Solved Exercises on Counting to 1000 by 10 in Grade 2

Master counting to 1000 by 10: 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 10 starting from 230. Write the next 5 numbers in the sequence.
Definition:

Skip counting by 10: Adding 10 to each number in a sequence

Skip counting method:
  1. Start with the given number
  2. Add 10 to get the next number
  3. Repeat for the desired number of terms
Starting number
230
Add 10
230+10=240
Step 1: Start with 230

230 is our starting point

Step 2: Add 10 to get next number

230 + 10 = 240

Step 3: Continue adding 10

240 + 10 = 250, 250 + 10 = 260, 260 + 10 = 270

230
→
240
→
250
→
260
→
270
230, 240, 250, 260, 270
Final answer:

The next 5 numbers are: 240, 250, 260, 270, 280

Applied rules:

• Place value rule: Only the tens digit changes when counting by 10

• Pattern recognition: Units digit stays the same

• Consistency: Same increment (10) applied each time

2 Missing number in sequence
Exercise 2
Find the missing number in this sequence: 450, 460, 470, ___, 490, 500
Definition:

Number sequence: A series of numbers following a specific pattern

Sequence
450, 460, 470, ?, 490, 500
Pattern
+10 each time
Missing
480
Step 1: Identify the pattern

460 - 450 = 10, 470 - 460 = 10

The pattern is adding 10 each time

Step 2: Apply the pattern

After 470: 470 + 10 = 480

Step 3: Verify with next number

480 + 10 = 490 ✓

450
→
460
→
470
→
480
→
490
→
500
450, 460, 470, 480, 490, 500
Final answer:

The missing number is 480

Applied rules:

• Pattern recognition: Identify consistent increments

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

• Place value understanding: Only tens digit changes

3 Place value analysis
Exercise 3
What happens to the hundreds, tens, and ones digits when you count by 10 starting from 190?
Definition:

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

Hundreds
1
Tens
9→0
Ones
0
Start
190
Add 10
190+10=200
Result
200
Step 1: Analyze 190

Hundreds: 1, Tens: 9, Ones: 0

Step 2: Add 10 to 190

190 + 10 = 200

Step 3: Analyze 200

Hundreds: 2, Tens: 0, Ones: 0

Step 4: Compare digits

Hundreds increased by 1, Tens changed from 9 to 0, Ones stayed 0

190 → 200: H+1, T:9→0, O:0
Final answer:

When counting by 10 from 190 to 200:
- Hundreds digit increases by 1 (1→2)
- Tens digit changes from 9 to 0
- Ones digit remains 0

Applied rules:

• Carry over rule: When tens reach 10, carry 1 to hundreds

• Place value system: Each position represents powers of 10

• Regrouping: 10 tens = 1 hundred

Rules and methods, laws,...
\(n + 10 = n + 10\)
Skip Counting by 10
Rule 1
Ones digit stays same
When counting by 10
Rule 2
Tens digit increases by 1
Unless it's 9 (then hundreds increase)
Rule 3
Pattern: +10 each time
Consistent increment
Key definitions:

Skip counting: Counting by a number other than 1

Place value: Value of a digit based on its position

Pattern: A repeated sequence or rule

Complete methodology:
  1. Identify the starting number
  2. Determine the increment (10 in this case)
  3. Apply the increment consistently
  4. Watch for place value changes when tens reach 9
  5. Verify the pattern continues correctly
Tip 1: When the tens digit is 9, adding 10 increases the hundreds digit.
Tip 2: The ones digit never changes when counting by 10.
Tip 3: Practice with number lines to visualize the pattern.
Tip 4: Count by 10s from different starting points.
Common errors: Forgetting to carry over when tens digit reaches 9, changing the ones digit.
Key insight: Skip counting builds the foundation for multiplication.
Formulas to know by heart:

• Count by 10: n → n+10 → n+20 → n+30...

