Solved Exercises on What is Place Value Strategy in Grade 2

Understanding place value strategy: tens and ones, addition and subtraction within 100 using place value strategies through these 5 detailed exercises.

Understanding Place Value Strategy: Exercises 1 to 3
1 Understanding place value
Exercise 1
What is the place value of each digit in the number 47?
Definition:

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

Place value method:
  1. Identify the position of each digit
  2. Understand that each position has a different value
  3. Rightmost digit is the ones place
  4. Next position to the left is the tens place
Number
47
Digit positions
4 in tens place, 7 in ones place
Value
40 + 7 = 47
Step 1: Identify the digits and their positions

Number: 47

Digit 4 is in the tens place

Digit 7 is in the ones place

Step 2: Understand the value of each position

Each position in a number has a different value

The rightmost position is the ones place

The next position to the left is the tens place

Step 3: Calculate the value of each digit

Digit 4 in the tens place: 4 × 10 = 40

Digit 7 in the ones place: 7 × 1 = 7

Step 4: Express the number in expanded form

47 = 40 + 7

47 = 40 + 7 (4 tens and 7 ones)
Final answer:

In the number 47: 4 is in the tens place (value 40) and 7 is in the ones place (value 7)

Applied rules:

• Place value: Each position has a different value

• Tens place: Represents groups of ten

• Ones place: Represents individual units

Understanding Place Value
📊
Number: 47

4 in tens place = 40

7 in ones place = 7

Expanded Form

47 = 40 + 7

47 = 4 tens + 7 ones

Visual Representation

47 = [4 groups of 10] + [7 individual units]

2 Using place value for addition
Exercise 2
Add 35 + 24 using place value strategy.
Definition:

Place value strategy: Breaking numbers into tens and ones to make calculations easier

Expression
35 + 24
Break apart
(30 + 5) + (20 + 4)
Result
59
Step 1: Break each number into tens and ones

35 = 30 + 5 (3 tens and 5 ones)

24 = 20 + 4 (2 tens and 4 ones)

Step 2: Add tens with tens and ones with ones

Tens: 30 + 20 = 50

Ones: 5 + 4 = 9

Step 3: Combine the results

50 + 9 = 59

35 + 24 = 59
Final answer:

35 + 24 = 59

Applied rules:

• Place value strategy: Break numbers into tens and ones

• Like place values: Add tens with tens and ones with ones

• Combining: Add the final tens and ones together

Place Value Addition Strategy
📊
Break Apart

35 = 30 + 5

24 = 20 + 4

Add Like Values

Tens: 30 + 20 = 50

Ones: 5 + 4 = 9

Final Calculation

50 + 9 = 59

3 Using place value for subtraction
Exercise 3
Subtract 58 - 23 using place value strategy.
Definition:

Place value subtraction strategy: Breaking numbers into tens and ones to make calculations easier

Expression
58 - 23
Break apart
(50 + 8) - (20 + 3)
Result
35
Step 1: Break each number into tens and ones

58 = 50 + 8 (5 tens and 8 ones)

23 = 20 + 3 (2 tens and 3 ones)

Step 2: Subtract tens from tens and ones from ones

Tens: 50 - 20 = 30

Ones: 8 - 3 = 5

Step 3: Combine the results

30 + 5 = 35

58 - 23 = 35
Final answer:

58 - 23 = 35

Applied rules:

• Place value strategy: Break numbers into tens and ones

• Like place values: Subtract tens from tens and ones from ones

• Combining: Add the final tens and ones together

Place Value Subtraction Strategy
📊
Break Apart

58 = 50 + 8

23 = 20 + 3

Subtract Like Values

Tens: 50 - 20 = 30

Ones: 8 - 3 = 5

Final Calculation

30 + 5 = 35

Complete Summary: What is Place Value Strategy
AB = A×10 + B
Place Value Formula
Key definitions:

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

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

Ones place: The rightmost digit, representing individual units

Place value strategy: Breaking numbers into their place values (tens and ones) to make calculations easier

Expanded form: Writing a number as the sum of its place values (e.g., 45 = 40 + 5)

Complete methodology:
  1. Recognize the number: Look at each digit and its position
  2. Break apart numbers: Write each number in expanded form (tens + ones)
  3. Operate on like place values: Add or subtract tens with tens, ones with ones
  4. Combine results: Add the final tens and ones together
Tip 1: Always write out the expanded form (tens + ones) to visualize the problem.
Tip 2: Remember that the rightmost digit is always the ones place.
Tip 3: Only add or subtract like place values (tens with tens, ones with ones).
Tip 4: Use base-10 blocks or drawings to physically represent tens and ones.
Tip 5: Practice with simple numbers first before moving to larger ones.
Common errors: Adding tens to ones, forgetting place value, misaligning digits.
Key concepts: Each position has a different value, 1 ten = 10 ones.
Memorization tips: "Same place values go together!" for addition/subtraction.
Essential rules to remember:

• Place value formula: Two-digit number AB = A×10 + B

• Like place values: Only operate on tens with tens and ones with ones

• Expanded form: Write numbers as the sum of their place values

• Strategy: Break numbers apart to make calculations easier

Examples progression
Understanding place value:

