Mathematics Grade 1: Place Value Tens and Ones

Grade 1 Mathematics Study Guide: Place Value – Tens and Ones

1. The Driving Question

If you have 24 crayons and want to count them fast, why can’t you just say “twenty-four” right away? How does breaking them into groups help you see the number in a way that makes sense—and how do those groups turn into the digits we write?

2. The Core Idea – Built, Not Listed

Imagine you’re at the playground with a big bucket of tennis balls. Counting one by one takes forever, so you stack them into tubes—each tube holds exactly 10 balls. Now, if you have 2 full tubes and 4 loose balls, you don’t have to count every single ball to know there are 24. The "2" in 24 stands for the 2 full tubes (20 balls), and the "4" stands for the 4 extra balls. That’s place value: the position of a digit tells you whether it’s counting tens or ones.

• Digit: A single symbol (0–9) used to write numbers. Example: In the number 35, both "3" and "5" are digits.
• Tens place: The digit on the left in a two-digit number; it tells how many groups of 10 there are. Example: In 52, the "5" means 5 groups of 10 (50).
• Ones place: The digit on the right in a two-digit number; it tells how many single items are left over. Example: In 17, the "7" means 7 ones.
• Place value: The value of a digit based on its position in a number. Example: The "1" in 16 means 10, but the "1" in 61 means 1.

3. Assessment Translation

How this appears in class: - Exit ticket: Draw 37 dots. Circle groups of 10. Write the number in tens and ones. - Show-your-work problem: You have 4 tens blocks and 8 ones blocks. What number do you have? Explain how you know.

Proficient vs. Developing Responses: - Proficient: Draws 3 full circles of 10 dots and 7 single dots. Writes "3 tens and 7 ones = 37." - Developing: Draws 37 dots but doesn’t group them. Writes "37" without explaining tens/ones.

Model Proficient Response: Prompt: You have 2 tens blocks and 5 ones blocks. What number is this? Response: "I have 2 groups of 10, which is 20, and 5 ones. So the number is 25."

4. Mistake Taxonomy

1. Question: Write the number for 6 tens and 3 ones.
2. Common wrong answer: "63" (correct) but with the explanation "6 ones and 3 tens."
3. Why it loses credit: The digits are in the wrong places. The "6" must be in the tens place.

4. Correct approach: "6 tens = 60, 3 ones = 3. 60 + 3 = 63. The ‘6’ goes first because it’s tens."

5. Question: Draw 24 using tens and ones.

6. Common wrong answer: Draws 24 single dots or writes "24" without grouping.
7. Why it loses credit: Doesn’t show understanding of place value as groups of 10.

8. Correct approach: Draw 2 circles with 10 dots each and 4 single dots. Label "2 tens, 4 ones."

9. Question: Which number has 5 tens and 0 ones?

10. Common wrong answer: "5" or "50 ones."
11. Why it loses credit: Confuses the value of the tens digit (5 tens = 50, not 5).
12. Correct approach: "5 tens = 50, 0 ones = 0. The number is 50."

5. Connection Layer

• Within math: Place value-Adding two-digit numbers. Understanding tens/ones makes it clear why we add the tens digits and ones digits separately (e.g., 24 + 35 = 59).
• Across subjects: Place value-Music (measures). A measure in music is like a "tens group"—it holds a set number of beats, just like a tens block holds 10 ones.
• Outside school: Place value-Money (dimes and pennies). A dime is like a tens block (10 cents), and a penny is like a ones block. 3 dimes and 2 pennies = 32 cents.

6. The Stretch Question

If you write the number "100," how many tens are in it? How many ones? Why does the "1" in 100 mean something different than the "1" in 10?

Pointer: The "1" in 100 is in the hundreds place, which is like having 10 tens blocks stacked together (10 × 10 = 100). The "1" in 10 is just 1 ten. This is why place value keeps growing—each new place is 10 times bigger than the last!