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Math Clip Art--Base Ten Blocks, Image 8
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Math Clip Art--Base Ten Blocks--8

Math Clip Art--Base Ten Blocks--8

This is a collection of clip art images that you can use to model different numbers. This complete collection models two- and three-digit numbers using base 10 blocks. To see the complete collection of these clip art images, click on this link. 

— CLICK THE PREVIEW BUTTON TO SEE THE CLIP ART IMAGE —

The following review provides basic information about place value.

The Base 10 Number System

When you first learned to count, you started at zero or one and counted to nine.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

After nine, the numbers started repeating.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

After 19, the pattern of numbers continues. In fact, counting numbers involves just using the digits from 0 to 9 in different combinations.

Why is that?

Our numbering system is called a base 10 system. This means there are ten digits, which you know as 0 to 9. All numbers in a base 10 system just use these digits.

Counting in a Base 10 System

When you look at a number, each digit represents a certain place value. Take a look at this three-digit number

The number 123.

The digit 3 is in the ones place. The digit 2 is in the tens place. The digit 1 is in the hundreds place.

Analysis of place value.

The digit 3 is in the ones place. The digit 2 is in the tens place. The digit 1 is in the hundreds place.

For whole numbers, place value increases 10-fold.

 

Place Value illustration.

Place Value in the Base 10 System

Place value determines the size of a number. Take a look at this number:

23

In the ones place is the digit 3, but int he tens place is the digit 2. Don't let the single digit fool you. The 2 in the tens place has a value of 20.

Now look at this number:

542

In the ones place is the digit 2. In the tens place is the digit 4. In the hundreds place is 5. If we were to separate these numbers, we would see this:

500

40

2

So, in going from left to right starting at the decimal point, each place value is ten times the value of the place value to the right.

If you're given a description of a number using just place value information, you can write a number. Here's an example. 

The digit in the ones place is 5. The digit in the tens place is 3. The digit in the hundreds place is 9. What is the number?

Using this description we write the following number: 935.

Number Systems with Other Bases

You've seen how the base 10 number system works, but why do we use a base 10 system? Are there other number systems?

Let's address the first question. The reason we use a base 10 system is probably because we have ten fingers to count with. Do you think it's a coincidence that our base 10 numbering system aligns with our 10 fingers to count?

But we have 10 fingers and 10 toes. Are there number systems that use base 20. Yes!

The Mayan culture used a base 20 system for counting. These are twenty symbols used to count.

Place Value

This numbering system uses just three symbols in different combinations: dots, dashes, and the shell. The shell represents zero. The dash represents an increment of five. The dot represents a value of one. Different combinations of these symbols can model any number.

Another, even more popular system is the binary system, which is used extensively with computers. With the binary system, there are only two digits: 0 and 1. This combination of digits can be used any number  equivalent to our base 10 numbers. Here are the first 10 numbers in binary and base 10.

Base 10 Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001

Why do computers use a binary, or base 2, system? What is the advantage of a binary system?

Computer circuitry and connections involve a lot of on-off switching. Many computer commands are basically combinations of these on-off switches. A binary system is ideal for modeling an on-off system. If you let 0 mean off and 1 mean on, then a binary code can be used to model not only numbers but any computer state.

Each number system has its own rules for writing numbers. Once you learn the rules, then you can write any number in any number system.

Number Models: Base Ten Blocks

One way to model base ten numbers is to use number models, and one of the best ones to use is to use base ten blocks. Base ten blocks are a visual model to represent numbers. Here is what these models look like.

For each of these models, place the correct number of blocks to model the digit in that place value.

This is a model for the number 24. There are two tens blocks in the tens place and four ones blocks in the ones place.

Here is a number to the hundreds place.

To model 250, put two hundreds blocks in the hundreds place, five tens blocks in the tens place, and no blocks in the ones place.
 


Note: The download is a PNG file.

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    Common Core Standards CCSS.MATH.CONTENT.K.NBT.A.1, CCSS.MATH.CONTENT.1.NBT.B.2, CCSS.MATH.CONTENT.2.NBT.A.1
    Grade Range K - 3
    Curriculum Nodes Arithmetic
        • Numbers and Patterns
            • Place Value
    Copyright Year 2021
    Keywords place value, base ten blocks
    Subscribe to Media4Math

     

    Princeton Review


    glossary

     

    Media4Math has a huge collection of instructional clip art covering a wide range of math topics. This collection of resources includes images that you can easily incorporate into your lesson plans. 

    There are several ways to access the math clip art library:

    • The table below has the clip art organized into different categories. These sub collections gather all the math clip art on that topic.
    • Use the keyword search field to look for a particular type of image or a math topic supported by clip art.
    • Browse the complete collection.

    Why use math clip art? Because math is sometimes best explained visually, these clip art images were developed with this idea in mind. A single image will show a concept or a sequence of images will develop a concept logically. This collection also includes animated clip art, for those cases where movement onscreen best clarifies a concept.

    Math Clip Art Collection on Media4Math

    Media4Math has an extensive collection of math clip art. Watch this video to learn more.
    Math Clip Art Collection on Media4Math

    The video was uploaded on 5/9/2022.

    You can view the video here.

    The video lasts for 2 minutes and 2 seconds.

    https://www.youtube.com/embed/kkR-eUhAqRQ
    https://youtu.be/kkR-eUhAqRQ?t={seek_to_second_number}

     

    3D Geometry Clock Faces Fractions--Pizza Slices Linear Functions Parallel Lines Cut by Transversal Statistics
    Adding Decimals Counting Functions and Relations Linear Function Tables Place Value Thermometers
    Angles Concepts Dice and Number Models Geometry Basics  Measurement Playing Cards Triangles
    Animated Clip Art Dividing Fractions by Whole Numbers Geometry Concepts Nets Quadratics  
    Applications of Linear and Quadratic Functions Equations Holiday-Themed Number Systems Ratios, Proportions, Percents  
    Base Ten Blocks Fraction Concepts Language of Math Order of Operations Spinners  

     

    The Evidence Basis for Instructional Clip Art

    The What Works Clearinghouse has a number of evidence-based Practice Guides that focus on math practices that are associated with effective teaching. For example the Practice Guide entitled Improving Mathematical Problem Solving in Grades 4 Through 8 has one recommendation involving showing visual representations of math concepts. Watch the following video to learn more about the three strategies, with special note of the use of visuals:

    In particular, make a note of this from the practice guide:

    A major task for any student engaged in problem solving is to translate the quantitative information in a problem into a symbolic equation—an arithmetic/algebraic statement— necessary for solving the problem. Visual representations help students solve problems by linking the relationships between quantities in the problem with the mathematical operations needed to solve the problem. Students who learn to visually represent the mathematical information in problems prior to writing an equation are more effective at problem solving.

    Visual representations include tables, graphs, number lines, and diagrams such as strip diagrams, percent bars, and schematic diagrams. Example 10 provides a brief explanation
    of how a few types of visual representations can be used to solve problems.68 In the
    panel’s opinion, teachers should consistently teach students to use a few types of visual representations rather than overwhelming them with many examples. In this recommendation, the panel offers suggestions for selecting appropriate visual representations to teach and methods for teaching students how to represent the problem using a visual representation.

    Media4Math's Clip Art Library includes thousands of images that can be used to visually represent quantities. For example, we have many fraction models that easily be incorporated into the lesson or discussion. When introducing fractions, the fraction clip art collection should be an essential part of your instruction.

    Fractions

    We also include a large number of geometric shapes that can be used in your geometry units. We have area models that can be used to model different processes.

    The Clip Art Library also includes visualizations of math manipulative. For example, algebra tiles, decimal blocks, fraction bars and other manipulative are available as downloadable clip art images.

    The Clip Art Library also includes animated clip art, which is an effective tool for visualizing concepts. Here is an example:

    Clip Art

    The Clip Art Library also includes sequenced images that are useful for showing a process, whether it involves a geometric construction or equation solving.


     

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