📚 First Grade Math: Counting and Number Patterns

Complete Study Notes & Formulas

1️⃣ Counting Review - Up to 10

✦ Basic Rule:

Count numbers in order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

✦ Formula:

Next Number = Current Number + 1

Example: If current number is 5, next number = 5 + 1 = 6

🔢 Count to Fill a Ten Frame

✦ What is a Ten Frame?

A rectangle with 10 boxes (5 on top, 5 on bottom)

✦ Filling Rule:

1. Fill the TOP row first (left to right)

2. Then fill the BOTTOM row (left to right)

✦ Key Formula:

Any Number up to 20 = 10 + Extra

Example: 13 = 10 + 3

Example: 17 = 10 + 7

2️⃣0️⃣ Counting Review - Up to 20

✦ Number Sequence:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

✦ Pattern Rule:

• Numbers 1-9: Single digit

• Numbers 10-19: Teen numbers (1 ten + ones)

• Number 20: 2 tens + 0 ones

3️⃣0️⃣ Counting Tens and Ones - Up to 30

✦ Place Value Formula:

Number = (Tens × 10) + Ones

Example: 23 = (2 × 10) + 3 = 20 + 3

Example: 30 = (3 × 10) + 0 = 30 + 0

✦ Quick Reference:

21 = 2 tens + 1 one | 25 = 2 tens + 5 ones

28 = 2 tens + 8 ones | 30 = 3 tens + 0 ones

4️⃣0️⃣ Count on Ten Frames - Up to 40

✦ Multiple Ten Frames Rule:

Total = (Full Ten Frames × 10) + Extra Counters

Example: 34 = (3 full frames × 10) + 4 = 30 + 4

Example: 40 = (4 full frames × 10) + 0 = 40 + 0

💯 Counting - Up to 100

✦ Pattern by Tens:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

✦ General Formula:

Any Two-Digit Number = (Tens Digit × 10) + Ones Digit

Example: 67 = (6 × 10) + 7 = 60 + 7

Example: 85 = (8 × 10) + 5 = 80 + 5

9️⃣9️⃣ Counting Tens and Ones - Up to 99

✦ Place Value Chart:

Number	Tens	Ones	Expanded Form
45	4	5	40 + 5
78	7	8	70 + 8
99	9	9	90 + 9

🖼️ Counting by Twos, Fives, and Tens with Pictures

✦ Visual Counting Rules:

• By 2s: Count pairs (like shoes, eyes)

• By 5s: Count groups of 5 (like fingers on one hand)

• By 10s: Count groups of 10 (like both hands)

⏭️ Counting by Twos, Fives, and Tens

✦ Skip Counting Formulas:

📌 Count by 2s: Add 2 each time

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

Formula: Next Number = Previous Number + 2

📌 Count by 5s: Add 5 each time

0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...

Formula: Next Number = Previous Number + 5

📌 Count by 10s: Add 10 each time

0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100...

Formula: Next Number = Previous Number + 10

⬅️➡️ Counting Forward and Backward

✦ Direction Rules:

▶️ Counting Forward: Add 1 (or skip count up)

Example: 15, 16, 17, 18, 19, 20

Formula: Next = Current + 1

◀️ Counting Backward: Subtract 1 (or skip count down)

Example: 20, 19, 18, 17, 16, 15

Formula: Previous = Current - 1

📏 Number Lines - Up to 100

✦ Number Line Rules:

• Numbers increase from LEFT to RIGHT

• Each mark = 1 unit (or skip count by 2, 5, 10)

• Moving RIGHT = Adding (+)

• Moving LEFT = Subtracting (-)

✦ Jump Formula:

Landing Number = Starting Number + (Jump Size × Number of Jumps)

Example: Start at 10, jump by 5, three times → 10 + (5 × 3) = 25

💯 Hundred Chart

✦ Structure:

10 rows × 10 columns = 100 numbers (1 to 100)

✦ Movement Formulas:

• Move RIGHT 1 space = Add 1

• Move LEFT 1 space = Subtract 1

• Move DOWN 1 row = Add 10

• Move UP 1 row = Subtract 10

✦ Pattern Rules:

• Each ROW starts with: 1, 11, 21, 31, 41, 51, 61, 71, 81, 91

• Each COLUMN has same ones digit

• Diagonal patterns show special number relationships

⚖️ Even or Odd

✦ Definitions:

🔵 EVEN Numbers: Can make perfect pairs (no leftovers)

Numbers that end in: 0, 2, 4, 6, 8

Examples: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

🔴 ODD Numbers: Have 1 leftover when making pairs

Numbers that end in: 1, 3, 5, 7, 9

Examples: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19...

