Solved Exercises on Counting to 1000 in Grade 2

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

Solution: Exercises 1 to 3
1 Skip Counting by 10s
Exercise 1
Fill in the missing numbers in this pattern:
100, 110, 120, ___, 140, 150, 160, ___, 180, 190
Definition:

Skip counting by 10s: Adding 10 to each number to get the next number in the sequence

Skip counting method:
  1. Identify the pattern (adding 10 each time)
  2. Add 10 to the previous number to find the next number
  3. Continue the pattern until the end
Pattern
100, 110, 120, ?, 140, 150, 160, ?, 180, 190
Rule
Add 10
Solution
130, 170
Step 1: Identify the pattern

110 - 100 = 10, so we're adding 10 each time

Step 2: Find the first missing number

120 + 10 = 130

Step 3: Find the second missing number

160 + 10 = 170

100, 110, 120, 130, 140, 150, 160, 170, 180, 190
Final answer:

The missing numbers are 130 and 170

Applied rules:

• Pattern Recognition: Identify the constant difference between consecutive numbers

• Place Value: Only the tens digit changes when skip counting by 10s

• Consistency: The same rule applies to all numbers in the sequence

2 Skip Counting by 100s
Exercise 2
Count backwards by 100s starting from 1000:
1000, 900, 800, ___, 600, 500, 400, ___, 200, 100
Definition:

Skip counting by 100s: Adding or subtracting 100 to move from one hundred to the next

Pattern
1000, 900, 800, ?, 600, 500, 400, ?, 200, 100
Rule
Subtract 100
Solution
700, 300
Step 1: Identify the pattern

1000 - 900 = 100, so we're subtracting 100 each time

Step 2: Find the first missing number

800 - 100 = 700

Step 3: Find the second missing number

400 - 100 = 300

1000, 900, 800, 700, 600, 500, 400, 300, 200, 100
Final answer:

The missing numbers are 700 and 300

Applied rules:

• Backward Counting: Subtract the same amount each time

• Place Value: Only the hundreds digit changes when skip counting by 100s

• Consistency: The same operation applies to all numbers in the sequence

3 Counting by 1s Across Hundreds
Exercise 3
Complete the sequence counting forward by 1s:
998, 999, ___, 1001, 1002, ___
Definition:

Sequential counting across hundreds: Adding 1 to numbers that cross hundreds boundaries

Pattern
998, 999, ?, 1001, 1002, ?
Rule
Add 1
Solution
1000, 1003
Step 1: Identify the pattern

999 - 998 = 1, so we're adding 1 each time

Step 2: Recognize the transition point

From 999 to the next number, all digits change (999→1000)

Step 3: Continue the pattern

999 + 1 = 1000, then 1002 + 1 = 1003

Step 4: Verify the sequence

1001 - 1000 = 1 ✓, confirming our pattern

998, 999, 1000, 1001, 1002, 1003
Final answer:

The missing numbers are 1000 and 1003

Applied rules:

• Pattern Recognition: Identify the constant difference (1) between consecutive numbers

• Place Value: Understand how digits change when crossing hundreds boundaries

• Verification: Check that the pattern holds between known numbers

Rules and methods, laws,...
Skip Counting: Start + Step × Position
Number Sequence Formula
Skip by 5s
Add 5
Pattern: 100, 105, 110, 115...
Skip by 10s
Add 10
Pattern: 100, 110, 120, 130...
Skip by 100s
Add 100
Pattern: 100, 200, 300, 400...
Key definitions:

Skip Counting: Counting by a number other than 1 (like 5s, 10s, 100s)

Place Value: Understanding hundreds, tens, and ones in 3-digit numbers

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

Transition Point: When counting reaches a boundary (like 999 to 1000) and place values change

Complete methodology:
  1. Analyze the sequence: Look at the first few numbers to identify the pattern
  2. Determine the step: Calculate the difference between consecutive numbers
  3. Apply the rule: Use the identified pattern to fill in missing numbers
  4. Verify your answer: Check that the pattern continues consistently
Tip 1: When counting by 10s, only the tens digit changes (120, 130, 140).
Tip 2: When counting by 100s, only the hundreds digit changes (100, 200, 300).
Tip 3: When counting by 5s, the ones digit alternates between 0 and 5 (100, 105, 110, 115).
Tip 4: Use your fingers or count aloud to check your pattern.

Common errors: Forgetting to change the correct digit, miscounting the step, not recognizing the pattern.
Key notes: Skip counting helps build multiplication skills and number sense.
Rules to know by heart:

• Skip by 5s: Add 5 each time (ones digit alternates 0, 5)

• Skip by 10s: Add 10 each time (tens digit increases by 1)

• Skip by 100s: Add 100 each time (hundreds digit increases by 1)

• Backward counting: Subtract the same amount each time

• Pattern consistency: The same rule applies throughout the sequence

Solution: Exercises 4 to 5
4 Mixed Skip Counting
Exercise 4
Identify the pattern and continue the sequence:
200, 210, 220, 225, 235, 245, 250, ___
Definition:

Mixed skip counting: A sequence that combines different counting patterns

Sequence
200→210→220→225→235→245→250→?
Pattern
+10, +10, +5, +10, +10, +5
Next
260
Step 1: Analyze the differences

210-200=10, 220-210=10, 225-220=5, 235-225=10, 245-235=10, 250-245=5

Step 2: Identify the repeating pattern

The pattern is: add 10, add 10, add 5 (then repeat)

Step 3: Apply the pattern

After 250 (which was +5 from 245), the next step is +10

Step 4: Calculate the next number

250 + 10 = 260

Next number: 260
Final answer:

The next number in the sequence is 260

Applied rules:

• Pattern Analysis: Calculate differences between consecutive numbers

• Repeating Pattern Recognition: Identify the cycle of operations

• Consistency Check: Verify the pattern repeats correctly

5 Place Value Understanding
Exercise 5
What comes next in this sequence?
898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, ___
Definition:

Place value transition: Understanding how numbers change when crossing hundreds boundaries

Sequence
898→899→900→...→910→?
Rule
Add 1
Result
911
Step 1: Identify the pattern

Each number increases by 1 (899-898=1, 900-899=1, etc.)

