Solved Exercises on Counting to 1000 by Ones in Grade 2

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

Solution: Exercises 1 to 3
1 Sequential counting
Exercise 1
Count by ones starting from 125. Write the next 10 numbers in the sequence.
Definition:

Counting by ones: Adding 1 to each number in a sequence

Counting by ones method:
  1. Start with the given number
  2. Add 1 to get the next number
  3. Each place value may change depending on the number
  4. Repeat for the desired number of terms
Starting number
125
Add 1
125+1=126
Step 1: Start with 125

125 is our starting point (1 hundred, 2 tens, 5 ones)

Step 2: Add 1 to get next number

125 + 1 = 126 (1 hundred, 2 tens, 6 ones)

Step 3: Continue adding 1

126 + 1 = 127, 127 + 1 = 128, 128 + 1 = 129, 129 + 1 = 130, 130 + 1 = 131, 131 + 1 = 132, 132 + 1 = 133, 133 + 1 = 134, 134 + 1 = 135

125
126
127
128
129
130
131
132
133
134
125
→
126
→
127
→
128
→
129
→
130
→
131
→
132
→
133
→
134
→
135
125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135
Final answer:

The next 10 numbers are: 126, 127, 128, 129, 130, 131, 132, 133, 134, 135

Applied rules:

• Sequential rule: Each number increases by 1

• Place value rule: Usually only the ones digit changes

• Carry over: When ones digit reaches 9, it resets to 0 and tens increase

2 Counting across place boundaries
Exercise 2
Count by ones starting from 198. Write the next 5 numbers in the sequence.
Definition:

Counting across boundaries: Counting that involves carrying over to higher place values

Sequence
198, 199, 200, 201, 202, 203
Pattern
+1 each time
Step 1: Start with 198

198 is our starting point (1 hundred, 9 tens, 8 ones)

Step 2: Add 1 to get 199

198 + 1 = 199 (1 hundred, 9 tens, 9 ones)

Step 3: Add 1 to get 200 (boundary crossing)

199 + 1 = 200 (2 hundreds, 0 tens, 0 ones)

Step 4: Continue adding 1

200 + 1 = 201, 201 + 1 = 202, 202 + 1 = 203

Hundreds
1→2
Tens
9→0
Ones
9→0→1
198
→
199
→
200
→
201
→
202
→
203
198, 199, 200, 201, 202, 203
Final answer:

The next 5 numbers are: 199, 200, 201, 202, 203

Applied rules:

• Boundary crossing: When ones digit is 9, adding 1 causes tens to change

• Carry over: 10 ones = 1 ten, 10 tens = 1 hundred

• Regrouping: Systematic exchange of place values

3 Place value analysis
Exercise 3
What happens to the hundreds, tens, and ones digits when you count by ones from 299 to 302?
Definition:

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

Hundreds
2→3
Tens
9→0→0
Ones
9→0→1→2
Start
299
Add 1
299+1=300
Continue
300→301→302
Step 1: Analyze 299

Hundreds: 2, Tens: 9, Ones: 9

Step 2: Add 1 to 299

299 + 1 = 300 (3 hundreds, 0 tens, 0 ones)

Step 3: Continue adding 1

300 + 1 = 301 (3 hundreds, 0 tens, 1 one)

301 + 1 = 302 (3 hundreds, 0 tens, 2 ones)

Step 4: Compare digits

From 299 to 302: H:2→3, T:9→0, O:9→0→1→2

299
→
300
→
301
→
302
299 → 300 → 301 → 302
Final answer:

When counting by ones from 299 to 302:
- Hundreds digit increases by 1 (2→3)
- Tens digit changes from 9 to 0
- Ones digit changes from 9 to 0, then increases to 1 and 2

Applied rules:

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

• Place value system: Each position represents powers of 10

• Regrouping: 10 ones = 1 ten, 10 tens = 1 hundred

Comprehensive Guide: Counting to 1000 by Ones
\(n + 1 = n + 1\)
Counting by Ones
Key definitions:

Counting by ones: Adding 1 to each number in a sequence to get the next number

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

Number sequence: A series of numbers that follow a specific pattern

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 1 to the number
  3. Handle place value changes: Watch for when ones or tens reach 9
  4. Continue the pattern: Repeat the process for desired number of terms
  5. Verify the result: Check that each number increases by 1
Tip 1: Usually only the ones digit changes when counting by ones.
Tip 2: When ones digit is 9, adding 1 changes both ones and tens digits.
Tip 3: Practice with number lines to visualize the sequence.
Tip 4: Count by ones from different starting points.
Tip 5: Use base-10 blocks to physically represent the counting process.
Pattern characteristics: Each number increases by 1, ones digit usually changes first.
Place value rules: When ones digit is 9, it resets to 0 and tens digit increases by 1.
Essential rules for counting by ones:

