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:

Ø Students will understand the meaning of and procedures for multiplying decimal numbers by whole numbers.

Ø 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.

Ø Students will further develop their ability to use these computations.

[Interest, Desire, Attitude]

Ø 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]

Ø Students will think about how to multiply and divide decimal numbers based on their understanding of multiplication and division of whole numbers.

Ø 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]

Ø Students will be able to calculate a decimal number x a whole number and a decimal number a whole number.

Ø Students will be able to represent the relationship between two quantities using such tools as double number lines.

[Knowledge, Understanding]

Ø 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. “Times as much” 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. “times as many/much”; 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

Today’s Lesson

Goals:

Ø 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]

Ø Students will be able to express the reason for writing a particular mathematical expression. [Mathematical Thinking][Representations, Procedures]

Flow of Lesson:

Ø Pose / understand the problem

Ø Develop a plan—group or individual

Ø Individual / group problem solving

Ø Whole class discussion—sharing student answers and reasoning; similarities and differences

Ø Summary (reflection)

Taken from Lesson Study Immersion Study handouts, Global Education Resources, 2007.

From “Curriculum” Guide:

Objectives (Grades 1 – 6): “The 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.” (p. 3)

Objectives (Grades 7 – 9): “The 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.” (p. 24)

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