Solved Exercises on Counting to 1000 by 100 in Grade 2

Master counting to 1000 by 100: skip counting patterns, place value understanding, number sequence recognition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Skip counting pattern
Exercise 1
Count by 100 starting from 100. Write the next 8 numbers in the sequence.
Definition:

Skip counting by 100: Adding 100 to each number in a sequence

Skip counting method:
  1. Start with the given number
  2. Add 100 to get the next number
  3. Only the hundreds digit changes
  4. Repeat for the desired number of terms
Starting number
100
Add 100
100+100=200
Step 1: Start with 100

100 is our starting point (1 hundred, 0 tens, 0 ones)

Step 2: Add 100 to get next number

100 + 100 = 200 (2 hundreds, 0 tens, 0 ones)

Step 3: Continue adding 100

200 + 100 = 300, 300 + 100 = 400, 400 + 100 = 500, 500 + 100 = 600, 600 + 100 = 700, 700 + 100 = 800, 800 + 100 = 900

100
200
300
400
500
600
700
800
900
100, 200, 300, 400, 500, 600, 700, 800, 900
Final answer:

The next 8 numbers are: 200, 300, 400, 500, 600, 700, 800, 900

Applied rules:

• Place value rule: Only the hundreds digit changes when counting by 100

• Pattern recognition: Tens and ones digits stay 0

• Consistency: Same increment (100) applied each time

2 Missing number in sequence
Exercise 2
Find the missing number in this sequence: 200, 300, 400, ___, 600, 700
Definition:

Number sequence: A series of numbers following a specific pattern

Sequence
200, 300, 400, ?, 600, 700
Pattern
+100 each time
Missing
500
Step 1: Identify the pattern

300 - 200 = 100, 400 - 300 = 100

The pattern is adding 100 each time

Step 2: Apply the pattern

After 400: 400 + 100 = 500

Step 3: Verify with next number

500 + 100 = 600 ✓

200
→
300
→
400
→
500
→
600
→
700
200, 300, 400, 500, 600, 700
Final answer:

The missing number is 500

Applied rules:

• Pattern recognition: Identify consistent increments of 100

• Verification: Check that the pattern continues after the missing number

• Place value understanding: Only hundreds digit changes

3 Place value analysis
Exercise 3
What happens to the hundreds, tens, and ones digits when you count by 100 starting from 800?
Definition:

Place value: The value of each digit based on its position

Hundreds
8
Tens
0
Ones
0
Start
800
Add 100
800+100=900
Result
900
Step 1: Analyze 800

Hundreds: 8, Tens: 0, Ones: 0

Step 2: Add 100 to 800

800 + 100 = 900

Step 3: Analyze 900

Hundreds: 9, Tens: 0, Ones: 0

Step 4: Compare digits

Hundreds increased by 1 (8→9), Tens and Ones stayed 0

800 → 900: H+1, T:0, O:0
Final answer:

When counting by 100 from 800 to 900:
- Hundreds digit increases by 1 (8→9)
- Tens digit remains 0
- Ones digit remains 0

Applied rules:

• Place value system: Each position represents powers of 10

• Consistency: Only hundreds digit changes when adding 100

• Pattern: Tens and ones digits remain constant

Comprehensive Guide: Counting to 1000 by 100
\(n + 100 = n + 100\)
Skip Counting by 100
Key definitions:

Skip counting: Counting by a number other than 1 (counting by 2s, 5s, 10s, 100s, etc.)

Place value: The value of a digit based on its position in a number (hundreds, tens, ones)

Number pattern: A sequence of numbers that follows a specific rule

Base-10 system: Our number system based on powers of 10

Complete methodology:
  1. Analyze the starting number: Identify hundreds, tens, and ones digits
  2. Apply the increment: Add or subtract 100 to the number
  3. Handle place value changes: Watch for when hundreds digit changes
  4. Continue the pattern: Repeat the process for desired number of terms
  5. Verify the result: Check that the pattern is consistent
Tip 1: When counting by 100, only the hundreds digit changes.
Tip 2: Tens and ones digits always remain the same when counting by 100.
Tip 3: Practice with number lines to visualize the pattern.
Tip 4: Count by 100s from different starting points.
Tip 5: Skip counting by 100s helps prepare for multiplication.
Pattern characteristics: Consistent increment of 100, tens and ones digits unchanged, hundreds digit increases by 1.
Place value rules: Counting by 100 affects only the hundreds place.
Essential rules for counting by 100:

• Hundreds digit: Increases by 1 each time (1→2→3...)

