Solved Exercises on Tens and Ones in Grade 1

Master tens and ones: place value, number decomposition, grouping strategies, and visual representations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Understanding Place Value
Exercise 1
Show the number 23 using tens and ones blocks.
Break down 23 into tens and ones.
Definition:

Place Value: In a 2-digit number, the left digit represents TENS and the right digit represents ONES.

Place Value Method:
  1. Identify the tens digit (leftmost) and ones digit (rightmost)
  2. Count how many groups of 10 are in the number
  3. Count the remaining single units
  4. Represent using visual blocks
23
→
2 TENS 3 ONES
10
10
1
1
1
Step 1: Analyze the number 23

23 has 2 in the tens place and 3 in the ones place

Step 2: Count the tens

2 tens = 2 × 10 = 20

Step 3: Count the ones

3 ones = 3 × 1 = 3

Step 4: Combine tens and ones

20 + 3 = 23

23 = 2 tens + 3 ones = 20 + 3
Final answer:

23 = 2 tens and 3 ones

Applied rules:

• Place Value Rule: Tens place is worth 10, ones place is worth 1

• Grouping Rule: 10 ones make 1 ten

• Addition Rule: Total = tens value + ones value

2 Number Decomposition
Exercise 2
Decompose 47 into tens and ones.
Show the expanded form of 47.
Definition:

Number Decomposition: Breaking a number into its place value parts (tens and ones).

47
→
4 TENS 7 ONES
10
10
10
10
1
1
1
1
1
1
1
Step 1: Identify digits in 47

4 is in the tens place, 7 is in the ones place

Step 2: Calculate tens value

4 tens = 4 × 10 = 40

Step 3: Calculate ones value

7 ones = 7 × 1 = 7

Step 4: Write expanded form

47 = 40 + 7

Step 5: Verify the decomposition

40 + 7 = 47 ✓

47 = 4 tens + 7 ones = 40 + 7
Final answer:

47 = 4 tens and 7 ones

Applied rules:

• Decomposition Rule: Separate tens and ones

• Value Calculation: Tens digit × 10, ones digit × 1

• Verification Rule: Sum should equal original number

3 Place Value Table
Exercise 3
Fill in the place value table for 56.
Show 56 using the place value chart.
Definition:

Place Value Chart: A table showing where each digit belongs (tens or ones).

TENS ONES
5 6
56
→
5 TENS 6 ONES
10
10
10
10
10
1
1
1
1
1
1
Step 1: Identify place values in 56

5 is in tens place, 6 is in ones place

Step 2: Fill the place value table

Tens column gets 5, Ones column gets 6

Step 3: Calculate actual values

5 tens = 50, 6 ones = 6

Step 4: Write expanded form

56 = 50 + 6

Step 5: Verify total

50 + 6 = 56 ✓

56 = 5 tens + 6 ones = 50 + 6
Final answer:

56 = 5 tens and 6 ones

Applied rules:

• Place Value Rule: Left digit = tens, right digit = ones

• Table Organization: Separate columns for each place

• Value Conversion: Digit × place value

Rules and methods, laws,...
Tens + Ones = Two-Digit Number
Place Value Formula
Rule 1
Tens = Digit × 10
Multiply tens digit by 10
Rule 2
Ones = Digit × 1
Multiply ones digit by 1
Rule 3
Total = Tens + Ones
Add tens and ones together
Key definitions:

Tens: Groups of 10 units (worth 10 each)

Ones: Single units (worth 1 each)

Place Value: Value depends on position in number

Complete methodology:
  1. Identify digits: Locate tens and ones positions
  2. Calculate values: Tens digit × 10, ones digit × 1
  3. Combine values: Add tens and ones together
  4. Verify result: Check if sum equals original number
Tip 1: Remember: 10 ones = 1 ten. Group 10 singles to make a ten.
Tip 2: Always write tens first, then ones (e.g., 34 = 3 tens, 4 ones).
Tip 3: Use visual blocks to represent numbers - helps understand concept.
Tip 4: Practice counting by tens: 10, 20, 30, 40, etc.
Common errors: Confusing tens and ones positions, forgetting to multiply by 10.
Memory aid: "Tens" comes first because it's bigger value than ones.
Formulas to know by heart:

• Place Value: For number AB: A tens + B ones

• Value Calculation: A × 10 + B × 1

• Expanded Form: AB = (A × 10) + (B × 1)

• Verification: (A × 10) + (B × 1) = AB

Visual Understanding

10
10
10
+
1
1
3 tens + 2 ones = 30 + 2 = 32
Solution: Exercises 4 to 5
4 Grouping Strategy
Exercise 4
If you have 38 blocks, how many groups of 10 can you make?
How many single blocks will remain?
Definition:

Grouping Strategy: Organizing items into groups of 10 to find tens and ones.

38
→
3 GROUPS OF 10 8 REMAINING
10
10
10
1
1
1
1
1
1
1
1
Step 1: Start with 38 blocks

We have 38 individual blocks to group

Step 2: Make groups of 10

38 ÷ 10 = 3 groups with remainder

Step 3: Count full groups

3 full groups of 10 = 30 blocks

Step 4: Count remaining blocks

38 - 30 = 8 remaining blocks

Step 5: Express in tens and ones

38 = 3 tens + 8 ones

3 groups of 10, 8 single blocks remain
Final answer:

You can make 3 groups of 10, with 8 blocks remaining

Applied rules:

• Division Rule: Number ÷ 10 gives tens count

• Remainder Rule: What's left over = ones count

• Grouping Rule: 10 singles = 1 ten

5 Addition Application
Exercise 5
Add 24 + 15 using tens and ones.
Show how place value helps with addition.
Definition:

Place Value Addition: Adding tens to tens and ones to ones separately.

24 + 15
→
24 = 2 tens + 4 ones 15 = 1 ten + 5 ones
Add tens: 2 + 1 = 3 tens Add ones: 4 + 5 = 9 ones
Step 1: Break down 24

24 = 2 tens + 4 ones = 20 + 4

Step 2: Break down 15

15 = 1 ten + 5 ones = 10 + 5

Step 3: Add tens together

2 tens + 1 ten = 3 tens = 30

Step 4: Add ones together

4 ones + 5 ones = 9 ones = 9

Step 5: Combine results

30 + 9 = 39

Step 6: Verify the answer

24 + 15 = 39 ✓

24 + 15 = 39 (3 tens + 9 ones)
Final answer:

24 + 15 = 39

Applied rules:

• Separation Rule: Add tens to tens, ones to ones

• Regrouping Rule: If ones sum ≥ 10, regroup to tens

• Combination Rule: Final answer = tens + ones

Complete Guide to Tens and Ones
AB = A × 10 + B × 1
Place Value Formula
Key definitions:

Tens: A group of 10 units, located in the second position from right

Ones: Single units, located in the first position from right

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

Complete methodology:
  1. Analyze the number: Identify the position of each digit
  2. Assign place values: Left digit = tens, right digit = ones
  3. Calculate actual values: Multiply each digit by its place value
  4. Combine values: Add tens value and ones value together
  5. Verify result: Ensure the sum equals the original number
Tip 1: Use visual aids like base-10 blocks to physically group items into tens and ones.
Tip 2: Practice skip counting by tens (10, 20, 30...) to build number sense.
Tip 3: Always read the number from left to right: "tens first, then ones".
Tip 4: Remember: 10 ones can be traded for 1 ten (regrouping).
Key Insight: Understanding place value is foundational for all future math operations.
Real-world use: Money counting, measuring, and organizing large quantities.
Essential Rules:

• Position Rule: Rightmost digit = ones, next digit left = tens

• Value Rule: Tens digit × 10, ones digit × 1

• Grouping Rule: 10 ones = 1 ten

• Addition Rule: Tens + ones = original number

• Comparison Rule: Tens are always greater than ones

Place Value Chart Examples

Number TENS ONES Expanded Form
12 1 2 10 + 2
35 3 5 30 + 5
48 4 8 40 + 8
60 6 0 60 + 0

Questions & Answers

Question: My child is confused about why 23 doesn't mean 2 and 3, but instead means 20 and 3. How can I explain place value clearly?

Answer: Great question! The key is helping children understand that the position of a digit determines its value:

  • In 23, the "2" is in the TENS place, so it represents 2 groups of 10 = 20
  • The "3" is in the ONES place, so it represents 3 single units = 3
  • Together: 20 + 3 = 23

Use physical objects: Have your child count out 23 blocks, then group them into 2 groups of 10 with 3 left over. This hands-on experience helps solidify the concept that "2" in the tens place means "2 groups of 10," not just "2."

Practice with various numbers and always emphasize: "What does this digit represent based on WHERE it sits in the number?"

Question: Some students struggle with the concept of trading 10 ones for 1 ten. What's an effective teaching strategy for regrouping?

Answer: The concept of regrouping is fundamental! Here's an effective strategy:

  1. Start with concrete materials: Use base-10 blocks, beans, or counters
  2. Build the concept gradually: Begin with numbers like 10, 20, 30
  3. Introduce the "trade": Show that 10 individual items can be exchanged for 1 group of 10
  4. Use consistent language: "Trade," "exchange," "make a ten"
  5. Connect to real life: Like trading 10 pennies for 1 dime

Create situations where students must regroup naturally: "If you have 13 blocks, can you make a group of 10? How many will be left over?" This builds the conceptual understanding before moving to abstract problems.

Question: How can I help students quickly identify tens and ones without counting each time?

Answer: Developing quick recognition requires pattern recognition and fluency building:

  • Visual patterns: Use ten frames and base-10 blocks consistently
  • Number talks: Daily discussions about number composition
  • Games and activities: Quick flash card identification, matching games
  • Verbal reinforcement: Always say "2 tens and 3 ones" for 23
  • Pattern practice: Work with number sequences (21, 22, 23...)

Focus on the structure: students should internalize that the first digit tells them how many tens (groups of 10), and the second digit tells them how many ones (single units). Repetition with immediate feedback strengthens this neural pathway.