47 = 40 + 7 (4 tens and 7 ones)

Addition with place value strategy:

35 + 24 = (30 + 5) + (20 + 4) = (30 + 20) + (5 + 4) = 50 + 9 = 59

Subtraction with place value strategy:

58 - 23 = (50 + 8) - (20 + 3) = (50 - 20) + (8 - 3) = 30 + 5 = 35

Understanding Place Value Strategy: Exercises 4 to 5
4 Word problem with place value strategy
Exercise 4
Sarah has 46 stickers. Her friend gives her 32 more stickers. How many stickers does Sarah have now?
Definition:

Word problems: Real-life situations requiring mathematical operations using place value strategies

Expression
46 + 32
Break apart
(40 + 6) + (30 + 2)
Result
78
Step 1: Identify the numbers in the problem

Sarah has 46 stickers

Her friend gives her 32 more stickers

This is an addition problem: 46 + 32

Step 2: Break each number into tens and ones

46 = 40 + 6 (4 tens and 6 ones)

32 = 30 + 2 (3 tens and 2 ones)

Step 3: Add tens with tens and ones with ones

Tens: 40 + 30 = 70

Ones: 6 + 2 = 8

Step 4: Combine the results

70 + 8 = 78

Step 5: State the answer in context

Sarah has 78 stickers now.

Sarah has 78 stickers now.
Final answer:

Sarah has 78 stickers now.

Applied rules:

• Problem solving: Identify operation needed from context

• Place value strategy: Break numbers into tens and ones

• Like place values: Add tens with tens and ones with ones

Word Problem Strategy
📊
Given Information

Sarah has: 46 stickers

Friend gives: 32 stickers

Operation: Addition

Break Apart

46 = 40 + 6

32 = 30 + 2

Calculate

Tens: 40 + 30 = 70

Ones: 6 + 2 = 8

Total: 70 + 8 = 78

5 Understanding place value relationships
Exercise 5
Explain why the number 53 is greater than the number 35, using place value strategy.
Definition:

Comparing numbers: Using place value to determine which number is greater by comparing digits in each place value

Numbers to compare
53 vs 35
Break apart
50 + 3 vs 30 + 5
Comparison
53 > 35
Step 1: Break each number into tens and ones

53 = 50 + 3 (5 tens and 3 ones)

35 = 30 + 5 (3 tens and 5 ones)

Step 2: Compare the tens places first

53 has 5 tens (50)

35 has 3 tens (30)

Since 50 > 30, we know 53 > 35

Step 3: Even though 35 has more ones

53 has 3 ones

35 has 5 ones

However, the tens place is more important than the ones place

Step 4: Conclusion

53 is greater than 35 because it has more tens

53 > 35 because 53 has 5 tens while 35 has only 3 tens
Final answer:

53 is greater than 35 because it has 5 tens (50) compared to 35's 3 tens (30). Even though 35 has more ones (5 vs 3), the tens place value is more significant.

Applied rules:

• Place value comparison: Compare digits starting from the highest place value

• Tens place: More significant than the ones place

• Value determination: Higher place value digits determine the larger number

Comparing Numbers with Place Value
📊
Number 53

5 tens = 50

3 ones = 3

Total: 50 + 3 = 53

Number 35

3 tens = 30

5 ones = 5

Total: 30 + 5 = 35

Comparison

50 > 30 (tens place)

Therefore: 53 > 35

Questions & Answers

Question: Why do we need to break numbers apart? Can't I just add them normally?

Answer: Great question! Breaking numbers apart helps you understand what you're really doing when you add. Let me explain:

  • When you see 23 + 15, you're actually adding 2 tens + 1 ten = 3 tens, and 3 ones + 5 ones = 8 ones
  • This equals 30 + 8 = 38
  • Breaking it apart makes it easier to see why 23 + 15 = 38
  • It also helps when you need to regroup later

Think of it like having bags of 10 marbles and loose marbles. It's easier to count 2 full bags + 1 full bag = 3 full bags, plus 3 loose + 5 loose = 8 loose.

Question: My child seems confused about which place is which. How can I help them remember?

Answer: Here are some strategies to help your child remember place values:

  • Teach them to read numbers from right to left: ones place, then tens place
  • Use physical manipulatives like base-10 blocks to visualize the difference
  • Create a chant: "Ones are on the right, tens are to the left!"
  • Point to each digit and say its value: "In 47, the 7 is 7 ones, the 4 is 4 tens"

Practice with simple numbers first: 12, 23, 34, etc., before moving to larger numbers.

Remind them that the rightmost digit is always the ones place!

Question: I want to understand place value better. Can you explain why it's so important?

Answer: Place value is fundamental to our entire number system! Here's why it's so important:

  • Base-10 system: Our number system is built on groups of 10
  • Efficiency: It allows us to represent large numbers with just 10 digits (0-9)
  • Calculations: Makes addition, subtraction, multiplication, and division possible
  • Future math: Essential for understanding decimals, fractions, and larger numbers

Without place value, we'd need a separate symbol for every number, which would be impossible!

Mastering place value now will make all future math much easier.