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Teach Multiplication, Division, and the Time Table All at the Same Time

An Instructional Guide for Learning Basic Math SkillsBy Andray McCuien

AuthorHouse

Copyright © 2011 Andray McCuien
All right reserved.
ISBN: 978-1-4567-2770-3

Contents

Title Page.....................................................1Content........................................................3Preface........................................................4How Students Learn.............................................5Reader Notes...................................................61 Multiplication and the Time Table............................112 Skip Counting................................................133 Introducing Long Division....................................154 Inverse Operation............................................295 Division Problems and Counting Up............................306 Counting-Up Strategy.........................................677 Counting-Up Strategy and Subtraction.........................69Conclusion.....................................................78Practice Pages for Instructors.................................79Scratch page...................................................82About the Author...............................................83

Chapter One

Multiplication and the Time Table Chart

At this point, students learn the rules for multiplying by 0 and 1. Rule for multiplying by 0: Any number multiplied by 0 is equal to 0.

0 × 1 = 0 0 × 4 = 0 0 × 7 = 0 0 × 10 = 0 0 × 2 = 0 0 × 5 = 0 0 × 8 = 0 0 × 11 = 0 0 × 3 = 0 0 × 6 = 0 0 × 9 = 0 0 × 12 = 0

Rule for multiplying by 1: Any number multiplied by 1 is equal to that same number.

1 × 1 = 1 1 × 4 = 4 1 × 7 = 7 1 × 10 = 10 1 × 2 = 2 1 × 5 = 5 1 × 8 = 8 1 × 11 = 11 1 × 3 = 3 1 × 6 = 6 1 × 9 = 9 1 × 12 = 12

To be sure students learn these two rules, have them write out the entire time table, multiplying each number from 1 to 12 by 0, showing the product of 0 for each set of two factors; have them repeat the same step to illustrate the second rule, multiplying each of the factors by 1 and showing the product.

These two rules are very simple and are usually easy for students to learn. It is usually not necessary to use the counting-up strategy to help students understand these two principles.

Now it is time to move on to the rest of the time table chart. Do not focus on how much of the time table chart students are able to remember at this point. This exercise is simply to help students become acquainted with the time table chart as a concept. Once students begin to apply the strategy of counting up, they will learn the time table chart in its entirety through repetition and practice.

Students should be given a time table chart to use when multiplication is introduced. This is simply to provide students with a visual aid to follow as the time tables are discussed.

Review each factor of the chart in its entirety. Because the rule of multiplying using the multiple of 1 has already been introduced, it should be reviewed briefly. Move on to the 2s, the 3s, and so forth, in sequence, until the entire time table chart from 1 to 12 has been introduced. Copies of the time table charts should not be used when students are applying the strategy of counting up.

Students tend to rely on the chart to determine the product of multiples rather than applying any type of problem-solving strategy. The charts should not be left in the possession of students, but passed out when the time tables are introduced and then collected at the conclusion of the lesson.

Time Table Chart and Basic Principles of Multiplication

Oral practice drills should be a 5- to 10-minute segment of daily instruction.

Chapter Two

Skip Counting

Now it is time to introduce students to the concept of skip counting by the numbers 2, 3, 5, and 10. Students must learn to add the number with which they are skip counting to each preceding product in sequence, using time table multiples, beginning with 1 and ending with 12. Students will learn to identify only the product of each set of multiples 1–12 multiplied by the table of 2, 3, 5, and 10.

Skip Counting by 2 Time Table of 2

2 × 1 = 2 2 × 4 = 8 2 × 7 = 14 2 × 10 = 20 2 × 2 = 4 2 × 5 = 10 2 × 8 = 16 2 × 11 = 22 2 × 3 = 6 2 × 6 = 11 2 × 9 = 18 2 × 12 = 24

Students will practice repeating the product of each set of multiples from the table of 2 in sequence until it is learned. Students are able to gesture using their fingers as they count aloud.

Practice Sequence

2 4 6 8 10 12 14 16 18 20 22 24

Skip Counting by 3 Time Table of 3

3 × 1 = 3 3 × 4 = 12 3 × 7 = 21 3 × 10 = 30 3 × 2 = 6 3 × 5 = 15 3 × 8 = 24 3 × 11 = 33 3 × 3 = 9 3 × 6 = 18 3 × 9 = 27 3 × 12 = 36

Students will practice repeating the product of each set of multiples from the table of 3 in sequence until it is learned. Students are able to gesture using their fingers as they count aloud.

Practice Sequence

3 6 9 12 15 18 21 24 27 30 33 36

Skip Counting by 5 Time Table of 5

5 × 1 = 5 5 × 4 = 20 5 × 7 = 35 5 × 10 = 50 5 × 2 = 10 5 × 5 = 25 5 × 8 = 40 5 × 11 = 55 5 × 3 = 15 5 × 6 = 30 5 × 9 = 45 5 × 12 = 60

Students will practice repeating the product of each set of multiples from the table of 5 in sequence until it is learned. Students are able to gesture using their fingers as they count aloud. While students may stop at 60, the illustrations continue up to 100.

Practice Sequence

5 10 15 20 25 30 35 40 45 50 55 60 65 70

75 80 85 90 95 100

Skip Counting by 10 Time Table of 10

10 × 1 = 10 10 × 4 = 40 10 × 7 = 70 10 × 10 = 100 10 × 2 = 20 10 × 5 = 50 10 × 8 = 80 10 × 11 = 110 10 × 3 = 30 10 × 6 = 60 10 × 9 = 90 10 × 12 = 120

Students will practice repeating the product of each set of multiples from the table of 10 in sequence until it is learned. Students are able to gesture using their fingers as they count aloud.

Practice Sequence

10 20 30 40 50 60 70 80 90 100 110 120

Chapter Three

Introducing Long Division

After students become familiar with multiplication, division can be introduced. I prefer to teach students long division using pencil and paper. It is very important to introduce students to key terms that are associated with division, such as inverse operations (operations that undo each other). The rules for dividing by 0 and 1 must also be introduced at this time.

Once students have become familiar with the terms associated with division, allow students to begin manual practice by assisting them as they solve several long-division problems using scratch paper and a pencil. Note the example below.

Long Division

6 [square root of 42]

Step 1: Help students determine the target number for the equation. The target number in this equation is 42.

Step 2: Students determine which multiplication table will be used to solve the equation. In this equation, the table of 6 will be used, because it must be determined how...