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.
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – 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. The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 1
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 1
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 1
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 1
The College of William and Mary Math On Wheels 2009‐2010
Transition into pictorial representation
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 1
The College of William and Mary Math On Wheels 2009‐2010
Pictorial Representations
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
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):
= flat
= rod
= unit
Shading techniques can also be used as a pictorial representation. (See following handout.)
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 2
The College of William and Mary Math On Wheels 2009‐2010
Place Value Titles
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 2
The College of William and Mary Math On Wheels 2009‐2010
Pictorial Representations
Laura Bitto – lebitt@wm.edu Jamie Riggs – 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):
= flat
= rod
= unit
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.
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – 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.
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 4
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Lesson 4
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – 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.
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Tenths grids
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Hundredths Grids
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Decimal Division
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Decimal Division
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Decimal Division
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu
Decimal Division
The College of William and Mary Math On Wheels 2009‐2010
Laura Bitto – lebitt@wm.edu Jamie Riggs – jlmoye@wm.edu