Mathematics Grade 1: Numbers 1-100 Counting and Writing

Grade 1 Mathematics Study Guide: Numbers 1–100 – Counting and Writing

1. The Driving Question

"If you’re playing hide-and-seek and the person counting yells ‘100!’ but you only know numbers up to 20, how do you keep track of all the numbers in between? And why do some numbers look like they’re made of two smaller numbers stuck together—like 21 or 57?"

2. The Core Idea – Built, Not Listed

Imagine you’re building a tower with blocks, one block at a time. The first block is 1, the second is 2, and so on. But what happens when you reach 10? Instead of starting over, you stack a new tower next to it—so 10 and 1 together make 11, 10 and 2 make 12, and so on. This is how numbers work: after 20, you’re really just saying “two tens” plus whatever comes next (21 = two tens + one). By the time you reach 100, you’ve stacked ten towers of ten blocks each—that’s why it’s called one hundred.

This system isn’t random. It’s like a secret code where the place of a digit (where it sits in the number) tells you its value. In 34, the 3 isn’t just “three”—it’s “three tens,” and the 4 is “four ones.” This is why 34 isn’t the same as 43, even though they use the same digits.

Key Vocabulary: - Digit – A single symbol (0, 1, 2, … 9) used to write numbers. Example: The number 72 has two digits: 7 and 2. - Place value – The value of a digit based on its position in a number. Example: In 56, the 5 is in the tens place (worth 50), and the 6 is in the ones place (worth 6). - Counting sequence – The order numbers follow when you count (1, 2, 3, … 100). Example: After 29 comes 30, not 210—because you’ve filled up the ones place and move to the next ten. - Decade number – A number that ends with a zero (10, 20, 30, … 100). Example: 40 is a decade number because it’s “four tens and zero ones.”

3. Assessment Translation

How this appears in Grade 1 assessments: - Exit tickets: “Write the number that comes after 49.” (Short constructed response) - Show-your-work problems: “Circle the group of 24 stars. Explain how you counted them.” (Visual + written explanation) - Classroom games: “Count by tens starting at 30. What number comes next?” (Oral or written)

What a proficient response looks like: - Developing: Writes 50 after 49 but hesitates or counts aloud one by one. - Proficient: Writes 50 immediately and explains, “After 49, the ones place is full, so I add one more ten.” - Advanced: Adds, “49 is four tens and nine ones, so the next number is five tens and zero ones—50.”

Model proficient response (to “Write the number that comes after 79”):

“After 79 comes 80. I know this because 79 is seven tens and nine ones. When the ones place is full (9), I add one more ten and reset the ones to zero. So seven tens + one more ten = eight tens, which is 80.”

4. Mistake Taxonomy

Mistake 1: Skipping numbers in the counting sequence - Prompt: “Count aloud from 58 to 65.” - Common wrong response: “58, 59, 60, 62, 63, 65” (skips 61 and 64). - Why it loses credit: The student doesn’t recognize the pattern of adding one each time. They might be guessing or misremembering. - Correct approach: - Say the numbers slowly: “58, 59, 60…” and pause to think, “What comes after 60? 61.” - Use a number line or fingers to track the count.

Mistake 2: Reversing digits in two-digit numbers - Prompt: “Write the number ‘thirty-seven.’” - Common wrong response: Writes 73 instead of 37. - Why it loses credit: The student hears the numbers but doesn’t connect the order to place value (tens come first, then ones). - Correct approach: - Think: “Thirty-seven means three tens and seven ones.” - Write the 3 in the tens place and the 7 in the ones place.

Mistake 3: Misidentifying the next decade number - Prompt: “What number comes after 99?” - Common wrong response: Writes 910 or 1000. - Why it loses credit: The student doesn’t understand that 100 is the next “full” hundred after 99 (ten tens). - Correct approach: - Remember: After 99, the tens and ones places are full, so you add one more hundred. - Say: “99 is nine tens and nine ones. The next number is ten tens, which is 100.”

5. Connection Layer

1. Within math: Numbers 1–100-Addition and subtraction within 100 Why it matters: If you don’t know how to count or write numbers, you can’t add 23 + 15 or subtract 47 – 12. The counting sequence is the foundation for all operations.

2. Across subjects: Numbers 1–100-Reading analog clocks (telling time) Why it matters: The numbers on a clock (1–12) are part of the counting sequence. If you can count to 100, you can learn to read 3:45 or 7:30 by understanding the pattern of numbers.

3. Outside school: Numbers 1–100-Sports jersey numbers Why it matters: Basketball jerseys (like 23 for Michael Jordan) or soccer jerseys (like 10 for Messi) use two-digit numbers. If you know place value, you’ll notice that 23 isn’t the same as 32—just like how a player’s number is unique!

6. The Stretch Question

“If you start counting at 1 and say one number every second, how long would it take to count to 100? What if you counted by tens instead—would it take the same amount of time? Why or why not?”

Pointer toward the answer: - Counting to 100 one by one would take 100 seconds (a little over a minute and a half). - Counting by tens (10, 20, 30, … 100) would take only 10 seconds because you’re saying fewer numbers. - The difference shows how grouping numbers (like by tens) can make counting faster—just like how place value groups ones into tens to make big numbers easier to write!