Solved Exercises on Standard Form Solutions in Grade 1

Master place value and standard form: ones, tens, number representation, expanded form conversion through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Converting Expanded to Standard Form
Exercise 1
Convert to standard form: 3 tens + 5 ones
Definition:

Standard form: Writing numbers in their normal way (e.g., 35)

Expanded form: Showing the value of each digit (e.g., 3 tens + 5 ones)

Conversion method:
  1. Identify the place value of each part
  2. Convert each part to its numerical value
  3. Add all parts together
Step 1: 3 tens = 3 × 10 = 30
Step 2: 5 ones = 5 × 1 = 5
Step 3: 30 + 5 = 35
Tens
Ones
3
→
5
3 tens + 5 ones = 30 + 5 = 35
Standard form: 35
Final answer:

3 tens + 5 ones = 35

Applied rules:

• Place value: Tens place is worth 10, ones place is worth 1

• Addition: Combine all place values

• Standard form: Write the final number without showing place values

2 Multiple Place Values
Exercise 2
Convert to standard form: 2 tens + 7 ones
Definition:

Place value system: Each position has a specific value (ones, tens, hundreds...)

Step 1: 2 tens = 2 × 10 = 20
Step 2: 7 ones = 7 × 1 = 7
Step 3: 20 + 7 = 27
Tens
Ones
2
→
7
2 tens + 7 ones = 20 + 7 = 27
Standard form: 27
Final answer:

2 tens + 7 ones = 27

Applied rules:

• Place value multiplication: Multiply digit by its place value

• Sequential addition: Add all converted values

• Standard notation: Write final number in regular form

3 Zero Place Values
Exercise 3
Convert to standard form: 4 tens + 0 ones
Definition:

Zero in place value: Zero represents no value in that position but maintains place value structure

Step 1: 4 tens = 4 × 10 = 40
Step 2: 0 ones = 0 × 1 = 0
Step 3: 40 + 0 = 40
Tens
Ones
4
→
0
4 tens + 0 ones = 40 + 0 = 40
Standard form: 40
Final answer:

4 tens + 0 ones = 40

Applied rules:

• Zero property: Any number multiplied by zero equals zero

• Place holder: Zero maintains positional value even if no units

• Standard form: Include zero in the ones place

Rules and methods, laws,...
3 tens + 5 ones = 35
Standard Form Conversion
Ones Place
×1
Tens Place
×10
Hundreds Place
×100
Key definitions:

Standard form: Regular way to write numbers (e.g., 45, 123)

Expanded form: Shows value of each digit (e.g., 40 + 5)

Place value: Position determines the value of each digit

Complete methodology:
  1. Identify place values: Determine which digits represent tens, ones, etc.
  2. Convert to numerical values: Multiply each digit by its place value
  3. Add all values: Sum all converted values
  4. Write in standard form: Present the final number
Tip 1: Remember: tens are worth 10 times more than ones.
Tip 2: Always write tens first, then ones in standard form.
Tip 3: Zero in ones place means no individual units.
Tip 4: Practice counting by tens to strengthen place value understanding.
Common errors: Forgetting to multiply by place value, misplacing digits, ignoring zeros.
Key insight: Place value helps us understand number magnitude and relationships.
Formulas to know by heart:

• Ones place value: digit × 1

• Tens place value: digit × 10

• Standard form: combine all place values

• Expanded form: separate each place value

Solution: Exercises 4 to 5
4 Mixed Place Values
Exercise 4
Convert to standard form: 1 ten + 9 ones
Definition:

Mixed place values: Combining different place value positions to form a number

Step 1: 1 ten = 1 × 10 = 10
Step 2: 9 ones = 9 × 1 = 9
Step 3: 10 + 9 = 19
Tens
Ones
1
→
9
1 ten + 9 ones = 10 + 9 = 19
Standard form: 19
Final answer:

1 ten + 9 ones = 19

Applied rules:

• Place value conversion: Multiply each digit by its respective value

• Addition principle: Combine all converted values

• Standard notation: Present final number in regular form

5 Maximum Single Digit
Exercise 5
Convert to standard form: 9 tens + 9 ones
Definition:

Maximum single digit: 9 is the highest single digit in our number system

Step 1: 9 tens = 9 × 10 = 90
Step 2: 9 ones = 9 × 1 = 9
Step 3: 90 + 9 = 99
Tens
Ones
9
→
9
9 tens + 9 ones = 90 + 9 = 99
Standard form: 99
Final answer:

9 tens + 9 ones = 99

Applied rules:

• Maximum digit rule: 9 is the highest value for any single place

• Place value multiplication: Each digit multiplied by its position value

• Summation: Add all place values to get standard form

Place Value Laws, Methods, Rules, and Definitions
2 tens + 3 ones = 23
Place Value Conversion
Key definitions:

Place value: The value of a digit based on its position in a number

Standard form: Normal way to write numbers (e.g., 45)

Expanded form: Breaking apart numbers to show place value (e.g., 40 + 5)

Tens place: Second digit from the right, worth 10 times the digit

Ones place: Rightmost digit, worth the digit itself

Complete methodology:
  1. Identify place values: Locate tens and ones positions
  2. Convert each digit: Multiply by respective place value (10 for tens, 1 for ones)
  3. Calculate totals: Perform multiplication for each digit
  4. Combine values: Add all calculated values together
  5. Write standard form: Present the final sum as the standard number
Tip 1: Count by tens (10, 20, 30...) to visualize place value.
Tip 2: Use base-10 blocks to physically represent tens and ones.
Tip 3: Remember that position matters - 12 is different from 21.
Tip 4: Practice reading numbers aloud to reinforce place value understanding.
Tip 5: Check your work by converting back to expanded form.
Place value law: Each position to the left is 10 times greater than the position to its right.
Zero rule: Zero maintains place value structure even when no units exist.
Maximum digit rule: Each place can hold a maximum of 9 units.
Essential formulas:

• Tens calculation: digit × 10

• Ones calculation: digit × 1

• Total value: (tens × 10) + (ones × 1)

• Standard form: combined result of all place values

Example: 47
40 + 7
Example: 82
80 + 2
Example: 15
10 + 5

Questions & Answers

Question: Why do we need to learn about standard form when we can just count the objects? For example, if I have 3 groups of 10 apples and 5 single apples, why convert to 35?

Answer: Great question! Learning standard form is crucial for several important reasons:

  • Efficiency: Writing "35" is much faster than saying "3 tens and 5 ones" every time
  • Communication: Standard form is the universal way to write numbers that everyone understands
  • Mathematical operations: Addition, subtraction, multiplication, and division are easier with standard form
  • Real-world applications: Prices, addresses, ages, and many other everyday numbers use standard form

Think of it like having a secret code that makes everything faster and clearer! When you know that 35 means 3 tens and 5 ones, you can work with numbers much more efficiently.

Question: I sometimes forget which is tens and which is ones. Is there a trick to remember?

Answer: Yes! Here are some helpful memory tricks:

  • "Tens" starts with "T" and "Ten" fingers = 10 fingers total
  • Ones are "on" the right side of the number
  • Remember: "Te" in "Tens" sounds like "Ten"
  • Count from right to left: ones, then tens, then hundreds

You can also think of it like this: If you had 35 cookies, you could make 3 groups of 10 cookies (the tens) and have 5 extra cookies (the ones).

Practice with physical objects like blocks or coins to make the concept more concrete!

Question: My child gets confused when we say "3 tens" - they think it means the number 3, not 30. How can I explain this better?

Answer: This is a very common confusion! Try these approaches:

  • Use concrete examples: Show 3 groups of 10 objects (like 3 bundles of 10 straws)
  • Count by tens: Count together: 10, 20, 30 (so 3 tens = 30)
  • Visual representation: Draw 3 circles with 10 dots in each circle
  • Physical grouping: Have them make 3 groups of 10 items

Emphasize that "3 tens" means "3 groups of 10", which equals 30. Once they understand that each group of 10 is worth 10, the connection becomes clearer.

Start with smaller numbers and gradually build up as they gain confidence!