Hands-On Math: Learning Multiplication and Division through Manipulative Activities - Softcover

Fletcher-Bacer, Dr. Kathleen

Softcover

ISBN 10: 1490767614 ISBN 13: 9781490767611

Verlag: Trafford, 2016

Inhaltsangabe

A Chinese proverb reads: “I hear and I forget. I see and I remember. I do and I understand.” In Hands-On Math, author Dr. Kathleen Fletcher-Bacer applies the basis of this proverb to help students understand abstract mathematical concepts. Known for her innovative and creative teaching techniques, Fletcher-Bacer shows how the use of manipulatives in the classroom is key to helping children learn the fundamentals of math. In Hands-On Math, she provides teachers with a realistic and step-by-step approach to teaching multiplication and division for conceptual understanding with the proper utilization of manipulatives. Divided into specific skill categories and levels of mastery, Fletcher-Bacer includes age-appropriate lesson plans and math activities. Based on her many years of teaching and teacher training, Fletcher-Bacer understands that children who discover foundational mathematical concepts for themselves retain those concepts and are able to transfer them to higher levels of mathematics. The lessons presented in Hands-On Math facilitate and enhance children’s learning.

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Hands-On Math

Learning Multiplication and Division through Manipulative Activities

By Kathleen Fletcher-Bacer

Trafford Publishing

Copyright © 2016 Kathleen Fletcher-Bacer
All rights reserved.

ISBN: 978-1-4907-6761-1

Contents

About this book, vii, 
Basic Multiplication Facts, 
Properties of Multiplication, 
Number Theory for Multiplication, 
Basic Multiplication Concepts: Games & Activities, 
Multi-Digit Multiplication, 
Basic Division Facts, 
Number Theory for Division, 
Basic Division Concepts: Games & Activities, 
Multi-Digit Division, 
Reinforcing Multiplication and Division, 
Appendix A: Manipulatives, 
Appendix B: Children's Literature that supports Multiplication and Division, 

CHAPTER 1

Basic Multiplication Facts

Building conceptual understanding of the basic multiplication facts is essential in helping students gain fluency with complex multiplication problems.

Basic Multiplication Facts: Using Physical Models for Conceptual Understanding

Multiplying Counters

(CCSS: 2.0A.C.3; 3.0A.A.1)

Manipulatives Needed:

• Counters of any kind (e.g., buttons, beans, washers, beads, small blocks, etc ...)

• Small bowls or containers for counters

Preparation:

• Distribute an ample supply of counters and up to 9 small bowls for each student or group of students.

• Copy and cut apart the Multiplying Counters cards (1 set for whole instruction and/or 1 set per group of students (pages 4-6)).

Procedure:

• Model a set of multiplication facts to the class. For example, model the 2 multiplication facts by illustrating with 2 bowls containing 1 counter each (2x1=2), 2 bowls with 2 counters (2x2=4) and continue through 2x9. As you model each fact, verbalize the mathematical sentence, e.g.,, I have 2 groups of 2 which equals 4.

• Shuffle the Multiplying Counter cards and use them to call out problems for students to represent with their counters and bowls. Students should share their findings.

Variation:

• Each group places a set of shuffled Multiplying Counters cards in the center of their workspace. Each student picks a card and creates the multiplication fact with their counters and bowls.

• Students should communicate their multiplication counter sets, e.g.,, I have 3 groups of 6, which equals 18.

Show me 3 x 6 (3 groups of 6). How many do you have altogether? 18 [3x6]

Multiplying Counters

[Card set to copy and cut out – page 1 of 3]

1x1 1x2 1x3 1x4 1x5 1x6
1x7 1x8 1x9 2x1 2x2 2x3
2x4 2x5 2x6 2x7 2x8 2x9
3x1 3x2 3x3 3x4 3x5 3x6
3x7 3x8 3x9 4x1 4x2 4x3

[Card set to copy and cut out – page 2 of 3]