• Place value: Hundreds, Tens, Ones

• Carry over: 10 tens = 1 hundred

• Pattern consistency: Same increment each time

Solution: Exercises 4 to 5
4 Counting backwards by 10
Exercise 4
Count backwards by 10 starting from 520. Write the next 5 numbers.
Definition:

Backwards skip counting: Subtracting 10 from each number in a sequence

Start
520
Subtract 10
520-10=510
Next
510
Step 1: Start with 520

520 is our starting point

Step 2: Subtract 10 to get next number

520 - 10 = 510

Step 3: Continue subtracting 10

510 - 10 = 500, 500 - 10 = 490, 490 - 10 = 480, 480 - 10 = 470

520
→
510
→
500
→
490
→
480
→
470
520, 510, 500, 490, 480, 470
Final answer:

The next 5 numbers are: 510, 500, 490, 480, 470

Applied rules:

• Reverse pattern: Subtract 10 instead of adding

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

• Borrowing: When tens digit is 0, decrease hundreds digit

5 Word problem application
Exercise 5
Sarah has 340 stickers. She gets 10 more stickers each day for a week. How many stickers does she have after one week?
Definition:

Word problem: Real-world scenario requiring mathematical solution

Initial
340
Days × 10
7×10=70
Total
340+70=410
Step 1: Identify initial amount

Sarah starts with 340 stickers

Step 2: Calculate total addition

She gets 10 stickers per day for 7 days: 10 × 7 = 70 stickers

Step 3: Add to initial amount

340 + 70 = 410 stickers

Step 4: Verify with skip counting

340 → 350 → 360 → 370 → 380 → 390 → 400 → 410 (7 steps)

340
→
350
→
360
→
370
→
380
→
390
→
400
→
410
340 + 70 = 410 stickers
Final answer:

Sarah has 410 stickers after one week

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

Comprehensive Guide: Counting to 1000 by 10
\(n + 10 = n + 10\)
Skip Counting by 10
Key definitions:

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

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

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

Complete methodology:
  1. Analyze the starting number: Identify hundreds, tens, and ones digits
  2. Apply the increment: Add or subtract 10 to the number
  3. Handle place value changes: Watch for when tens digit becomes 10 or 0
  4. Continue the pattern: Repeat the process for desired number of terms
  5. Verify the result: Check that the pattern is consistent
Tip 1: The ones digit never changes when counting by 10.
Tip 2: When tens digit is 9, adding 10 increases the hundreds digit.
Tip 3: Use number lines to visualize the counting pattern.
Tip 4: Practice counting by 10s from different starting points.
Tip 5: Remember that skip counting is foundational for multiplication.
Pattern characteristics: Consistent increment of 10, ones digit unchanged, tens digit increases by 1 (with exceptions).
Place value rules: When tens digit is 9, it resets to 0 and hundreds digit increases by 1.
Essential rules for counting by 10:

• Ones digit: Always remains the same

• Tens digit: Increases by 1 each time (except when it's 9)

• Hundreds digit: Increases by 1 when tens goes from 9 to 0

• Pattern consistency: Always add or subtract 10

• Carry/borrow rule: 10 tens = 1 hundred

\(n, n+10, n+20, n+30...\)
General Pattern Formula

Questions & Answers

Question: Why does the ones digit stay the same when we count by 10? I don't understand why it doesn't change.

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

  • When we count by 10, we're adding exactly 1 ten and 0 ones
  • For example: 230 + 10 = 240. We add 1 to the tens place (3→4) but add 0 to the ones place (0→0)
  • This is because 10 is made up of 1 ten and 0 ones

Think of it like money: if you have $230 and someone gives you $10 more, you now have $240. The dollar amount ($0) in the ones place doesn'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 transition from 190 to 200 when counting by 10s?

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

  • Use manipulatives: Show with base-10 blocks how 10 tens make 1 hundred
  • Visual aids: Use number lines or hundreds charts to show the jump visually
  • Verbal explanation: Explain that when we have 10 tens, we group them into 1 hundred
  • Practice in small chunks: Focus specifically on transitions like 190→200, 290→300

The key is helping students understand that 190 means 1 hundred, 9 tens, and 0 ones. When we add 10 (1 more ten), we have 10 tens, which equals 1 hundred. So we now have 2 hundreds, 0 tens, and 0 ones = 200.

Question: My child is having trouble with backwards counting by 10s. How can I make this easier for them?

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

  • Start with smaller numbers: Practice 100, 90, 80, etc. before going to larger numbers
  • Use real-life contexts: Countdown situations like rocket launches or timer countdowns
  • 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 10s follows the same rules as forwards counting, just in reverse: the ones digit stays the same, and the tens digit decreases by 1 each time.