🎯 First Grade Math: Place Values

Complete Study Notes & Formulas

🔟 Place Value Models - Tens and Ones

✦ What is Place Value?

Place value tells us the value of a digit based on its position in a number.

✦ Two-Digit Numbers Structure:

Every two-digit number has TWO places:

TENS place (Left) | ONES place (Right)

✦ Base Ten Blocks:

🔵 ONES = Small cubes (individual units)

🟧 TENS = Long bars/rods (10 ones grouped together)

✦ Core Formula:

Number = (Tens × 10) + Ones

Example: 34 = (3 × 10) + 4 = 30 + 4

3 tens = 3 groups of 10 = 30

4 ones = 4 individual units = 4

✦ Visual Model Examples:

Number	Tens Rods	Ones Cubes	Place Value
23	2 rods	3 cubes	2 tens + 3 ones
47	4 rods	7 cubes	4 tens + 7 ones
50	5 rods	0 cubes	5 tens + 0 ones

✦ Expanded Form:

Standard Form → Expanded Form

25 = 20 + 5 = 2 tens + 5 ones

68 = 60 + 8 = 6 tens + 8 ones

91 = 90 + 1 = 9 tens + 1 one

💯 Place Value Models - Up to Hundreds

✦ Three-Digit Numbers Structure:

Three-digit numbers have THREE places:

HUNDREDS (Left) | TENS (Middle) | ONES (Right)

✦ Base Ten Blocks for Hundreds:

🟩 ONES = Small cubes (1 unit)

🟦 TENS = Long rods (10 ones = 1 ten)

🟥 HUNDREDS = Flat squares (10 tens = 100 ones = 1 hundred)

✦ Three-Digit Formula:

Number = (Hundreds × 100) + (Tens × 10) + Ones

Example: 347 = (3 × 100) + (4 × 10) + 7

= 300 + 40 + 7

= 347

✦ Place Value Chart:

Number	Hundreds	Tens	Ones	Expanded Form
123	1	2	3	100 + 20 + 3
456	4	5	6	400 + 50 + 6
789	7	8	9	700 + 80 + 9
900	9	0	0	900 + 0 + 0

✦ Relationship Between Places:

1 Hundred = 10 Tens = 100 Ones

1 Ten = 10 Ones

Example: 200 = 20 tens = 200 ones

3️⃣0️⃣ Write Tens and Ones - Up to 30

✦ Number Range: 1 to 30

Numbers 1-9: 0 tens + ones

Numbers 10-19: 1 ten + ones

Numbers 20-29: 2 tens + ones

Number 30: 3 tens + 0 ones

✦ Writing Formula:

Write: ___ tens and ___ ones

Step 1: Find the tens digit (left number)

For 24 → 2 is in the tens place

Step 2: Find the ones digit (right number)

For 24 → 4 is in the ones place

Step 3: Write the answer

24 = 2 tens and 4 ones

✦ Complete Examples (1-30):

Number	Tens and Ones	Number	Tens and Ones
10	1 ten, 0 ones	21	2 tens, 1 one
11	1 ten, 1 one	22	2 tens, 2 ones
12	1 ten, 2 ones	23	2 tens, 3 ones
15	1 ten, 5 ones	25	2 tens, 5 ones
19	1 ten, 9 ones	30	3 tens, 0 ones

✦ Special Cases:

⚠️ Numbers 1-9 have 0 tens

Example: 7 = 0 tens and 7 ones

⚠️ Numbers ending in 0 have 0 ones

Example: 20 = 2 tens and 0 ones

💯 Write Tens and Ones - Up to 100

✦ Number Range: 1 to 100

All numbers from 1-99 have at most 9 tens and 9 ones

Number 100 = 10 tens and 0 ones OR 1 hundred

✦ Universal Formula for Two-Digit Numbers:

AB = A tens and B ones

Where:

• A = First digit (tens place)

• B = Second digit (ones place)

Examples:

67 → 6 tens and 7 ones

82 → 8 tens and 2 ones

99 → 9 tens and 9 ones

✦ Complete Reference Chart:

Tens	Range	Pattern	Example
0	1-9	0 tens + ones	5 = 0 tens, 5 ones
1	10-19	1 ten + ones	17 = 1 ten, 7 ones
2	20-29	2 tens + ones	24 = 2 tens, 4 ones
3	30-39	3 tens + ones	36 = 3 tens, 6 ones
4	40-49	4 tens + ones	48 = 4 tens, 8 ones
5	50-59	5 tens + ones	55 = 5 tens, 5 ones
6	60-69	6 tens + ones	63 = 6 tens, 3 ones
7	70-79	7 tens + ones	71 = 7 tens, 1 one
8	80-89	8 tens + ones	85 = 8 tens, 5 ones
9	90-99	9 tens + ones	97 = 9 tens, 7 ones
10	100	10 tens + 0 ones	100 = 10 tens, 0 ones