This exercise introduces the fundamental concept of converting tens and ones into standard form. The workbook format includes clear visual representations and step-by-step solutions that help students understand the relationship between place value components and standard form numbers.
Standard form: Writing a number using digits (e.g., 43)
Place value: The value of a digit depends on its position in the number
Note: In grade 1, we focus on tens and ones. Each ten represents 10 ones.
- Count the tens: 4 tens = 40
- Count the ones: 3 ones = 3
- Add tens and ones together: 40 + 3 = 43
4 tens = 4 × 10 = 40
3 ones = 3 × 1 = 3
40 + 3 = 43
The standard form of 4 tens and 3 ones is 43
• Place value: Tens place represents groups of 10
• Standard form: Write number using digits
• Addition: Combine tens and ones values
• Practice Tip: Use base ten blocks to visualize: 4 long rods (tens) and 3 small cubes (ones)
- 2 tens and 5 ones = 25
- 1 ten and 8 ones = 18
- 5 tens and 0 ones = 50
- Each ten is worth 10 ones
- The tens digit goes in the tens place (second from right)
- The ones digit goes in the ones place (rightmost)
Q: What if I have more than 9 ones?
A: Regroup 10 ones as 1 ten. For example, 3 tens and 13 ones = 4 tens and 3 ones = 43.
Q: How do I write 0 tens and 7 ones?
A: That's just 7 ones = 7. We don't usually write 07, just 7.
Digit analysis: Breaking down a number to identify tens and ones
Note: In any two-digit number, the left digit is tens and the right digit is ones.
- Identify the tens digit: leftmost digit
- Identify the ones digit: rightmost digit
- State the number as tens and ones
In 56, the tens digit is 5
In 56, the ones digit is 6
56 = 5 tens and 6 ones
56 represents 5 tens and 6 ones
• Position rule: Left digit is tens, right digit is ones
• Value rule: Tens digit × 10 + ones digit
• Representation: Show as groups of tens and ones
• Practice Tip: Count by tens: 10, 20, 30, 40, 50, then add ones: 51, 52, 53, 54, 55, 56
- 34 = 3 tens and 4 ones
- 78 = 7 tens and 8 ones
- 60 = 6 tens and 0 ones
- Always read from left to right: tens first, then ones
- 56 means 5 groups of 10 and 6 individual units
- Count by tens first, then count ones
Q: What if the number is less than 10?
A: Single-digit numbers have 0 tens and the number as ones. For example, 6 = 0 tens and 6 ones.
Q: How do I know which digit is tens?
A: In a two-digit number, the left digit is always the tens place.
Base ten blocks: Visual tools representing tens (long rods) and ones (small cubes)
Note: Each tens block equals 10 ones blocks. This helps visualize place value.
- Count the tens blocks and multiply by 10
- Count the ones blocks
- Add the values together
3 tens blocks = 3 × 10 = 30
9 ones blocks = 9 × 1 = 9
30 + 9 = 39
The standard form is 39
• Base ten concept: Each tens block equals 10 ones
• Counting: Separate tens and ones before adding
• Standard form: Write total as a number
• Practice Tip: Draw the blocks to visualize: 3 long rectangles and 9 small squares
- 2 tens and 4 ones blocks = 24
- 5 tens and 0 ones blocks = 50
- 1 ten and 9 ones blocks = 19
- Each tens block is worth 10 individual units
- Count tens first, then add ones
- Visual representation helps understand place value
Q: Can I trade 10 ones blocks for 1 tens block?
A: Yes! This is called regrouping. 10 ones = 1 ten.
Q: What if I have 10 tens blocks?
A: 10 tens = 1 hundred. In grade 1, we focus on tens and ones.
Expanded form: Writing a number showing the value of each digit (e.g., 72 = 70 + 2)
Note: This shows the actual value each digit contributes to the whole number.
- Identify the tens digit and its value
- Identify the ones digit and its value
- Write as a sum of these values
7 in the tens place = 7 × 10 = 70
2 in the ones place = 2 × 1 = 2
72 = 70 + 2
72 in expanded form is 70 + 2
• Place value: Each position has a specific value
• Expanded form: Shows value of each digit separately
• Standard form: The usual way to write numbers
• Practice Tip: Expanded form helps understand what each digit represents
- 35 = 30 + 5
- 82 = 80 + 2
- 40 = 40 + 0
- Expanded form shows the actual value of each digit
- Tens digit × 10 + ones digit × 1
- This connects to standard form: 70 + 2 = 72
Q: Why do we learn expanded form?
A: It helps understand place value and makes addition/subtraction easier.
Q: Can I write expanded form for single digits?
A: Yes! For example, 7 = 0 + 7 or just 7.
Place value chart: Organizes digits by their place (tens, ones)
Note: Charts help organize thinking about place value and make it easier to understand.
- Identify the tens digit
- Identify the ones digit
- Fill the chart accordingly
In 94, the tens digit is 9
In 94, the ones digit is 4
Tens: 9, Ones: 4, Total: 94
Tens: 9, Ones: 4, Standard Form: 94
• Organization: Charts help organize place value thinking
• Position rule: Left digit is tens, right digit is ones
• Value calculation: Digit × place value
• Practice Tip: Use charts to double-check your work
- For 45: Tens=4, Ones=5
- For 80: Tens=8, Ones=0
- For 27: Tens=2, Ones=7
- Charts help organize thinking about place value
- Always fill tens first, then ones
- Check that your chart adds up to the original number
Q: Do I need to use a chart for every problem?
A: Not always, but charts are helpful when learning or checking work.
Q: What if I have more than two digits?
A: Grade 1 focuses on tens and ones. Later grades add hundreds, thousands, etc.