Standard Form Exercises in Grade 1 - Mathematics - Exercises with solutions

Master standard form in place value: tens and units, expanded to standard form, base ten blocks through these 10 detailed exercises.

Solutions: Exercises 1 to 10
1 Tens and Units
Exercise 1
What is the standard form of 3 tens and 4 units?
Difficulty: Beginner Time: ~2 minutes Skills: Place Value Understanding
Definition:

Standard form: The normal way of writing numbers using digits (e.g., 34)

Place value: The value of each digit depends on its position (tens, units)

Step-by-step conversion method:
  1. Identify the number of tens and units
  2. Write the tens digit in the tens place
  3. Write the units digit in the units place
Given
3 tens and 4 units
Standard Form
34
Step 1: Identify tens and units

3 tens means 3 in the tens place

4 units means 4 in the units place

Step 2: Write in standard form

Tens place: 3, Units place: 4

Step 3: Combine the digits

Standard form: 34

3 tens and 4 units = 34
Final answer:

34

Applied rules:

• Place value: Tens place is the second digit from right

• Standard form: Write digits in order from left to right

• Value calculation: 3 tens = 30, 4 units = 4, total = 34

• Practice Tip: Count by tens (10, 20, 30) then add units

Related Examples:
  • 2 tens and 5 units = 25
  • 4 tens and 0 units = 40
  • 1 ten and 7 units = 17
Quick Tips:
  • Always put tens digit first, then units digit
  • If there are 0 units, just write the tens digit followed by 0
  • Count tens: 10, 20, 30, 40, 50, 60, 70, 80, 90
Frequently Asked Questions:

Q: What if I have more than 9 units?
A: That's impossible in basic place value. 10 units equal 1 ten.

Q: How do I know which digit goes where?
A: Tens digit comes first (left), units digit comes second (right)

2 Base Ten Blocks
Exercise 2
If I have 2 rods (tens) and 6 cubes (units), what is the standard form?
Difficulty: Beginner Time: ~3 minutes Skills: Visual Representation
Definition:

Base ten blocks: Visual tools where rods represent tens and cubes represent units

Rod: Represents 10 units (ten)

Cube: Represents 1 unit

Step-by-step conversion method:
  1. Count the number of rods (tens)
  2. Count the number of cubes (units)
  3. Write the tens digit in tens place, units digit in units place
Given
2 rods and 6 cubes
Standard Form
26
Step 1: Count rods (tens)

2 rods = 2 tens = 20

Step 2: Count cubes (units)

6 cubes = 6 units = 6

Step 3: Write in standard form

Tens digit: 2, Units digit: 6

Standard form: 26

2 rods and 6 cubes = 26
Final answer:

26

Applied rules:

• Base ten blocks: Rods = tens, cubes = units

• Visual counting: Count each type of block separately

• Standard form: Write tens digit first, units digit second

• Practice Tip: Draw or visualize the blocks to reinforce understanding

Related Examples:
  • 3 rods and 2 cubes = 32
  • 1 rod and 9 cubes = 19
  • 4 rods and 0 cubes = 40
Quick Tips:
  • Rods are longer (representing tens) and cubes are small (representing units)
  • Each rod equals 10 cubes
  • Count rods first, then count cubes
Frequently Asked Questions:

Q: What if I have 10 cubes?
A: Trade 10 cubes for 1 rod. 10 cubes = 1 ten.

Q: How do I know if I'm counting correctly?
A: Count rods and cubes separately, then combine: 2 rods + 6 cubes = 26

3 Expanded to Standard Form
Exercise 3
Convert 50 + 3 to standard form.
Difficulty: Beginner Time: ~2 minutes Skills: Expanded Form Conversion
Definition:

Expanded form: Writing a number as the sum of its tens and units (e.g., 50 + 3)

Standard form: The normal way of writing numbers using digits (e.g., 53)

Step-by-step conversion method:
  1. Identify the tens part (multiple of 10)
  2. Identify the units part (single digit)
  3. Combine the tens and units digits
Given
50 + 3
Standard Form
53
Step 1: Identify tens part

50 represents 5 tens (5 × 10)

Step 2: Identify units part

3 represents 3 units

Step 3: Write in standard form

Tens digit: 5, Units digit: 3

Standard form: 53

50 + 3 = 53
Final answer:

53

Applied rules:

• Expanded form: Shows the value of each place separately

• Conversion: Combine tens and units digits

• Place value: 50 means 5 in tens place, 3 means 3 in units place

• Practice Tip: Think of expanded form as showing what makes up the number

Related Examples:
  • 40 + 7 = 47
  • 20 + 9 = 29
  • 60 + 0 = 60
Quick Tips:
  • The first number is always a multiple of 10 (tens)
  • The second number is always less than 10 (units)
  • Just put the tens digit and units digit together
Frequently Asked Questions:

Q: What if the units part is 0?
A: Just write the tens part. Example: 40 + 0 = 40.

Q: Can the tens part be 0?
A: No, if tens = 0, it would just be a single digit number.

Solutions: Exercises 4 to 5
4 Number Recognition
Exercise 4
What number has 7 in the tens place and 2 in the units place?
Definition:

Number recognition: Identifying numbers based on place value positions

Tens place: Second digit from the right

Units place: Rightmost digit

Step-by-step identification method:
  1. Identify the digit in the tens place
  2. Identify the digit in the units place
  3. Write the tens digit first, then the units digit
Given
7 in tens, 2 in units
Standard Form
72
Step 1: Identify tens digit

Tens place: 7

Step 2: Identify units digit

Units place: 2

Step 3: Write in standard form

Standard form: 72

7 tens and 2 units = 72
Final answer:

72

Applied rules:

• Place value positions: Tens is second from right, units is first from right

• Digit placement: Tens digit comes first, units digit comes second

• Number formation: Combine digits in order

• Practice Tip: Remember: TENS come before UNITS in writing

Related Examples:
  • 3 in tens place, 8 in units place = 38
  • 9 in tens place, 0 in units place = 90
  • 1 in tens place, 5 in units place = 15
Quick Tips:
  • Tens place is always the second digit when reading from right to left
  • Units place is always the rightmost digit
  • Put the tens digit first, then the units digit
Frequently Asked Questions:

Q: What if I mix up tens and units?
A: Remember: TENS are bigger, so they come first in the number.

Q: Can the tens digit be 0?
A: Only if it's a single-digit number. For two-digit numbers, tens cannot be 0.

5 Place Value Chart
Exercise 5
Using a place value chart, what is the standard form of 4 tens and 9 units?
Definition:

Place value chart: A table showing the value of each digit position

Tens Units
4 9
Step-by-step chart method:
  1. Fill the tens column with the tens digit
  2. Fill the units column with the units digit
  3. Read the digits from left to right
Given
4 tens, 9 units
Place Value Chart
Tens Units
4 9
Standard Form
49
Step 1: Fill the chart

Tens column: 4, Units column: 9

Step 2: Read from left to right

First digit (tens): 4, Second digit (units): 9

Step 3: Write the number

Standard form: 49

4 tens and 9 units = 49
Final answer:

49

Applied rules:

• Place value chart: Organizes digits by their position value

• Column organization: Tens column holds tens digit, units holds units digit

• Reading order: Read digits from left to right

• Practice Tip: Use charts to visualize place value relationships

Related Examples:
  • 2 tens, 3 units →
    TU
    23
    = 23
  • 6 tens, 0 units →
    TU
    60
    = 60
  • 8 tens, 5 units →
    TU
    85
    = 85
Quick Tips:
  • Always fill the chart from left to right: tens first, then units
  • The place value chart helps organize digits correctly
  • Read the filled chart from left to right to get the standard form
Frequently Asked Questions:

Q: What if I have more than 9 in the units column?
A: That's not possible. Units can only be 0-9. 10 units = 1 ten.

Q: Can I use this method for larger numbers?
A: Yes, extend the chart: Hundreds, Tens, Units for three-digit numbers.

Solutions: Exercises 6 to 10
6 Word to Standard Form
Exercise 6
What is the standard form of "sixty-four"?
Definition:

Word form: Numbers written in words (e.g., sixty-four)

Standard form: Numbers written with digits (e.g., 64)

Step-by-step conversion method:
  1. Identify the tens word ("sixty" = 6 tens)
  2. Identify the units word ("four" = 4 units)
  3. Write the tens digit first, then the units digit
Given
"sixty-four"
Tens and Units
6 tens, 4 units
Standard Form
64
Step 1: Break down the word

"sixty" means 6 tens (60)

"four" means 4 units (4)

Step 2: Identify digits

Tens digit: 6, Units digit: 4

Step 3: Write in standard form

Standard form: 64

"sixty-four" = 64
Final answer:

64

Applied rules:

• Word recognition: Know what each number word represents

• Part breakdown: Separate tens part from units part

• Digit placement: Tens digit first, units digit second

• Practice Tip: Learn number words from 11 to 99 for better recognition

Related Examples:
  • "thirty-two" = 32
  • "eighty-seven" = 87
  • "fifty" = 50 (no units part)
Quick Tips:
  • Words ending in "-ty" usually indicate tens (twenty, thirty, forty...)
  • Numbers like "seventeen" mean 10 + 7 = 17
  • Memorize common number words: eleven, twelve, thirteen through nineteen
Frequently Asked Questions:

Q: What about "seventeen"?
A: "seven-teen" means 10 + 7 = 17. Teen numbers are special: 11-19.

Q: How do I know if there are zero units?
A: Words like "thirty" (not "thirty-zero") have zero units: 30.

7 Comparing Numbers
Exercise 7
Which is greater: 45 or 54? Explain using standard form.
Definition:

Number comparison: Determining which number is larger by comparing place values

Standard form comparison: Compare digits starting from the left (highest place value)

Step-by-step comparison method:
  1. Compare the tens digits first
  2. If tens are equal, compare the units digits
  3. Higher digit in the first differing place value determines the larger number
Numbers to Compare
45 vs 54
Tens Comparison
4 vs 5
Result
54 > 45
Step 1: Compare tens digits

45 has 4 tens, 54 has 5 tens

Since 5 > 4, 54 > 45

Step 2: Confirm with place value

45 = 4 tens + 5 units = 40 + 5 = 45

54 = 5 tens + 4 units = 50 + 4 = 54

Step 3: State the comparison

54 is greater than 45

54 > 45
Final answer:

54 is greater than 45 because 5 tens is greater than 4 tens.

Applied rules:

• Comparison order: Always start with the highest place value

• Place value importance: Tens place is more significant than units place

• Digit comparison: Higher digit in first place value wins

• Practice Tip: Remember: 54 has more tens than 45, so it's larger

Related Examples:
  • 23 vs 32 → 32 > 23 (3 tens > 2 tens)
  • 67 vs 61 → 67 > 61 (same tens, 7 units > 1 unit)
  • 89 vs 98 → 98 > 89 (9 tens > 8 tens)
Quick Tips:
  • Always compare from left to right (highest place value first)
  • If tens are the same, compare units
  • More tens always means a larger number
Frequently Asked Questions:

Q: What if the tens are the same?
A: Compare the units. Example: 45 vs 47 → 47 > 45 because 7 > 5.

Q: Does the number of digits matter?
A: For two-digit numbers, start with tens comparison.

8 Missing Tens/Units
Exercise 8
If the standard form is 87, what are the tens and units?
Definition:

Digit identification: Finding the value of each place in a standard form number

Standard form breakdown: Separating a number into its tens and units components

Step-by-step identification method:
  1. Identify the tens digit (second from right)
  2. Identify the units digit (rightmost)
  3. State how many tens and how many units
Given
87
Tens Digit
8
Units Digit
7
Step 1: Identify tens digit

In 87, the tens digit is 8 (second from right)

Step 2: Identify units digit

In 87, the units digit is 7 (rightmost digit)

Step 3: State the values

87 has 8 tens and 7 units

87 = 8 tens and 7 units
Final answer:

8 tens and 7 units

Applied rules:

• Digit position: Tens digit is second from right, units is rightmost

• Place value: Each position has a specific value

• Number breakdown: Standard form shows all place values

• Practice Tip: Practice identifying digits in various positions

Related Examples:
  • 53 = 5 tens and 3 units
  • 91 = 9 tens and 1 unit
  • 20 = 2 tens and 0 units
Quick Tips:
  • Count digits from right to left: units (1st), tens (2nd)
  • The leftmost digit is always the tens digit for two-digit numbers
  • The rightmost digit is always the units digit
Frequently Asked Questions:

Q: What if the units digit is 0?
A: There are 0 units. Example: 40 = 4 tens and 0 units.

Q: Can the tens digit be 0?
A: Only for single-digit numbers. For two-digit numbers, tens ≥ 1.

9 Drawing Base Ten
Exercise 9
Draw base ten blocks for the number 36 and write the standard form.
Definition:

Base ten block drawing: Visual representation using rods (tens) and cubes (units)

Rod: Long rectangle representing 10 units

Cube: Small square representing 1 unit

Step-by-step drawing method:
  1. Identify the tens and units in the number
  2. Draw the correct number of rods (tens)
  3. Draw the correct number of cubes (units)
  4. Confirm the standard form matches the drawing
Given Number
36
Drawing
3 rods, 6 cubes
Standard Form
36
Step 1: Identify tens and units

36 has 3 tens and 6 units

Step 2: Draw base ten blocks

Draw 3 rods (each representing 10)

Draw 6 cubes (each representing 1)

Step 3: Confirm standard form

3 rods = 30, 6 cubes = 6

30 + 6 = 36

36 = 3 rods and 6 cubes
Final answer:

Draw 3 rods and 6 cubes for the number 36.

Applied rules:

• Visual representation: Rods = tens, cubes = units

• Accurate counting: Draw exact number of rods and cubes

• Verification: Check that drawing matches standard form

• Practice Tip: Drawing helps visualize the concept of place value

Related Examples:
  • 24 = 2 rods + 4 cubes
  • 50 = 5 rods + 0 cubes
  • 19 = 1 rod + 9 cubes
Quick Tips:
  • Draw rods first (long rectangles), then cubes (small squares)
  • Each rod represents 10 cubes worth of value
  • Count your drawn blocks to verify they match the number
Frequently Asked Questions:

Q: What if I run out of space for cubes?
A: Organize cubes in rows or groups to keep drawing neat.

Q: Can I draw partial rods?
A: No, rods always represent exactly 10 units.

10 Mixed Problems
Exercise 10
Write 2 tens and 8 units in standard form, expanded form, and word form.
Definition:

Multiple representations: Same number shown in different formats

Standard form: Digits (e.g., 28)

Expanded form: Sum of place values (e.g., 20 + 8)

Word form: Written in words (e.g., twenty-eight)

Step-by-step conversion method:
  1. Start with the given information (2 tens and 8 units)
  2. Convert to standard form (write digits)
  3. Convert to expanded form (show tens and units as addition)
  4. Convert to word form (write the number in words)
Given
2 tens, 8 units
Standard Form
28
Expanded Form
20 + 8
Word Form
twenty-eight
Step 1: Write standard form

2 tens = 2 in tens place, 8 units = 8 in units place

Standard form: 28

Step 2: Write expanded form

2 tens = 20, 8 units = 8

Expanded form: 20 + 8

Step 3: Write word form

2 tens = "twenty", 8 units = "eight"

Combined: "twenty-eight"

2 tens and 8 units = 28 (standard), 20 + 8 (expanded), twenty-eight (word)
Final answer:

Standard form: 28, Expanded form: 20 + 8, Word form: twenty-eight

Applied rules:

• Multiple representations: Same value in different formats

• Consistency: All forms represent the same quantity

• Conversion: Each form can be converted to others

• Practice Tip: Practice converting between all three forms regularly

Related Examples:
  • 4 tens and 5 units = 45, 40 + 5, forty-five
  • 1 ten and 9 units = 19, 10 + 9, nineteen
  • 7 tens and 0 units = 70, 70 + 0, seventy
Quick Tips:
  • Start with one form and convert to others systematically
  • Always verify that all representations have the same value
  • Practice moving fluidly between all three forms
Frequently Asked Questions:

Q: Why learn multiple forms?
A: It helps understand place value and number relationships better.

