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In this lesson, we will try to gain a deeper understanding of place values, how to compare multi-digits based on the digits in the different place values, and how to round numbers based on place value.
See the fact file below for more information on the generalizing place value for multi-digit whole numbers or alternatively, you can download our 34-page Generalizing Place Value for Multi-digit Whole Numbers worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- Let’s have a review session.
- Ones stands for one digits. Moving to the left, tens means x10, and then as we move from tens to hundreds, we multiply the 10 (from tens) by another 10, which will give us 100.
RELATION TO TEN (10)
- Now, let’s understand how the number ten is related to place values.
- What is the relationship between 7, 70, 700, and 7000?
- Let’s understand this place value by place value.
- Therefore, we can say that a digit in the ones place value multiplied by ten will give us a two-digit number, which in our case is 70. This understanding is applicable to the succeeding place values.
- We can say that, as we multiply a number by 10, the number increases in value and becomes 10 times larger.
- We can use this understanding to relate this to division.
- This time, whenever we divide a number by 10, the number decreases in value and becomes 10 times smaller.
- Notice also that, whenever we multiply the number by 10, an additional zero (0) gets inserted on the right side of the number. On the other hand, whenever we divide the number by 10, we remove a zero from the right side of the number.
READ AND WRITE
- In this section, we will try to understand how to read and write numbers in numeric form, expanded form, and word form.
- Let’s start with how we will write the given number above in numeric form. We will just write the given number without the boxes and the place values.
- Now, let’s write it in expanded form.
- 1,000 + 10 + 1
- Since we have a digit in the thousands place value, writing it in word form would be one thousand.
- Next, we do not have any digit in the hundreds place value.
- Since we know that a two-digit number does not mention tens or ones, and we know that 11 is called eleven, we will just add it.
- Therefore, the number 1,011 in word form is:
- ONE THOUSAND ELEVEN
- In this section, we will try to understand how we can compare values of numbers using their place values, as well as how we can create numbers that are smaller, larger, or equal to a certain number.
- First, let’s figure out how to compare numbers.
- First, look at the numbers per place value. To start comparing numbers, we should look at the leftmost digit first.
- The first number has 3 in the hundreds place value, while the second number has 4 in the hundreds place value. Now, we know that 4 is greater than 3.
- 406 > 305
- Therefore, we can conclude that 406 is greater than 305.
- What if the digits in the hundreds place value are the same, though?
- The numbers above have the same digits in the hundreds place value.
- If this is the case, we should move to the next place value to the right, which is the tens place value.
- Now, we have two different digits. The first number has 2 in the tens place value, while the second number has 1.
- We know that 2 is greater than one.
- 325 > 315
- If both of the digits in the hundreds place value and tens place value are the same for both numbers, we will move to the next place value to the right, which is the ones place value. This is applicable to numbers with more than 3 digits.
- Now, how can we use this knowledge to create a larger number, a smaller number, or a number of equal value?
- Look at the number above. We want to write a number larger than that number. How would you do that?
- First, look at the digit on the leftmost side. The digit is 2. To write a 3-digit number larger than 250, the leftmost number must be greater than 2.
- 350 > 250
- 350 is a number greater than 250.
- What if you want the leftmost digits to be the same? Then, we can look at the digit to the right side of the leftmost digit. Write a number wherein the number in that place value is larger than the given number.
- 260 > 250
- What if we want to write a number smaller than 250?
- Just as we wrote a number larger than 250, we can look at
the digits and write a number with smaller digits.
- 150 < 250
- What if we want to write a number with the same value as 250?
- 250 = 250
- In this section, we will try to understand how to round numbers to any place value.
- Throughout this section, we will use the number above as a guide.
- Let’s round the number to the nearest hundred.
- Now that we have identified the digit in the hundreds place value, we will look at the digit to the right of the hundreds place value.
- The digit on the right side of 7 is 6.
- The number line will serve as a guide of whether we will round up or round down.
- To round up, we add one to the digit we are rounding, and then replace all the digits to the right with zeros.
- To round down, we retain the digit we are rounding, and we replace all the digits to the right with zeros.
- How would we know if we are to round up or round down? Let’s use the number line!
- If the digit to the right side of the digit we are rounding is 0, 1, 2, 3, or 4, we will round down. If the digit is 5, 6, 7, 8, or 9, we will round up.
- Let’s look at the digit to the right of the hundreds place value. The digit is 6. Therefore, we will round up.
- Thus, if we round 45,762 to the nearest hundred, we will get 45,800.
- Now, let’s understand how rounding down works.
- Let’s round the number to the nearest ten.
- The number to the right of the tens place value is 2.
- Looking at the number line, 2 belongs to the group wherein we have to round down.
- Therefore, we will round down.
- Thus, if we round 45,762 to the nearest ten, we will get 45,760.
Generalizing Place Value for Multi-digit Whole Numbers Worksheets
This is a fantastic bundle which includes everything you need to know about the generalizing place value for multi-digit whole numbers across 34 in-depth pages. These are ready-to-use Generalizing Place Value for Multi-digit Whole Numbers worksheets that are perfect for teaching students about the place values, how to compare multi-digits based on the digits in the different place values, and how to round numbers based on place value.
Complete List Of Included Worksheets
- Lesson Plan
- Generalizing Place Value for Multi-digit Whole Numbers
- To Number
- Compare Them
- The Line
- Write It
- Round Round
- Figure Out
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Use With Any Curriculum
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