4x4 4x5 4x6 4x7 4x8 4x9
5x1 5x2 5x3 5x4 5x5 5x6
5x7 5x8 5x9 6x1 6x2 6x3
6x4 6x5 6x6 6x7 6x8 6x9
7x1 7x2 7x3 7x4 7x5 7x6

[Card set to copy and cut out – page 3 of 3]

7x7 7x8 7x9 8x1 8x2 8x3
8x4 8x5 8x6 8x7 8x8 8x9
9x1 9x2 9x3 9x4 9x5 9x6
9x7 9x8 9x9

Basic Multiplication Facts: Using Physical Models for Conceptual Understanding

Unlocking the Facts

(CCSS: 2.0A.C.3; 3.0A.A.1)

Manipulatives Needed:

• Unifix™ cubes (up to 9 colors) or Interlocking cubes

Preparation:

• Supply each group of 4 students plenty of Unifix ™ or Interlocking cubes. They will need up to 9 different colors to accommodate all the facts.

• Duplicate 9 copies of Unlocking the Facts (page 9) for each group to record their findings.

Procedure:

• Guide students through the process of constructing groups of colored cubes to represent the basic multiplication facts. It is essential to utilize the colors and the order of the fact, e.g.,, 3 groups of 5 in each group = 15. At this point do not introduce the communicative property. See the chart below to assist you in directing students to build various facts.

• Students record their findings on the Unlocking the Facts worksheets (page _____)

3x5=15

Special variations:

• You may also use this activity as a learning center in the classroom.

• If you don't have enough manipulatives, you can easily build the foundation through 5's and then have students use crayons to represent the rest of the facts using the Unlocking the Facts worksheets. You may find this an effective strategy once they have conceptual understanding.

Answers: Use the fact charts to correct their work.

Unlocking the Facts

1's 2's 3's 4's 5's 6's 7's 8's 9's

1. Circle the multiplication fact above that you are working on.

2. Color in squares that match your work and write the multiplication sentence for each. For example, if working on 2's, use 2 colors and color in 2 groups of 1 each and write 2x1=2.

Name ____________________________ Date ________

Basic Multiplication Facts: Using Physical Models for Conceptual Understanding

Linking Lego™ Array

(CCSS: 2.0A.C.3; 2.0A.C.4; 3.0A.A.1)

Manipulatives Needed:

• Lego™ blocks (up to 9 different colors)

• Lego™ building plates

Preparation:

• Supply each student or group of students an ample supply of legos and 1 10"x10" lego building plate per student/group. They will need up to 9 different colors to accommodate all the facts.

• Copy the Multiplying Counters cards (1 set for whole instruction and/or 1 set per group of students (pages 4-6).

Procedure:

• Model how to represent the basic multiplication facts with legos. For example 3x4=12 would be 3 different colors of legos with 4 in each row snapped into the lego building plate grid. Instruct students to leave a small space between the lego blocks so that each is distinguishable.

• Use the chart on page 9 to guide in the building of all the facts and to correct students' work.

Variations:

• This activity can easily be set up as a learning center. You may use graph paper to have them record their findings as they build various multiplication facts.

Lego Races

• Divide students up into teams to race against each other in building multiplication facts with their legos.

• Use the cards to draw and call out different multiplication fact problems. The team who displays the array the fastest stands up and says, for example, "3x4=12" and shows their board to the class.

Basic Multiplication Facts: Using physical models for Conceptual Understanding

Multiplication Book

(CCSS:2.0A.C.3; 2.0A.C.4; 3.0A.A.1)

Manipulatives Needed:

• 1 in graph paper (10 sheets per student) (page 13)

• 1 cm graph paper (10 sheets per student) (page 14)

• 9 different colors of crayons, markers, or colored pencils

• 9x12 in. light-colored construction paper (15 sheets per student)

• Scissors

• Glue or glue sticks

• 9 different colors of 1" colored squares (for teacher...

Details zur Ausgabe

• Verlag: Trafford
• Erscheinungsdatum: 2016
• Sprache: Englisch
• ISBN 10: 1490767614
• ISBN 13: 9781490767611
• Einband: Taschenbuch
• Anzahl der Seiten: 238
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland