Solved Exercises on Strategies Based on Place Value in Grade 2

Master strategies based on place value: decomposing numbers, regrouping, expanded form, and using place value for efficient addition and subtraction through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Decomposing Strategy
Exercise 1
Decompose 93 and add 15 using strategies based on place value
Definition:

Decomposing Strategy: Breaking numbers into their place values (tens and ones) to make calculations easier.

Decomposing Method:
  1. Break each number into tens and ones
  2. Add the tens together
  3. Add the ones together
  4. Combine the sums
  5. Regroup if necessary
Problem
93 + 15
Decompose
90+3 + 10+5
Add by place
100+8=108
Step 1: Decompose each number into tens and ones

93 = 90 + 3 and 15 = 10 + 5

Step 2: Add the tens together

90 + 10 = 100

Step 3: Add the ones together

3 + 5 = 8

Step 4: Combine the sums

100 + 8 = 108

93 + 15 = 108
Final answer:

93 + 15 = 108

Applied rules:

• Decomposing: Breaking numbers into their place values

• Place Value Addition: Adding digits with the same place value

• Regrouping: When ones sum to 10+, convert to tens and ones

2 Regrouping Strategy
Exercise 2
Solve using strategies based on place value: 67 + 28
Definition:

Regrouping Strategy: Converting 10 ones to 1 ten when adding, or 1 ten to 10 ones when subtracting.

Problem
67 + 28
Decompose
(60+7)+(20+8)
Add by place
80+15=95
Step 1: Decompose both numbers into tens and ones

67 = 60 + 7 and 28 = 20 + 8

Step 2: Add the tens together

60 + 20 = 80

Step 3: Add the ones together

7 + 8 = 15

Step 4: Regroup when ones sum to 10+

15 ones = 10 ones + 5 ones = 1 ten + 5 ones

Step 5: Add the regrouped ten to the tens sum

80 + 10 = 90, then 90 + 5 = 95

67 + 28 = 95
Final answer:

67 + 28 = 95

Applied rules:

• Place Value Addition: Add digits with the same place value

• Regrouping: When ones sum to 10 or more, convert to tens and ones

• Number Composition: Reassemble the final sum from its components

3 Subtraction with Regrouping
Exercise 3
Solve using strategies based on place value: 81 - 47
Definition:

Subtraction with Regrouping: Converting 1 ten to 10 ones when the top ones digit is smaller than the bottom ones digit.

Problem
81 - 47
Decompose
(80+1)-(40+7)
Regroup
80+1=70+11
Step 1: Decompose both numbers into tens and ones

81 = 80 + 1 and 47 = 40 + 7

Step 2: Check if ones can be subtracted

1 - 7 cannot be done, so we need to regroup

Step 3: Regroup from tens to ones

Take 1 ten from 80 (leaving 70) and add to 1 ones: 70 + 11

Step 4: Subtract tens and ones separately

70 - 40 = 30 and 11 - 7 = 4

Step 5: Combine the results

30 + 4 = 34

81 - 47 = 34
Final answer:

81 - 47 = 34

Applied rules:

• Place Value Subtraction: Subtract digits with the same place value

• Regrouping: When the top digit is smaller, borrow from the next higher place

• Number Composition: Reassemble the final difference from its components

Rules and methods, laws,...
93 = 90 + 3 (decomposing strategy)
Decomposing Strategy
Strategy 1
Decomposing
Breaking numbers into tens + ones
Strategy 2
Regrouping
Converting between place values
Strategy 3
Place Value
Working with same place values
Key definitions:

Strategies Based on Place Value: Methods that use the value of digits based on their position in a number

Decomposing: Breaking a number into its component parts (tens and ones)

Regrouping: Converting from one place value to another (borrowing in subtraction, carrying in addition)

Expanded Form: Writing a number as the sum of its place values (e.g., 93 = 90 + 3)

Complete methodology:
  1. Identify place values: Determine the tens and ones in each number
  2. Separate by place: Work with tens and ones separately
  3. Perform operations: Add or subtract digits in the same place
  4. Regroup when necessary: Borrow or carry between places
  5. Combine results: Put the tens and ones back together
Tip 1: Always decompose numbers to see the tens and ones clearly.
Tip 2: In subtraction, if the top ones digit is smaller than the bottom ones digit, you must regroup.
Tip 3: Remember: 1 ten = 10 ones (for regrouping purposes).
Tip 4: Always check your answer by using the inverse operation.
Common errors: Forgetting to regroup when necessary, adding tens and ones together before completing operations, misidentifying place values.
Key strategies: Practice decomposing numbers, visualize with base-10 blocks, check answers with inverse operations.
Place value rules:

• In 2-digit numbers, the left digit is the tens place, right digit is the ones place

• When adding, add tens to tens and ones to ones

• When subtracting, subtract tens from tens and ones from ones

• Regroup when the top digit is smaller than the bottom digit in subtraction

• 1 ten = 10 ones (for regrouping purposes)

Solution: Exercises 4 to 5
4 Mixed Operations Strategy
Exercise 4
Solve using strategies based on place value: 54 + 38 - 26
Definition:

Mixed Operations Strategy: Perform operations sequentially using place value methods.