• Tens digit: Always remains the same

• Ones digit: Always remains the same

• Pattern consistency: Always add or subtract 100

• Base-10 relationship: 100 = 10 tens = 100 ones

\(n, n+100, n+200, n+300...\)
General Pattern Formula
Solution: Exercises 4 to 5
4 Counting backwards by 100
Exercise 4
Count backwards by 100 starting from 900. Write the next 6 numbers.
Definition:

Backwards skip counting: Subtracting 100 from each number in a sequence

Start
900
Subtract 100
900-100=800
Next
800
Step 1: Start with 900

900 is our starting point (9 hundreds, 0 tens, 0 ones)

Step 2: Subtract 100 to get next number

900 - 100 = 800 (8 hundreds, 0 tens, 0 ones)

Step 3: Continue subtracting 100

800 - 100 = 700, 700 - 100 = 600, 600 - 100 = 500, 500 - 100 = 400, 400 - 100 = 300

900
800
700
600
500
400
300
900, 800, 700, 600, 500, 400, 300
Final answer:

The next 6 numbers are: 800, 700, 600, 500, 400, 300

Applied rules:

• Reverse pattern: Subtract 100 instead of adding

• Place value rule: Only hundreds digit changes (decreases by 1)

• Consistency: Same decrement (100) applied each time

5 Word problem application
Exercise 5
A school has 400 books in the library. They buy 100 more books every month for 3 months. How many books are in the library after 3 months?
Definition:

Word problem: Real-world scenario requiring mathematical solution

Initial
400
Months × 100
3×100=300
Total
400+300=700
Step 1: Identify initial amount

The library starts with 400 books

Step 2: Calculate total addition

They buy 100 books per month for 3 months: 100 × 3 = 300 books

Step 3: Add to initial amount

400 + 300 = 700 books

Step 4: Verify with skip counting

400 → 500 → 600 → 700 (3 steps of 100)

400
→
500
→
600
→
700
400 + 300 = 700 books
Final answer:

The library has 700 books after 3 months

Applied rules:

• Real-world application: Connect math to practical scenarios

• Problem solving: Break down word problems into steps

• Verification: Use multiple methods to confirm answer

Questions & Answers

Question: Why do the tens and ones digits stay the same when we count by 100? I don't understand why they don't change.

Answer: Great question! This happens because of how our number system works:

  • When we count by 100, we're adding exactly 1 hundred, 0 tens, and 0 ones
  • For example: 200 + 100 = 300. We add 1 to the hundreds place (2→3) but add 0 to the tens and ones places
  • This is because 100 is made up of 1 hundred, 0 tens, and 0 ones

Think of it like money: if you have $200 and someone gives you $100 more, you now have $300. The tens and ones amounts ($00) don't change.

This is a fundamental part of our base-10 number system where each place value is 10 times the previous one.

Question: How can I help my students who struggle with the concept that counting by 100 only changes the hundreds digit?

Answer: This is a common challenge! Here are effective strategies:

  • Use manipulatives: Show with base-10 blocks how adding 100 only adds to the hundreds place
  • Visual aids: Use place value charts to highlight which digit changes
  • Color coding: Use different colors for hundreds, tens, and ones digits
  • Verbal emphasis: Repeatedly emphasize that only the hundreds digit changes

The key is helping students understand that 100 means 1 hundred, 0 tens, and 0 ones. So when we add 100, we only add to the hundreds place.

Question: My child is having trouble with backwards counting by 100s. How can I make this easier for them?

Answer: Backwards counting can be challenging! Try these approaches:

  • Start with smaller numbers: Practice 300, 200, 100 before going to larger numbers
  • Use real-life contexts: Elevator scenarios (going down floors) or countdown situations
  • Connect to forward counting: Show that backwards counting undoes forward counting
  • Use visual aids: Number lines going left show decreasing values

Remind your child that backwards counting by 100s follows the same rules as forwards counting, just in reverse: the tens and ones digits stay the same, and the hundreds digit decreases by 1 each time.