Solved Exercises on What is Place Value Strategy in Math in Grade 2

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

Understanding Place Value Strategy in Math: Exercises 1 to 3
1 Understanding place value in math
Exercise 1
What is the place value of each digit in the number 58 in math?
Definition:

Place value in math: The value of a digit based on its position in a number, fundamental to mathematical operations

Place value method in math:
  1. Identify the position of each digit
  2. Understand that each position has a different value in math
  3. Rightmost digit is the ones place
  4. Next position to the left is the tens place
Number
58
Digit positions
5 in tens place, 8 in ones place
Value
50 + 8 = 58
Step 1: Identify the digits and their positions in math

Number: 58

Digit 5 is in the tens place

Digit 8 is in the ones place

Step 2: Understand the value of each position in math

Each position in a number has a different value in mathematical operations

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 in math

Digit 5 in the tens place: 5 × 10 = 50

Digit 8 in the ones place: 8 × 1 = 8

Step 4: Express the number in expanded form in math

58 = 50 + 8

58 = 50 + 8 (5 tens and 8 ones)
Final answer:

In the number 58 in math: 5 is in the tens place (value 50) and 8 is in the ones place (value 8)

Applied rules in math:

• Place value in math: Each position has a different value

• Tens place in math: Represents groups of ten

• Ones place in math: Represents individual units

Understanding Place Value in Math
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Number: 58

5 in tens place = 50

8 in ones place = 8

Expanded Form

58 = 50 + 8

58 = 5 tens + 8 ones

Visual Representation

58 = [5 groups of 10] + [8 individual units]

2 Using place value strategy in math for addition
Exercise 2
Add 42 + 36 using place value strategy in math.
Definition:

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

Expression
42 + 36
Break apart
(40 + 2) + (30 + 6)
Result
78
Step 1: Break each number into tens and ones in math

42 = 40 + 2 (4 tens and 2 ones)

36 = 30 + 6 (3 tens and 6 ones)

Step 2: Add tens with tens and ones with ones in math

Tens: 40 + 30 = 70

Ones: 2 + 6 = 8

Step 3: Combine the results in math

70 + 8 = 78

42 + 36 = 78
Final answer:

42 + 36 = 78

Applied rules in math:

• Place value strategy in math: Break numbers into tens and ones

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

• Combining in math: Add the final tens and ones together

Place Value Addition Strategy in Math
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Break Apart

42 = 40 + 2

36 = 30 + 6

Add Like Values

Tens: 40 + 30 = 70

Ones: 2 + 6 = 8

Final Calculation

70 + 8 = 78

3 Using place value strategy in math for subtraction
Exercise 3
Subtract 67 - 24 using place value strategy in math.
Definition:

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

Expression
67 - 24
Break apart
(60 + 7) - (20 + 4)
Result
43
Step 1: Break each number into tens and ones in math

67 = 60 + 7 (6 tens and 7 ones)

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

Step 2: Subtract tens from tens and ones from ones in math

Tens: 60 - 20 = 40

Ones: 7 - 4 = 3

Step 3: Combine the results in math

40 + 3 = 43

67 - 24 = 43
Final answer:

67 - 24 = 43

Applied rules in math:

• Place value strategy in math: Break numbers into tens and ones

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

• Combining in math: Add the final tens and ones together

Place Value Subtraction Strategy in Math
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Break Apart

67 = 60 + 7

24 = 20 + 4

Subtract Like Values

Tens: 60 - 20 = 40

Ones: 7 - 4 = 3

Final Calculation

40 + 3 = 43

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

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

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

Ones place in math: The rightmost digit, representing individual units

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

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

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

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

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

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

• Strategy in math: Break numbers apart to make calculations easier

Examples progression in math
Understanding place value in math:

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

Addition with place value strategy in math:

42 + 36 = (40 + 2) + (30 + 6) = (40 + 30) + (2 + 6) = 70 + 8 = 78

Subtraction with place value strategy in math:

67 - 24 = (60 + 7) - (20 + 4) = (60 - 20) + (7 - 4) = 40 + 3 = 43

Understanding Place Value Strategy in Math: Exercises 4 to 5
4 Word problem with place value strategy in math
Exercise 4
Tom has 54 marbles. His friend gives him 28 more marbles. How many marbles does Tom have now? Use place value strategy in math.
Definition:

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

Expression
54 + 28
Break apart
(50 + 4) + (20 + 8)
Result
82
Step 1: Identify the numbers in the math problem

Tom has 54 marbles

His friend gives him 28 more marbles

This is an addition problem: 54 + 28

Step 2: Break each number into tens and ones in math

54 = 50 + 4 (5 tens and 4 ones)

28 = 20 + 8 (2 tens and 8 ones)

Step 3: Add tens with tens and ones with ones in math

Tens: 50 + 20 = 70

Ones: 4 + 8 = 12

Step 4: Handle the result in math

Since 12 ≥ 10, we need to regroup: 12 = 1 ten + 2 ones

Add this extra ten to our tens: 70 + 10 = 80

Step 5: Combine the results in math

80 + 2 = 82

Step 6: State the answer in context in math

Tom has 82 marbles now.

Tom has 82 marbles now.
Final answer:

Tom has 82 marbles now.

Applied rules in math:

• Problem solving in math: Identify operation needed from context

• Place value strategy in math: Break numbers into tens and ones

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

• Regrouping in math: When ones add to 10 or more, convert to tens

Word Problem Strategy in Math
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Given Information

Tom has: 54 marbles

Friend gives: 28 marbles

Operation: Addition

Break Apart

54 = 50 + 4

28 = 20 + 8

Calculate

Tens: 50 + 20 = 70

Ones: 4 + 8 = 12

Regroup: 12 = 1 ten + 2 ones

Total: 70 + 10 + 2 = 82

5 Understanding place value relationships in math
Exercise 5
Explain why the number 72 is greater than the number 27 in math, using place value strategy.
Definition:

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

Numbers to compare
72 vs 27
Break apart
70 + 2 vs 20 + 7
Comparison
72 > 27
Step 1: Break each number into tens and ones in math

72 = 70 + 2 (7 tens and 2 ones)

27 = 20 + 7 (2 tens and 7 ones)

Step 2: Compare the tens places first in math

72 has 7 tens (70)

27 has 2 tens (20)

Since 70 > 20, we know 72 > 27

Step 3: Even though 27 has more ones in math

72 has 2 ones

27 has 7 ones

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

Step 4: Conclusion in math

72 is greater than 27 because it has more tens in math

72 > 27 because 72 has 7 tens while 27 has only 2 tens
Final answer:

72 is greater than 27 in math because it has 7 tens (70) compared to 27's 2 tens (20). Even though 27 has more ones (7 vs 2), the tens place value is more significant in mathematical comparison.

Applied rules in math:

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

• Tens place in math: More significant than the ones place

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

Comparing Numbers with Place Value in Math
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Number 72

7 tens = 70

2 ones = 2

Total: 70 + 2 = 72

Number 27

2 tens = 20

7 ones = 7

Total: 20 + 7 = 27

Comparison

70 > 20 (tens place)

Therefore: 72 > 27

Questions & Answers in Math

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

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

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

Think of it like having bags of 10 marbles and loose marbles in math. 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 in math. How can I help them remember?

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

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

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

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

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

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

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

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

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