Q: Which form is most important?
A: Standard form is most commonly used, but all forms are valuable.

Key Concepts, Rules, and Definitions
3 tens + 4 units = 34
Place Value Relationship
Key definitions:

Standard form: Writing numbers using digits (e.g., 45)

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

Tens place: The second digit from the right, representing groups of 10

Units place: The rightmost digit, representing individual units

Complete methodology:
  1. Identify place values: Recognize tens and units in a number
  2. Understand relationships: Know that 1 ten = 10 units
  3. Convert between forms: Move between standard, expanded, and word forms
  4. Apply knowledge: Use place value to compare and manipulate numbers
Tip 1: Always remember: tens come before units when writing numbers.
Tip 2: Use base ten blocks to visualize the relationship between tens and units.
Tip 3: When comparing numbers, start with the tens place.
Tip 4: Practice converting between different number forms daily.
Common errors: Reversing tens and units digits, misreading number words, forgetting place value positions.
Exam preparation: Practice identifying digits in each place, converting between forms, comparing numbers.
Rules to remember:

• Position matters: Tens place is second from right, units place is rightmost

• Value relationship: 1 ten = 10 units

• Writing order: Tens digit first, then units digit

• Comparison rule: Compare tens first, then units if tens are equal

• Zero handling: If units are zero, still write the tens digit followed by 0

Rules and Methods for Standard Form
5 tens + 3 units = 53
Standard Form Conversion
Place Value
Tens and Units
Two-digit numbers have tens and units places
Standard Form
Tens digit + Units digit
Write digits in order: tens first, units second
Expanded Form
(Tens × 10) + Units
Show the value of each place separately

Key Takeaways

  • Standard form uses digits to represent numbers
  • Tens place is the second digit from the right
  • Units place is the rightmost digit
  • Always compare numbers starting from the tens place
  • Practice converting between different number representations

Questions & Answers

Question: I'm confused about tens and units. How do I know which digit is which in a number like 47?

Answer: Great question! Here's how to identify tens and units in a two-digit number:

  • Count from the right: The rightmost digit is always the units place
  • Next to the right: The second digit from the right is always the tens place

For 47:

  • The digit "7" is in the units place (rightmost)
  • The digit "4" is in the tens place (second from right)

So 47 means 4 tens (40) and 7 units (7), which equals 40 + 7 = 47.

Memory trick: "Units" sounds like "ones," and it's the ones place!

Question: My child is struggling with converting expanded form like "30 + 5" to standard form. How can I help?

Answer: Here's a step-by-step approach to help your child:

  • Identify the tens part: In "30 + 5", the 30 represents 3 tens
  • Identify the units part: The 5 represents 5 units
  • Write the tens digit: From 30, the tens digit is 3
  • Write the units digit: From 5, the units digit is 5
  • Combine: Put the tens digit first, then the units digit

So 30 + 5 becomes 35.

Practice tip: Use physical objects like straws bundled in groups of 10 to represent tens, and individual straws for units.

This hands-on approach helps children visualize the connection between expanded and standard forms.

Question: Why is 54 bigger than 45? They have the same digits!

Answer: Even though 54 and 45 use the same digits, they're in different places, which changes their value!

Let's break down each number:

  • 54 = 5 tens + 4 units = 50 + 4 = 54
  • 45 = 4 tens + 5 units = 40 + 5 = 45

Even though 54 has fewer units (4) than 45 (5), it has more tens (5 tens = 50) compared to 45 (4 tens = 40).

Since tens are worth more than units (10 > 1), having more tens makes the whole number bigger.

Rule: Always compare the tens place first when comparing two-digit numbers!

Place Value Glossary

Standard Form
The normal way of writing numbers using digits, like 45 or 78. This is how we usually write numbers.
Place Value
The value of a digit based on its position in a number. In 23, the 2 has a place value of 20 because it's in the tens place.
Tens Place
The second digit from the right in a number. It represents groups of ten. In 47, the 4 is in the tens place and represents 40.
Units Place
The rightmost digit in a number. It represents individual units. In 47, the 7 is in the units place and represents 7.
Expanded Form
A way to write numbers showing the value of each digit. For example, 35 in expanded form is 30 + 5.

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