Step 2: Understand place value transition

From 899 to 900, the tens digit goes from 9 to 0, and the hundreds digit increases

Step 3: Calculate the next number

910 + 1 = 911

Step 4: Verify the pattern

910 + 1 = 911, maintaining the skip counting by 1s pattern

Next number: 911
Final answer:

The next number in the sequence is 911

Applied rules:

• Place Value Understanding: Know how digits change when reaching 9 in any place

• Hundreds Transition: When tens reach 90 and add 1, hundreds increase

• Pattern Consistency: Maintain the same skip counting rule throughout

Detailed Summary: Counting to 1000
nth Term = Start + (n-1) × Step
Arithmetic Sequence Formula
Key definitions:

Skip Counting: Counting forward or backward by a consistent interval (2, 5, 10, 100)

Place Value: Understanding that each digit position represents hundreds, tens, or ones

Number Pattern: A sequence of numbers that follows a predictable rule

Transition Point: When counting reaches a boundary (like 999 to 1000) and place values change

Complete methodology:
  1. Observe the sequence: Look at the first few numbers to understand the starting point
  2. Calculate differences: Find the difference between consecutive numbers to determine the step
  3. Identify the pattern: Determine if it's skip counting by 2s, 5s, 10s, 100s, etc.
  4. Apply the rule: Use the identified step to continue the sequence
  5. Verify results: Check that the pattern continues consistently throughout
Tip 1: When skip counting by 10s, the last digit stays the same while the tens digit changes.
Tip 2: When skip counting by 100s, the last two digits stay the same while the hundreds digit changes.
Tip 3: Use your hands to count by 5s: 5, 10, 15, 20, etc. (each finger represents 5).
Tip 4: Practice counting forward and backward to strengthen number sense.

Common errors: Forgetting to carry over when reaching 9 in any place value, misidentifying the pattern, not maintaining consistency in the skip counting step.
Memory aids: Remember that skip counting by 10s changes only the tens digit, skip counting by 100s changes only the hundreds digit.
Formulas to know by heart:

• Skip counting by 5s: Add 5 each time (100, 105, 110, 115...)

• Skip counting by 10s: Add 10 each time (100, 110, 120, 130...)

• Skip counting by 100s: Add 100 each time (100, 200, 300, 400...)

• Backward counting: Subtract the same amount each time

• Transition rule: When a place value reaches its maximum (9), it resets to 0 and the next higher place value increases

Questions & Answers

Question: I don't understand why when I count from 999 by 1s, it goes 999, 1000. Why does the 999 become 1000?

Answer: Great question! This happens because of place value rules:

  • In 999, the hundreds digit is 9, the tens digit is 9, and the ones digit is 9
  • When you add 1 to 999, you're adding to the ones place: 9 + 1 = 10
  • But 10 ones equals 1 ten, so you carry the 1 to the tens place
  • This makes the ones digit go back to 0, and the tens digit becomes 9 + 1 = 10
  • But 10 tens equals 1 hundred, so you carry the 1 to the hundreds place
  • This makes the tens digit go back to 0, and the hundreds digit becomes 9 + 1 = 10
  • But 10 hundreds equals 1 thousand, so you carry the 1 to the thousands place
  • This makes the hundreds digit go back to 0, and the thousands digit increases from 0 to 1

So: 999 + 1 = 1000 (0 thousands, 9 hundreds, 9 tens, 9 ones becomes 1 thousand, 0 hundreds, 0 tens, 0 ones)

Think of it like having 999 pennies and adding 1 penny - you now have $10.00, not 999001 cents!

Question: How can I remember whether to add or subtract when skip counting?

Answer: Here are some helpful strategies to remember:

  • Forward counting: Going up (like climbing stairs) means adding
  • Backward counting: Going down (like going down stairs) means subtracting
  • Look for direction words: "forward," "up," "more" usually mean addition
  • Look for direction words: "backward," "down," "less" usually mean subtraction

For example: "Count forward by 10s" means add 10 each time. "Count backward by 100s" means subtract 100 each time.

Tip: Practice with a number line - moving right is adding, moving left is subtracting!

Question: What's the easiest way to learn skip counting by 5s? I keep getting confused.

Answer: Here are effective strategies for skip counting by 5s:

  • Use your hands: Count your fingers - each hand has 5 fingers, so 2 hands = 10, 4 hands = 20, etc.
  • Notice the pattern: Numbers ending in 0 or 5 alternate (100, 105, 110, 115...)
  • Connect to money: Nickels are worth 5 cents, so count nickels: 5¢, 10¢, 15¢, 20¢...
  • Count in groups: Think of pairs of hands: 1 pair = 10 fingers, 2 pairs = 20 fingers, etc.

Practice saying: "100, 105, 110, 115, 120, 125..." rhythmically. The rhythm helps your brain remember the pattern!

Start with smaller ranges (like 100-200) before attempting larger ranges (like 100-1000).