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Base Ten Blocks

The Uses of Place Value Blocks

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Learning Intentions and Success Criteria

We are learning how base ten blocks can be used to represent and understand our base ten number system. Moreover, we are learning how to use base ten blocks to perform various different operations in mathematics.

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Mathing

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“Pinning Down a Clue”

Important Note:

If you can see this box, then the slide show is not playing and the reveal won’t work.

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Here is the solution:

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If you are using PowerPoint,

click on Slide Show,

then click on From Current Slide.

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If you are using Google Slides,

click on View then Present.

www.stevewyborney.com

Steve Wyborney

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As the clues appear, use the information to narrow the possibilities to a smaller set. After each clue, use estimation again to determine which of the remaining answers is the most reasonable.

How many clothespins

are in the vase?

Write down your first estimate. After each clue, you’ll see if your estimate is still a possibility. After each clue, if it is no longer possible write down a new estimate – and be prepared to explain why you chose it.

www.stevewyborney.com

Steve Wyborney

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Clue #1

Clue #2

Clue #3

Clue #4

Clue #5

Clue #1

The answer is greater than 20

and less than 70.

Clue #2

The answer is part of this pattern: 22, 25, 28…

Clue #3

The answer is an even number,

but it is not 46.

Clue #4

The answer is not equal to

½ of 56.

Clue #5

The answer does not include

the digit 5.

The answer is not a multiple of 5.

www.stevewyborney.com

Steve Wyborney

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After seeing the clues, you have narrowed the possibilities to a small set of numbers. Before you see the answer, select your final estimate. Write it down, and explain to someone why you chose that number.

www.stevewyborney.com

Steve Wyborney

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64 clothespins

The Reveal

Click to see the answer.

Important Note:

If you can see this box, then the slide show is not playing and the reveal won’t work.

​

Here is the solution:

​

If you are using PowerPoint,

click on Slide Show,

then click on From Current Slide.

​

If you are using Google Slides,

click on View then Present.

www.stevewyborney.com

Steve Wyborney

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Why is Place Value difficult for students?

  • Place value is a foundational element of the mathematics curriculum.
  • By learning our number system, students build an understanding of basic operations with whole numbers and later with decimals. Understanding place value allows students to think strategically and flexibly with numbers.

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Why is Place Value difficult for students?

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  • Using representations of numbers is vital in helping students understand place value.
  • Using manipulatives such as Base Ten Blocks allows students to touch, feel, and see the numbers.
  • Without this strong foundation, things like regrouping and operations with multi-digit numbers and decimals lose any meaning.

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What does Base Ten Mean?

  • A number system, regardless of base, is simply a way to express numbers.
  • The “base” of any number system refers to the number of digits used to express numbers in that system.
  • The relationships between the values represented by each digit's place in our number system are the same for whole numbers and decimals.
  • The value of each place is always ten times the value to its immediate right.
  • And the value one place to the right is divided by ten.

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What are Base Ten Blocks?

  • Base Ten Blocks provide a model of our base ten number system. Although there are several different names given to the individual blocks, their relationship to each other remains the same.

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What are Base Ten Blocks?

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  • Base Ten Blocks or MAB were developed to portray the most basic principles of the number system as a simple structure regardless of the base.
  • The different shapes of the blocks represent the structure of that number system.

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What do you use Base Ten Blocks For?

  • Base Ten Blocks are perfect for allowing students to represent whole numbers and decimals and place value concepts.
  • Addition, subtraction, multiplication, and division can all be modeled using Base Ten Blocks.
  • Base Ten Blocks allow students to see the concept of breaking apart and regrouping—which can be arduous when done with the physical versions.

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As with any other manipulative, it is important to give students some “play” time during their first exposure to the materials

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The Parts

What do you notice?

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What do you wonder?

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The Parts Continued

  • The smallest blocks, called “units,” measure one unit on each side and represent ones.
  • The long, narrow blocks, called “rods,” consist of ten of the “unit” cubes and represent tens.
  • The flat, square blocks, known as “flats,” are comprised of ten rods or one hundred units and represent one hundred.
  • The largest block is called a “cube.” It measures ten units per side and represents a thousand.

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Representing Numbers

Examples:

  1. 7
  2. 14
  3. 123
  4. 1234

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Addition

Examples:

  1. 8 + 9
  2. 64 + 58
  3. 123 + 143

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Subtraction

Examples:

  1. 17- 8
  2. 45 - 17
  3. 123- 52

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Multiplication

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Division

Example:

  1. 164 ÷ 3

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Represent Decimal Numbers

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Adding Decimals Using Base Ten Blocks

Example:

  1. 0.35 + 0.25
  2. 1.15 + 2.06

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Subtracting Decimals

Examples

  1. 0.85 - 0.25
  2. 1.54 - 0.15
  3. 23.4 - 22.1

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Multiplication of Decimals

Examples:

  1. 0.70 ⋅ 0.8 =
  2. 0.5 ⋅ 1.7 =
  3. 0.1 ⋅ 2.1 =

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Dividing Decimals

Example:

  1. 3.4 ÷ 0.4

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Additional Uses

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Perimeter and Area

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Volume

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Surface Area

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Contact Information

Todd Robert Martin

District Instructional Specialist

Secondary Mathematics

(e): tmartin2@apslearns.org

(p): (330) 761-3252