✦ Division Formula:

Even Number ÷ 2 = Whole Number (no remainder)

Example: 8 ÷ 2 = 4 (Even)

Odd Number ÷ 2 = Has remainder of 1

Example: 9 ÷ 2 = 4 remainder 1 (Odd)

🔍 Identify Numbers as Even or Odd

✦ Quick Identification Rule:

Look at the LAST DIGIT (ones place) ONLY!

If last digit is 0, 2, 4, 6, or 8 → EVEN

If last digit is 1, 3, 5, 7, or 9 → ODD

✦ Examples:

34 ends in 4 → EVEN | 47 ends in 7 → ODD

88 ends in 8 → EVEN | 91 ends in 1 → ODD

📏 Even or Odd Numbers on Number Lines

✦ Pattern on Number Line:

Even and Odd numbers ALTERNATE

1(O), 2(E), 3(O), 4(E), 5(O), 6(E), 7(O), 8(E)...

✦ Skip Counting Pattern:

Count by 2s from 0 or any even number = All EVEN

0, 2, 4, 6, 8, 10, 12...

Count by 2s from 1 or any odd number = All ODD

1, 3, 5, 7, 9, 11, 13...

⬅️➡️ Which Even or Odd Number Comes Before or After?

✦ Same Type Navigation:

🔵 Next EVEN number = Current Even + 2

Example: After 8 → 8 + 2 = 10

Before 8 → 8 - 2 = 6

🔴 Next ODD number = Current Odd + 2

Example: After 7 → 7 + 2 = 9

Before 7 → 7 - 2 = 5

📊 Skip-Counting Patterns - With Tables

✦ Skip Counting Table:

Skip By	Pattern	Formula
2s	2, 4, 6, 8, 10...	n × 2
5s	5, 10, 15, 20, 25...	n × 5
10s	10, 20, 30, 40, 50...	n × 10

(where n = position: 1st, 2nd, 3rd, 4th...)

🔢 Sequences - Count Up and Down by 1, 2, 3, 5, and 10

✦ Sequence Formulas:

⬆️ COUNTING UP (Ascending):

Next Term = Current Term + Step Size

⬇️ COUNTING DOWN (Descending):

Next Term = Current Term - Step Size

✦ Examples:

Up by 3: 5, 8, 11, 14, 17... (add 3 each time)

Down by 5: 50, 45, 40, 35, 30... (subtract 5 each time)

💯 Sequences - Count Up and Down by 100

✦ Hundred Jump Formula:

⬆️ Counting UP by 100:

Next Number = Current Number + 100

Example: 100, 200, 300, 400, 500, 600...

⬇️ Counting DOWN by 100:

Next Number = Current Number - 100

Example: 600, 500, 400, 300, 200, 100, 0

🥇 Ordinal Numbers

✦ What are Ordinal Numbers?

Numbers that show POSITION or ORDER (not quantity)

✦ First 20 Ordinal Numbers:

Number	Ordinal	Number	Ordinal
1	1st (First)	11	11th (Eleventh)
2	2nd (Second)	12	12th (Twelfth)
3	3rd (Third)	13	13th (Thirteenth)
4	4th (Fourth)	14-19	Add "th"
5-10	Add "th"	20	20th (Twentieth)

✦ Rule for Larger Numbers:

Numbers ending in 1 → add "st" (21st, 31st, 41st...)

Numbers ending in 2 → add "nd" (22nd, 32nd, 42nd...)

Numbers ending in 3 → add "rd" (23rd, 33rd, 43rd...)

All other numbers → add "th" (24th, 25th, 30th...)

EXCEPT: 11th, 12th, 13th (always "th")

✍️ Writing Numbers in Words

✦ Basic Number Words (1-20):

1 = One	6 = Six	11 = Eleven	16 = Sixteen
2 = Two	7 = Seven	12 = Twelve	17 = Seventeen
3 = Three	8 = Eight	13 = Thirteen	18 = Eighteen
4 = Four	9 = Nine	14 = Fourteen	19 = Nineteen
5 = Five	10 = Ten	15 = Fifteen	20 = Twenty

✦ Tens Words:

10 = Ten | 20 = Twenty | 30 = Thirty | 40 = Forty | 50 = Fifty

60 = Sixty | 70 = Seventy | 80 = Eighty | 90 = Ninety | 100 = One Hundred

✦ Two-Digit Number Formula:

For numbers 21-99:

Write: [Tens word] + hyphen (-) + [Ones word]

Examples:

34 = Thirty-four

67 = Sixty-seven

89 = Eighty-nine

✦ Important Rule:

⚠️ Always use a hyphen (-) between tens and ones!

✅ Correct: Twenty-five, Forty-two

❌ Wrong: Twenty five, Fortytwo

📌 Quick Reference Summary

🔢 Basic Counting:

Next = Current + 1

Previous = Current - 1

🔟 Place Value: