**What Is The Value Of W** – Place value is a difficult concept to master. Use this strategy to help third, fourth, and fifth graders expand their understanding of place value as they construct (or “make”) four-digit numbers.

In the early elementary grades, students must understand that the value of a number depends on its position in the number. They did this mostly by creating two- and three-digit numbers.

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## What Is The Value Of W

Using this strategy, students will create four-digit numbers using manipulatives called place value discs. These place value discs (sometimes called place value chips) are round objects, each representing 1, 10, 100, or 1,000.

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For example, in the number 6, 142, the number 6 is represented by six thousand discs, the number 1 by a hundred discs, the number 4 by four decimal discs, and the number 2 by two discs. . .

Before you begin, make sure your students understand place value with two- and three-digit numbers. (You may want to use straw bundles as a more concrete way of displaying the digit value.) Then you can move on to the strategy of using more disks of digit values.

Gather the materials. Give each student a place value mat and a set of place value discs. Have students cut the discs.

Students struggling with fine motor skills may find it difficult to cut or replace paper discs. Discs may be too small for students with low vision. It’s important for students to be able to use manipulatives in this strategy, so consider these options:

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1. Introduce vocabulary. Clearly review the academic vocabulary required for the course, such as place value, one, ten thousand, one hundred, one thousand. Use the Matte digit value to mark each column heading.

For English Learners (ELLs): talk about the difference between the words skin and skin. Explain that ten (or 10) denotes a number greater than 9 but less than 11. Show ten using a collection of individual objects, such as 10 pens. Explain that ten refers to how many groups of 10 are used to make a number. For example, the number 60 means that there are six tens or six groups of 10. “Remember when we showed six ten before?” Ask Show students 10 groups using straws (or other objects) to remind them of previous lessons.

2. Explains digit value discs. Explain to students that they will use the place value discs to help them understand the place value. View each disc — 1, 10, 100, 1,000. Mark different colors for each disc type.

Model how to count 10 units disks and then transfer to 1 tens disk. Do this for all 10 decimal disks and change to 1 hundred disks. Then count 10 hundred discs again and trade 1 thousand discs. Students can practice doing this with their discs. To represent this idea another way, count to 10, then write a text frame on the board: “____ one disc makes ____ tens.” Fill in the blanks in the sentence frame as a class: “10 discs make 1 tense disc.”

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This is a good opportunity to talk about the relationship between each place. For example, the thousands digit is 10 times the hundreds digit.

3. Start with concrete. Use the concrete-representational-abstract (CRA) instruction sequence to have students construct (or “make”) a number using the place value mat and discs. Model how the place value discs can be changed to create a four-digit number. For example, you can make 2, 418 with a 2 thousand diskette, 4 hundred diskette, 1 decimal diskette and 8 unity disk.

Think out loud as you model how to place the discs on the mat. For example, you might say, “I know I need two thousand disks to make two thousand disks, so here are a thousand disks, here are a thousand more disks.” Then invite students to do this with a few numbers. Give them feedback as they work.

Teaching Tip: To relate numbers to real-world uses, you can identify four-digit numbers around your school, such as the year the school was built. You can also use numbers that are important to students, such as the year they were born.

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4. Switch to the demonstration. After students learn how to make numbers with discs, move on to the representational level. Model drawing a circle on a place value mat: Draw a circle in the appropriate column and write the number (1, 10, 100, or 1,000) that corresponds to the circle. (Students can find coins if they have trouble drawing a circle.)

For example, draw 5 thousand circles, 6 hundred circles, 4 tens circles, and 2 ones circles to represent the number 5,642. Next, have students draw circles in the appropriate columns on their place value mat to make the four-digit number.

Provide ample opportunities for training and feedback. Invite students to explain what is entered in each column and say the standard number. Many students, including ELLs and students who struggle with expressive language, can benefit from using sentence frames to share their numbers. You can use this frame and display: “My number is ____. ____ thousand, ____ one hundred, ____ ten thousand, and ____ one.

Teaching Tip: To reuse the space-saving mats throughout the lesson, put the mats inside the dry-wipe pockets. Have students use dry erase markers to record their answers. Then they can clean it up and move on to the next instance. You can also pocket copies of sentence frames.

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5. Conclude with a summary. Once you’ve mastered the representational level, move on to the abstract level. On the place value mat, have students construct a number using only the written numbers, such as 8 thousand, 7 hundred, 1 ten thousand, and 7 equals 8,717. Both can write the number and read it aloud.

If students are having trouble getting to the abstract level, encourage them to return to using the place value discs and then the drawings. Do not rush to abstraction until you have mastered these scaffolds.

6. Continue to use the discs. Place value discs and thousands of mats can support students as they continue to work with multi-digit numbers. Mats and discs help students round to the nearest ten, hundred or thousand. These resources can help students understand how to work with multi-digit numbers. For example, you can use mats and disks to help students use extended notation when adding and subtracting.

Students who learn and think differently may find it difficult to make a connection between our basic 10 number system and the language we use for numbers. This is because the language we use for numbers is not directly translated. For example, we write “2, 316”, not “2000 300 10 6”.

## What Is The Value Of W?

Writing down numbers using place value discs helps students make connections between the number system and language. The discs show students that a number is the sum of its parts. Discs also help students compare the value of each place.

Using multiple models, including place value discs, straw bundles, and drawings, will help all students understand place value. They learn from support and feedback as they move from concrete representations of a number to abstract representations.

Once students understand the concept of place value, they will have a solid foundation for more advanced math operations including rearrangement, multiplication, and addition with fractions and decimals.

Families may be familiar with place value, but may have learned it differently in elementary school.

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Explain how you taught place value in your classroom newsletter or at a school activity. Share resources that families can use to practice the concept of place value at home, including how to use multi-sensory techniques for place value and other math concepts. If you teach fourth grade, you can also share information about why math is difficult at this grade level.

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From Learning Disability Research and Practice, “Using Concrete-Representative-Abstract Sequencing with Integrated Strategy Teaching to Teach Deduction with Reconstruction to Students with Learning Disabilities.

The Editor-in-Chief is Kim Green, MA. As a former primary school teacher and certified reading specialist, she is passionate about developing resources for teachers.

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