Problem
54 + 38 - 26
First: 54 + 38
90 + 12 = 102
Then: 102 - 26
90 + 12 - 26 = 76
Step 1: First perform 54 + 38 using place value

54 = 50 + 4, 38 = 30 + 8, so (50 + 30) + (4 + 8) = 80 + 12 = 92

Step 2: Now perform 92 - 26 using place value

92 = 90 + 2, 26 = 20 + 6

Step 3: Since 2 < 6, regroup 90 + 2 to 80 + 12

Now we have (80 + 12) - (20 + 6)

Step 4: Subtract tens and ones separately

80 - 20 = 60, and 12 - 6 = 6

Step 5: Combine the results

60 + 6 = 66

54 + 38 - 26 = 66
Final answer:

54 + 38 - 26 = 66

Applied rules:

• Order of Operations: Perform operations from left to right

• Place Value Strategy: Use decomposition for each operation

• Regrouping: Apply when needed in each step

5 Comparison Strategy
Exercise 5
Which is greater: 74 - 39 or 68 - 25? Use strategies based on place value.
Definition:

Comparison Strategy: Solve each expression using place value methods, then compare the results.

First: 74 - 39
70+4 - 30+9 = 60+14 - 30+9 = 35
Second: 68 - 25
60+8 - 20+5 = 40+3 = 43
Compare
35 < 43
Step 1: Solve 74 - 39 using place value

74 = 70 + 4, 39 = 30 + 9

Step 2: Since 4 < 9, regroup 70 + 4 to 60 + 14

Now we have (60 + 14) - (30 + 9)

Step 3: Subtract tens and ones separately

60 - 30 = 30, and 14 - 9 = 5

Step 4: Combine the results

30 + 5 = 35

Step 5: Solve 68 - 25 using place value

68 = 60 + 8, 25 = 20 + 5, so (60 - 20) + (8 - 5) = 40 + 3 = 43

Step 6: Compare the results

35 < 43, so 68 - 25 is greater

74 - 39 = 35, 68 - 25 = 43, so 68 - 25 > 74 - 39
Final answer:

68 - 25 is greater than 74 - 39

Applied rules:

• Place Value Subtraction: Apply decomposition method to both expressions

• Comparison: Once both expressions are simplified, compare the results

• Regrouping: Apply when needed in each expression

Strategies Based on Place Value Concepts and Techniques
93 = 90 + 3 (decomposing strategy)
Place Value Decomposition
Key definitions:

Strategies Based on Place Value: Methods that use the value of digits based on their position in a number

Decomposing: Breaking a number into its component parts (tens and ones)

Regrouping: Converting between place values (1 ten = 10 ones)

Expanded Form: Writing a number as the sum of its place values (e.g., 93 = 90 + 3)

Complete methodology:
  1. Identify place values: Look at each digit and determine its value
  2. Separate by place: Group tens and ones separately
  3. Perform operations: Work with tens and ones separately
  4. Regroup when necessary: Convert between places when needed
  5. Combine results: Put the final answer together
Tip 1: Think of tens as bundles of 10 ones - this helps visualize regrouping
Tip 2: Use base-10 blocks or drawings to physically represent the numbers
Tip 3: In subtraction, always check if you need to regroup BEFORE subtracting
Tip 4: Practice with number lines to see how place value affects the magnitude of numbers
Common errors: Forgetting to regroup when necessary, adding tens and ones together before completing operations, misidentifying place values.
Success habits: Regular practice with decomposing numbers, visualizing with manipulatives, checking answers.
Strategies based on place value:

• Decompose numbers into tens and ones before operating

• Add/subtract digits with the same place value

• Regroup when necessary (10 ones = 1 ten)

• Check your answer by using the inverse operation

• Use visual models to support understanding

Strategies Based on Place Value Workflow

🔢
Step-by-Step Process
1
Identify place values
2
Decompose numbers
3
Operate by place
4
Regroup if needed
5
Combine results
Place Value Visualization
Understanding place value helps us see that 93 is actually 9 tens and 3 ones, making operations easier to manage.
Master Strategies Based on Place Value for Strong Math Foundation!

Questions & Answers

Question: Why do we need to use strategies based on place value? Can't I just add or subtract the regular way?

Answer: Great question! Strategies based on place value actually make math easier and help you understand what you're doing:

  • They organize the work: Instead of trying to add 67 + 28 all at once, you add 60 + 20 = 80, then 7 + 8 = 15, then 80 + 15 = 95
  • They prevent mistakes: You won't accidentally add 7 tens to 8 ones
  • They build number sense: You understand that 67 really means 6 tens and 7 ones
  • They prepare you for bigger numbers: This same strategy works for hundreds and thousands later

Think of it like organizing your toys - it's easier to count if you group similar items together!

Question: How can I help my child practice strategies based on place value at home?

Answer: Here are effective ways to practice strategies based on place value at home:

  • Use manipulatives: Base-10 blocks, straws bundled in tens, or groups of 10 beans
  • Play number games: Have your child build numbers with place-value cards
  • Real-world connections: Use money to show tens and ones (dimes and pennies)
  • Drawings: Have your child draw sticks for tens and dots for ones

Start with simple numbers like 12, 23, 34 and practice decomposing them: 12 = 10 + 2. Once comfortable, move to larger numbers and operations.

Make it visual and hands-on - the more concrete experiences your child has with tens and ones, the better they'll understand abstract place value concepts.

Question: I still don't understand regrouping. Can you explain it in a simpler way?

Answer: Sure! Think of regrouping like trading. Let's say you have 81 cents and want to give someone 47 cents:

  • You have 8 dimes and 1 penny (81 cents)
  • But you need to give 7 pennies and you only have 1 penny
  • So you trade 1 dime for 10 pennies (regrouping)
  • Now you have 7 dimes and 11 pennies
  • You can give 7 pennies and keep 4 pennies
  • Then give 4 dimes and keep 3 dimes
  • You're left with 3 dimes and 4 pennies = 34 cents

Regrouping is just trading between place values to make the math easier!