• Sequential rule: Each number is exactly 1 more than the previous number

• Ones digit: Usually increases by 1 (0→1→2...→9)

• Boundary crossing: When ones digit is 9, it becomes 0 and tens digit increases

• Carry over: 10 ones = 1 ten, 10 tens = 1 hundred

• Consistency: The same increment (1) applied each time

\(n, n+1, n+2, n+3...\)
General Pattern Formula
Solution: Exercises 4 to 5
4 Counting backwards by ones
Exercise 4
Count backwards by ones starting from 205. Write the next 6 numbers.
Definition:

Backwards counting: Subtracting 1 from each number in a sequence

Start
205
Subtract 1
205-1=204
Next
204
Step 1: Start with 205

205 is our starting point (2 hundreds, 0 tens, 5 ones)

Step 2: Subtract 1 to get next number

205 - 1 = 204 (2 hundreds, 0 tens, 4 ones)

Step 3: Continue subtracting 1

204 - 1 = 203, 203 - 1 = 202, 202 - 1 = 201, 201 - 1 = 200, 200 - 1 = 199

205
204
203
202
201
200
199
205
→
204
→
203
→
202
→
201
→
200
→
199
205, 204, 203, 202, 201, 200, 199
Final answer:

The next 6 numbers are: 204, 203, 202, 201, 200, 199

Applied rules:

• Reverse pattern: Subtract 1 instead of adding

• Place value rule: Usually only ones digit changes (decreases by 1)

• Borrowing: When ones digit is 0, decrease tens digit and ones becomes 9

5 Word problem application
Exercise 5
Sarah is reading a book with 120 pages. She has read 87 pages so far. How many more pages does she need to read to finish the book?
Definition:

Word problem: Real-world scenario requiring mathematical solution

Total
120
Read
87
Remaining
120-87=33
Step 1: Identify total pages

The book has 120 pages total

Step 2: Identify pages read

Sarah has read 87 pages

Step 3: Calculate remaining pages

120 - 87 = 33 pages left to read

Step 4: Verify by counting forward

87 + 1 = 88, 88 + 1 = 89, ..., up to 120 (33 additions)

87
88
89
90
91
92
93
94
95
96
87
→
88
→
89
→
90
→
91
→
92
→
93
→
94
→
95
→
96
→
97
→
98
→
99
→
100
→
101
→
102
→
103
→
104
→
105
→
106
→
107
→
108
→
109
→
110
→
111
→
112
→
113
→
114
→
115
→
116
→
117
→
118
→
119
→
120
120 - 87 = 33 pages
Final answer:

Sarah needs to read 33 more pages to finish the book

Applied rules:

• Real-world application: Connect math to practical scenarios

• Problem solving: Break down word problems into steps

• Verification: Use counting by ones to confirm subtraction

Questions & Answers

Question: Why does the tens digit change from 9 to 0 when counting by ones? For example, why does 199 become 200?

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

  • Our number system only uses digits 0-9 in each place
  • When we have 9 ones and add 1 more, we now have 10 ones
  • But we can't write "10" in the ones place, so we regroup: 10 ones = 1 ten
  • Similarly, when we have 9 tens and add 1 more ten, we get 10 tens = 1 hundred
  • This is why 199 + 1 = 200: we go from 1 hundred 9 tens 9 ones to 2 hundreds 0 tens 0 ones

Think of it like having 9 pennies. When you get 1 more penny, you now have 10 pennies, which equals 1 dime. So you exchange 10 pennies for 1 dime and have 0 pennies left.

This is called "regrouping" and it's a fundamental part of our base-10 number system.

Question: How can I help my students understand the difference between counting by ones and skip counting?

Answer: Here are effective strategies:

  • Use concrete examples: Show with manipulatives how counting by ones adds 1 each time vs skip counting adding more
  • Visual patterns: Use number grids to highlight different patterns
  • Compare and contrast: Show counting by ones (1, 2, 3, 4...) vs skip counting (5, 10, 15, 20...)
  • Physical movement: Have students take 1 step for ones vs 5 steps for fives

The key is helping students see that counting by ones creates a steady, gradual pattern where each number increases by exactly 1, while skip counting creates bigger jumps.

Question: My child struggles with backwards counting by ones. How can I help them?

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

  • Start with smaller numbers: Practice 10, 9, 8, 7... before going to larger numbers
  • Use real-life contexts: Rocket countdowns, timers, or elevator floors going down
  • 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 ones follows the same place value rules as forwards counting, just in reverse: usually only the ones digit decreases by 1, but watch for when it goes from 0 to 9.