# Place Value, Rounding, Addition, and Subtraction

## Objective

Build numbers to 1,000,000 and write numbers to that place value in standard and unit form.

## Common Core Standards

### Core Standards

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• 4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

• 4.NBT.A.2 — Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

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• 2.NBT.A.1

• 2.NBT.A.2

• 3.NBT.A.3

## Criteria for Success

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1. Extend the place value system to the millions (or higher), recognizing the patterns within place value (i.e., ones, tens, and hundreds repeat within triples of units, thousands, millions, etc.) (MP.7).
2. Visualize the magnitude of 1 million.
3. Appropriately place commas within numbers up to 1 million when they are presented in standard and unit forms.
4. Convert between unit and standard form (i.e., 24,078 = 2 ten thousands 4 thousands 7 tens 8 ones).
5. Read numbers in word form (e.g., 24,078 as “twenty-four thousand, seventy-eight). (Note: Students will not yet write numbers in word form.)

## Tips for Teachers

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Before the Problem Set or at any point to give students more practice with reading numbers, you could have students play "Digit Ski" from Building Conceptual Understanding and Fluency Through Games by the Public Schools of North Carolina.

### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from discussion) and Anchor Task 3 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Look at your paper base ten blocks. The ones piece is the smallest square. Then tens piece is a 10 x 1 strip. The hundreds piece is the larger 10 x 10 square.

1. Use the paper base ten blocks to construct 1,000. Use tape as needed.
2. Use the paper base ten blocks to construct 10,000. Use tape as needed.
3. What comes next? How much bigger will it be?

#### References

John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II)Activity 10.15

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Modified by Fishtank Learning, Inc.

### Problem 2

1. Look at the ones, tens, hundreds, and thousands base ten blocks.
1. What would you expect a ten thousands base ten block to look like?
2. What would you expect a hundred thousands base ten block to look like?
3. What comes next? What would you expect its base ten block to look like?
2. What pattern do you notice in the shapes of the base ten blocks? What pattern do you notice in the names of the place values? ​​​​​​

#### References

John A. Van de Walle Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II)Activity 10.15 and Figure 10.8

Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.

Modified by Fishtank Learning, Inc.

### Problem 3

When we write really large numbers, writing commas in between groups of them can help make it easier to write them. We place commas every three place values from the right, starting with the ones place. For example, we write 5,678 with the comma placed three place values from the right.

1. Write 430325 in standard form with the correct placement of commas. Then read the number name.
2. Write 3 hundred thousands 2 ten thousands 4 hundreds 5 tens 7 ones in standard form with the correct placement of commas. Then read the number name.
3. Read 50,438 out loud. Then write it in unit form.

## Problem Set & Homework

### Discussion of Problem Set

• How do you know where to place commas in a number? How is this related to three-dimensional representations of numbers? How is it related to the place value names?
• How is the placement of commas related to how we read numbers?
• What are the similarities and differences between standard and unit form? When might we use one over the other?
• Look at #4. Explain how you knew the place value names without ever having hear them before.

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### Problem 1

Write the following numbers in standard form. Be sure to place commas where appropriate.

a.   9 thousands 3 hundreds 4 ones

b.   6 ten thousands 2 thousands 7 hundreds 8 tens 9 ones

c.   1 hundred thousand 8 thousands 9 hundreds 5 tens 3 ones

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic A > Lesson 3Exit Ticket

Grade 4 Mathematics > Module 1 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

### Problem 2

Write the following numbers in unit form.

a.   23,091

b.   8,530

c.   360,467