Solved Exercises on Base 10 Operations in Grade 1

Master base 10 operations: place value, tens and ones, addition and subtraction, regrouping, number sense through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Adding Using Base 10
Exercise 1
Add 23 + 15 using base 10 blocks.
Definition:

Base 10 addition: Adding numbers by combining tens and ones separately

Base 10 addition method:
  1. Break numbers into tens and ones
  2. Add tens together
  3. Add ones together
  4. Combine the results
Numbers
23 + 15
Break Down
(20 + 3) + (10 + 5)
Result
38
Step 1: Break down 23

23 = 2 tens + 3 ones = 20 + 3

Step 2: Break down 15

15 = 1 ten + 5 ones = 10 + 5

Step 3: Add tens together

20 + 10 = 30

Step 4: Add ones together

3 + 5 = 8

Step 5: Combine results

30 + 8 = 38

23 + 15 = 38
Final answer:

23 + 15 = 38

Applied rules:

• Place value: Separate tens and ones before adding

• Grouping: Add tens with tens, ones with ones

• Combining: Put tens and ones back together

2 Subtracting Using Base 10
Exercise 2
Subtract 37 - 14 using base 10 blocks.
Definition:

Base 10 subtraction: Subtracting numbers by removing tens and ones separately

Numbers
37 - 14
Break Down
(30 + 7) - (10 + 4)
Result
23
Step 1: Break down 37

37 = 3 tens + 7 ones = 30 + 7

Step 2: Break down 14

14 = 1 ten + 4 ones = 10 + 4

Step 3: Subtract tens

30 - 10 = 20

Step 4: Subtract ones

7 - 4 = 3

Step 5: Combine results

20 + 3 = 23

37 - 14 = 23
Final answer:

37 - 14 = 23

Applied rules:

• Place value: Separate tens and ones before subtracting

• Grouping: Subtract tens from tens, ones from ones

• Combining: Put tens and ones back together

3 Regrouping with Base 10
Exercise 3
Add 28 + 15 using base 10 blocks. Show regrouping if needed.
Definition:

Regrouping: When ones add up to 10 or more, convert 10 ones to 1 ten

Numbers
28 + 15
Break Down
(20 + 8) + (10 + 5)
Regroup
3 tens + 13 ones = 4 tens + 3 ones
Result
43
Step 1: Break down 28

28 = 2 tens + 8 ones = 20 + 8

Step 2: Break down 15

15 = 1 ten + 5 ones = 10 + 5

Step 3: Add tens

20 + 10 = 30 (3 tens)

Step 4: Add ones

8 + 5 = 13 (13 ones)

Step 5: Regroup

13 ones = 1 ten + 3 ones

Step 6: Combine

3 tens + 1 ten + 3 ones = 4 tens + 3 ones = 43

28 + 15 = 43
Final answer:

28 + 15 = 43

Applied rules:

• Regrouping: When ones ≥ 10, convert 10 ones to 1 ten

• Place value: Maintain correct positions after regrouping

• Combining: Add all tens and all ones separately

Rules and methods, laws,...
23 + 15 = 38
Base 10 Addition
Rule 1
Tens + Tens
Add tens together
Rule 2
Ones + Ones
Add ones together
Rule 3
Regroup if ≥ 10
10 ones = 1 ten
Key definitions:

Base 10 system: Number system using groups of ten

Regrouping: Converting 10 ones to 1 ten when needed

Place value: Value of a digit based on its position

Complete methodology:
  1. Separate: Break numbers into tens and ones
  2. Add separately: Tens with tens, ones with ones
  3. Check for regrouping: If ones ≥ 10, regroup
  4. Combine: Put tens and ones back together
Tip 1: Use base-10 blocks to visualize the process.
Tip 2: Always add tens with tens and ones with ones.
Tip 3: Look for regrouping when ones add up to 10 or more.
Tip 4: Practice with numbers up to 99.
Common errors: Adding tens and ones together without separation, forgetting to regroup.
Key concepts: Place value, regrouping, base-10 system.
Formulas to know by heart:

• Base 10 addition: (Tens₁ + Tens₂) + (Ones₁ + Ones₂)

• Regrouping: 10 ones = 1 ten

• Base 10 subtraction: (Tens₁ - Tens₂) + (Ones₁ - Ones₂)

Solution: Exercises 4 to 5
4 Subtraction with Regrouping
Exercise 4
Subtract 32 - 17 using base 10 blocks. Show regrouping if needed.
Definition:

Borrowing: When ones in minuend are less than ones in subtrahend, borrow 1 ten

Numbers
32 - 17
Break Down
(30 + 2) - (10 + 7)
Borrow
2 tens + 12 ones - (1 ten + 7 ones)
Result
15
Step 1: Break down 32

32 = 3 tens + 2 ones = 30 + 2

Step 2: Break down 17

17 = 1 ten + 7 ones = 10 + 7

Step 3: Check for borrowing

2 ones < 7 ones, so we need to borrow

Step 4: Borrow 1 ten

32 = 2 tens + 12 ones (take 1 ten and add 10 to ones)

Step 5: Subtract tens

2 tens - 1 ten = 1 ten

Step 6: Subtract ones

12 ones - 7 ones = 5 ones

Step 7: Combine results

1 ten + 5 ones = 15

32 - 17 = 15
Final answer:

32 - 17 = 15

Applied rules:

• Borrowing: When ones in minuend < ones in subtrahend, borrow 1 ten

• Conversion: 1 ten = 10 ones

• Subtraction: Subtract tens from tens, ones from ones

5 Mixed Operations
Exercise 5
Solve 45 + 23 - 18 using base 10 operations.
Definition:

Mixed operations: Performing multiple operations in sequence using base 10 principles

Operations
45 + 23 - 18
First Add
68
Then Subtract
50
Step 1: Add 45 + 23

45 = 4 tens + 5 ones, 23 = 2 tens + 3 ones

4 tens + 2 tens = 6 tens, 5 ones + 3 ones = 8 ones

6 tens + 8 ones = 68

Step 2: Subtract 68 - 18

68 = 6 tens + 8 ones, 18 = 1 ten + 8 ones

6 tens - 1 ten = 5 tens, 8 ones - 8 ones = 0 ones

5 tens + 0 ones = 50

Step 3: Final result

45 + 23 - 18 = 50

45 + 23 - 18 = 50
Final answer:

45 + 23 - 18 = 50

Applied rules:

• Order of operations: Work from left to right

• Base 10 principles: Apply to each operation

• Consistency: Maintain place value throughout

Base 10 Operations Guide: Laws, Methods, Definitions, Expressions
23 + 15 = 38
Base 10 Operation
Key definitions:

Base 10 system: Number system using groups of ten

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

Regrouping: Converting 10 ones to 1 ten (or vice versa)

Complete methodology:
  1. Identify components: Break numbers into tens and ones
  2. Perform operation: Add/subtract tens with tens, ones with ones
  3. Check for regrouping: If needed, convert between tens and ones
  4. Combine results: Put tens and ones back together
  5. Verify: Check that the result makes sense
Tip 1: Use base-10 blocks (rods for tens, cubes for ones) to visualize operations.
Tip 2: Always work with tens and ones separately.
Tip 3: Remember: 10 ones = 1 ten, and 1 ten = 10 ones.
Tip 4: Practice with numbers up to 99 to master the concept.
Common errors: Forgetting to regroup when needed, mixing tens and ones incorrectly.
Exam preparation: Master addition and subtraction with regrouping up to 99.
Formulas to know by heart:

• Base 10 addition: (T₁ + T₂) + (O₁ + O₂)

• Base 10 subtraction: (T₁ - T₂) + (O₁ - O₂)

• Regrouping: 10 ones = 1 ten

• Borrowing: 1 ten = 10 ones

Questions & Answers

Question: Why do we need to break numbers into tens and ones? Can't we just add them normally?

Answer: Great question! Breaking numbers into tens and ones helps us understand what we're doing:

  • Understanding: It shows us WHY 23 + 15 = 38 (not just memorizing it)
  • Accuracy: It prevents mistakes like adding 2 + 5 = 7 instead of 20 + 5 = 25
  • Foundation: It builds the foundation for bigger numbers later

Think of it like organizing toys: it's easier to count 2 boxes of 10 toys plus 3 extra toys than to count 23 toys all mixed up!

Example: 34 + 25 = (30 + 20) + (4 + 5) = 50 + 9 = 59

Question: My child gets confused about when to regroup. How can I help them remember?

Answer: Here are helpful strategies:

  • Addition regrouping: When ones add up to 10 or more, regroup
  • Subtraction regrouping: When top number is smaller than bottom number in ones place
  • Memory trick: "More than 9 in ones? Make a new ten!"
  • Visual aids: Use base-10 blocks to show the exchange

You can also have them circle the ones column before deciding whether to regroup.

Tip: Practice with problems that don't require regrouping first, then introduce regrouping gradually.

Question: How can I help my students who struggle with base 10 operations?

Answer: Here's a systematic approach for struggling students:

  1. Concrete first: Use physical base-10 blocks for hands-on experience
  2. Visual representations: Draw tens and ones separately
  3. Step-by-step routine: Create a consistent process they can follow
  4. Frequent practice: Daily short sessions with immediate feedback

Teach them to draw lines: "Tens | Ones" to separate the columns visually.

Provide anchor charts with the steps visible in the classroom for reference.

Base 10 Operations: Complete Learning Summary

Key Definitions

Base 10 System: Number system using groups of ten

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

Tens Place: The position where tens digits go (left side of two-digit numbers)

Ones Place: The position where ones digits go (right side of two-digit numbers)

Regrouping: Converting 10 ones to 1 ten (or vice versa)

Core Rules & Laws

Separation Rule: Always work with tens and ones separately

Regrouping Rule: When ones ≥ 10, convert 10 ones to 1 ten

Borrowing Rule: When subtracting and top ones < bottom ones, borrow 1 ten

Combination Rule: Add/subtract tens with tens, ones with ones

Conversion Rule: 1 ten = 10 ones, 10 ones = 1 ten

Step-by-Step Method

Step 1: Break numbers into tens and ones

Step 2: Perform the operation on tens

Step 3: Perform the operation on ones

Step 4: Check for regrouping/borrowing if needed

Step 5: Combine tens and ones to get the final answer

Examples & Applications

Addition: 23 + 15 = (20 + 10) + (3 + 5) = 30 + 8 = 38

Subtraction: 37 - 14 = (30 - 10) + (7 - 4) = 20 + 3 = 23

With regrouping: 28 + 15 = (20 + 10) + (8 + 5) = 30 + 13 = 43

With borrowing: 32 - 17 = (20 - 10) + (12 - 7) = 10 + 5 = 15

Mixed operations: 45 + 23 - 18 = 68 - 18 = 50

Tips & Common Pitfalls

Tip 1: Use base-10 blocks to visualize operations

Tip 2: Always separate tens and ones before operating

Tip 3: Check for regrouping after adding ones

Pitfall: Don't add tens and ones together without separation

Pitfall: Forget to regroup when ones ≥ 10

Key Takeaways

Memorize: 10 ones = 1 ten, 1 ten = 10 ones

Remember: Work with tens and ones separately

Practice: Work with numbers up to 99

Verify: Always check your answers

Master: Regrouping and borrowing are crucial skills