Number and Operations · 6 min read
Place Value to 100,000
Section Overview
This section covers Number and Operations in the Grade 3 TEKS (3.2, 3.3, 3.4, and 3.7A). These skills are tested in STAAR Reporting Category 1 (Numerical Representations and Relationships) and Reporting Category 2 (Computations and Algebraic Relationships). You will read and write numbers to 100,000, compare and round numbers, add and subtract within 1,000, count money, multiply and divide, and work with fractions. Remember that STAAR math is taken without a calculator, so each topic shows mental math and paper-and-pencil strategies.
Digits, Places, and Values
Our number system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The spot where a digit sits is its place. The place tells the digit's value. The value is how much the digit is worth.
In 47,382, the digit 4 is in the ten thousands place, so its value is 40,000. The digit 7 is in the thousands place, so its value is 7,000.
- Step 1: Name the places from the right: 5 is in the ones, 1 is in the tens, 8 is in the hundreds, and 6 is in the thousands.
- Step 2: The value of a digit is the digit times its place: 6 × 1,000 = 6,000.
- Answer: The value of the 6 is 6,000.
Building Numbers with Base-Ten Blocks
Base-ten blocks show place value with objects. A small cube is 1. A rod is 10 ones, or 10. A flat is 10 rods, or 100. A big cube is 10 flats, or 1,000.
To name the number, count each kind of block. Then add the values: 1,000 + 300 + 20 + 5 = 1,325.
- Step 1: 2 big cubes are 2 thousands, or 2,000.
- Step 2: There are 0 flats, so there are 0 hundreds. Write 0 in the hundreds place.
- Step 3: 4 rods are 4 tens, or 40. 9 small cubes are 9 ones.
- Step 4: Add: 2,000 + 0 + 40 + 9 = 2,049.
- Answer: 2,049
Standard Form, Word Form, and Expanded Notation
You can write the same number in different ways. Every form names the same amount.
| Form | What it uses | Example |
|---|---|---|
| Standard form | Digits, with a comma | 58,604 |
| Word form | Words | fifty-eight thousand, six hundred four |
| Expanded notation | A sum of the value of each digit | 50,000 + 8,000 + 600 + 4 |
| Expanded notation with multiplication | Each digit times its place value | (5 × 10,000) + (8 × 1,000) + (6 × 100) + (4 × 1) |
In word form, use a hyphen in numbers like fifty-eight and twenty-one. Put a comma after the word thousand. Do not say and when you read a whole number. Say 58,604 as fifty-eight thousand, six hundred four.
- Step 1: Find each place. 70,000 means 7 ten thousands. 3,000 means 3 thousands. 90 means 9 tens. 1 means 1 one.
- Step 2: There is no hundreds part in the sum, so the hundreds digit is 0.
- Step 3: Write the digits in order: 7 ten thousands, 3 thousands, 0 hundreds, 9 tens, 1 one.
- Answer: 73,091
- Step 1: Read the digits before the comma: 15. Say fifteen thousand.
- Step 2: Read the last three digits: 240. Say two hundred forty.
- Step 3: Put the parts together with a comma after thousand.
- Answer: fifteen thousand, two hundred forty
Each Place Is 10 Times the Place to Its Right
Place value follows a pattern. Each place is worth 10 times as much as the place to its right. This pattern keeps going all the way to the hundred thousands place.
| Regroup | Equals |
|---|---|
| 10 ones | 1 ten (10) |
| 10 tens | 1 hundred (100) |
| 10 hundreds | 1 thousand (1,000) |
| 10 thousands | 1 ten thousand (10,000) |
| 10 ten thousands | 1 hundred thousand (100,000) |
- Step 1: The 4 in the thousands place has a value of 4 × 1,000 = 4,000.
- Step 2: The 4 in the hundreds place has a value of 4 × 100 = 400.
- Step 3: Compare: 400 × 10 = 4,000. The thousands place is one place to the left of the hundreds place.
- Answer: The 4 in the thousands place is worth 10 times as much as the 4 in the hundreds place.
Composing and Decomposing Numbers
To decompose a number means to break it into parts. To compose a number means to put parts together. There is more than one way to break apart a number.
- 4,560 = 4 thousands + 5 hundreds + 6 tens
- 4,560 = 45 hundreds + 6 tens
- 4,560 = 456 tens
- 4,560 = 3 thousands + 15 hundreds + 6 tens
All four lines name the same number. The last line traded 1 thousand for 10 hundreds. That is still 4,560.
- Step 1: 3 boxes of 1,000 is 3,000 beads.
- Step 2: 12 bags of 100 is 12 hundreds. Regroup: 10 hundreds = 1 thousand, so 12 hundreds = 1,000 + 200 = 1,200.
- Step 3: Add the parts: 3,000 + 1,200 + 5 = 4,205.
- Answer: Mia has 4,205 beads.
- Value means how much the digit is worth, not the digit itself.
- Name the places from the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands.
- If a picture shows 10 or more of one kind of block, regroup before you write the number.
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