TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Decimal Operations Using Base-10 Blocks

This kit contains: • 10 bags of “Base 10 Cube Blue” (set of 1)

• 10 bags of “Base 10 Flats Blue” (set of 10) • 10 bags of “Base 10 Rods Blue” (set of 50) • 10 bags of “Base 10 Units Blue” (set of 100) • 1 bag of “Overhead Base 10 Blocks Blue” (set of 50) • 1 activity binder Video demonstrations of the following lessons can be found at: http://tidewaterteam.wm.edu/VideoManipulatives/index.php

Overview of Lesson 1 Getting to Know Base-10 Blocks In this lesson, students will explore the relationships between

decimals using Base-10 Blocks. Often, students need time to explore and “play” with the new manipulative before they are ready to be guided through computations using the manipulative. Allow students time to explore relationships between the Base-10 Blocks. In order to promote higher-level thinking and to develop number sense, have students work with establishing new values based on different pieces being considered the unit. After students have become familiar with assigning values to the blocks, students will use the blocks to show values the teacher specifies as well as name the value the teacher demonstrates with the blocks. See the video, Exploring the Relationships of Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php for a demonstration of this lesson.

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Overview of Lesson 2 Adding Decimals Using Base-10 Blocks In this lesson students will use the Base-10 blocks to model

decimal addition. Examples with and without regrouping will be done within the same lesson. After students are comfortable with adding decimals using the Base-10 Blocks, pictorial representations should be used and connections to the written algorithm should be emphasized. See the video, Adding Decimals Using Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php for a demonstration of this lesson.

Overview of Lesson 3 Subtracting Decimals Using Base-10 Blocks In this lesson students will use the Base-10 blocks to model

decimal subtraction. Examples with and without regrouping will be done within the same lesson. After students are comfortable with subtracting decimals using the Base-10 Blocks, pictorial representations should be used and connections to the written algorithm should be emphasized. See the video, Subtracting Decimals Using Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php for a demonstration of this lesson.

Overview of Lesson 4 Multiplying Decimals Using Base-10 Blocks In this lesson students will use the Base-10 blocks to model

decimal multiplication. This model will may come naturally to students that are familiar and comfortable with whole number multiplication arrays. Teachers should choose their examples very carefully. Not all decimal multiplication problems are successfully represented with this model. This model is best used to introduce the meaning of decimal multiplication, and then move into pictorial and abstract representations. See the video, Multiplying Decimals Using Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php for a demonstration of this lesson.

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 1

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 1

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 1

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 1 Transition into pictorial representation

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Lesson 1 Pictorial Representations

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Lesson 2

Teacher Notes

Students should make a place value mat to lay the base-10 blocks on while performing the addition problems. The following page has place value titles that can be cut out to manipulate as a place value mat. Teachers can also develop their own mats as well. For an example of a mat and lesson, view the video Adding Decimals Using Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php.

Some examples of addition decimal problems to model with base-10 blocks may be:

• Example 1: 0.05 + 0.13 0.05 + 0.13 = 0.18

• Example 2: 1.16 + 0.57 1.16 + 0.57 = 1.73

• Example 3: 1.83 + 0.21 1.83 + 0.21 = 2.04

After students become comfortable with performing the operation with the manipulative. Transition the students into pictorial representations and then into the algorithm. Base-10 blocks can be drawn free hand using the following symbols (or variation of the following):

Shading techniques can also be used as a pictorial representation. (See following handout.)

= flat = rod = unit

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 2 Place Value Titles

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 2 Pictorial Representations

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 3

Teacher Notes

Students can use a place value mat to lay the base-10 blocks on while performing the subtraction problems. (Use the titles on previous page, or create your own.) For an example of a mat and lesson, view the video Subtracting Decimals Using Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php.

Some examples of addition decimal problems to model with base-10 blocks may be:

• Example 1: 0.4 – 0.2 o 0.4 – 0.2 = 0.2

• Example 2: 0.40-0.06 o 0.40-0.06 = 0.34

• Example 3: 1.26 – 0.18 o 1.26 – 0.18 = 1.08

After students become comfortable with performing the operation with the manipulative. Transition the students into pictorial representations and then into the algorithm. Base-10 blocks can be drawn free hand using the following symbols (or variation of the following):

When drawing subtraction problems, students should cross out what is being taken away in the problem. That is, draw the subtrahend, cross out the minuend, and what is left is the difference. Regrouping can also be represented pictorially.

= flat = rod = unit

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 4

Teacher Notes

In this lesson students will use the Base-10 blocks to model decimal multiplication. This model will may come naturally to students that are familiar and comfortable with whole number multiplication arrays. Teachers should choose their examples very carefully. Not all decimal multiplication problems are successfully represented with this model. This model is best used to introduce the meaning of decimal multiplication, and then move into pictorial and abstract representations.

See the video, Multiplying Decimals Using Base Ten Blocks at http://tidewaterteam.wm.edu/VideoManipulatives/index.php for a demonstration of this lesson.

The following pages include pictorial representations of decimal multiplication.

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 4

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Lesson 4

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Additional Resources

The following pages are additional related resources. They include blank grids that can be used for shading in representations of decimals and/or decimal operations. Also, pictorials representations of decimal division are included.

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Tenths grids

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Hundredths Grids

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Decimal Division

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Decimal Division

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Decimal Division

TheCollegeofWilliamandMary LauraBitto–lebitt@wm.eduMathOnWheels2009‐2010 JamieRiggs–jlmoye@wm.edu

Decimal Division