Solved Exercises on Understanding Tens and Ones in Grade 1

Master place value: understanding tens and ones, base-10 system, and number composition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Identifying tens and ones
Exercise 1
Identify the tens and ones in these numbers:
37, 52, 84, 19, 60
Definition:

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

Place value identification method:
  1. Look at the leftmost digit (tens place)
  2. Look at the rightmost digit (ones place)
  3. Count how many tens and how many ones
  4. Express as expanded form if needed
Number Tens Place Ones Place Expanded Form
37 3 7 30 + 7
52 5 2 50 + 2
84 8 4 80 + 4
19 1 9 10 + 9
60 6 0 60 + 0
Step 1: Identify the tens digit

For 37, the tens digit is 3 (represents 3 groups of 10)

Step 2: Identify the ones digit

For 37, the ones digit is 7 (represents 7 individual units)

Step 3: Express in expanded form

37 = 30 + 7 (3 tens + 7 ones)

10
10
10
1
1
1
1
1
1
1
37: 3 tens, 7 ones
52: 5 tens, 2 ones
84: 8 tens, 4 ones
19: 1 ten, 9 ones
60: 6 tens, 0 ones
Final answer:

37: 3 tens, 7 ones, 52: 5 tens, 2 ones, 84: 8 tens, 4 ones, 19: 1 ten, 9 ones, 60: 6 tens, 0 ones

Applied rules:

• Position matters: Left digit = tens, right digit = ones

• Base-10 system: Each ten is worth 10 ones

• Zero placeholder: Zero in ones place still represents value

2 Expanded form representation
Exercise 2
Write these numbers in expanded form:
46, 73, 91, 28, 50
Definition:

Expanded form: Writing a number to show the value of each digit

Number Tens Ones Expanded Form Base-10 Blocks
46 4 6 40 + 6 4 tens + 6 ones
73 7 3 70 + 3 7 tens + 3 ones
91 9 1 90 + 1 9 tens + 1 one
28 2 8 20 + 8 2 tens + 8 ones
50 5 0 50 + 0 5 tens + 0 ones
46 =
40
+
6
10
10
10
10
1
1
1
1
1
1
Step 1: Identify tens and ones

46: 4 tens and 6 ones

Step 2: Calculate tens value

4 tens = 4 × 10 = 40

Step 3: Calculate ones value

6 ones = 6 × 1 = 6

Step 4: Combine with addition

46 = 40 + 6

46 = 40 + 6
73 = 70 + 3
91 = 90 + 1
28 = 20 + 8
50 = 50 + 0
Final answer:

46 = 40 + 6, 73 = 70 + 3, 91 = 90 + 1, 28 = 20 + 8, 50 = 50 + 0

Applied rules:

• Place value multiplication: Tens digit × 10, ones digit × 1

• Expanded form: Sum of each place value

• Zero handling: Include zeros in expanded form

3 Base-10 blocks representation
Exercise 3
Show these numbers using base-10 blocks:
24, 37, 51, 40, 63
Definition:

Base-10 blocks: Visual representation using sticks for tens and units for ones

Number Tens Ones Base-10 Blocks Total Value
24 2 4 2 sticks + 4 units 24
37 3 7 3 sticks + 7 units 37
51 5 1 5 sticks + 1 unit 51
40 4 0 4 sticks + 0 units 40
63 6 3 6 sticks + 3 units 63
10
10
1
1
1
1
Step 1: Identify tens and ones

For 24: 2 tens and 4 ones

Step 2: Draw base-10 blocks

Draw 2 long sticks (each representing 10) and 4 small squares (each representing 1)

Step 3: Verify total

(2 × 10) + (4 × 1) = 20 + 4 = 24

24 =
20
+
4
24: 2 tens + 4 ones
37: 3 tens + 7 ones
51: 5 tens + 1 one
40: 4 tens + 0 ones
63: 6 tens + 3 ones
Final answer:

24: 2 tens + 4 ones, 37: 3 tens + 7 ones, 51: 5 tens + 1 one, 40: 4 tens + 0 ones, 63: 6 tens + 3 ones

Applied rules:

• Base-10 representation: Each stick = 10, each unit = 1

• Visual grouping: Tens are grouped separately from ones

• Total verification: Sum of blocks equals original number

Place Value System and Base-10
Number = (Tens × 10) + (Ones × 1)
Place Value Formula
Tens Place
× 10
Left digit value
Ones Place
× 1
Right digit value
Base-10
10 digits
Our number system
Key definitions:

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

Tens place: The leftmost digit in a two-digit number, representing groups of 10

Ones place: The rightmost digit in a number, representing individual units

Base-10 system: Our number system based on groups of 10

Expanded form: Writing a number as the sum of each place value

Place value methodology:
  1. Identify positions: Locate tens and ones places
  2. Determine values: Calculate the value of each digit
  3. Express relationship: Show how digits contribute to total value
  4. Verify accuracy: Ensure place values sum to original number
Tip 1: Remember: 1 ten = 10 ones (they're equal in value).
Tip 2: Use base-10 blocks to visualize the concept.
Tip 3: Practice with expanded form to reinforce the concept.
Tip 4: Zero in ones place still represents a value (e.g., 50 = 5 tens + 0 ones).
Base-10 system: We use 10 digits (0-9) to represent all numbers.
Position significance: The same digit has different values based on position.
Place value rules to remember:

• Tens place: Left digit × 10

• Ones place: Right digit × 1

• Total value: Tens value + Ones value

• Expanded form: (Tens × 10) + (Ones × 1)

• Zero placeholder: Still contributes to number's value

Base-10 System Guide
📊
Tens Place
Left digit represents groups of 10
47: 4 tens = 40
Ones Place
Right digit represents individual units
47: 7 ones = 7
Expanded Form
Breaking number into place values
47 = 40 + 7
Base-10 Blocks
Visual representation of tens and ones
47: 4 sticks + 7 units
Solution: Exercises 4 to 5
4 Converting from expanded form
Exercise 4
Convert these expanded forms to standard form:
30 + 5, 60 + 8, 40 + 0, 20 + 9, 70 + 4
Definition:

Standard form: Writing a number in its normal form using digits

Expanded Form Tens Ones Standard Form Base-10 Blocks
30 + 5 3 5 35 3 sticks + 5 units
60 + 8 6 8 68 6 sticks + 8 units
40 + 0 4 0 40 4 sticks + 0 units
20 + 9 2 9 29 2 sticks + 9 units
70 + 4 7 4 74 7 sticks + 4 units
30
+
5
=
35
10
10
10
1
1
1
1
1
Step 1: Identify tens and ones

30 + 5: 30 represents 3 tens, 5 represents 5 ones

Step 2: Combine tens and ones

3 tens and 5 ones = 35

Step 3: Write in standard form

35

30 + 5 = 35
60 + 8 = 68
40 + 0 = 40
20 + 9 = 29
70 + 4 = 74
Final answer:

30 + 5 = 35, 60 + 8 = 68, 40 + 0 = 40, 20 + 9 = 29, 70 + 4 = 74

Applied rules:

• Reverse expansion: Addition of place values gives standard form

• Tens identification: First digit represents tens place

• Ones identification: Second digit represents ones place

5 Problem solving with place value
Exercise 5
Sarah has 4 tens and 7 ones. How many total does she have? Write in standard form.
Definition:

Problem solving: Applying place value knowledge to solve real-world scenarios

Description Tens Ones Calculation Result
Sarah's tens 4 - 4 × 10 = 40 40
Sarah's ones - 7 7 × 1 = 7 7
Total 4 7 40 + 7 = 47 47
4 tens + 7 ones =
40
+
7
=
47
10
10
10
10
1
1
1
1
1
1
1
Step 1: Identify given information

Sarah has 4 tens and 7 ones

Step 2: Calculate value of tens

4 tens = 4 × 10 = 40

Step 3: Calculate value of ones

7 ones = 7 × 1 = 7

Step 4: Find total value

40 + 7 = 47

Sarah has 47 total
Final answer:

Sarah has 47 total (standard form)

Applied rules:

• Problem translation: Convert words to mathematical expressions

• Place value calculation: Multiply digits by their place values

• Summation: Add place values to get total

Comprehensive Summary: Understanding Tens and Ones
N = (T × 10) + (O × 1)
Base-10 Place Value System
Key definitions:

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

Tens place: The leftmost digit in a two-digit number, representing groups of 10

Ones place: The rightmost digit in a number, representing individual units

Base-10 system: Our decimal number system based on groups of 10

Expanded form: Writing a number as the sum of each place value

Standard form: Writing a number in its normal form using digits

Complete place value methodology:
  1. Identify positions: Locate tens and ones places in the number
  2. Determine digit values: Calculate the actual value of each digit
  3. Express relationships: Show how each digit contributes to total value
  4. Convert forms: Move between expanded and standard forms
  5. Verify accuracy: Ensure all conversions are correct
Tip 1: Remember: 1 ten stick equals 10 individual units in value.
Tip 2: Always multiply the tens digit by 10 to get its true value.
Tip 3: Zero in ones place still represents a meaningful value (e.g., 50 ≠ 5).
Tip 4: Use visual aids like base-10 blocks to reinforce understanding.
Base-10 foundation: Our entire number system is built on groups of 10.
Position significance: Same digit has different values in different positions.
Essential place value rules:

• Tens calculation: Tens digit × 10

• Ones calculation: Ones digit × 1

• Total value: Tens value + Ones value

• Expanded form: (Tens × 10) + (Ones × 1)

• Standard form: Combined digits in their respective positions

Place Value Mastery Framework
📊
Tens Place Value
Left digit represents groups of 10
57: 5 tens = 50
Ones Place Value
Right digit represents individual units
57: 7 ones = 7
Expanded Form
Breaking number into place values
57 = 50 + 7
Standard Form
Combined digits in correct positions
50 + 7 = 57
Key takeaways:

• Place value is the foundation of our number system

• Understanding tens and ones enables advanced mathematical concepts

• Visual representations like base-10 blocks enhance comprehension

• Practice converting between different number forms builds fluency

Questions & Answers

Question: Why do we say "4 tens" when we have 40? Isn't 4 much smaller than 40?

Answer: Great question! When we say "4 tens", we mean 4 groups of 10:

  • 4 tens = 4 groups of 10
  • 4 groups of 10 = 10 + 10 + 10 + 10 = 40
  • So: 4 tens = 40

Think of it like having 4 bags, and each bag has 10 candies. You have 40 candies total!

The "4" tells us HOW MANY groups, and "tens" tells us WHAT KIND OF GROUP (groups of 10).

Question: My child gets confused when there's a zero in the ones place. How can I help them understand numbers like 50?

Answer: Zero in the ones place is a common source of confusion! Here's how to clarify:

  • Zero means "none": In 50, there are 5 tens and 0 ones
  • Use base-10 blocks: Show 5 long sticks (tens) and 0 small cubes (ones)
  • Count together: "50, 51, 52..." - there are no extra ones after the 50
  • Real examples: 50 dollars = 5 tens of dollars, no extra dollars

Emphasize that the zero holds the ones place and tells us there are no extra ones beyond the tens.

Practice with round numbers (10, 20, 30, 40, 50, etc.) to build comfort!

Question: How do I know which digit is the tens and which is the ones? Sometimes I mix them up!

Answer: Here's a simple way to remember:

  • Left digit = Tens place (the bigger value)
  • Right digit = Ones place (the smaller value)
  • Memory trick: "Left is Large" - the left digit represents the larger value (tens)
  • Counting order: We read numbers from left to right, starting with tens

For example, in 63: 6 is on the left (tens place) and 3 is on the right (ones place).

Practice pointing to each digit and saying "This is the tens digit, this is the ones digit"!

The tens digit is always worth more than the ones digit!

Question: How can I make place value more concrete for my child?

Answer: Use hands-on materials and real-life examples:

  • Base-10 blocks: Long sticks for tens, small cubes for ones
  • Straws: Bundle 10 straws with rubber bands to make tens
  • Candy or coins: Group 10 pieces together to make tens
  • Money: Dimes represent tens, pennies represent ones

Create games: "Show me 34 using blocks" or "How many tens are in 57 straws?"

Tip: Start with physical manipulation before moving to abstract numbers!

Question: How does understanding tens and ones prepare students for higher math?

Answer: Place value understanding is foundational for all advanced mathematics:

  • Addition: Understanding regrouping (carrying) requires place value
  • Subtraction: Borrowing relies on understanding tens and ones
  • Multiplication: Partial products use place value concepts
  • Division: Place value helps with long division algorithms
  • Decimal system: All our number work builds on base-10

Students who master tens and ones develop stronger computational skills.

Example: Understanding that 45 = 40 + 5 helps with 45 + 23 = (40 + 20) + (5 + 3).

This foundation supports mathematical reasoning throughout schooling!