Introduction
“Good morning, mathematicians!
Today, we are going to learn different ways to show numbers using place value.”
“Even though we are learning online and don’t have blocks or sticks, we can still picture, draw, and think about numbers.”
“By the end of this lesson, you will be able to show numbers using hundreds, tens, and ones, and write them in standard form, expanded form, and word form.”
Review Place Value
“Let’s review place value.”
“Think about a place-value chart:
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Hundreds
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Tens
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Ones”
“Remember:
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10 ones make 1 ten
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10 tens make 1 hundred.”
“When we group numbers, we make them easier to understand.”
Showing the Number 235
“Let’s work with the number 235.”
“First, imagine we have 235 ones. That’s a lot, so we group them.”
“Let’s make groups of 10 ones.”
“Think with me:
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235 ones can be grouped into 23 groups of ten
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That leaves 5 ones left over.”
“So right now, we have:
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23 tens
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5 ones”
“Now let’s trade again.”
“If we take 10 tens, we can trade them for 1 hundred.”
“So now we have:
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2 hundreds
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3 tens
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5 ones”
“Say it with me:
235 = 2 hundreds, 3 tens, and 5 ones.”
Writing 235 in Different Forms
“Now let’s write 235 in different ways.”
“First, standard form:
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That’s just the number we usually write: 235”
“Next is expanded form.”
“235 has:
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2 hundreds = 200
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3 tens = 30
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5 ones = 5”
“So expanded form is:
235 = 200 + 30 + 5”
“Now let’s write it in word form.”
“235 is written:
two hundred thirty-five.”
The Number 321
“Now let’s try another number: 321.”
“Look at the digits:
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3 is in the hundreds place
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2 is in the tens place
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1 is in the ones place.”
“So we know:
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3 hundreds
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2 tens
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1 one”
“That means:
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Expanded form is 300 + 20 + 1
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Word form is three hundred twenty-one.”
Lesson Wrap Up
“Today you learned how to:
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Group ones into tens
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Trade tens for hundreds
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Show numbers using place value
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Write numbers in standard, expanded, and word form.”
“Now you are ready to answer the questions on your worksheet.”
“Remember to ask yourself:
How many hundreds? How many tens? How many ones?”
“Take your time and show your thinking.”
“You’ve got this—let’s begin!”
Ways to Show Numbers Student Activity
Materials (Virtual):
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Paper and pencil or a digital whiteboard, drawing tool, or math app
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Optional: online place-value chart or base-ten blocks tool
Showing the Number 124
There are many ways to show the number 124. Answer questions 1–9 to learn how.
Imagine or draw 124 ones on your paper or screen.
Circle groups of 10 to make tens.
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How many groups of ten can you make?
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How many ones are left over?
Now imagine combining 10 groups of ten to make 1 hundred.
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How many hundreds are there?
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How many tens are left?
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How many ones are left?
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How many are there in all?
Writing the Number 124
The number 124 can be written in different ways.
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Standard form:
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124 = ___ hundred ___ tens ___ ones
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OR ___ tens ___ ones
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Expanded form:
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124 = 100 + ___ + ___
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Word form:
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124 is written one hundred twenty-___
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Showing the Number 238
There are also different ways to write 238. Answer questions 10–12.
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Place-value form:
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238 = ___ hundreds ___ tens ___ ones
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OR ___ tens ___ ones
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Expanded form:
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238 = ___ + ___ + ___
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Word form:
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238 is written _______________________________
Write each number in expanded form.
___________________________________
Challenge:
1. Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right.
The clues below describe the 4 digits of a mystery number that contains the digits 3, 4, 7, 8.
• The value of the 8 is 10 times the value of the 8 in 3,518.
• The value of the 7 is 100 times the value of the 7 in 1,273.
• The value of the 4 is 100 times the value of the 4 in 7,284.
• The missing place value is the 3.
What is the number?
a. 7,483
b. 8,743
c. 7,834
d. 4,738
How to:
Step-by-Step Explanation
Step 1: Remember the Place-Value Rule
When a digit moves:
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One place to the left, its value becomes 10 times larger
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One place to the right, its value becomes 10 times smaller
Step 2: Use the Clue About the Digit 8
The value of the 8 is 10 times the value of the 8 in 3,518.
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In 3,518, the 8 is in the ones place
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Its value is 8
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Ten times 8 is 80
So, in the mystery number, 8 must be in the tens place.
Step 3: Use the Clue About the Digit 7
The value of the 7 is 100 times the value of the 7 in 1,273.
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In 1,273, the 7 is in the tens place
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Its value is 70
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100 times 70 is 7,000
So, in the mystery number, 7 must be in the thousands place.
Step 4: Use the Clue About the Digit 4
The value of the 4 is 100 times the value of the 4 in 7,284.
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In 7,284, the 4 is in the ones place
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Its value is 4
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100 times 4 is 400
So, in the mystery number, 4 must be in the hundreds place.
Step 5: Place the Digit 3
The missing place value is the 3.
So far, we have:
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Thousands place: 7
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Hundreds place: 4
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Tens place: 8
The only place left is the ones place, so 3 goes in the ones place.
Step 6: Write the Number
Putting the digits together by place value:
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 7 | 4 | 8 | 3 |
2. Read and write multi-digit whole numbers from 0 to 1,000,000 using standard form, expanded form, and word form.
Select all the ways to rename the number 2,340.
a. 234 tens
b. 2,340 ones
c. 234 thousands
d. 2 hundreds and 34 ones
e. 2 thousands and 34 tens
f. 2 thousands and 34 ones
g. 2 thousands and 34 hundreds
Explanation:
Let’s check each choice by rewriting it as a number and seeing if it equals 2,340.
Given Number: 2,340
a. 234 tens
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234 × 10 = 2,340
✅ Correct
b. 2,340 ones
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2,340 × 1 = 2,340
✅ Correct
c. 234 thousands
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234 × 1,000 = 234,000
❌ Not correct
d. 2 hundreds and 34 ones
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2 hundreds = 200
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34 ones = 34
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200 + 34 = 234
❌ Not correct
e. 2 thousands and 34 tens
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2 thousands = 2,000
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34 tens = 340
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2,000 + 340 = 2,340
✅ Correct
f. 2 thousands and 34 ones
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2,000 + 34 = 2,034
❌ Not correct
g. 2 thousands and 34 hundreds
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2,000 + 3,400 = 5,400
❌ Not correct
✅ Correct Answers:
a, b, e
These are all valid ways to rename 2,340.
Answers:
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