problem solving
¯ Whole class discussion—sharing student answers
and reasoning; similarities and differences
¯ Summary (reflection)
Taken from Lesson Study Immersion
Study handouts, Global Education Resources, 2007.
From ÒCurriculumÓ Guide:
Objectives (Grades 1 –
6): ÒThe aims are to help children develop their abilities to consider their
daily-life phenomena insightfully and logically, acquiring the fundamental
knowledge and skills regarding numbers, quantities and geometrical figures, and
thereby to foster their attitude to appreciate the mathematical coping with and
to willingly make use of it in their lives.Ó (p. 3)
Objectives (Grades 7 –
9): ÒThe aims are to help students deepen their understanding of the basic
concepts, principles and rules concerning numbers, quantities and figures, and
acquire the way of mathematically representing and coping with, and to enhance
their abilities of mathematically considering things, as well as to help them
appreciate the mathematical way of viewing and thinking, and thereby to foster
their attitudes of willingly applying them.Ó (p. 24)